tag:blogger.com,1999:blog-24672026395982380632016-10-25T21:33:23.198-05:00misscalcul8Elissa Millernoreply@blogger.comBlogger602125tag:blogger.com,1999:blog-2467202639598238063.post-51047563431898190582016-10-10T23:41:00.001-05:002016-10-10T23:41:57.858-05:00#DITL Monday, October 10th, 2016<br />Today is Columbus Day which means we are out of school. We actually have a 3.5 day weekend. On Friday we had our Regional Teachers Institute until noon. I'm always excited for long weekends so I can catch up on the extra stuff I have to do or put off.<br /><br />Nothing this weekend went as planned. I did not even touch my school stuff until today. Which was not the plan.<br /><br />8:48 Wake up. Make myself go back to sleep.<br /><br />11:00 Wake up again. No shame since I average 5 hours of sleep or less during the school week. Eat breakfast, scripture journal, straighten up the house.<br /><br />11:45 Get to work on my laptop. Update my trig lesson on finding an angle with trig ratios to include text problems where students have to draw their own diagram, Updated notebook file that goes with it. Create solving trigonometric equations interactive notebook pages, a pong review game powerpoint, and a quiz for my senior math class. Next it's on to Geometry- I update the interactive notebook pages I already made for conditional statements with a foldable I made a few years ago since I feel like it is a better fit. Update notebook file to match. Next create new interactive notebook pages for deductive reasoning, a pong review game, and a quiz.<br /><br />3:00 Eat lunch while watching Jimmy Fallon. When I'm done eating I walk around the house watching tv on my ipad so I can get steps in. My goal is 12,000 a day and when you don't go to work and spend hours on your laptop, it's hard. When my show is over I start walking around with my Bible...gotta get those steps.<br /><br />5:15 Back to work. I need to make a practice activity for Algebra I inequality word problems. So I google problems and create...you guessed it- a pong review game powerpoint. It's my go to activity. Then I, you guessed it again- made a quiz. It's almost the end of the quarter so I make up a binder check 'quiz'.<br /><br />6:00 I have more work to do but I'm running low on motivation so I start wasting time on e-mail and social media. Then I realize I haven't read any blogs lately so I catch up on those.<br /><br />7:30 I remember I need to create and print posters for our Student Council Socktober drive. Cue google images and pinterest.<br /><br />8:00 Realize I should eat dinner. Eat while watching TV and again finish my show with walking around the house. I'm only up to 7700 steps.<br /><br />9:00 Spend 30 minutes doing my workout and walking around for a cool down. Pack my lunch and get my breakfast ready for tomorrow. Pick out my outfit.<br /><br />10:00 Shower.<br /><br />10:15 Get out the ol ipad and go for another walk. I walk until I reach my 12,000 goal which brings us to<br /><br />11:15. I sit down to start this blog post and realize that I forgot about the 92 bell ringers I need to respond to plus the 9 trig quizzes, 10 Algebra 2 tests, and 8 geometry quizzes I have to grade. And I wanted to paint my fingernails.<br /><br />This was an embarrassing post to write- I don't know if it's because I'm bad at managing my time or because I feel like I have to justify how I spend it. Or maybe it's because my job is like a second job on the nights and weekends. I never feel like I've done enough. Not to mention I have a painting project in my downstairs bathroom that I didn't even get to touch this weekend.<br /><br /><b>1) Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?</b><br /><br />Zero teacher moves today.<br /><br /><b>2) Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?</b><br /><br />I spend so much time putting together notes, practice, and quizzes from my curriculum. It's mostly formatting and copying and pasting. As soon as I feel accomplished for having everything prepared, I start questioning if it's the best way to teach it. I can't feel content.<br /><br /><b>3) We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.</b><br /><br />I've been getting along better with a colleague at school. Although it's been unintentional, I know that it's healthier. I'm still getting better at laughing and sharing things with the students. Although I've always felt like I shared a lot with students but somehow this year seems different.<br /><b><br /></b><b>4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?</b><br /><br />Keep working on a better work/life balance. My weekends are consumed with school work in an attempt to free up my week nights but I still can't seem to leave school before 5:00. I do know that next year will be a million times better. With my curriculum, I am finally aligning things in a way I am mostly satisfied with. I'm making notes of things to change or fix for next year and even doing some now if they are quick fixes. NO MORE STARTING OVER.<br /><b><br /></b><b>5) What else happened this month that you would like to share?</b><br /><br />I've been teaching trig identities for the first time. I have struggled, actually sat with the kids and worked the problems along with them, and got to the point where I could make up problems for the students to practice.<br /><br />11:41 Off to do at least another hour of work!<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com3tag:blogger.com,1999:blog-2467202639598238063.post-47980791632487459872016-09-26T23:45:00.000-05:002016-09-26T23:45:02.725-05:00We Don't Know EverythingReading Dan's post, <a href="http://blog.mrmeyer.com/2016/what-should-math-teachers-do-when-they-dont-know-the-math/">What Should Math Teachers Do When They Don't Know the Math?</a>, really resounded with me and the timing was ironic.<br /><br />We were working on constructions in Geometry and we were working through notes from the curriculum. Admittedly, I had not looked made an answer key as I had performed the constructions in past years, albeit not according to these directions.<br /><br />There was one step I just could not figure out. I read, reread it, positioned my compass, re-positioned my compass. I stopped and stared at it for an awkward amount of silence.<br /><br />And then I turned around to tell the kids, "We're going to skip this one and come back to it tomorrow."<br /><br />S: "So you don't know how to do it?"<br /><br />Me: "No, I'll have to figure it out and then tell you tomorrow."<br /><br />S#2: "But you're the one who is supposed to be teaching us."<br /><br />Me: "Teachers are humans too. We don't know everything. Would you rather me lie to you and tell you the wrong way to do it?"<br /><br />S#3: "Yes. Then we would feel better about knowing how to do it."<br /><br />Me: *mind blown"<br /><br />The next day at the beginning of class another student was quick to ask, "Did you figure out that problem from yesterday?"<br /><br />Me: "Yes I did! Let's start on that one now since some of you were hating on me for not knowing how to do something.<br /><br />S: We weren't hating....<br /><br />Me: "How would you feel if I treated you that way when you don't know something?"<br /><br />Silence...<br /><br />And we went on with class and it wasn't brought up again.<br /><br /><b>So...what do we do when it becomes clear, in front of a class, that we don't understand math like we thought.</b><br /><b><br /></b>Admit it. Show room for growth, Use growth mindset on your own set of teaching skills. Explain your old thinking and how that changed or hit an obstacle. Explain your new thinking.<br /><br />And the ability to do this comes from the confidence and purpose that you feel inside. It comes from a place of being prepared and experienced. It's embarrassing for like 10 seconds and then my brain switches to "Well, I guess I'm going to learn something new today. Glad I won't have to make this mistake again."<br /><br />That's worth sharing.<br /><br />Students aren't used to that at first but the older they get and especially as they advance through higher math with me, I am very open about my math abilities and struggles. This year more than ever I've had students ask me why I decided to teach math and what my favorite subject was in school. I'm open about all of that. I did very well in high school and hit a wall in college. I passed most of my college courses with a C. I don't understand calculus at all. I don't even know how I passed any of those classes. I struggle with trig and some of the more advanced topics in Algebra 2. I used to call my mom every day in college, crying, telling her I didn't think I could do this.<br /><br />How can I teach math when I don't understand it myself?<br /><br />And then somehow I wound up in the classroom, magically able to do most of the things I have to teach with ease, and not really knowing how it happened.<br /><br />But in case I ever forget, there is always a moment like I mentioned to humble me and remind what it is like to struggle, feel unsure, and be embarrassed.<br /><br />I'm really trying to communicate to my students how important it is to continually better yourself. Not try to just get through things and get things over worth. Not just distract yourself and waste time with social media and video games and YouTube. But to really think about, on purpose, areas of weakness or how to make things better.<br /><br />I hope it's working.<br /><br />I hope they see mistakes going hand in hand with success.<br /><br />I hope they see a real person can be good at their job and make mistakes.<br /><br />I hope they see that making mistakes doesn't have to ruin your confidence or your day and that you grow because of and in spite of, making mistakes.<br /><br />I hope it becomes normal and comfortable for them to mess up and see me mess up and learn and go on with our lives.<br /><br />I just read this quote yesterday but already forgot from where, "Successful people feel comfortable being wrong."<br /><br />I hope when they see me, they see both.<br /><br />That's what I'm here for.<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com4tag:blogger.com,1999:blog-2467202639598238063.post-48837861088315205342016-09-10T23:01:00.000-05:002016-09-17T19:02:54.218-05:00#DITL Saturday, September 10th, 2016My normal routine is to do all my shopping and errands on Friday nights so that I have nowhere to go on Saturdays and I can do all my work and clean all day Saturday.<br /><br />I have a lunch date with my bestie on the second Saturday of every month so my plans were already thrown off. I thought that I would stay at school and work a lot on Friday, get groceries after my lunch with my friend, then come home and do the rest of my work.<br /><br />Friday my sisters messages me at the end of school and needs me to baby-sit my niece and nephew. Well there goes my working Friday plans.<br /><br />My mom sets up a birthday lunch for my Grandma, who is visiting from Florida, for Saturday at 6:00 at a place an hour away.<br /><br />Well there goes my working Saturday plans.<br /><br />I am a routine person so I really really really hate when my routine is interrupted by someone other than me.<br /><br />Routinely throughout the day, I just stopped myself from worrying about school.<br /><br />Mental speech: "You still have Sunday to get things done that must be done. No, you can't do everything you wanted to do. Yes, you will have to work more weeknights this week than you want to. But enjoy the moment! You are having lunch with your best friend and dinner with your grandma! Those are fun things that you like doing. So do them!"<br /><br />Even when I am not at school, or doing school work, I'm planning/worrying about school work. But I can't let that overtake my actual life.<br /><br />One of my New Year's Resolutions was to create a better work/life balance.<br /><br />I'm doing it.<br /><br />I'm not perfect.<br /><br />But I am present.<br /><br /><b>1) Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal? </b><br /><br />I am proud that I chose to put my personal life above my professional life and enjoy my weekend. It was all ideal. =)<br /><br /><b>2) Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately? </b><br /><br />I am looking forward to a school year when I don't have to slave over everything. A challenge for me lately is getting things done on my plan period. It is the last hour of the day and I am so tired and spent that I zone out on my e-mail and the Internet rather than accomplishing anything. Then I have to stay after school and do it anyway. I feel like I have no time at home and I work late at school and still have things to take home.<br /><br /><b>3) We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently. </b><br /><br />Overall I feel like I am way more open and relational with my students this year. I can think of several moments in the past weeks where I told them stories from my life and we laughed together or when students have asked my advice on clothes or boys or asked me to look things up or give my opinions on the election and so on. One student has been confiding in me about relationships and I've been trying really hard to change her focus and build her confidence.<br /><b><br /></b><b>4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?</b><br /><br />Keep working on a better work/life balance. Continue asking good questions, asking students to notice similarities and differences, asking students to try a problem before they know what to do, asking for strategies, and doing number talks.<br /><br /><b>5) What else happened this month that you would like to share?</b><br /><br />I've been posting some #teach180 photos and I've never done that before.Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-84442958808108460112016-08-30T23:49:00.001-05:002016-08-30T23:53:01.536-05:00Guys, I'm Killing It<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" width="320" /></a></div><br />I don't know exactly what gave me my teacher mojo back but I definitely know that last year was my seven year slump.<br /><br />I've had good things that I've wanted to blog every day but my internet has been lame at home and I'm still so tired every day that I've gotten behind.<br /><br />Day 1 and I already knew everyone's names.<br /><br />My biggest class is 18 and my smallest is 5.<br /><br />I've tried so many new things already: number talks, Google classroom, Google forms, a clothesline activity, asking students to notice things before we start working, introducing growth mindset, using my Plickers multiple times, and my questioning skills have greatly improved.<br /><br />Here are some highlights from the past two weeks:<br /><br />Using a beach ball every Monday at the beginning of class- we hit it while we talk about our weekends and we stop when no one else has anything to share. This has been a GREAT way to get energy flowing on a Monday and to get more students talking and for longer amounts of time. And almost every class will ask me about my weekend too- maybe to just keep hitting the ball longer.<br /><br />I asked our tech person about the possibility of sharing some Chrome books with the two teachers who have classroom sets and she showed up at my door the next day with six that are mine to keep, one per table group. I literally teared up at her kindness.<br /><br />During my growth mindset discussion with my seniors I kindddddddd of went off on a tangent about being a confident woman and how important it is to make being with yourself a safe place and being successful in the future and etc.....when I finally finished a student said, "Wow, you should be like a coach or something." {I've always wanted to write a book and I think I might have just stumbled on the topic}.<br /><br />I tweeted about my <a href="https://twitter.com/misscalcul8/status/768537643399249920">favorite problem of all time</a> and in my freshman class, the first person to get the correct answer was the student who spent the first week of school telling me how math was not her subject and to please not call on her when she doesn't know the answer. I said "I thought math wasn't your thing and yet you were the first one done." She said, "Well I thought it wasn't!" She worked really hard the rest of the class period.<br /><br />I was talking to a group of students when one almost let a cuss word slip; she cut herself off and said "This is why you shouldn't make me like you so much- then I talk normal around you." Lol<br /><br />Number talks have been going well but they really prefer dot talks to anything else so far. Some students are purposely counting them in an unusual order just so they can share their thinking. I've had multiple hands go up to share their thinking and it feels like everyone is comfortable with that.<br /><br />I feel like it was so easy to just jump right into how I want my classes to run- I already feel like I've known my freshman students for a long time and it's such a testament to how being consistent and building routines and procedures can enhance your classroom culture.<br /><br />I taught the same piecewise functions lesson that I always teach but I started by asking them to notice things about the function and then notice things about the graph. It seemed like the lesson went so much smoother because they made connections all the way through.<br /><br />It's only week three I know but I haven't really had to beg people to work; I feel like I have a good mixture of students that helped make this happen.<br /><br />A few students have made real efforts since last year to change their attitude and effort and it's so cool to see them grow.<br /><br />I feel so blessed to get to be in their lives year after year and to know them so well that I can see change and growth over time. Also after reading tweets and blog posts, I also feel blessed to be in a school that provides me with all the colored paper {and most school supplies} that I want and that my biggest class size is smaller than most people's small class size.<br /><br />I still love when students come in and love the way my room smells- I didn't it was so odd for a teacher to buy air fresheners. ;)<br /><br />A student asked me how much I spend on all of this stuff and I just appreciated that she noticed the extra that I put in.<br /><br />This was the first year I didn't dread back to school time, the first year I had no school nightmares, and the first year {that I can remember} that I don't have that one class that I'm just dreading.<br /><br />I can't really explain how my questioning skills have improved but it's like I am self-editing in real time- I'll have my next question on the tip of my tongue and it's like my brain says 'Here's a better idea!" and a more interesting question comes out.<br /><br />Three lessons that I already had resources for meant I could think deeper about how to present them in a more conceptual way- this is another area I see improvement in myself over time.<br /><br />I still maintain that Jesus gives me supernatural patience and I can feel the moment I enter into it- helping students one on one I always reach a point where I want to walk away and it's like this supernatural patience washes over me and I just continue like nothing happened.<br /><br />I don't know why but I think it is so cute when students tell me bye as they leave. It's not every student but it's just endearing.<br /><br />I've started almost every paragraph with 'I' so far but as hard as we are on ourselves, I think we can all stand to brag on ourselves. One of my gifts is making connections with people and I love seeing that come to fruition- this year feels just like a continuation of last year rather than a new start. Maybe it's not the best thing but I felt like starting school as a tee again- I loved hearing the updates of what all my friends did over the summer and what was going on in their lives.<br /><br />I feel like finally all of my experience and ups and downs and talents and strengths and weaknesses are coming together and I'm approaching the ever elusive peak of 'actually knowing what I'm doing'.<br /><br />My career is on an uphill swing and that is definitely <a href="https://onegoodthingteach.wordpress.com/">ONE GOOD THING</a>.<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com6tag:blogger.com,1999:blog-2467202639598238063.post-85504214273746674342016-08-27T18:10:00.001-05:002016-08-27T18:10:26.068-05:00Plan With Me...Infinite and No SolutionsSo I'm planning this lesson for the upcoming week and I have 3 slides that I feel like are a good start. I'm just about to tweet them out and ask what I can add to them when I decide to check the <a href="http://www.fishing4tech.com/mtbos.html">MTBoS search engine</a> first. I land on this <a href="https://jennvadnais.com/2015/08/19/combining-like-terms-w-desmos/">great blog post</a> about using Desmos to check answers after combining like terms by graphing.<br /><br />And instantly my lesson just got better. I get to use Desmos for the first time with my freshman and we are just beginning!<br /><br />Here's a general outline and my thought process.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-4RQ-nNiCHwQ/V8IbKcwDW4I/AAAAAAAAFTU/-dE9TjuUPAwVlgl9QSayHpJq2rDW8LPUACLcB/s1600/Slide1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-4RQ-nNiCHwQ/V8IbKcwDW4I/AAAAAAAAFTU/-dE9TjuUPAwVlgl9QSayHpJq2rDW8LPUACLcB/s320/Slide1.JPG" width="320" /></a></div><br />I will ask students to share out some answers and I will write them on the board. I will have one chrome book per group of three students and ask them to each take turns typing in an expression from the board (I'm thinking 6 so each student types in 2 and purposely include wrong ones). But what if I don't get very many answers?<br /><br />I will ask them what they notice as they type in each equation.<br /><br />We will discuss the connection between the expression and the line.<br /><br />Next:<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-mFKpIdln1OA/V8IclqOhsoI/AAAAAAAAFTc/MuJH9ZRXqKAEZdzzP9sg9cAi3yJvVWhzQCLcB/s1600/Slide3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-mFKpIdln1OA/V8IclqOhsoI/AAAAAAAAFTc/MuJH9ZRXqKAEZdzzP9sg9cAi3yJvVWhzQCLcB/s320/Slide3.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>I will ask students to prove me right or wrong. I'm thinking I'll have to explain that they either need to solve for x or plug in random values and see what happens. Some kind of work will happen which will lead us to graphing it in Desmos and seeing if it is the same line or not.<br /><br />Third:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-c-dAxjFrssI/V8IcdA-nG8I/AAAAAAAAFTY/rqzOenWS4UUp0TYsn1gSji7HAKTnBDseQCEw/s1600/Slide2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-c-dAxjFrssI/V8IcdA-nG8I/AAAAAAAAFTY/rqzOenWS4UUp0TYsn1gSji7HAKTnBDseQCEw/s320/Slide2.JPG" width="320" /></a></div><br />Some kind of work happening, either with Algebra or Desmos leading up to the fact that they graph two parallel lines which have no intersecting solution and how they simplify to the same slope with different y-intercepts.<br /><br />Is that it? Now we just practice?<br /><br />What are some good questions I can ask? What needs to go in their notes?<br /><br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com7tag:blogger.com,1999:blog-2467202639598238063.post-74515874646445844872016-08-20T22:24:00.003-05:002016-08-20T22:24:56.948-05:00First Days 2016-2017<br />I was <i>not</i> ready. I spent my last few days getting my classroom ready and not preparing actual activities. This should have been an 'easy' week for me since it's the only time I can get away with doing the same thing every hour. Instead I didn't go to bed earlier than midnight all week. =( Definitely making a check list so this doesn't happen next year.<br /><div><br /><b>Monday</b><br />Today we did Mental Math Monday and got our binders ready: dividers, tabs, names on the spine, pencil bags, new pencils, and dry erase markers. We folded our name tents; I loved having students write to me every day. The name tent part was not really necessary since we are so small and everybody knows everybody. Next year I might not use an actual name tent. It also took me up to an hour and a half each night too respond. I would say it is worth it but I definitely couldn'tdo it all year.We did our first <a href="https://saravanderwerf.com/2016/06/27/secondary-number-talks-ill-convince-you-with-ducks/">number talk</a>!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-TZI01n1UZCs/V7jj2FKwjfI/AAAAAAAAFSg/ONeo2zGES9sNuETSVmmmQNuWnffOCBOkQCLcB/s1600/Day%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-TZI01n1UZCs/V7jj2FKwjfI/AAAAAAAAFSg/ONeo2zGES9sNuETSVmmmQNuWnffOCBOkQCLcB/s320/Day%2B1.jpg" width="320" /></a></div><br /><br /><b>Tuesday</b></div>I used Google Classroom for the first time today and I think I was successful. Students used an ipad to sign in to their account add my class by code. I posted a question asking them they're favorite animated movie. Then I posted a google form for estimation180. They commented and opened the form. I showed a picture on the board and they gave me a too low, too high, and estimate. We looked at the answers on the spreadsheet and then I showed the correct answer. I had 4-5 students guess correctly throughout the day and that has never happened. Google Forms FTW? Next, we did Amy Zimmer's <a href="https://docs.google.com/presentation/d/1ePSYmbQ_UvmjA3UKmBFzeVj9ujhq9-yH528cG9lfuoU/edit">icebreaker</a> to set up groups and group roles. I noticed that the designated time keeper kept time for the rest of the period, even after the activity ended. From there we went straight to Sara's<br /><a href="https://saravanderwerf.com/2015/12/07/100-numbers-to-get-students-talking/">1-100 task</a> making groups work. The kids LOVED it!! In between rounds we discussed strategies for working together and improving their times.<br /><b><br /></b><b>Wednesday</b><br />We started with our Work It Wednesday problem, how can you arrange 8 8's to add up to 1000? From there I showed them pictures from the previous day's 1-100 task.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-HaPR5p2-pLo/V7kAkDxIGUI/AAAAAAAAFSw/55-lriVS5d0r4ANGviaO4xCOBqdPNvPygCLcB/s1600/IMG_6309.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-HaPR5p2-pLo/V7kAkDxIGUI/AAAAAAAAFSw/55-lriVS5d0r4ANGviaO4xCOBqdPNvPygCLcB/s320/IMG_6309.JPG" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-xvMAnBvSWg0/V7kAnYkZX4I/AAAAAAAAFS4/rS2NvqyOClkP0_rFM4xgQQ9UCHnDiVp0QCLcB/s1600/IMG_6310.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-xvMAnBvSWg0/V7kAnYkZX4I/AAAAAAAAFS4/rS2NvqyOClkP0_rFM4xgQQ9UCHnDiVp0QCLcB/s320/IMG_6310.JPG" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-i0Gak9PAaj4/V7kAlPnUXEI/AAAAAAAAFS0/qD6xJjV76hUFp9qPgEXDPebeAnJ6Wb5EwCLcB/s1600/IMG_6311.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-i0Gak9PAaj4/V7kAlPnUXEI/AAAAAAAAFS0/qD6xJjV76hUFp9qPgEXDPebeAnJ6Wb5EwCLcB/s320/IMG_6311.JPG" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-zsrjuZN7gxg/V7kBBxO1PeI/AAAAAAAAFS8/mgP-oCEGjskQkasfevM9udu4ctRHCxVtwCLcB/s1600/IMG_6320.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-zsrjuZN7gxg/V7kBBxO1PeI/AAAAAAAAFS8/mgP-oCEGjskQkasfevM9udu4ctRHCxVtwCLcB/s320/IMG_6320.JPG" width="240" /></a></div><br />They could not believe that I took pictures! Not a single student in any class noticed I was taking pictures. Not even in a class of 5! They have already asked to do it again. My best group made it all the way to 91 and two groups made it to the 80's. We reviewed the group work strategies and from there we went to Sarah's <a href="http://mathequalslove.blogspot.com/2016/07/broken-circles-planning-for-day-1.html">Broken Circle</a> task. This only took 2-3 minutes since my students were in groups of 3. We finished the day by <a href="http://misscalculate.blogspot.com/2014/08/day-5-7-interactive-notebook-setup-and.html">setting up our INBs</a>.<br /><b><br /></b><b>Thursday</b><br />Thursday are my designated day for number talks and it started out rough. Read more <a href="http://misscalculate.blogspot.com/2016/08/my-first-number-talks.html">here</a>. We again used Google Classroom to open a pdf of my syllabus. I tried Brigid's idea of doodle notes using this <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwigrJHYw9HOAhUI7B4KHXKZAuIQFggeMAA&url=http%3A%2F%2Fwww.mathgiraffe.com%2Fblog%2Fsyllabus-for-math-class-doodle-style-free-printable&usg=AFQjCNEn3TUTQScqITg4JIXo_zPWhaS7NA&sig2=Yt4GU0XGLYXP6ToY9Ymmcw">doodle syllabus</a>. I still have mixed feelings about this. My artistic students really appreciated it. The students did agree that taking notes from the pdf was better than listening to me talk the whole time. But most of these students have had me for years and know my policies and procedures. More than one person asked why we were doing this and most people didn't even get it finished in a class period because they spent so much time doing what I asked...doodling! I can see it working much better in a lecture heavy class but thankfully, I am heading in the opposite direction of that.<br /><b><br /></b><b>Friday</b><br />We ended the week by taking our end of course exam which will be given again in December and May. I spent my time making answer keys and updating my spreadsheet data.<br /><br />Comparing the first administration last year to this year<br /><br />Algebra I 15% to 24%<br />Geometry 18% to 20%<br />Algebra II 16.5% to 24%<br />Trig 30% to 19%<br /><br />I'm using new exams except for Trig so those numbers basically mean nothing but I like that they are moving up. Except what the heck happened in trig?<br /><br />I'm so glad that thanks to my blog, I have a record of everything I've tried during the first days of school. If you teach in a small school, you know you can't repeat activities until four years have passed. Check out my <a href="http://misscalculate.blogspot.com/search/label/First%20Days">first days tag</a> if you need more ideas!<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com3tag:blogger.com,1999:blog-2467202639598238063.post-35038556011193165132016-08-19T22:09:00.001-05:002016-08-20T22:06:13.736-05:00My First Number Talk<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">I was inspired by </span><a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiK9Mbq_87OAhUH7B4KHSgVDtEQFggeMAA&url=https%3A%2F%2Fsaravanderwerf.com%2F2016%2F06%2F27%2Fsecondary-number-talks-ill-convince-you-with-ducks%2F&usg=AFQjCNH4PRx4zCXTs5vLhPgGkAxG1Ehhiw&sig2=OxNxnehW37F96-AD5pNHpw" style="text-align: left;">Sara Van Der Werf's post</a><span style="text-align: left;"> to finally start doing number talks. I haven't read any of the books yet so forgive me if I'm screwing this up.</span></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">It took me three days of number talks before I realized I should start saving these pictures.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">They are pretty terrible but I'd like to have a starting point to look back at.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The first two days were counting items in a picture so when I threw this one at them, I realized maybe a fraction problem was not the best one to use first.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We had a <i>rough</i> start but there was about one interesting answer per period so all was not lost.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-SPe70wB-fgs/V7fG99VT7cI/AAAAAAAAFSE/SWFYSsaeLgcz4By-DKvOD1j74Z1VbfTVwCLcB/s1600/10%2BNumber%2BTalks_1.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-SPe70wB-fgs/V7fG99VT7cI/AAAAAAAAFSE/SWFYSsaeLgcz4By-DKvOD1j74Z1VbfTVwCLcB/s320/10%2BNumber%2BTalks_1.jpeg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-BpVRelL01dE/V7fG_WRisEI/AAAAAAAAFSI/t_9n-ZNoZlEJ3cJ7o0xE72s0sfm8u7ICQCLcB/s1600/10%2BNumber%2BTalks_4.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-BpVRelL01dE/V7fG_WRisEI/AAAAAAAAFSI/t_9n-ZNoZlEJ3cJ7o0xE72s0sfm8u7ICQCLcB/s320/10%2BNumber%2BTalks_4.jpeg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-_t9N2A3tD8g/V7fHBGJZD0I/AAAAAAAAFSM/5U6luTi9gqcm-HxfPrqhGRknISMS5c2MACLcB/s1600/10%2BNumber%2BTalks_5.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-_t9N2A3tD8g/V7fHBGJZD0I/AAAAAAAAFSM/5U6luTi9gqcm-HxfPrqhGRknISMS5c2MACLcB/s320/10%2BNumber%2BTalks_5.jpeg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-Hu16skRbBGM/V7fHCcvU_VI/AAAAAAAAFSQ/Z9D7gFkpexU7gzkDhLddJLNc9Q78j8ZrQCLcB/s1600/10%2BNumber%2BTalks_8.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://2.bp.blogspot.com/-Hu16skRbBGM/V7fHCcvU_VI/AAAAAAAAFSQ/Z9D7gFkpexU7gzkDhLddJLNc9Q78j8ZrQCLcB/s320/10%2BNumber%2BTalks_8.jpeg" width="320" /></a></div><br />A lot of them chose 5/8 because they said they learned that the smaller fractions are bigger pieces.<br /><br />I'm really trying to put the emphasis on how we are thinking about things over right answers.<br /><br />I also used <a href="https://saravanderwerf.com/2016/08/07/week-1-day-1-name-tents-with-feedback/">Sara's name tent idea</a> and more than one student wrote that they liked how we were learning about different ways to think and that they appreciate me letting them be creative.<br /><br />Be still my heart.<br /><br />It was much easier to get them to talk about counting dots and footballs but I'm not giving up!<br /><br />Suggestions appreciated.<br /><br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com1tag:blogger.com,1999:blog-2467202639598238063.post-82178653277339957442016-08-18T22:27:00.001-05:002016-08-18T22:28:12.973-05:00Pharaohs<br /><div style="text-align: center;"><img src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" /></div><br />Things I want to instill in my students or that I hope they 'inherit' from me and my classroom!<br /><br />P-persistence. Let's get it right and get it done!<br /><br />H- happiness. I'm really working on two things: to operate out of love and to let life be on my lips. How can I speak life, love, and happiness each day to my 90 students?<br /><br />A- assertive. Learn the difference between aggressive and assertive. Know how and when to stand up for yourself and others. Learn how to not back down graciously.<br /><br />R- resilient. You wouldn't believe the things that four of my students in particular are facing this early in the school year. I hope they see in me the 'fighting spirit' to show up every day and do hard work well.<br /><br />A- attitude. As we learn together about growth mindset, I want to teach them the importance of their attitude and how it sets the tone of each day and the future.<br /><br />O- original. I think I am pretty good at standing out and being unique. Hopefully my students take away that it is okay to have strong passions and interests and to put them on display.<br /><br />H- honor. I'm trying my best to start off honoring the different ways of thinking my students have, honoring their identity by asking them to share it, and honoring the important of our relationship by building it.<br /><br />S- spirit. Take pride in who you are and where you are from. If it's not the best place, then try making it better. Give back. Be successful and share how you got there.<br /><br />Pharaoh Pride!Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-30348595798395846172016-08-12T23:43:00.000-05:002016-09-17T19:10:51.660-05:00#DITL Back to School! Year 8<br />I don't count today as our first day because I only saw my kids for five minutes per period. But this was one of the best starts we've had and an all around positive day so you know I have to share.<br /><br />The day started with the Principal giving updates to the students for about 20 minutes. Then students were released to their classes for 5 minutes each.<br /><br />This was enough time for me to have students write down their birthdays and favorite candy. I gave them an address label with my Remind number and code. I asked them to get composition notebooks and then I said good-bye!<br /><br />I asked my freshman class how many of them liked math and none of them raised their hand. I !asked them how many were good at math but didn't like it. No one. I asked them if we could all agree to think positive and that this is going to be a good year of math class. All smiles and head nods. So now it is my personal mission to ask that question at the end of the year and have a majority of the hands go up.<br /><br />We rotated through all of our classes and then around 9:30 we went to the gym. A student group had some cute games planned but it wasn't super organized. Middle school students had a blast and most of the high school sat on the bleachers and talked. We were there until lunch at 11:30 which was a little long considering we are having air conditioner problems but I made my way around talking to students.<br /><br />It just felt so nice to be reminded of relationships I've been building for years and the comfort of being surrounded by students I know and I like. I have no classes I'm dreading this year. I spent most of the day smiling and chatting with students and that was just enjoyable!<br /><br />We had a 12:00 dismissal and then a Google training from 12:30-2:30 which means we also had an hour lunch.<br /><br />I really love having Back to School night on Thursday and an early dismissal Friday.<br /><br />Have a great weekend!Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-19580396868783530732016-08-11T23:45:00.000-05:002016-09-17T19:10:27.677-05:00#DITL Back to School NightMy day did not start out very positive. Nobody likes their Teacher Institute to start with the principal reading a 22 point packet out loud word for word of new rules and expectations.<br /><br />But that is not what I came to write about.<br /><br />We revamped our Back to School Night and I really enjoyed it so I wanted to share with you. It started at 5:00 where students get their schedules in the lobby and sign up for door prizes. Then they travel around to each classroom and have their teachers sign their schedule. Showing your schedule with all the teacher signatures earned you ice cream in the cafeteria.<br /><br />Students were in the gym doing face painting and hosting sign up sheets for clubs. This was also the time for students to find their locker, test the lock, etc.<br /><br />In the library there were videos from last school year playing on a loop.<br /><br />At 6:30, everyone returns to the gym where the Principal speaks about announcements and updates.<br /><br />Then names were pulled for door prizes and that wrapped up the night!<br /><br />If only the air conditioning worked correctly...<br /><br />I was surprised to see a large group of people in the lobby at 5:00 on the dot.<br /><br />Only one student I talked to today told me they didn't like math!<br /><br />Our community 4H group donated Back to School baskets for us- so thoughtful!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-JaYiEEUicck/V64X2oCP4sI/AAAAAAAAFRs/fY--1GA13bYFjOAq5emvJDfiqatc8Y9OACLcB/s1600/IMG_6275.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-JaYiEEUicck/V64X2oCP4sI/AAAAAAAAFRs/fY--1GA13bYFjOAq5emvJDfiqatc8Y9OACLcB/s320/IMG_6275.JPG" width="240" /></a></div><br /><br />I went home feeling energized which is a lot better than the day began.<br /><br />I can't explain the growth I've experienced since January...or why. But there has definitely been a shift. I have a lot of things to do and get ready still but I'm not overwhelmed. I'm going to take it a day at a time- and it's going to be fine! I'm doing good work. I'm also doing good work to sustain my energy levels. My students deserve the best Ms. Miller I can be right now- not the best Ms. Miller I will ever be.<br /><br />My motto for the year is 'Add good things to the pile- no more starting over!"<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com3tag:blogger.com,1999:blog-2467202639598238063.post-12123191639453906722016-08-10T23:59:00.000-05:002016-09-17T19:03:30.225-05:00#DITL August 10th, 2016 <br />9:00 AM Woke up....second to last day to sleep in. =(<br /><br />10:15 AM Got to school to finish decorating my classroom. Tomorrow is a half day teacher institute from 1-5 and then Back to School Night from 5-7.<br /><br />Things I accomplished today:<br /><br /><ul><li>Cleaned all 6 carts and drawers and put new labels on each drawer (120 drawers)</li><li>Attached new labels inside plastic bins to put in the cart</li><li>Took my pentaminoes, tangrams, and counters into ziplock bags for each cart</li><li>Refilled the cart with supplies</li><li>Finished my Instagram/Milligram bulletin board</li><li>Decorated my door with my lovely chevron stickers</li><li>Rehung my chevron borders around each whiteboard (I'm never taking them down again!)</li><li>Cut out balloon and star shapes on our die cut machine for student birthdays</li><li>Printed out my Plicker cards</li><li>Took the chairs down</li><li>Printed new number placards for each group of desks</li><li>Took down streamers and paper lanterns that I didn't want anymore</li><li>Finished hanging my 'custom' wall clock</li><li>Changed three bags of trash</li><li>Swept the floor</li></ul><div>5:15 PM Got home and made dinner; changed clothes and went shopping</div><div><br /></div><div>Shopping included MORE classroom stuff:</div><div><ul><li>Wal-Mart: (plastic unit tubs, washi tape, air fresheners, and groceries)</li><li>Aldi (sugar and biscuits lol)</li><li>Walgreens (pictures for my bulletin board)</li><li>Hobby Lobby (light switch covers, silver hanging decorations, foam letters, scrapbook paper, poster board)</li><li>Dollar Tree (plastic bins and baby washcloths for dry erase markers)</li><li>Target (washi tape for binders)</li><li>Staples (my fave green Staedtler pencils)</li><li>Chinese food for a celebratory lunch tomorrow</li><li>Half price shakes at Sonic since I never ate lunch</li></ul><div>10:15 Then because I'm a crazy person I went BACK to school to finish some things so I won't be rushed tomorrow</div></div><div><br /></div><div><ul><li>Rehung my diploma frame that fell and broke</li><li>Hung up my pictures from Walgreens</li><li>Added the baby washcloths to their labeled white bins</li><li>Added scissors labels to their bins</li><li>Hung up the silver hanging decorations </li><li>Set up the air fresheners</li><li>Switched out the light switch cover</li><li>Put out my pencils in my pencil holder</li></ul><div>11:30 Finally home. Unload my crap and pick out my outfit for tomorrow. I always like to dress up more for Back to School Night since I look younger. Got everything ready for tomorrow because I hate mornings- even though I don't have to be at school until 1:00, I don't want to get up any earlier than 9:00 and I don't want to be rushed.</div></div><div><br /></div><div>And that's a normal day for me- I do crazy things at crazy times all in the name of creating!</div><div><br /></div><div>I got 12,354 steps today and walked 5.48 miles. I also drank 64 ounces of water.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-g5xMn0fn5gM/V6wcGAKjO0I/AAAAAAAAFQY/-Z5DQpIlV8oN1gqdx2cWdDLvxqBMHaUNwCLcB/s1600/IMG_6250.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-g5xMn0fn5gM/V6wcGAKjO0I/AAAAAAAAFQY/-Z5DQpIlV8oN1gqdx2cWdDLvxqBMHaUNwCLcB/s400/IMG_6250.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-riLCgRkDNPs/V6wcAHSXElI/AAAAAAAAFQU/g-3IqDIZ2xoHfZW0WqouuQfAG5x-W1-cQCLcB/s1600/IMG_6252.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-riLCgRkDNPs/V6wcAHSXElI/AAAAAAAAFQU/g-3IqDIZ2xoHfZW0WqouuQfAG5x-W1-cQCLcB/s400/IMG_6252.JPG" width="300" /></a></div><div style="text-align: center;"> <a href="https://1.bp.blogspot.com/-Ae3L9hPxc2U/V6wb96yPprI/AAAAAAAAFQQ/V_D8Ih0XfRQjUw1lqM99Yks7za7jHdIpgCLcB/s1600/IMG_6255.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="400" src="https://1.bp.blogspot.com/-Ae3L9hPxc2U/V6wb96yPprI/AAAAAAAAFQQ/V_D8Ih0XfRQjUw1lqM99Yks7za7jHdIpgCLcB/s400/IMG_6255.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-R4QHkGovINE/V6wcbiJ1IBI/AAAAAAAAFQc/qPrE7aDnajwEhIOjI4ah0SKwu74u0jYxwCLcB/s1600/IMG_6256.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-R4QHkGovINE/V6wcbiJ1IBI/AAAAAAAAFQc/qPrE7aDnajwEhIOjI4ah0SKwu74u0jYxwCLcB/s400/IMG_6256.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-Y2tnHna_7pU/V6wchCyaV6I/AAAAAAAAFQg/awKIfPFR9-YsSNEhgiS-6JlBGRed8sSGwCLcB/s1600/IMG_6257.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-Y2tnHna_7pU/V6wchCyaV6I/AAAAAAAAFQg/awKIfPFR9-YsSNEhgiS-6JlBGRed8sSGwCLcB/s400/IMG_6257.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; 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margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-itUVPmDYhnA/V6wdgTPRNsI/AAAAAAAAFQ8/tnmp_BuAc4QDgFmw0bq7PKAOSkzfQxk0ACLcB/s400/IMG_6260.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-fNCwZSvX7Pk/V6wddMKDWyI/AAAAAAAAFQ4/A3uBFUMKe2EDv4YXXY5cqhXrVrDbxJX7ACLcB/s1600/IMG_6261.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-fNCwZSvX7Pk/V6wddMKDWyI/AAAAAAAAFQ4/A3uBFUMKe2EDv4YXXY5cqhXrVrDbxJX7ACLcB/s400/IMG_6261.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-SQqR5Jfvdi8/V6wd4XFgCKI/AAAAAAAAFRE/AXV2lbxIkBoENo6mmzjY7xEFBwsm-9pnACLcB/s1600/IMG_6262.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-SQqR5Jfvdi8/V6wd4XFgCKI/AAAAAAAAFRE/AXV2lbxIkBoENo6mmzjY7xEFBwsm-9pnACLcB/s400/IMG_6262.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-_tPqrJWLpP4/V6wd_71Ms5I/AAAAAAAAFRM/KcoqFo8wFsEVCDRtOA3XQ7WnkWZpfdqRgCLcB/s1600/IMG_6263.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-_tPqrJWLpP4/V6wd_71Ms5I/AAAAAAAAFRM/KcoqFo8wFsEVCDRtOA3XQ7WnkWZpfdqRgCLcB/s400/IMG_6263.JPG" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-cdYgVwou6rM/V6wd9YXtBCI/AAAAAAAAFRI/Wdgnu8VkUxYWGBPFsMiJ1Qnj-hB-mEs-gCLcB/s1600/IMG_6264.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-cdYgVwou6rM/V6wd9YXtBCI/AAAAAAAAFRI/Wdgnu8VkUxYWGBPFsMiJ1Qnj-hB-mEs-gCLcB/s400/IMG_6264.JPG" width="300" /></a></div><br /><div><br /></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com4tag:blogger.com,1999:blog-2467202639598238063.post-28209349511913523842016-08-09T23:13:00.002-05:002016-08-09T23:13:24.317-05:00How To...Teacher Assessment<i style="background-color: white; color: #666666; font-family: Neucha; font-size: 15.84px; line-height: 22.176px; text-align: center;">In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To" style="color: #741b47; text-decoration: none;">tag</a> to the right for more posts!</i><br /><div><div style="text-align: center;"><span style="color: #666666; font-family: "neucha";"><span style="font-size: 15.84px; line-height: 22.176px;"><i><br /></i></span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" width="320" /></a></div>Again, let me just say that assessment is not something I claim to be any type of expert at. I steal most of my assessments/questions, I don't feel great about the way I grade, etc etc.<br /><br />But the least I can do is try new things and talk about them.<br /><br />So here goes!<br /><br /></div><br /><ul><li><b>Class Discussion:</b> This doesn't happen often or well in my classes, tbh. Mostly students asking me questions and me asking them questions- not much 'discussing'. I really like the idea of using controversial words like always, sometimes, never, best, and worst to spark debate among students. That feels like something I can try.</li><li><b><a href="http://desmos.com/">Desmos</a>:</b> So far I've only used activity builder for some investigations but it's great for formative assessment because I can see all student responses at the same time or individually.</li><li><b>Feedback Quiz</b>: <a href="http://misscalculate.blogspot.com/2015/07/tmc15-feedback-quizzes.html">link here</a> </li><li><b><a href="https://kahoot.it/">Kahoot</a>:</b> Students LOVE Kahoot but unfortunately iPads don't. I've only used them for formative assessment, more like practice but they definitely inspire the kids to try harder. Time limits are the only drawback for me but I like that there are so many public Kahoots that I can use and that creating my own is easy. </li><li><b>Participation Quiz:</b> <a href="https://samjshah.com/2011/07/12/participation-quizzes/">link here</a> </li><li><b><a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwi7_dfX_LXOAhVoJcAKHdimAhgQFggeMAA&url=https%3A%2F%2Fplickers.com%2F&usg=AFQjCNHejsr59XgNV930brkdRF43xJowXA&sig2=RJ0tP-fULTY3RUIvHrqzig">Plickers</a></b>: The students also LOVE plickers and they always point out to me that we didn't used them enough...like once or twice a year. But behold, thanks to <a href="https://twitter.com/jschool0218">Jonathan Schoolcraft</a>, we will now use them EVERY Friday for <a href="http://wodb.ca/">Which One Doesn't Belong</a>. Hooray!</li><li><b>Quiz</b>: Just your standard quiz. I quiz over every concept but considering combining 2-3 concepts per quiz. Although I always have less grades in the gradebook than anyone else considering I only grade quizzes and tests. Hmm...</li><li><b>Self-Check Quiz</b>: <a href="https://noschese180.wordpress.com/2011/10/07/day-22-quiz-day/">link here</a>; I read about this years ago and it seems to fit feek with self-quizzing concepts mentioned in <a href="http://misscalculate.blogspot.com/2016/07/tmc16-make-it-stick-applications-in.html">Make It Stick</a>.</li><li><b>Unit Test:</b> enough said</li><li><b>Whiteboard Practice:</b> I mostly use this in my smaller classes which is not awesome but there is something magical about it; students just automatically teach each other or self-correct which is great formative assessment</li></ul>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-78879746035201921602016-08-08T23:30:00.001-05:002016-08-09T01:32:29.980-05:00How To...Self and Peer Assessment<i style="background-color: white; color: #666666; font-family: Neucha; font-size: 15.84px; line-height: 22.176px; text-align: center;">In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To" style="color: #741b47; text-decoration: none;">tag</a> to the right for more posts!</i><br /><br /><div class="separator" style="background-color: white; clear: both; color: #666666; font-family: Neucha; font-size: 15.84px; line-height: 22.176px; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="color: #741b47; margin-left: 1em; margin-right: 1em; text-decoration: none;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" style="border: none; position: relative;" width="320" /></a></div><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;">Thanks to </span><a href="https://mathbythemountain.wordpress.com/" style="background-color: white; font-family: neucha; font-size: 15.84px; line-height: 22.176px; text-decoration: none;">mathbythemountain</a><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"> for suggesting this post; after </span><a href="http://misscalculate.blogspot.com/2016/08/how-tocreate-pacing-guide.html" style="background-color: white; font-family: neucha; font-size: 15.84px; line-height: 22.176px; text-decoration: none;">my last post</a><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;">, she asked me to explain each activity.</span><br /><br style="background-color: white; font-family: neucha; font-size: 15.84px; line-height: 22.176px;" /><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;">So here goes! Let me first say....I haven't done any of these and some of them I just learned about this summer.</span><br /><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b><br /></b></span><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b>Self-Assessment:</b></span><br /><ul><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Brain dump:</b> <a href="http://www.ericaleebeaton.com/how-to-download-and-do-a-brain-dump/">link here</a>; although it's pretty self-explanatory. I'm thinking of doing this for the first five minutes of <a href="http://misscalculate.blogspot.com/2016/05/mtbos30-study-guide-day.html">study guide day</a></span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Circle Graph Reflection:</b> blogged about <a href="http://misscalculate.blogspot.com/2016/07/inb-goodies.html">here</a> with an INB download</span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>End of unit summary INB sheet:</b> <span style="font-size: 15.84px; line-height: 22.176px;">blogged about </span><a href="http://misscalculate.blogspot.com/2016/07/inb-goodies.html" style="font-size: 15.84px; line-height: 22.176px;">here</a><span style="font-size: 15.84px; line-height: 22.176px;"> with an INB download</span></span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Reflection question on quiz/</b></span><span style="background-color: transparent;"><b>test:</b> inspired by Pam Wilson and mentioned in my "Make it Stick" <a href="http://misscalculate.blogspot.com/2016/07/tmc16-make-it-stick-applications-in.html">post</a>, I also read about this in Mathematical Mindsets. Seems really easy to implement and useful for both students and me, and apparently students can be very accurate at it.</span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Rubric:</b> this is pretty generic and I don't have any examples to share but it could be used for any assessment or project</span></span></li></ul><ul></ul><div><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b><br /></b></span><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b>Peer-Assessment:</b></span></div><div><ul><li><b>Nominations:</b> <a href="http://misscalculate.blogspot.com/2016/07/tmc16-my-favorites.html">link here</a></li><li><b>Rubric:</b> same as above</li><li><b>Two Stars and a Wish:</b> <a href="https://www.nwea.org/blog/2012/classroom-techniques-formative-assessment-idea-number-six/">link here</a></li></ul><div><br />I'm obviously weak in both of these areas. Do you have ideas to add to this?</div><div><br /></div></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-31481903709086765872016-08-08T23:30:00.000-05:002016-08-09T01:32:02.653-05:00How To...Self and Peer Assessment<i style="background-color: white; color: #666666; font-family: Neucha; font-size: 15.84px; line-height: 22.176px; text-align: center;">In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To" style="color: #741b47; text-decoration: none;">tag</a> to the right for more posts!</i><br /><br /><div class="separator" style="background-color: white; clear: both; color: #666666; font-family: Neucha; font-size: 15.84px; line-height: 22.176px; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="color: #741b47; margin-left: 1em; margin-right: 1em; text-decoration: none;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" style="border: none; position: relative;" width="320" /></a></div><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;">Thanks to </span><a href="https://mathbythemountain.wordpress.com/" style="background-color: white; font-family: neucha; font-size: 15.84px; line-height: 22.176px; text-decoration: none;">mathbythemountain</a><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"> for suggesting this post; after </span><a href="http://misscalculate.blogspot.com/2016/08/how-tocreate-pacing-guide.html" style="background-color: white; font-family: neucha; font-size: 15.84px; line-height: 22.176px; text-decoration: none;">my last post</a><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;">, she asked me to explain each activity.</span><br /><br style="background-color: white; font-family: neucha; font-size: 15.84px; line-height: 22.176px;" /><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;">So here goes! Let me first say....I haven't done any of these and some of them I just learned about this summer.</span><br /><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b><br /></b></span><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b>Self-Assessment:</b></span><br /><ul><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Brain dump:</b> <a href="http://www.ericaleebeaton.com/how-to-download-and-do-a-brain-dump/">link here</a>; although it's pretty self-explanatory. I'm thinking of doing this for the first five minutes of <a href="http://misscalculate.blogspot.com/2016/05/mtbos30-study-guide-day.html">study guide day</a></span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Circle Graph Reflection:</b> blogged about <a href="http://misscalculate.blogspot.com/2016/07/inb-goodies.html">here</a> with an INB download</span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>End of unit summary INB sheet:</b> <span style="font-size: 15.84px; line-height: 22.176px;">blogged about </span><a href="http://misscalculate.blogspot.com/2016/07/inb-goodies.html" style="font-size: 15.84px; line-height: 22.176px;">here</a><span style="font-size: 15.84px; line-height: 22.176px;"> with an INB download</span></span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Reflection question on quiz/</b></span><span style="background-color: transparent;"><b>test:</b> inspired by Pam Wilson and mentioned in my "Make it Stick" <a href="http://misscalculate.blogspot.com/2016/07/tmc16-make-it-stick-applications-in.html">post</a>, I also read about this in Mathematical Mindsets. Seems really easy to implement and useful for both students and me, and apparently students can be very accurate at it.</span></span></li><li><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><span style="background-color: transparent;"><b>Rubric:</b> this is pretty generic and I don't have any examples to share but it could be used for any assessment or project<br /></span></span></li></ul><ul></ul><div><span style="background-color: white; font-family: "neucha"; font-size: 15.84px; line-height: 22.176px;"><b>Peer-Assessment:</b></span></div><div><ul><li><b>Nominations:</b> <a href="http://misscalculate.blogspot.com/2016/07/tmc16-my-favorites.html">link here</a></li><li><b>Rubric:</b> same as above</li><li><b>Two Stars and a Wish:</b> <a href="https://www.nwea.org/blog/2012/classroom-techniques-formative-assessment-idea-number-six/">link here</a></li></ul><div>I'm obviously weak in both of these areas. Do you have ideas to add to this?</div><div><br /></div></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-62739261893941133952016-08-07T23:27:00.000-05:002016-08-08T01:28:47.157-05:00How To...Implement Activities<br /><i style="background-color: white; color: #666666; font-family: Neucha; font-size: 15.84px; line-height: 22.176px; text-align: center;">In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To" style="color: #741b47; text-decoration: none;">tag</a> to the right for more posts!</i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" width="320" /></a></div><br />Thanks to <a href="https://mathbythemountain.wordpress.com/">mathbythemountain</a> for suggesting this post; after <a href="http://misscalculate.blogspot.com/2016/08/how-tocreate-pacing-guide.html">my last post</a>, she asked me to explain each activity.<br /><br />So here goes!<br /><br /><b>Activities:</b><br /><ul><li><b>Dry Erase Practice:</b> my students can write on their desks with dry erase markers so I guess you could just call this desk practice. If I have problems prepared, then they work it on the desk and I show the answer. If I don't, then I walk around and look at their work, Or both.</li><li><b>Task Cards:</b> these are kind of popular now but basically they are problems printed individually on cardstock. I set them on the whiteboard ledge and students or groups come get one card and work it and then return it. Each group should only have one card. Sometimes the cards have answers on them so they can self-check. Sometimes I walk around with an answer key.</li><li><b>Investigation:</b> for me, this is basically a scaffolded activity that leads them through new instruction. It usually involves a lot of questions, maybe some color coding, maybe some matching, sorting, or calculator directions.</li><li><b><a href="http://desmos.com/">Desmos:</a></b> So far I have only used Activity Builder, which is amazing, but over the summer they introduced marble slides and card sorts so I can't wait to use those. Desmos is also great for verifying things with graphs, showing visuals, and introducing transformations.</li><li><b>Card Sort:</b> these are my favorite of all time and I plan on blogging a 'how to' post about creating them. Basically, if there is something you know students mix up or something they never notice, make a card sort out of it. Ask them to sort the pieces into groups and explain how they sorted. Then give them hints until they find it such as: you should have four groups, each group should have the same amount, etc. SO much more meaningful than you just telling students to look for or pay attention to something- let them discover it on their own.</li><li><b>Grudge Ball:</b> <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwih8dzzkrHOAhXJ54MKHR8lCMQQFgghMAA&url=http%3A%2F%2Ftoengagethemall.blogspot.com%2F2013%2F02%2Fgrudgeball-review-game-where-kids-attack.html&usg=AFQjCNFyHWuJ4FXm6bwfEoDYoJcIB58A6w&sig2=219de_axYLJ6pVah2lwXng">link here</a> </li><li><b>Row Game:</b> <a href="http://function-of-time.blogspot.com/2009/10/row-game.html">link here</a> </li><li><b>Four in a Row:</b> <a href="http://mathequalslove.blogspot.com/2016/01/quick-and-easy-review-games.html">link here</a></li><li>Triples: usually a set of 15 problems, students in pairs/groups work them out and then at the end they sort into 5 groups of 3 that have the same answer. If they can't find three cards with the same answer, they work together to find their mistakes</li></ul><div><b><br /></b><b>Activities that Involve Movement:</b></div><div><ul><li><b>Chalk Talk:</b> <a href="https://pamjwilson.wordpress.com/2013/03/29/chalk-talk-part-1-makthinkvis/">link here</a></li><li><b>Centers/Stations: </b>students rotate to stations that focus on different topics; answer key to previous station provided after rotating; usually used to review.</li><li><b>Cornhole Review:</b> <a href="http://www.mathgiraffe.com/blog/review-strategies-games">link here</a> </li><li>Gallery Walk: <a href="https://pamjwilson.wordpress.com/2014/04/01/gallery-walk-ppschat-challenge/">link here</a></li><li>Hedbanz: <a href="https://samjshah.com/2014/07/29/rational-function-headbandz/">link here</a> </li><li>Pong Review: <a href="http://misscalculate.blogspot.com/2011/03/fish-pong-review-game.html">link here</a></li><li>Scavenger Hunt: <a href="http://everybodyisageniusblog.blogspot.com/2012/09/math-scavenger-hunt.html">link here</a> </li><li>Speed Dating: <a href="http://function-of-time.blogspot.com/2009/10/speed-dating.html">link here</a></li><li>Trashketball: tape a line on the floor some distance away from the trash can and set out a ream of paper. Students work in groups, everyone works the problem, the group answer that is correct sends one person to shoot. Make up your own rules. I put tape for 2 and 3 pointers. If they don't get the problem correct then they don't get to shoot.</li><li>Vertical Whiteboards: <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwi50rbFlbHOAhUs5oMKHaoIDwIQFggeMAA&url=http%3A%2F%2Fslamdunkmath.blogspot.com%2F2014%2F08%2Fvertical-non-permanent-surfaces-and.html&usg=AFQjCNFLz3IHB86qi8uT2m64J-UXVrdajg&sig2=FnRIK2XZY97TGy8iA2SRwg">link here</a></li></ul><div><br />Next up I will explain the assessments mentioned in my <a href="http://misscalculate.blogspot.com/2016/08/how-tocreate-pacing-guide.html">previous post</a>. Thanks again Audrey!</div><div><br /></div></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com2tag:blogger.com,1999:blog-2467202639598238063.post-7928118468917653322016-08-06T23:55:00.000-05:002016-08-07T00:19:39.425-05:00How To...Create a Pacing Guide<div style="text-align: center;"><i><br />In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To">tag</a> to the right for more posts!</i></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" width="320" /></a></div><br />I'm not going to claim to be an expert in any of these '<a href="http://misscalculate.blogspot.com/search/label/How%20To">how to</a>' posts but I've made quite a few pacing guides and I can at least explain my thinking behind it.<br /><br />Here is my Algebra I rough draft. Look at it first so that I can break down each decision.<br /><br /><center><iframe allowfullscreen="" frameborder="0" height="400" msallowfullscreen="" src="https://app.box.com/embed/preview/3o2y7h4dw3zhh1b4iqdjkp2dc0tppawp?direction=ASC&theme=dark" webkitallowfullscreen="" width="450"> </iframe></center><br /><br />First of all, I want a clear list of topics that I plan on teaching. I want those nestled inside cozy little units. I want a specific number of units that spans the course of a year.<br /><br />I want these things so I can break them down into small, manageable chunks. I will be starting my eighth year of teaching and to be honest, I usually get about halfway through my pacing guide. That's pretty terrible.<br /><br />I've just decided: no more starting over!!! I want to focus on adding.<br /><br />I've started with Algebra I. There are 12 units...which means 3 units per quarter which means 3 weeks per unit. I have 6 or less skills per unit which means 2 skills per week. This is the goal I'm shooting for while knowing that some units will go faster or slower than I predict, the weather will mess up my good intentions several times, and instead of getting upset, I will focus on getting farther and farther along in my pacing guide each year.<br /><br />I also align my pacing guide to the final exam or end of course exam. This means that next to each skill, I put the question number from the exam that corresponds to that skill. This way at the end of the year, I have a list of each question that students *should* be able to do (since I never get through everything).<br /><br />This year I added activity structures to check off, mainly because I want to see how often I use certain activities and I want to make sure I include movement more often.<br /><br />I also included the mathematical practices because I've never done a good job at focusing on them.<br /><br />Reflection, seld-assessment, and peer-assessment came up a lot in my reading and at TMC this year so I added those sections as well. As you can see, this is a weakness of mine since I have very few ideas to attempt.<br /><br />I put a 'notes' section at the bottom because I'm trying to get better at reflecting.<br /><br />For next year, I would like to add vocabulary words, good questions, and prerequisite skills. I will try to add those things along the way so that next year: no more starting over! Hopefully I will remember to update this post in the next month or so with *this year's* final draft.<br /><br />Oh, and the color strip at the top of each page will be color coded for each course and to that course's INB...of course.<br /><br />This will also be a great tool to include in my teacher evaluation binder!<br /><br />What else would you include in a pacing guide that will help you focus? What are some of your favorite strategies for self and peer assessment?<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com8tag:blogger.com,1999:blog-2467202639598238063.post-61386639728712700442016-08-05T18:38:00.002-05:002016-08-05T18:38:25.847-05:00Classroom Instruction from A to Z<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s1600/blaugust.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://2.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/iboq_-my2qkSQ9kuTLUQNpQf-HFTLqsIwCPcB/s320/blaugust.jpg" width="320" /></a></div><br /><a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwj31tj1s6vOAhUp2oMKHT1tDQoQFggeMAA&url=https%3A%2F%2Fwww.amazon.com%2FClassroom-Instruction-Barbara-R-Blackburn%2Fdp%2F159667038X&usg=AFQjCNH_37ttQ2h0v71pHPp8m8-sewV4Zw&sig2=tRE-0dcE8mOkWVQQUVCPMw">Classroom Instruction from A to Z</a><br />Barbara Blackburn<br /><br />It isn't the strategy- it's how you use the strategy that makes a difference.<br /><br />My goal is to give them information and let them internalize and give it back; not just force-fed info and make them regurgitate it. I want to give them an opportunity to internalize and express [their learning].<br /><br />If they are allowed to choose how they will show that they understand the content, many students will invest more time and effort in the task.<br /><br />Start with one idea and build on your success.<br /><br />"Learning and teaching is messy stuff. It doesn't fit into bubbles." -Michele Forman<br /><br />Think of data analysis like a triangle: classroom performance and standardized test scores should be evaluated together with a third data point, your teacher judgment.<br /><br />Data shouldn't replace your judgment; it should help you make decisions.<br /><br />Our students are not in their final state when we are teaching them.<br /><br />The word <i>but</i> can serve as a red light or a stop sign for progress, The word <i>and</i> is like a green light.<br /><br />Your language reflects your beliefs, and your students follow your model. If they hear you using words as an excuse, so will they.<br /><br />Give students your BEST: belief, encouragement, support, time<br /><br />Many students do not have a vision of anything more than where they are right now. You can help them create a vision for themselves through your words, actions, and activities so they they support each other.<br /><br />"Students learn over half of what they know from visual images." -Mary Alice White<br /><br />If your form of delivery isn't working, then find a different way to deliver it.<br /><br />Rigor is not just about difficulty. Rigor is also about helping out students learn to critically think about their learning.<br /><br />Complexity isn't about doing more work, it's about doing less drill and practice and more higher-level thinking activities.<br /><br />Allowing students to take a zero reflects lowered expectations. It permits a student to get by without actually doing the work and says to the student, "You don't have to learn this."<br /><br />Less is more. Give students small amounts of focused work that requires them to apply knowledge and evaluate information.<br /><br />Our mode of instruction says, "Trust me. I know where we are going, so you don't need to." But students don't always respond positively to that approach.<br /><br />Effective homework can be completed independently with minimal and appropriate support. If the assignment is too difficult, students are more likely to ask someone else to complete it for them.<br /><br />"The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask him which he finds it hard to answer." -Alice Wellington Rollins<br /><br />As you create questions for your students, remember to build in questions that are open ended, those that have more than one answer.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-fm-T8IX2z3Q/V6UjZJ6tMhI/AAAAAAAAFP8/n4KZE4PeB9cU8BvThKUsMtUTYFu4oD9fQCLcB/s1600/Qumaker.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="223" src="https://3.bp.blogspot.com/-fm-T8IX2z3Q/V6UjZJ6tMhI/AAAAAAAAFP8/n4KZE4PeB9cU8BvThKUsMtUTYFu4oD9fQCLcB/s320/Qumaker.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">There are three types of reflection for students: reflecting on what they have learned, reflecting on how they learn, and reflecting on their progress.</div><div class="separator" style="clear: both; text-align: left;"><br /></div>Checking Prior Knowledge- First, she gives students three minutes to answer a short true/false questionnaire. Next, in pairs, students compare responses and use the textbook to check their answers. Each set of partners must rewrite any false statements so that they are true. She ends with a whole class discussion to ensure understanding.<br /><br />During "Three Alike", she writes three words on the board or overhead projector. Students then have to explain what the words have in common.<br /><br />I shuffle playing cards and each student takes one. While they are taking their cards, I make up the rules. Find your group by matching either the suit, the number, or picture. I prepare the deck ahead of time so that I will have the correct number of cards that will create the desired number of groups.<br /><br />Just because we do something a lot doesn't mean it works.Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com2tag:blogger.com,1999:blog-2467202639598238063.post-32568862661622287682016-08-04T08:25:00.000-05:002016-08-07T00:20:29.667-05:00How To...Mathematical Mindsets: How Do I Start?<i style="text-align: center;"><br />In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To">tag</a> to the right for more posts!<br /></i><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://statteacher.blogspot.com/2016/07/mtbosblaugust-participating-blogs-2016.html"><img border="0" height="105" src="https://1.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/kxvDiiEC6RMqy7GgP2Xgnb29vbnDgYFRwCEw/s320/blaugust.jpg" width="320" /></a></div>If you're like me, the last five posts were probably overwhelming.<br /><br />Part 1 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-1.html">{here}</a><br />Part 2 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-2.html">{here}</a><br />Part 3<a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-3.html">{here}</a><br />Part 4 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-4.html">{here}</a><br />Part 5 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-5.html">{here}</a><br /><br /><a href="https://www.amazon.com/Mathematical-Mindsets-Unleashing-Potential-Innovative/dp/0470894520/ref=sr_1_1?ie=UTF8&qid=1469836771&sr=8-1&keywords=mathematical+mindsets">Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching</a><br />Jo Boaler<br /><br />There's a lot of things to change, fixm and improve. I tried to break this massive shift to my brain into categories of practical things to do.<br /><br />Easy: things I can do from day one this school year with no prep<br />Medium: things I can do in the next couple of months or with some prep<br />Hard: things to think about this year and plan to do over next summer<br /><br /><b><u>Easy</u></b><br /><ul><li>Ask students to think visually first</li><li>Ask students for the different ways they see and solve problems</li><li>Ask students to look for patterns, similarities, and differences</li><li>In every math conversation, ask students to reason, to explain why they chose particular methods and why they made sense.</li><li>Honor hard work and the struggle over effortless achievement</li><li>Think of all the ways to be mathematical. No one is good at all of these ways of working, but everyone is good at some of them.</li><li>Classroom mantra/poster: Always give help when needed, always ask for help when you need it.</li><li>Do not include early assignments {review?} from math class in the end-of-class grade .</li><li>Do not include homework, if given, as any part of grading.</li><li><div>Honor student thinking- say, "incorrect but helpful"-there is always some logic there.</div></li><li><div>When students want me to tell them how to do a problem say, "Do you want my brain to grow or do you want to grow your brain today?”</div></li><li><div>Praise people for having good thinking and for being accomplished, learned, hard working, and persistent; not being smart or fast or for effortless achievement</div></li><li><div>To take student thinking deeper say, "You may know a rule for solving this question, but the rule doesn't matter today, I want you to make sense of your answer, to explain why your solution makes sense."</div></li><li><div>Teachers can encourage students to use intuition with any math problem simply by asking them what they think would work, <i>before</i> they are taught a method.</div></li><li><div>Tell students, "I am not concerned about you finishing math problems quickly; what I really like to see is an interesting representation of ideas, or a creative method or solution."</div></li><li><div>Ask students to draw connections between concepts in mathematics when working on problems. Encourage students to propose different methods to solve problems and then ask them to draw connections between methods, discussing for example, how they are similar and different</div></li><li>Ask students to play the role of being the skeptic; explain that they need to <i>demand</i> to be fully convinced. Students really enjoy challenging each other for convincing reasons, and this helps them learn mathematical reasoning and proof. When students act as a skeptic, they get an opportunity to question other students without having to take on the role of someone who doesn't understand.</li><li><div>Offer all students high-level math content and believe they can do it</div></li><li>"One of the greatest gifts you can give to your students is your knowledge, ideas, and feedback on their mathematical development, when phrased positively and with growth messages".</li></ul><b><u>Medium</u></b><br /><br /><ul><li>For definitions, give nonexamples and barely examples instead of perfect examples</li><li>Introduce and build a growth mindset!</li><li>Introduce the headache before the aspirin</li><li>Replace class lectures with instructing reporters who go back and instruct their group.</li><li><div>Participation quizzes! {<a href="https://samjshah.com/2011/07/12/participation-quizzes/">Yay Sam!</a>}</div></li><li><div>Put student questions on posters,</div></li><li><div>Always allow students to resubmit any work or test for a higher grade {I already do quiz retakes but I let students use their notes on tests. Should still allow them to redo tests as well?}</div></li><li><div>Take students' ideas and make incorrect statements for the students to challenge</div></li><li><div>Instead of asking students to simplify ask students to find all the ways they can represent that are equivalent.</div></li><li><div>Tell students what they should know and let them reflect on how much of it they know. Frequently.</div></li><li><div>Self and peer-assessment {"Questions that ask students to think about errors or confusions are particularly helpful in encouraging students' self-reflection, and they will often result in the students' understanding the mathematics for the first time."}</div></li><li>Number Talks</li><li>Ask students to compare and choose methods to problem solve</li></ul><b><u>Hard</u></b><br /><ul><li>Grade multidimensionally</li><li>Give group tests and randomly choose one paper from the group to grade.</li><li>Learn more about Assessment for Learning, A4L</li><li>Do not use a 100-point scale.</li><li>Give diagnoistic comments instead of grades. "The students receiving comments learned twice as fast as the control group, the achievement gap between male and female students disappeared, and student attitudes improved."</li><li><div>Study after study shows that grading reduces the achievement of students. Share grades with school administrators but not with the students.</div></li><li><div>Give students rich mathematical tasks that are low floor, high ceiling</div></li><li>Open up the task so that there are multiple methods, pathways, and representations. </li><li>Include inquiry opportunities.</li></ul><br /><div>Do you feel better now, seeing that the easy section has the most things to do?<br /><br />Did you notice that most of them include the verbs ask, tell, show, say, show, think, honor, encourage? Those are all forms of talking and I don't know about you, but I am pretty dang good at that.<br /><br />Look how we can make great change with small changes in our words and demeanor. I am encouraged that there are so many positive things I can do for my students RIGHT AWAY.</div><br />Hooray.<br /><br />All day.<br /><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com6tag:blogger.com,1999:blog-2467202639598238063.post-19120392620201639702016-08-03T11:25:00.000-05:002016-08-03T11:25:00.169-05:00Mathematical Mindsets: The Highlights {Part 5}<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://statteacher.blogspot.com/2016/07/mtbosblaugust-participating-blogs-2016.html"><img border="0" height="105" src="https://1.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/kxvDiiEC6RMqy7GgP2Xgnb29vbnDgYFRwCEw/s320/blaugust.jpg" width="320" /></a></div>This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!<br /><br />It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.<br /><br />Enjoy!<br /><br />Part 1 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-1.html">{here}</a><br />Part 2 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-2.html">{here}</a><br />Part 3<a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-3.html">{here}</a><br />Part 4 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-4.html">{here}</a><br /><br /><a href="https://www.amazon.com/Mathematical-Mindsets-Unleashing-Potential-Innovative/dp/0470894520/ref=sr_1_1?ie=UTF8&qid=1469836771&sr=8-1&keywords=mathematical+mindsets">Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching</a><br />Jo Boaler<br /><br /><b><u>Chapter 9: Teaching Mathematics for a Growth Mindset</u></b><br /><br /><b style="background-color: yellow;">I believe in every one of them, that there is no such thing as a math brain or a math gene, and that I expect all of them to achieve at the highest levels. I love mistakes. Every time they make a mistake their brain grows. Failure and struggle do not mean that they cannot do math—these are the most important parts of math and learning. I don't value students' working quickly; I value their working in depth, creating interesting pathways and representations. I love student questions and will put these onto posters that I hang on the walls for the whole class to think about.</b><br /><br />Math is a very creative subject that is, at its core, about visualizing patterns and creating solution paths that others can see, discuss, and critique.<br /><br />To run a participation quiz, choose a task for students to work on in groups, then show them the ways of working that you value.<br /><br />Once you have shown these to students, you can start them working. As they work together in groups, walk around the room watching group behavior, writing down comments.<br /><br />As you circulate and take notes, quote students' actual words when they are noteworthy.<br /><br />But it is even more important to communicate positive beliefs and expectations to students who are slow, appear unmotivated, or struggle. <b style="background-color: yellow;">It is also important to realize that the speed at which students appear to grasp concepts is not indicative of their mathematics potential (Schwartz, 2001).</b><br /><br />The most productive classrooms are those in which students work on complex problems, are encouraged to take risks, and can struggle and fail and still feel good about working on hard problems.<br /><br />We must also resist valuing “effortless achievement”—praising students who are fast with math. Instead, <b style="background-color: yellow;">we should value persistence and hard thinking.</b><br /><br /><b style="background-color: yellow;">When students fail and struggle it does not mean anything about their math potential; it means that their brains are growing, synapses are firing, and new pathways are being developed that will make them stronger in the future.</b><br /><br />Instead of saying “You are so smart,” it is fine to say to students something like “It's great that you have learned that,” or “I love how you are thinking about the problem.”<br /><br />My undergraduates have really worked on this and now <b style="background-color: yellow;">praise people for having good thinking and for being accomplished, learned, hard working, and persistent.</b><br /><b style="background-color: yellow;"><br /></b><b style="background-color: yellow;">There is always some logic in students' thinking, and it is good to find it, not so that we avoid the “failure” idea, but so that we honor students' thinking.</b><br /><br />I recently read about a second-grade teacher, Nadia Boria, who offers this response to students when they ask for help: “Let's think about this for a minute. <b style="background-color: yellow;">Do you want my brain to grow or do you want to grow your brain today?</b>” (Frazier, 2015).<br /><br />Mathematics tasks should offer plenty of space for learning. Instead of requiring that students simply give an answer, they should give students the opportunity to explore, create, and grow.<br /><br />Open up math tasks:<br /><br /><ul><li>Instead of asking students to answer the question 1/2 divided by 1/4, ask them to make a conjecture about the answer to 1/2 divided by 1/4 and make sense of their answer, including a visual representation of the solution. As I described in Chapter Five , when Cathy Humphreys asked students to solve 1 ÷ 2/3 she started by saying, <b style="background-color: yellow;">“You may know a rule for solving this question, but the rule doesn't matter today, I want you to make sense of your answer, to explain why your solution makes sense.” </b></li><li>Instead of asking students to simplify 1/3(2x + 15) + 8, a common problem given in algebra class, <b style="background-color: yellow;">ask students to find all the ways they can represent that are equivalent.</b></li><li>Instead of asking students how many squares are in the 100th case, <span style="background-color: yellow;"><b>ask them how they see the pattern growing</b></span>, and to use that understanding to generalize to the 100th case</li></ul><br />Ask students to discuss:<br /><br /><ul><li>Ways of seeing the mathematics </li><li>Ways of representing ideas </li><li>The different pathways through the problem and strategies </li><li>The different methods used: “Why did you choose those methods? How do they work?”</li></ul><br />Encourage students to propose different methods to solve problems and then ask them to draw connections between methods, discussing for example, how they are similar and different or why one method may be used and not another. This could be done with methods used to solve number problems, such as those shown in Figure 5.1 , in Chapter Five .<br /><br />Ask students to draw connections between concepts in mathematics when working on problems.<br /><br />In my own teaching of mathematics, I encourage student creativity by posing interesting challenges and valuing students' thinking. <b style="background-color: yellow;">I tell students I am not concerned about their finishing math problems quickly; what I really like to see is an interesting representation of ideas, or a creative method or solution. When I introduce mathematics to students in this way, they always surprise me with their creative thinking.</b><br /><br /><b style="background-color: yellow;">Teachers can encourage students to use intuition with any math problem simply by asking them what they think would work, before they are taught a method.</b><br /><br /><b style="background-color: yellow;">The teacher provocatively took the students' ideas and made incorrect statements for the students to challenge, and the class considered together all of the possible relationships of angles that preserve the definitions.</b><br /><br />In the lesson in China, the teacher did not ask complete-this-sentence questions; she listened to students' ideas and made provocative statements in relation to their ideas that pushed forward their understanding. Her statements caused the students to respond with conjectures and reasons, thinking about the relationships between different angles.<br /><br />If you give students the opportunity to extend problems, they will almost always come up with creative and rich opportunities to explore mathematics in depth, and that is a very worthwhile thing for them to do.<br /><br /><b style="background-color: yellow;">He points out that students currently spend 80% of the time they spend in math classrooms performing calculations, when they should instead be working on the other three parts of mathematics—setting up models, refining them, and using them to solve real problems.</b><br /><br />In my own teaching experience, when I have asked students in classrooms to consider a situation and pose their own question, they have become instantly engaged, excited to draw on their own thinking and ideas. This is an idea for math classrooms that is very easy to implement and needs to be used only some of the time. Students should be able to experience this in school so that they are prepared to use it later in their mathematical lives.<br /><br />It is so important that employees describe their mathematical pathways to others, in teams, because others can then use those pathways in their own work and investigations and can also see if there are errors in thinking or logic. This is the core of mathematical work; it is called reasoning.<br /><br /><b style="background-color: yellow;">When students act as a skeptic, they get an opportunity to question other students without having to take on the role of someone who doesn't understand.</b>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com2tag:blogger.com,1999:blog-2467202639598238063.post-1966362185626865462016-08-02T11:01:00.000-05:002016-08-02T11:01:00.148-05:00Mathematical Mindsets: The Highlights {Part 4}<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://statteacher.blogspot.com/2016/07/mtbosblaugust-participating-blogs-2016.html"><img border="0" height="105" src="https://1.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPw/kxvDiiEC6RMqy7GgP2Xgnb29vbnDgYFRwCEw/s320/blaugust.jpg" width="320" /></a></div>This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!<br /><br />It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.<br /><br />Enjoy!<br /><br />Part 1 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-1.html">{here}</a><br />Part 2 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-2.html">{here}</a><br />Part 3<a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-3.html">{here}</a><br /><br /><a href="https://www.amazon.com/Mathematical-Mindsets-Unleashing-Potential-Innovative/dp/0470894520/ref=sr_1_1?ie=UTF8&qid=1469836771&sr=8-1&keywords=mathematical+mindsets">Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching</a><br />Jo Boaler<br /><b><u><br /></u></b><b><u>Chapter 7: From Tracking to Growth Mindset Grouping</u></b><br /><br />The strong messages associated with tracking are harmful to students whether they go into the lowest or highest groups (Boaler, 1997; Boaler, 2013a; Boaler & Wiliam, 2001; Boaler, Wiliam, & Brown, 2001).<br /><br />In the Third International Mathematics and Science Study, for example, the United States was found to have the greatest variability in student achievement—that is, the most tracking. T<b style="background-color: yellow;">he country with the highest achievement was Korea, which was also the country with the least tracking</b> and the most equal achievement. The United States also had the strongest links between achievement and socioeconomic status, a result that has been attributed to tracking (Beaton & O'Dwyer, 2002). <b style="background-color: yellow;">Countries as different as Finland and China top the world in mathematics performance, and both countries reject ability grouping, teaching all students high-level content.</b><br /><br />They found that the students who worked without advanced classes took more advanced math, enjoyed math more, and passed the state test in New York a year earlier than students in tracks. Further, researchers showed that the advantages came across the achievement spectrum for low-and high-achieving students (Burris, Heubert, & Levin, 2006). These findings have been repeated in study after study (see, for example, Boaler, 2013b). <b style="background-color: yellow;">A substantial body of research points to the harmful effects of tracking, yet the practice is used in most schools across the country.</b><br /><br />Most of the unmotivated and bad behavior that happens in classrooms comes from students who do not believe that they can achieve.<br /><br />In all of my experience teaching heterogeneous groups of students, <b style="background-color: yellow;">I have found that when students start to believe they can achieve, and they understand that I believe in them, bad behavior and lack of motivation disappear.</b><br /><br />They discovered that when they gave open tasks, all students were interested, challenged, and supported. Over time the students they thought of as low-achieving started working at higher levels, and the classroom was not divided into students who could and students who could not; it was a place full of excited students learning together and helping each other.<br /><br />The choice or the challenge must always be available to all students.<br /><br />A one-dimensional math class, of which there are many in the United States, is one in which one practice valued above all others—usually that of executing procedures correctly.<br /><br />In a multidimensional math class, teachers think of all the ways to be mathematical. No one is good at all of these ways of working, but everyone is good at some of them.<br /><br />A stunning 97% of students from the traditional approach said the same thing: “Pay careful attention.” This is a passive learning act that is associated with low achievement (Bransford, Brown, & Cocking, 1999).<br /><br />In the Railside classes, when we asked students the same question, they came up with a range of ways of working, such as:<br /><br /><ul><li>Asking good questions </li><li>Rephrasing problems </li><li>Explaining </li><li>Using logic </li><li>Justifying methods </li><li>Using manipulatives </li><li>Connecting ideas </li><li>Helping others</li></ul><br />A student named Rico said in an interview, “Back in middle school the only thing you worked on was your math skills. But here you work socially and you also try to learn to help people and get help. Like you improve on your social skills, math skills, and logic skills” (Railside student, year 1).<br /><br />Another student, Jasmine, added, “With math you have to interact with everybody and talk to them and answer their questions. You can't be just like ‘Oh here's the book, look at the numbers and figure it out.’” When we asked, “Why is that different for math?” she said, “It's not just one way to do it. It's more interpretive. It's not just one answer. There's more than one way to get it. And then it's like: ‘Why does it work?’” (Railside student, year 1).<br /><br />A theme of the algebra course, and then later all the courses in the school, was multiple representations—students were frequently asked to represent their ideas in different ways, such as through words, graphs, tables, symbols, and diagrams. Students were also encouraged to color code, representing ideas in the same color—for example, using the same color for the x in an expression, diagram, graph, table, and paragraph (see Exhibit 7.4 ).<br /><br /><b style="background-color: yellow;">Many more students were successful because there were many more ways to be successful.</b><br /><br />Although the standardized state tests the students had to take under the State of California requirements did not value multidimensional mathematics, the students achieved at high levels because they had learned to be successful in class and to feel good about mathematics. They also approached the state tests as confident problem solvers willing to try any question.<br /><br />Students were able to get started through encouraging each other, rereading questions, and asking each other questions.<br /><br />What is the question asking us?<br />How could we rephrase this question?<br />What are the key parts of the problem?<br /><br />But teachers frequently need to inject a new piece of information or a new direction into the group work. In complex instruction, teachers do not try to do this by quieting the whole class. Instead, they call the recorder/reporters out to join the teacher for a huddle. The recorder/reporters meet as a group with the teacher, who can give information that each recorder/reporter takes back to the groups. This not only helps the teacher but also gives the students responsibility that is intrinsically valuable in helping them feel empowered mathematically.<br /><br />An interesting and subtle approach recommended in the complex instruction pedagogy is that of assigning competence . This practice involves teachers' raising the status of students who they think may be lower status in a group—by, for example, praising something they have said or done that has intellectual value, and bringing it to the group's or the whole class's attention. For example, teachers may ask a student to present an idea or publicly praise a student's work in a whole class setting.<br /><br />An activity I always like groups to work on before introducing any math work is to ask them to discuss together the things they do and don't like other group members to do and say when they are working in a group on math.<br /><br />I find that when students think for themselves about positive and negative group discussions and come up with their own lists, they are more thoughtful about the ways they interact in groups.<br /><br /><b style="background-color: yellow;">I also start classes by explaining to students what is important to me. I say that I do not value speed or people racing through math; I value people showing how they think about the math, and I like creative representations of ideas.</b><br /><br />Yet another way the Railside teachers encouraged group responsibility is a method that is shocking to some, but that really communicates the idea that group members are responsible for each other. Occasionally the teachers gave what they called “group tests.” Students would take the test individually, but the teachers would take in only one test paper per group (randomly chosen) and grade it. That grade would then be the grade for all the students in the group. This was a very clear communication to students that they needed to make sure all of their group members understood the mathematics.<br /><br /><b style="background-color: yellow;">As the approach they experienced became more multidimensional, they came to regard each other in more multidimensional ways, valuing the different ways of seeing and understanding mathematics that different students brought to problems.</b><br /><br />Many parents worry about high achievers in heterogeneous classes, thinking that low achievers will bring down their achievement, but this does not usually happen. High achievers are often high achievers in the U.S. system because they are procedurally fast. Often these students have not learned to think deeply about ideas, explain their work, or see mathematics from different perspectives because they have never been asked to do so. When they work in groups with different thinkers they are helped, both by going deeper and by having the opportunity to explain work, which deepens their understanding. Rather than groups being lowered by the presence of low achievers, group conversations rise to the level of the highest-thinking students. Neither the high nor the low achievers would be as helped if they were grouped only with similar achieving students.<br /><br />Two practices I have come to regard as particularly important in promoting equity, and that were central to the responsibility students showed for each other, are justification and reasoning.<br /><br />Always give help when needed, always ask for help when you need it.<br /><br /><b><u>Chapter 8: Assessment for a Growth Mindset</u></b><br /><br /><b style="background-color: yellow;">Students with no experience of examinations and tests can score at high levels because the most important preparation we can give students is a growth mindset, positive beliefs about their own ability, and problem-solving mathematical tools that they are prepared to use in any mathematical situation.</b><br /><br /><b style="background-color: yellow;">Study after study shows that grading reduces the achievement of students.</b><br /><br /><b style="background-color: yellow;">The students receiving comments learned twice as fast as the control group, the achievement gap between male and female students disappeared, and student attitudes improved.</b><br /><br />When we give assessments to students, we create an important opportunity. Well-crafted tasks and questions accompanied by clear feedback offer students a growth mindset pathway that helps them to know that they can learn to high levels and, critically, how they can get there.<br /><br />I have seen this shift happen with many teachers with whom I have worked. It comes about when teachers are treated as the professionals they are and are invited to use their own judgment, helped by research ideas, to create positive learning and assessment experiences for their students.<br /><br />He went on to describe how the valuing of different mathematics strategies allowed him to feel he could work with mathematics in any way he wanted, to explore ideas and learn about numbers.<br /><br />When students are given scores that tell them they rank below other students, they often give up on school, deciding that they will never be able to learn, and they take on the identity of an underperforming student.<br /><br />The grades and scores given to students who are high achieving are just as damaging. Students develop the idea that they are an “A student” and start on a precarious fixed mindset learning path that makes them avoid harder work or challenges for fear that they will lose their A label. Such students often are devastated if they get a B or lower, for any of their work.<br /><br />When students develop interest in the ideas they are learning, their motivation and their achievements increase.<br /><br />They found something amazing: a form of assessment so powerful that if teachers shifted their practices and used it, it would raise the achievement of a country, as measured in international studies, from the middle of the pack to a place in the top five.<br /><br />In A4L, students become knowledgeable about what they know, what they need to know, and ways to close the gap between the two. Students are given information about their flexible and growing learning pathways that contributes to their development of a growth mathematics mindset.<br /><br />One important principle of A4L is that it teaches students responsibility for their own learning.<br /><br />Assessment for learning can be thought of as having three parts: (1) clearly communicating to students what they have learned, (2) helping students become aware of where they are in their learning journey and where they need to reach, and (3) giving students information on ways to close the gap between where they are now and where they need to be (see Figure 8.3 ).<br /><br /><b style="background-color: yellow;">The researchers concluded that a large part of the students' previous low achievement came not from their purported lack of ability but from the fact that previously they had not known what they should really be focusing upon.</b><br /><b><span style="color: yellow;"><br /></span></b><b style="background-color: yellow;">The two main strategies for helping students become aware of the math they are learning and their broader learning pathways are self-and peer assessment.</b><br /><br />If students start each unit of work with clear statements about the mathematics they are going to learn, they start to focus on the bigger landscape of their learning journeys—they learn what is important, as well as what they need to work on to improve.<br /><br />Studies have found that when students are asked to rate their understanding of their work through self-assessment, they are incredibly accurate at assessing their own understanding, and they do not over-or underestimate it (Black et al., 2002).<br /><br /><b style="background-color: yellow;">In addition to receiving the criteria, students need to be given time to reflect upon their learning, which they can do during a lesson, at the end of a lesson, or even at home.</b><br /><br />Peer assessment is a similar strategy to self-assessment, as it also involves giving students clear criteria for assessment, but they use it to assess each other's work rather than their own. When students assess each other's work they gain additional opportunities to become aware of the mathematics they are learning and need to learn.<br /><b style="background-color: yellow;"><br /></b><b style="background-color: yellow;">P</b><b style="background-color: yellow;">eer assessment has been shown to be highly effective, in part because students are often much more open to hearing criticism or a suggestion for change from another student, and peers usually communicate in ways that are easily understood by each other.</b><br /><br /><span style="background-color: yellow;"><b>When students are given information that communicates clearly what they are learning, and they are asked, at frequent intervals, to reflect on their learning, they develop responsibility for their own learning.</b></span><br /><br />An effective way for students to become knowledgeable about the ideas they are learning is to provide some class time for reflection. Ask students at the end of a lesson to reflect using questions such as those in Exhibit 8.4.<br /><br />As I noted in Chapter Four, brain science tells us that the most powerful learning occurs when we use different pathways in the brain.<br /><br />They tell us that mathematics learning, particularly the formal abstract mathematics that takes up a lot of the school curriculum, is enhanced when students are using visual and intuitive mathematical thinking, connected with numerical thinking.<br /><br />In this realm there is one method that stands above all others in its effectiveness: the process of teachers giving students diagnostic comments on their work. <b style="background-color: yellow;">One of the greatest gifts you can give to your students is your knowledge, ideas, and feedback on their mathematical development, when phrased positively and with growth messages.</b><br /><br />Always allow students to resubmit any work or test for a higher grade<br /><br />Share grades with school administrators but not with the students.<br /><br />Use multidimensional grading.<br /><br />Do not use a 100-point scale.<br /><br />Do not include early assignments {review?} from math class in the end-of-class grade .<br /><br />Do not include homework, if given, as any part of grading.<br /><div><br /></div><br />Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-88178794200852366592016-08-01T09:09:00.000-05:002016-08-01T23:27:23.228-05:00Mathematical Mindsets: The Highlights {Part 3}<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://statteacher.blogspot.com/2016/07/mtbosblaugust-participating-blogs-2016.html"><img border="0" height="105" src="https://1.bp.blogspot.com/-01mhQRqGT-w/V6Agb7-4gFI/AAAAAAAAFPs/YyvqdHG5fqIRPi98qKD9qiiKUH5z3joXACLcB/s320/blaugust.jpg" width="320" /></a></div><br />This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!<br /><br />It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.<br /><br />Enjoy!<br />See Part 1<a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-1.html">{here}</a>and Part 2 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-2.html">{here}</a><br /><br /><a href="https://www.amazon.com/Mathematical-Mindsets-Unleashing-Potential-Innovative/dp/0470894520/ref=sr_1_1?ie=UTF8&qid=1469836771&sr=8-1&keywords=mathematical+mindsets">Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching</a><br />Jo Boaler<br /><br /><b><u>Chapter 5: Rich Mathematical Tasks</u></b><br /><br />Teachers are the most important resource for students. They are the ones who can create exciting mathematics environments, give students the positive messages they need, and take any math task and make it one that piques students' curiosity and interest. <b style="background-color: yellow;">Studies have shown that the teacher has a greater impact on student learning than any other variable (Darling-Hammond, 2000).</b><br /><br />This is intrinsically interesting, but it's also true that most people I meet, even high-level mathematics users, have never realized numbers can be so open and number problems can be solved in so many ways. When this realization is combined with visual insights into the mathematical ways of working, engagement is intensified.<br /><br />I have learned through this that people are fascinated by flexibility and openness in mathematics. Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people.<br /><br /><b style="background-color: yellow;">Teachers can create such mathematical excitement in classrooms, with any task, by asking students for the different ways they see and can solve tasks and by encouraging discussion of different ways of seeing problems.</b><br /><br />They tried out ideas with each other, many of which were <b style="background-color: yellow;">incorrect but helpful</b> in ultimately forming a pathway to the solution.<br /><br />Important observations that reveal opportunities to improve the engagement of all students:<br /><br /><ul><li>The task is challenging but accessible .</li><li>The boys saw the task as a puzzle</li><li>The visual thinking about the growth of the task gave the boys understanding of the way the pattern grew</li><li>They had all developed their own way of seeing the pattern growth</li><li>The classroom had been set up to encourage students to propose ideas without being afraid of making mistakes</li><li>We had taught the students to respect each other's thinking</li><li>The students were using their own ideas,</li><li>The boys were working together</li><li>The boys were working heterogeneously.</li></ul><br /><br /><b style="background-color: yellow;">When we don't ask students to think visually, we miss an incredible opportunity to increase their understanding.</b><br /><br />Additionally, students did not think they were finding a standard answer for us; they thought they were exploring methods and using their own ideas and thoughts, which included their own ways of seeing mathematical growth.<br /><br />The researchers found that when students were given problems to solve, and they did not know methods to solve them, but they were given opportunity to explore the problems, they became curious, and their brains were primed to learn new methods, so that when teachers taught the methods, students paid greater attention to them and were more motivated to learn them.<br /><br /><b style="background-color: yellow;">The teacher taught them the methods when they were needed, rather than the usual approach of teaching a method that students then practiced.</b><br /><br />When students are asked to think intuitively, many good things happen. First, they stop thinking narrowly about single methods and consider mathematics more broadly. Second, they realize they have to use their own minds—thinking, sense making, and reasoning. They stop thinking their task is just to repeat methods, and they realize their task is to think about the appropriateness of different methods. And third, as the Schwartz and Bransford research study showed, their brains become primed to learn new methods (Schwartz & Bransford, 1998).<br /><br />When teachers are designers, creating and adapting tasks, they are the most powerful teachers they can be.<br /><br />Making math tasks richer:<br />1. Can You Open the Task to Encourage Multiple Methods, Pathways, and Representations?<br />2. Can You Make It an Inquiry Task?<br />When students think their role is not to reproduce a method but to come up with an idea, everything changes (Duckworth, 1991).<br />The mathematics is more complex and exciting because students are using their ideas and thoughts.<br />3. Can You Ask the Problem Before Teaching the Method?<br />4. Can You Add a Visual Component?<br />5. Can You Make It Low Floor and High Ceiling?<br />When students are invited to ask a harder question, they often light up, totally engaged by the opportunity to use their own thinking and creativity.<br />6. Can You Add the Requirement to Convince and Reason?<br /><br /><b style="background-color: yellow;">In every math conversation, students were asked to reason, explaining why they had chosen particular methods and why they made sense.</b> This opened up mathematical pathways and allowed students who had not understood to both gain understanding and ask questions, adding to the understanding of the original student.<br /><br />She explains that there are three levels of being convincing (Boaler & Humphreys, 2005):<br /><br /><ul><li>Convince yourself </li><li>Convince a friend </li><li>Convince a skeptic </li></ul>It is fairly easy to convince yourself or a friend, but you need high levels of reasoning to convince a skeptic. Cathy tells her students that they need to be skeptics, pushing other students to always give full and convincing reasons.<br /><br /><b style="background-color: yellow;">When I ask students to play the role of being the skeptic, I explain that they need to demand to be fully convinced. Students really enjoy challenging each other for convincing reasons, and this helps them learn mathematical reasoning and proof.</b><br /><span style="background-color: yellow;"><br /></span><b style="background-color: yellow;">Open up the task so that there are multiple methods, pathways, and representations. Include inquiry opportunities. Ask the problem before teaching the method. Add a visual component and ask students how they see the mathematics. Extend the task to make it lower floor and higher ceiling. Ask students to convince and reason; be skeptical.</b><br /><b style="background-color: yellow;"><br /></b><b><u>Chapter 6: Mathematics and the Path to Equity</u></b><br /><br /><b style="background-color: yellow;">When we have gifted programs in schools we tell students that some of the students are genetically different; this message is not only very damaging but also incorrect.</b><br /><br /><b style="background-color: yellow;">Some people who have excelled in math choose not to be proud of the hard work and struggle they went through; they prefer to think they were born with a gift. There are many problems with this idea, one being that students who are successful through hard work often think that they are imposters because their achievement was not effortless.</b><br /><br />The researchers went on to study the factors in the students' environment that led to different feelings of belonging, and they found that two factors worked against feelings of belonging. One was the message that math ability is a fixed trait; the other was the idea that women have less ability than men. These ideas shaped women's, but not men's, sense of belonging in math. The women's lowered sense of belonging meant that they pursued fewer math courses and received lower grades. <b style="background-color: yellow;">Women who received the message that math ability is learned were protected from negative stereotypes—they maintained a high sense of belonging in math and remained intent on pursuing mathematics in the future.</b><br /><br /><b style="background-color: yellow;">We need all teachers to believe in all students, to reject the idea of some students being suitable for higher-level math and others not, and to work to make higher-level math available to all students, whatever their prior achievement, skin color, or gender.</b><br /><br />Some teachers believe that some students cannot achieve at high levels of high school because they live in poverty or because of their previous preparation. In Chapter One I gave an example of high school teachers who made this argument to their school board, but teachers such as those at Life Academy are proving this wrong every day, through teaching high-level mathematics and positive messages to all students.<br /><br /><b style="background-color: yellow;">This is unfortunate, as we know that students who are advanced in math from an early age are more likely to drop math when they get the opportunity and achieve at lower levels.</b><br /><br />Making math more equitable:<br /><b>1. Offer all students high-level content</b><br /><b>2. Work to change ideas about who can achieve in mathematics</b><br />The studies also show, encouragingly, that students who have a growth mindset are able to shrug off stereotyped messages and continue to success; this speaks again to the huge need for students, and teachers, to develop growth mindset beliefs about their own subjects and transmit growth mindset messages to students.<br /><b>3. Encourage students to think deeply about mathematics</b><br />Unfortunately, the procedural nature of mathematics teaching in many classes means that deep understanding is often not available, and when girls cannot gain deep understanding they underachieve, turn away from mathematics, and often develop anxiety. Girls have much higher levels of anxiety about mathematics than boys do (Organisation for Economic Co-operation and Development [OECD], 2015), and the unavailability of deep understanding is one main reason for this (Boaler, 2014a).<br /><b>4. Teach students to work together</b><br />When the Chinese American students found mathematics difficult, they were supported—first by knowing that everyone was struggling and then by working together to solve problems.<br /><b>5. Give girls and students of color additional encouragement to learn math and science</b><br />The researchers found that the levels of anxiety held by women elementary teachers predicted the achievement of the girls in their classes, but not the boys (Beilock et al., 2009).<br />Researchers found that when mothers told their daughters “I was no good at math in school” their daughter's achievement immediately went down (Eccles & Jacobs, 1986). Teachers need to replace sympathetic messages such as “Don't worry, math isn't your thing” with positive messages such as “You can do this, I believe in you, math is all about effort and hard work.” Subsequent experiments showed that women underachieved when they simply marked their gender in a box before taking the test, compared to those who did not have to do that. Role models are extremely important to students—and one of the reasons it is so important to diversify the teaching force.<br /><b>6. Eliminate (or at least change the nature of) homework</b><br />PISA, the international assessment group, with a data set of 13 million students, recently made a major announcement. After studying the relationships among homework, achievement, and equity, they announced that homework perpetuates inequities in education (Program for International Student Assessment [PISA], 2015).<br /><br />Additionally, they questioned whether homework has any academic value at all, as it did not seem to raise achievement for students. <b style="background-color: yellow;">This is not an isolated finding; academic research has consistently found homework to either negatively affect or not affect achievement. Baker and LeTendre (2005), for example, compared standardized math scores across different countries and found no positive link between frequency of math homework and students' math achievement. </b><br /><br /><b style="background-color: yellow;">Mikki (2006) found that countries that gave more math homework had lower overall test scores than those that gave less math homework (Mikki, 2006).</b> Kitsantas, Cheema, and Ware (2011) examined 5,000 15-and 16-year-olds across different income levels and ethnic backgrounds and also found that the more time students spent on math homework, the lower their math achievement across all ethnic groups.<br /><br /><b style="background-color: yellow;">When we assign homework to students, we provide barriers to the students who most need our support. This fact, alone, makes homework indefensible to me.</b><br /><b style="background-color: yellow;"><br /></b><b style="background-color: yellow;">It is unfair and unwise to give students difficult problems to do when they are tired, sometimes even exhausted, at the end of the day. I wonder if teachers who set homework think that children have afternoon hours to complete it, with a doting parent who does not work on hand. If they do not think this, then I do not understand why they feel they can dictate how children should spend family time in the evenings.</b><br /><b style="background-color: yellow;"><br /></b><b style="background-color: yellow;">The value of most math homework across the United States is low, and the harm is significant.</b><br /><br /><span style="background-color: yellow;"></span><br />Homework should be given only if the homework task is worthwhile and draws upon the opportunity for reflection or active investigation around the home.<br /><div><br /></div><div><br /></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-40290078520935895992016-07-31T07:50:00.000-05:002016-08-01T01:16:04.767-05:00Mathematical Mindsets: The Highlights {Part 2}This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!<br /><br />It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.<br /><br />Enjoy!<br /><br /><a href="https://www.amazon.com/Mathematical-Mindsets-Unleashing-Potential-Innovative/dp/0470894520/ref=sr_1_1?ie=UTF8&qid=1469836771&sr=8-1&keywords=mathematical+mindsets">Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching</a><br />Jo Boaler<br /><br />See Part 1 <a href="http://misscalculate.blogspot.com/2016/07/mathematical-mindsets-highlights-part-1.html">{here}</a><br /><br /><b><u>Chapter 3: The Creativity and Beauty in Mathematics</u></b><br /><br />But mathematics, real mathematics, is a subject full of uncertainty; it is about explorations, conjectures, and interpretations, not definitive answers.<br /><br />But Hersh points out that it is the questions that drive mathematics. Solving problems and making up new ones is the essence of mathematical life.<br /><br />Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it—which is the essence of real mathematics—they become more deeply engaged and perform at higher levels.<br /><br /><b style="background-color: yellow;">What employers need, he argues, is people who can ask good questions, set up models, analyze results, and interpret mathematical answers. It used to be that employers needed people to calculate; they no longer need this. What they need is people to think and reason.</b><br /><br /><b style="background-color: yellow;">Parents often do not see the need for something that is at the heart of mathematics: the discipline. Many parents have asked me: What is the point of my child explaining their work if they can get the answer right? My answer is always the same: Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.</b><br /><br />Mathematics is a very social subject, as proof comes about when mathematicians can convince other mathematicians of logical connections.<br /><br />Group and whole class discussions are really important. Not only are they the greatest aid to understanding—as students rarely understand ideas without talking through them—and not only do they enliven the subject and engage students, but they teach students to reason and to critique each other's reasoning, both of which are central in today's high-tech workplaces.<br /><br />We also want students reasoning in mathematics classrooms because the act of reasoning through a problem and considering another person's reasoning is interesting for students. Students and adults are much more engaged when they are given open math problems and allowed to come up with methods and pathways than if they are working on problems that require a calculation and answer.<br /><br /><b style="background-color: yellow;">What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.</b><br /><b style="background-color: yellow;"><br /></b><b style="background-color: yellow;">The powerful thinkers are those who make connections, think logically, and use space, data, and numbers creatively.</b><br /><div><br /></div><div><br /></div><div><div><b><u>Chapter 4: Creating Mathematical Mindsets: The Importance of Flexibility with Numbers</u></b></div><div><br /></div><div><b style="background-color: yellow;">The best and most important start we can give our students is to encourage them to play with numbers and shapes, thinking about what patterns and ideas they can see.</b></div><div><br /></div><div>Successful math users have an approach to math, as well as mathematical understanding, that sets them apart from less successful users. They approach math with the desire to understand it and to think about it, and with the confidence that they can make sense of it. Successful math users search for patterns and relationships and think about connections. They approach math with a mathematical mindset , knowing that math is a subject of growth and their role is to learn and think about new ideas. We need to instill this mathematical mindset in students from their first experiences of math.</div><div><br /></div><div>When students see math as a broad landscape of unexplored puzzles in which they can wander around, asking questions and thinking about relationships, they understand that their role is thinking, sense making, and growing.</div><div><br /></div><div>Instead of approaching numbers with flexibility and number sense, they seemed to cling to formal procedures they had learned, using them very precisely, not abandoning them even when it made sense to do so. <b style="background-color: yellow;">The low achievers did not know less , they just did not use numbers flexibly—probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts instead of interacting with numbers flexibly (Boaler, 2015a). The researchers pointed out something else important—the mathematics the low achievers were using was a harder mathematics. It is much easier to subtract 5 from 20 than to start at 21 and count down 16 numbers.</b></div><div><br /></div><div>Notably, the brain can only compress concepts; it cannot compress rules and methods. <b style="background-color: yellow;">Therefore students who do not engage in conceptual thinking and instead approach mathematics as a list of rules to remember are not engaging in the critical process of compression, so their brain is unable to organize and file away ideas; instead, it struggles to hold onto long lists of methods and rules. This is why it is so important to help students approach mathematics conceptually at all times.</b></div><div><br /></div><div>The left side of the brain handles factual and technical information; the right side brain handles visual and spatial information. Researchers have found that mathematics learning and performance are optimized when the two sides of the brain are communicating (Park & Brannon, 2013).</div><div><br /></div><div>The implications of this finding are extremely important for mathematics learning, as they tell us that learning the formal abstract mathematics that makes up a lot of the school curriculum is enhanced when students are using visual and intuitive mathematical thinking.</div><div><br /></div><div>The antithesis of this approach is a focus on rote memorization and speed. <b style="background-color: yellow;">The more we emphasize memorization to students, the less willing they become to think about numbers and their relations and to use and develop number sense.</b></div><div><br /></div><div>The hippocampus, like other brain regions, is not fixed and can grow at any time, as illustrated by the London Black Cab studies (Woollett & Maguire, 2011), but it will always be the case that some students are faster or slower when memorizing, and this has nothing to do with mathematics potential. </div><div><br /></div><div><b style="background-color: yellow;">All subjects require the memorization of some facts, but mathematics is the only subject in which teachers believe they should be tested under timed conditions.</b> Why do we treat mathematics in this way? We have the research evidence that shows students can learn math facts much more powerfully with engaging activities; now is the time to use this evidence and liberate students from mathematics fear.</div><div><br /></div><div>It is important to revisit mathematical ideas, but the “practice” of methods over and over again is unhelpful. <b style="background-color: yellow;">When you learn a new idea in mathematics, it is helpful to reinforce that idea, and the best way to do this is by using it in different ways. We do students a great disservice when we pull out the most simple version of an idea and give students 40 questions that repeat it. Worksheets that repeat the same idea over and over turn students away from math, are unnecessary, and do not prepare them to use the idea in different situations.</b></div><div><br /></div><div>First, practicing isolating methods induces boredom in students; many students simply turn off when they think their role is to passively accept a method (Boaler & Greeno, 2000) and repeat it over and over again.</div><div><br /></div><div>Second, most practice examples give the most simplified and disconnected version of the method to be practiced, giving students no sense of when or how they might use the method.</div><div><br /></div><div>When textbooks introduce only the simplest version of an idea, students are denied the opportunity to learn what the idea really is.</div><div><br /></div><div><b style="background-color: yellow;">When learning a definition, it is helpful to offer different examples—some of which barely meet the definition and some of which do not meet it at all—instead of perfect examples each time.</b></div><div><br /></div><div>Students are given uncomplicated situations that require the simple use of a procedure (or often, no situation at all). They learn the method, but when they are given realistic mathematics problems or when they need to use math in the world, they are unable to use the methods (Organisation for Economic Co-operation and Development, 2013). Real problems often require the choice and adaptation of methods that students have often never learned to use or even think about.</div><div><b style="background-color: yellow;"><br /></b></div><div><b style="background-color: yellow;">One significant problem the students from the traditional school faced in the national examination—a set of procedural questions—was that they did not know which method to choose to answer questions. They had practiced methods over and over but had never been asked to consider a situation and choose a method.</b></div><div><br /></div><div>It is also part of the reason that students do not develop mathematical mindsets; they do not see their role as thinking and sense making; rather, they see it as taking methods and repeating them. Students are led to think there is no place for thinking in math class.</div><div><br /></div><div>In a second study, conducted in the United States, we asked students in a similar practice model of math teaching what their role was in the math classroom (Boaler & Staples, 2005). A stunning 97% of students said the same thing: their role was to “pay careful attention.” This passive act of watching—not thinking, reasoning, or sense making—does not lead to understanding or the development of a mathematical mindset.</div><div><br /></div><div><b style="background-color: yellow;">Large research studies have shown that the presence or absence of homework has minimal or no effects on achievement (Challenge Success, 2012) and that homework leads to significant inequities.</b></div><div><br /></div><div>Research also shows that the only time homework is effective is when students are given a worthwhile learning experience, not worksheets of practice problems, and when homework is seen not as a norm but as an occasional opportunity to offer a meaningful task.</div><div><br /></div><div>Two innovative teachers I work with in Vista Unified School District, Yekaterina Milvidskaia and Tiana Tebelman, developed a set of homework reflection questions that they choose from each day to help their students process and understand the mathematics they have met that day at a deeper level. They typically assign one reflection question for students to respond to each night and one to five mathematical questions to work on (depending on the complexity of the problems).</div><div><br /></div><div><b style="background-color: yellow;">Questions that ask students to think about errors or confusions are particularly helpful in encouraging students' self-reflection, and they will often result in the students' understanding the mathematics for the first time.</b></div><div><b style="background-color: yellow;"><br /></b></div><div><b style="background-color: yellow;">Number talks are the best pedagogical method I know for developing number sense and helping students see the flexible and conceptual nature of math.</b></div><div><br /></div><div>A growth mindset is important, but for this to inspire students to high levels of mathematics learning, they also need a mathematics mindset. We need students to have growth beliefs about themselves and accompany these with growth beliefs about the nature of mathematics and their role within it.</div></div><div><br /></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-19826489849923693902016-07-30T09:28:00.000-05:002016-07-30T09:28:05.230-05:00Mathematical Mindsets: The Highlights {Part 1}<br />This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!<br /><br />It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.<br /><br />Enjoy!<br /><br /><a href="https://www.amazon.com/Mathematical-Mindsets-Unleashing-Potential-Innovative/dp/0470894520/ref=sr_1_1?ie=UTF8&qid=1469836771&sr=8-1&keywords=mathematical+mindsets">Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching</a><br />Jo Boaler<br /><br /><b><u>Introduction: The Power of Mindset</u></b><br />When students get the idea they cannot do math, they often maintain a negative relationship with mathematics throughout the rest of their lives.<br /><br />Research studies have established that the more math classes students take, the higher their earnings ten years later.<br /><br />Research has also found that students who take advanced math classes learn ways of working and thinking—especially learning to reason and be logical—that make them more productive in their jobs. Students taking advanced math learn how to approach mathematical situations so that once they are employed, they are promoted to more demanding and more highly paid positions than those who did not take mathematics to advanced levels (Rose & Betts, 2004).<br /><br />That single belief—that math is a “gift” that some people have and others don't—is responsible for much of the widespread math failure in the world.<br /><br />Math is conveyed as a really hard subject that is uninteresting, inaccessible, and only for “nerds”; it is not for cool, engaging people, and it is not for girls. It is no wonder that so many children in schools disengage from math and believe they cannot do well.<br /><br />Part of the change we need to see in mathematics is acknowledgment of the creative and interpretive nature of mathematics. Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making, and interpretation of methods; it is a set of ideas that helps illuminate the world; and it is constantly changing. Math problems should encourage and acknowledge the different ways in which people see mathematics and the different pathways they take to solve problems. When these changes happen, students engage with math more deeply and well.<br /><br />They believe that mathematics ability is a sign of intelligence and that math is a gift, and if they don't have that gift then they are not only bad at math but they are unintelligent and unlikely to ever do well in life.<br /><br /><b><u>Chapter 1: The Brain and Mathematics Learning</u></b><br /><br />If you learn something deeply, the synaptic activity will create lasting connections in your brain, forming structural pathways, but if you visit an idea only once or in a superficial way, the synaptic connections can “wash away” like pathways made in the sand. Synapses fire when learning happens, but learning does not happen only in classrooms or when reading books; synapses fire when we have conversations, play games, or build with toys, and in the course of many, many other experiences.<br /><br />If brains can change in three weeks, imagine what can happen in a year of math class if students are given the right math materials and they receive positive messages about their potential and ability.<br /><br />The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math, and everyone can achieve at the highest levels in school.<br /><br /><b style="background-color: yellow;">What I am saying is that any brain differences children are born with are nowhere near as important as the brain growth experiences they have throughout life.</b><br /><br /><b style="background-color: yellow;">Every second of the day our brain synapses are firing, and students raised in stimulating environments with growth mindset messages are capable of anything.</b><br /><br />A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn. The very best opportunities to learn come about when students believe in themselves.<br /><br />In other studies, researchers have shown that students' (and adults') mindsets can change from fixed to growth, and when that happens their learning approach becomes significantly more positive and successful (Blackwell et al., 2007).<br /><br /><b style="background-color: yellow;">The highest-achieving students in the world are those with a growth mindset, and they outrank the other students by the equivalent of more than a year of mathematics (see Figure 1.6 ).</b><br /><br />It turns out that even believing you are smart—one of the fixed mindset messages—is damaging, as students with this fixed mindset are less willing to try more challenging work or subjects because they are afraid of slipping up and no longer being seen as smart. Students with a growth mindset take on hard work, and they view mistakes as a challenge and motivation to do more.<br /><br />When students are given fixed praise—for example, being told they are smart when they do something well—they may feel good at first, but when they fail later (and everyone does) they think that means they are not so smart after all.<br /><br />Praise feels good, but when people are praised for who they are as a person (“You are so smart”) rather than what they did (“That is an amazing piece of work”), they get the idea that they have a fixed amount of ability.<br /><br />Telling students they are smart sets them up for problems later. As students go through school and life, failing at many tasks—which, again, is perfectly natural—they evaluate themselves, deciding how smart or not smart this means they really are. <b style="background-color: yellow;">Instead of praising students for being smart, or any other personal attribute, it's better to say things like: “It is great that you have learned that,” and “You have thought really deeply about this.</b><b style="background-color: yellow;">”</b><br /><b style="background-color: yellow;"><br /></b><b><u>Chapter 2: The Power of Mistakes and Struggle</u></b><br /><b><br /></b>“Every time a student makes a mistake in math, they grow a synapse.”<br /><br />One reason it is so significant is that it speaks to the huge power and value of mistakes, although students everywhere think that when they make a mistake it means that they are not a “math person” or worse, that they are not smart.<br /><br />When teachers ask me how this can be possible, I tell them that the best thinking we have on this now is that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged, and this is the time when the brain grows the most.<br /><br />First, the researchers found that the students' brains reacted with greater ERN and Pe responses—electrical activity—when they made mistakes than when their answers were correct. Second, they found that the brain activity was greater following mistakes for individuals with a growth mindset than for individuals with a fixed mindset.<br /><br />The study also found that individuals with a growth mindset had a greater awareness of errors than individuals with a fixed mindset, so they were more likely to go back and correct errors.<br /><br /><b style="background-color: yellow;">It tells us that the ideas we hold about ourselves—in particular, whether we believe in ourselves or not—change the workings of our brains. If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake.</b><br /><br />He points out: “Imperfection is a part of any creative process and of life, yet for some reason we live in a culture that has a paralyzing fear of failure, which prevents action and hardens a rigid perfectionism. It's the single most disempowering state of mind you can have if you'd like to be more creative, inventive, or entrepreneurial.”<br /><br />He also summarizes the habits of successful people in general, saying that successful people:<br /><br /><ul><li>Feel comfortable being wrong </li><li>Try seemingly wild ideas </li><li>Are open to different experiences </li><li>Play with ideas without judging them </li><li>Are willing to go against traditional ideas </li><li>Keep going through difficulties </li></ul><br />It's also a good time to reinforce important messages—that when the student made this mistake, it was good, because they were in a stage of cognitive struggle and their brain was sparking and growing.<br /><div><b style="background-color: yellow;"><br /></b></div><div><div><b style="background-color: yellow;">I said “Do you know what just happened? When you got that answer wrong your brain grew, but when you got the answer right, nothing happened in your brain; there was no brain growth.”</b></div><div><b style="background-color: yellow;"><br /></b></div><div><b style="background-color: yellow;">If we want students to be making mistakes, we need to give them challenging work that will be difficult for them, that will prompt disequilibrium.</b></div><div><b style="background-color: yellow;"><br /></b></div><div><b style="background-color: yellow;">In workshops with Carol Dweck I often hear her tell parents to communicate to their children that it is not impressive to get work correct, as that shows they were not learning.</b></div><div><br /></div><div>This is a radical message, but we need to give students strong messages to override an idea they often get in school—that it is most important to get everything correct, and that correctness is a sign of intelligence.</div><div><br /></div><div>When mathematics is taught as an open and creative subject, all about connections, learning, and growth, and mistakes are encouraged, incredible things happen.</div></div><div><br /></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0tag:blogger.com,1999:blog-2467202639598238063.post-69070262210131689612016-07-29T02:48:00.001-05:002016-08-07T00:21:35.071-05:00How To...Teacher Moves<h4 style="text-align: center;"><i style="font-weight: normal;">In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the <a href="http://misscalculate.blogspot.com/search/label/How%20To">tag</a> to the right for more posts!</i></h4><div><i style="font-weight: normal;"><br /></i></div>This is a collection of ideas and resources that I've read and wanted to use or have already used.<br /><br />Get presenter’s to the front. One can only speak and the other can only point. They explain their thinking for one pair. Keep this light, safe and fun. If a student does not explain clearly enough or missing key elements, just let it go, they will most likely come out in later explanations.<br /><br />Ask a student in the class to re-explain the presenter’s thinking.<br /><br />"Get low" in the classroom so students don't look to you as the answer keeper.<br /><br />Students write two truths and a lie about a function or math problem; <a href="http://mrorr-isageek.com/better-questions-two-truths-one-lie/">see here</a> for variations; include these type of questions on assessments.<br /><br />Grade or give feedback with <a href="http://drawingonmath.blogspot.com/2016/05/follow-up-grading-with-highlighters.html">two</a> or <a href="http://fawnnguyen.com/giving-feedback-with-a-highlighter/">more</a> highlighters.<br /><br />When students say:<br /><br /><ul><li>"What do I do next?" reply with "What do you think?"</li><li>"What do I do next?" reply with "How did you start?"</li><li>"Is this right?" reply with "What did you do?"</li><li>"Can you help me?" reply with "What should you do first?"</li><li>"I got the wrong answer." reply with "Can you find a mistake in your work?"</li></ul><div>When asking students to share their responses with the class, say "Thank you" to acknowledge their answers without confirming if it's right or wrong. Practice that poker face!</div><div><br /></div><div>Put self-assessment questions on quizzes and tests for students to reflect on what they think they know.</div><div><br /></div><div>Include quadratic equations when teaching solving systems by substitution. {Great idea <a href="http://www.megcraig.org/?p=1247">Meg</a>!}</div><div><br /></div><div>Help address gaps, spiral content, self-test, study, or review by giving students index card problems as they enter the room. You can make an answer key or have students line up or sit down based on the answers they get. {Thanks <a href="http://simplifyingradicals2.blogspot.com/2016/01/entrance-questions.html">Nora</a>!}</div><div><br /></div><div>You can jump a few DOK levels by reversing the question....give students math problems and ask them what they solve instead of asking them to <i>do</i> the calculation. {Learn more from <a href="http://fawnnguyen.com/reversing-the-question/">Fawn</a>}</div><div><br /></div><div>Here are three quick games to play when you have extra time in class that involve some strategy and logic. Always be prepared; this is a great back up. {Thanks to <a href="https://fractionfanatic.wordpress.com/2016/03/29/5-minutes-of-fun-or-more/">Julie</a>!}</div><div><br /></div><div>Sarah Carter shares <a href="http://mathequalslove.blogspot.com/2016/01/quick-and-easy-review-games.html">four of her favorite review games</a>. I know I always have my default games so it's great to mix it up with some new ideas. Here's <a href="http://mathtalesfromthespring.blogspot.com/search/label/Review%20Activities">another collection</a> from Kim that I really loved and have gotten away from.</div><div><br /></div><div>I am a huge fan of <a href="http://misscalculate.blogspot.com/search/label/Sorting">card sorts</a> but this post really inspired me to kick mine up a notch. These ideas work great for INBs, individual studying, and pair practice. {Love <a href="http://www.mathgiraffe.com/blog/3-ways-to-use-card-sorts-in-high-school-math">these</a> Brigid!}</div><div><br /></div><div><br /></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com2tag:blogger.com,1999:blog-2467202639598238063.post-28774459609309579722016-07-28T23:59:00.000-05:002016-07-29T02:20:08.511-05:00Bell Ringers 3.0<br />One disadvantage of teaching in a tiny school is that you can't just reuse everything because you have the same students for three years in a row. So every year I have to find new first day of school activities and change things like my daily bell ringers.<br /><br />Every year I find a new obsession so I would probably just change it anyway.<br /><br />Updates from <a href="http://misscalculate.blogspot.com/2015/08/bell-ringers-20.html">last year</a>:<br /><ul><li>Changed the colors to match better</li><li>Took off the week labels {how is it that we got to school for 180 days but it's more than 36 weeks....so confusing}</li><li>Changed "Weigh It Wednesday" balance bender puzzles to "Work It Wednesday" brain teasers {thanks to weekly KenKen pdfs for educators!}</li><li>Changed "Thoughtful Q's Thursday" to "Number Talks Thursday" {excited but completely unprepared for these}</li><li>Updated estimation180 and WODB photos with new ones {thanks everyone who submits those!}</li></ul><div><br />Here is THE powerpoint!</div><div><br /></div><div><center><iframe allowfullscreen="" frameborder="0" height="400" msallowfullscreen="" src="https://app.box.com/embed/preview/yvlg8hjny6lzfrjrnfo408w526ghk1lg?direction=ASC&theme=dark" webkitallowfullscreen="" width="450"> </iframe></center></div><div><br /></div><div>Now I have some questions. Last year I printed out <a href="https://app.box.com/s/tkdwhddwftgd8oqh8r4u">front and back handouts</a> every week for students. I know some people use Google Classroom for warm ups but I just don't think I can rely on our Internet on a daily basis. </div><div><br /></div><div>I know for sure I want students to write on Mental Math Mondays. </div><div><br /></div><div>I'm thinking I could use Google Forms for Tough Guess Tuesday estimation180 photos. Most people did not or could not calculate the error and error percentage. Do I <i>need</i> them to do that? Do I <i>need </i>them to write a description and a reason? How would I display the information in a useful way? </div><div><br /></div><div>Work It Wednesday are brain teasers that don't necessarily require writing...students could use dry erase markers on their desk. Do I <i>need</i> them to write anything?</div><div><br /></div><div>For Number Talk Thursday, it's supposed to be mental so students could use marker again. But I also used some dot images so I could print those on paper for students to write on. I kind of like the idea of printing more than one of the same image so they can practice seeing different strategies. </div><div><br /></div><div>I know for sure I want students to use Plickers for Freaky Friday WODB. They love Plickers and I only use them a couple times of year. But do I want them to write their reasons? Or just call on random people to share their answers? I obviously don't grade these so do I NEED them to write?</div><div><br /></div><div>I guess what I'm truly struggling with is....will they do it if I don't make them write it down and turn it in?</div><div><br /></div><div>It would be great if I could use less paper...maybe fit one week per side, cutting the amount of copies I need in half. But my favorite part of last year's handouts was the questions I asked every week. They were random and let me get to know the students so much better. I guess I could use Google Classroom for those too...how would you do that? Every Friday post a question?</div><div><br /></div><div>How do you guys handle your warm ups in a way that makes your heart smile? :-)</div><div><br /></div>Elissa Millerhttps://plus.google.com/110542622977827264599noreply@blogger.com0