2011-2012 Class Schedule

1st- 10th Grade Social Development
2nd- 11th Grade Test Prep (ACT)
3rd- 8th Grade Algebra I
4th- Plan
5th- Algebra 1
6th- Geometry Lab
7th- Geometry
8th- Algebra Lab

I'm super pumped about this schedule!

Social Development is basically advisory or what I like to call 'mothering'. That's my heart. I would rather do that all day every day if I could! The plan for that is on Monday- Character Education, Tuesday- Sustained Silent Reading for everyone (including the teacher!), Wednesday- Test Prep, Thursday- Study Hall, Friday- Team Building/Service Projects. How fun is that?

The test prep for 11th grade is broken up among four of us: math, reading, english, science. So we will have a group of kids for 4-5 weeks and then they will rotate to a different content area. I am in love with this because it's not that much of an extra prep, kind of a mini prep. The plan is that Monday through Wednesday is test prep (not sure what that will consist of yet) then Thursday is a study hall and Friday again with the team building and service projects.

The Algebra and Geometry labs will probably be the hardest thing for me to deal with. Our instructional team is starting to plan assessments together and after that we want to move on to planning the curriculum/activities for those lab classes. We know for sure we want to incorporate probability, statistics, and measurement since those are the first things to get cut out of the normal curriculum. My heart for this class is to meet with students individually and work on skills they haven't mastered yet. We also would like to use ALEKS (or I'm leaning toward TenMarks) or some computer program a couple days of week for students to work on at their own pace. I think the first thing to do is plan a routine like we have for the social development and test prep classes. That way students and teachers know what to expect on a daily/weekly basis. And makes planning a lot simpler.

Other changes to our schedule is that the school day is extended from 3:06 to 3:20. Teachers had to stay until 3:20 anyway so now we can leave as soon as the bell rings.

In the morning, we have to be here by 7:45 and class starts at 8:03. The new schedule gives us team meeting time (vertical, instructional, student support, leadership, etc) from 7:45 to 8:15 every day. As far as teachers are concerned, we have to be there the same amount of time. We went from seven to eight periods so I'm sure some teachers have extra preps and are not happy about that! But, so far, I haven't heard any complaints.

Our lunch period is now common between middle school and high school. Remember, smallllll school. While that may cause some issues, it opens up more options for middle school students to take as 'exploratory' classes.

Another change is that all juniors/seniors will have gym first hour and all freshmen/sophomores will have gym second hour. We're kind of going on a fitness initiative. More aerobics and such because research shows that getting those endorphins pumping helps students think better. The FACS teacher will be pulling students during their gym time to create individual nutrition plans as well.

All in all, I have to say I am surprised and impressed that my administration came up with this. Of course I'm biased since I like my schedule, but I do think this is a good way to fulfill a lot of different needs that our school currently has.

The attitude and atmosphere is slowly changing and becoming more positive. Teachers have been coming up with cross-curriculum projects and new ideas. Since I've spent a lot of time complaining, I thought I would share some positive things now.

  • The elementary has started an intramural basketball team for boys and girls.
  • We're brainstorming ways to update, rearrange, and change the atmosphere of the library to a place people want to be.
  • The history and English department are doing a joint study of the Holocaust that culminates in a trip to a Holocaust museum with a tour given by a Holocaust survivor.
  • The band teacher wants to design his own band uniform with measurement help from algebra/geo students, measurement predictions from the statistics class, design/color ideas from the art classes, and mock-up patterns sewn by the FACS classes.
  • I'm stealing a project from Mimi where students design their own logo and then shrink or enlarge it (to practice percents) and with the help of the art teacher, we will blow it up or shrink it and use the printing press to create an actual print of the logo.
  • The fine arts department is planning a Math Olympics day where students sign up and compete for math related activities such as counting back change, doing mental math, telling time from an analog clock, etc.
  • We will be using Career Cruising with students as a way to kind of build a portfolio of sorts for college/careers after school as well as a way of setting goals and recording student accomplishments.
  • We've formed a Communications Committee to work on communication between administrators and teachers, teachers and parents, etc.
Pretty impressive if I do say so myself.


Classroom Management Workshop

Effective Classroom:
-Mutual Respect

What Do You Want to Know?
-how to deal with the one problem child
-bag of tricks
-how to deal with bullying
-managing cooperative learning and transitions
-beginning activities

Collaborative Norms
-Equity of voice
-Active listening
-Safety to share different perspectives

Come to the Edge poem

3 Characteristics of an Effective Teacher
1. Positive expectations for student success
2. Extremely good classroom manager
3. Knows how to design lessons for student mastery

Efficient is not the same as effective.

Creating Acceptance
-Make eye contact with each student 
-Call all students by preferred name (Should we call students by Mr. or Ms. since we expect them to respond to us in that manner?) 
-Move toward and stay close to learners

Give-one-get-one strategy. Give students a grid of nine squares. They fill in three with their own ideas. Then find another student to exchange one idea with. Keep rotating students until grid is full.

Effective teachers manage their classrooms.
Ineffective teachers discipline their classrooms.

Focus on procedures to limit dealing with behavior.

Discipline has penalties and rewards. Procedures don't.

Students Should Know:
Where to get materials
What to do when they have a question
Where to work
Where to put work
What the rules are

Rules are concerned with behavior, not academic work.

There's no reason to have a rule that's not important. If you don't enforce it, don't make it a rule.

Be firm, fair, consistent.

Teaching Procedures
1. Explain, model, demonstrate
2. Rehearse, practice
3. Review

The number one problem in the classroom is not discipline; it is the lack of routines and procedures.

Discuss inappropriate behaviors quietly, calmly, and privately as often as you can.

http://www.disciplinehelp.com Library of scenarios and how to deal with specific behaviors.

New Culture of Teaching: Alan November

Closing the Gap Conference
Keynote Speaker- Alan November

3 Job Skills
1. Dealing with an overwhelming amount of information and being able to sift through to find what's useful and needed.
2. Global communication- being able to complete things that you can't finish on your own, working with people not in the same room
3. Self-directed- being able to work on your own efficiently without a boss.

2 Tech Tools
1. Skype
2. Screen casting tool (Jing)

Teachers should have access to any website with the complete trust that they will make the right decision. Only in the US are websites blocked.

Record people  (that children are familiar with) reading books aloud to encourage reading. Use Skype to create a 'grandparent network'.

Build a video library of tutorials made BY students, FOR students that spans the entire curriculum. Over time, show different cases/ method. Students need to see other students homework more than the teacher does. The role of the teacher is now more important than ever: all content goes through and mist be approved by teacher. Ttt

We have underestimated students willingness to work harder than the teacher. Homework is not purposeful work.

Search Google using site extensions like .gov, .k13.il.us, to limit results from quality sites. Site:

Students are going to publish content on the Internet anyway. Why not be a role model for how to publish appropriate content? They're posting crap on the Internet because they've never been taught otherwise.

The majority of students have inaccurate notes. We don't have time to check for quality.

Google and Gates are paying Khan to cover the entire American curriculum. If students can get every lecture ever needed on their phone/laptop, we no longer need to lecture. Homework becomes classwork and there is no homework. Homework needs immediate feedback or it does no good. 

We are blocking the most powerful tool ever invented for learning because of our fear of lack of control.

With Wolfram-Alpha, we no longer have to focus on mechanics. We can spend time on application.

Live demonstration of polleverywhere.com

Video of Eric Mazoir: Students at Harvard can get high scores on tests without understanding anything. This is our American curriculum. Even if NCLB completely succeeded, the nation would fail.

Students should read, write, and reflect before the lecture.

In the classroom 'flip', everyone wins. But we won't actually do it because of tradition. Students need immediate feedback and they cam get that now with clickers. We can know what kids are thinking! Students need to learn logic, reasoning, and how to think. They no longer need the teacher for transfer of knowledge. We've bought billions of dollars of technology but we haven't changed the process of learning. Who owns the learning in your classroom?

Use Google Docs to take collaborative notes. One person can't take better notes than three people working together.

Teach students to deal with content, not block it.    


SOHCAHTOA Graph Project

Update on my trig ratio graph lesson that I blogged about here. I talked to my pre-calc teacher and he said if I wanted to do this it would be good. So it wasn't necessary and I wasted a lot of time but I still think it was a good lesson. Thanks to @approx_normal for suggesting I test this out on Excel on my own. After some trial and error, I figured out that students would get a good picture of the graph by using multiples of 3 up to 90 degrees. We kept the y window the same, going up to 1 by increments of .1.

I gave them a page with three blank graphs, one for each trig ratio. And then ta-da, I made up another investigation! The hardest part for students was figuring out how to label the graphs. Especially after we realized that the y window for the tangent graph needed to go from 0 to 20 by 2s. (Note: I didn't change that yet so if you use it, that's something you need to look for.)

Then once I got them started on calculating the degrees, it was pretty much smooth sailing. The next stumbling block was when it came to predictions. I had them draw a curve through all the dots. 

After using the line to predict certain trig values, I wanted them to use the calculator. But, they just wanted to try it by typing in sin(42). I probably should have shown them how to graph the trig functions on the calculator earlier. But, after they graphed the function, I had them hit trace and type in the necessary angle measure.

To sum things up, I made a Powerpoint with pictures of trig graphs from real life scenarios. The first slide is a graphic organizer which we used to take notes about nonlinear, nonquadratic, discrete, and continuous. I briefly introduced the concept of asymptotes as well.

For homework, students answered the reflection questions on the back about their process. And to be honest, the answers weren't that great. But then again, neither was the assignment.


Review Pong

I got this game off of the ilovemath.org wiki but I had to change some of the problems since we hadn't done all of that yet. It's a review game based on the 'win a fish' carnival game.

Original Directions:
Remember the game at the fair where you try to toss a ball in a fish bowl and if so, you take home the fish?  Same kind of concept.

My "fish pond" is made from the lid of the copier paper box. I then taped down some plastic cups. Since I needed 3 different colors, I took overhead pens and went around the inside top part of the cup (red, black, and red). I filled the lid full of cups trying to not have any spaces. I just put tape on the bottom of the cups. I have a ping pong too.

Students are in groups. I take turns asking groups for a problem. Everyone works the problem. Each group shows me 1 answer. One point for correct answer, extra points are gained by getting the ping pong ball in a cup.

I have the lid of cups on a desk and another desk in front of that. The students stand behind a line that is about 2 or 3 feet away. I ask that they toss the ping pong ball so that it hits the first desk and bounces it in to the cups. If it bounces out, no points, if it gets stuck on top of all of the cups, no points.

My Take:
I didn't give any points for the right answer. I put colored post-it flags inside the cups that were worth different points. But I also noticed there were yellow, green, and blue plastic cups at Wal-Mart so I will be picking some of those up soon.

In the picture above, I ran out of cups AND they were out of the right size so I filled the rest with small cups. I don't know if that made it harder or easier but it's what I'm working with. So then the students win different points depending on what color they win.

The students like this game because they think it will be so easy and they will be great at it. The truth is, they suck. They complain that our desks are slanted and that throws off their ability to bounce but I just make fun of them and play on. And if you haven't already made the connection, students refer to this as beer pong. I originally called it fish pong and now I call it nothing, I just bring out the box.

I made my own game for similar triangles and one for trig ratio practice.


Balloon Pop: A Review Game

I learned about this game at a Pippin's math conference which I blogged about here. It's sad that that was almost a year ago and I'm just now using it. You can use a regular review worksheet or my personal favorite, a Powerpoint of review problems.


Students are in teams. You create a sheet with balloons on it and a place to write a team name. Or you can steal mine. Print this on paper and stick it in side of a page protector. Students write their name on it with dry erase marker.

Show a problem. Each team works it, which means every person works it. They agree on a team answer. Now reveal the correct answer. Whichever team(s) gets the correct answer gets to pop another team's balloon by using the dry erase marker to draw an X on it. If a team's balloons all get popped, then they can erase a popped balloon instead of popping someone else's balloon. But that's only an option after all of their balloons have been popped. Whichever team has the most unpopped balloons left at then end, wins.

My students loved this. The fun thing is to watch different teams try to form alliances and get other teams out. My students said it was like playing survivor because you never knew which teams were working together. Students were surprised by how fast time went by and thought it was fun. They actually asked to do it again.

Here is my balloon pop Powerpoint for solving systems of equations by substitution. I put the answers at the bottom of each slide and covered it with a white rectangle. Then I used the animations to make the box disappear and show the answer.

Coming Attractions: New Year Resolutions

Since my school has received this school improvement grant, I plan to work my butt off this summer to take full advantage of my instructional coach.

I decided to go ahead and start my list so that as soon as school ends, I know exactly where to start. (Some are ideas and things I don't need to create or that I can't do until school starts.)

What I Want For Next Year
  1. Binders I don't use textbooks so everything is a worksheet/handout and they are everywhere. I am too anal to let this continue. So everyone will have binders with dividers and a little bag to hold all of their supplies in. My AP suggested making them classroom binders to keep things simple. I can have a weekly TA who's job is to come in and immediately pass them out. I just want to get rid of bottle neck traffic jams.
  2. Writing/Blogging I need to incorporate way more reading and writing. I don't know to make it work time-wise but I want each student to write a blog and comment on others' as well. I have Nonfiction Writing Prompts from the Write to Know Series for Algebra and Geometry to use as a starting place. How can I make it all work?
  3. Develop Class Writing/Blogging Rubric I definitely want to assess these blogs but I would like to use examples of their own writing to have students help me create a rubric based on what they think is important in their writing. So as a class we will model critiquing and feedback to develop a rubric so that students can then self-assess, peer-tutor, or just understand my assessment process better.
  4. Visual Procedure Rubrics Speaking of rubrics, I want to take pictures of important procedures that we do all the time in class. For example: paying attention in class. I would take 3 different pictures. When students were acting appropriately that would be a 1, when some are off task would be a 2, and chaos would be a 3. Then I can post pictures of the most important procedures and easily assess them: "Class you're at a 2 and I need you at a 1." Everyone knows what is expected.
  5. Practice Procedures/Transitions I plan to spend the beginning of class literally practicing procedures and timing students on transitions until we can quickly and efficiently move from place to place, task to task, without losing so much instructional time. This is where the visual rubrics will come into play. As we practice, I can photograph each stage and use as a reminder.
  6. Math/Art/Writing Projects I'd like to develop an art project involving math for every unit or every other unit as a motivator to get work done correctly and efficiently in class to make time to work on their project. Obviously it would be something I would grade and display, it would appeal to kinesthetic and visual learners, it would hopefully tie concepts together, and make class a little more enjoyable. If I can do it, I'd like to create a project per unit which may include art, writing, 'inventing', etc.
  7. Formal Team Roles I've been doing group work without really holding students accountable. It has helped in some ways because they are teaching each other but I know so much more could be done. I basically want to follow Riley Lark's structure because I love how clearly it is explained. As we practice procedures, we can easily model the roles described here.
  8. Formatives With Clickers I recently started using clickers and the students love it but it hasn't been super useful to me yet. I've been using them on bell ringers and exit slips as a way to hopefully guide my instruction. It is cool to watch but we waste time waiting for people to click and obviously some still guess. So next year, I want to have formative already developed on slides so students can easily click and I will know what to do with that information.
  9. Display Team Results Combining the previous two, I want to use the data from our formatives and summatives to compare teams within classes. I tried this by comparing two periods but then one period just called themselves the slower class. So someone suggested I compare teams with a class which makes sense, especially because students will rotate teams. My clicker software has awesome 3d graphs which would be easy to print and display. In color.
  10. Write Multiple Versions of Every Assessment In order to make sbg finally work for me, I HAVE to do this.
  11. Remediation/Scaffolded Worksheets I want to have these made so that if students do not make my cut off score (I'm thinking 80%) then I immediately have a worksheet for them to complete before retesting. I will have examples worked out plus answers to the problems they complete on their own so that they can self check. I hope to use Nasco's Algebra 1 and Geometry Worksheets for that.
  12. Index Card Flip Charts I'm totally stealing Julie's idea because some of my kids are so obsessed with taking notes. I need to do this because I give so much paper since I don't use textbooks. Plus, I'm requiring binders so it will be very easy to keep things organized. Also, in my notes/homework/investigations I can point students back to a particular concept that they need to remember. And what a great tool to study for final exams!
  13. Math Dictionary On that same note, my friend over at Ms. Mathemagician has her students make their own math dictionary on a key ring. I can't remember the specifics (hint, hint, *blog post* cough, cough) but I think she gives a weekly vocab quiz. Mix that with an idea from @graceachen, who lets students use a certain amount of cards on the quiz but less and less cards as time goes on until they are not using any cards at all.
  14. Embed Review at Appropriate Places I want do this right now because I love lists so much but I want to make a list of the units I need to teach broken down into prerequisite skills and new skills. From there, I can start each unit by reviewing the appropriate material and leading into the new material. Hopefully, I can eliminate wasting much of the first quarter reviewing and get into the real focus of Algebra I.
  15. Performance Events On the one hand, I want to love sbg because I love breaking things down into manageable pieces and simplifying and organizing. On the other hand, I love investigations that tie things together in a neat package. If I'm going to try sbg skill tests again, I want to somehow incorporate performance events which will tie concepts together and definitely hit that critical thinking gap where students need to be familiar with multi-step problems. Maybe skill quizzes could be short and frequent and then every so often (end of unit, every 3 weeks, etc?) we have a performance event accompanied by a write-up that would serve more as a 'test' than quiz.
I know someone will tell me to pick one or two things to focus on and build on those but I don't have time for all that. I have resources available that I might never have again. I'm going to do my best to get as much done as I can. I will crash and burn on my own at some point so please don't discourage me ahead of time.

Don't steal my fire; just let me burn!


Critical Thinking Skills

In our instructional team meeting, we've been looking at data. Which is quite depressing. But what we've noticed is that basically, our students are not retaining information. The more we talked about it, the more we decided that the real issue is critical thinking. Students can only do exact duplicates of problems we've done in class without being able to apply that concept in a different setting. From there, we are brainstorming what we can do. Here's what we came up with as a group:
  • Include an entire unit of story problems
  • Use brainteasers/puzzles/riddles to get students in the habit of thinking and working multi-step problems in a 'fun' setting with no pressure.
  • More practice reading math problems 
  • More practice working multi-step problems
  • Teaching students to persevere and try different methods rather than giving up
 On a personal note, here are some ideas I want to try next year:
  • Error Analysis- Having students analyze work to find and fix the problem.
  • Journaling- Getting students to think through mathematical processes.
  • Peer editing- Have students read/assess each others journal entries.
  • Multi-Step problems- Make every problem more than one step if at all possible, including on assessments
That's all I can remember at the moment.

What are your suggestions? How do you  kick things up a notch? How do you write assessments that aren't just asking them to remember or memorize something?


PLC Readiness Survey

In my PLC class, we are simulating PLC's and worked together to create a PLC readiness survey to give to the other teachers in our school who are not taking the class. We started out by all writing our own questions on issues we thought needed to be addressed. Our instructor compiled them and tried to cluster them together. We went through and voted on the ones we liked the most. Every group has the same first 11 questions. Then each group added 3-5 of their own depending on who they were giving their surveys to: elementary, middle, or high. My group was the high school group.

I wanted to share this survey in case it was something that other schools who want to implement the PLC model might find useful or at least a stepping stone to the PLC mindset.

We based the first questions on the Likert scale and then threw in some open ended questions.
  1. I feel comfortable with my peers observing my class
  2. The faculty works well together to explore skills and strategies to improve student learning.
  3. I am committed to continuously seeking out opportunities to improve my teaching.
  4. Our school has a supportive environment for students.
  5. Our school has a supportive environment for staff.
  6. Our district has a culture of trust and commitment.
  7. Instructors have a voice and ownership in our school.
  8. I value collaborative planning and sharing among faculty.
  9. I am willing to collaborate with my peers.
  10. I use the results of assessments to guide student learning.
  11. Our school would see improved student achievement data as a result of implementing a system of teacher collaboration and data analysis.
  12. I am willing to talk to faculty members about my teaching methods and my ideas.
  13. Staff members work together to search for solutions to address diverse student needs.
  14. What concerns you most about peer observation? (Open-ended)
  15. How can we use assessment data toward more positive outcomes? (Open-ended)
  16. What disadvantages do you see with collaborative planning periods? (Open-ended)



My instructional coach sent me a link to a great little unit on right triangle trig. If you take a look at it, it's a pretty cool way of grouping students and having them measure angles and sides to find some patterns and ratios.

I also like the visual way of using string and clothes pins to illustrate  the opposite, adjacent, and hypotenuse. I had three students hold the strings of the triangle and stretch all the way across the room. I made the rest of the students sit in the floor inside of the triangle. I made colorful signs and one of them had a bunch of thermometers on it that said 'Degrees'.

 I had a student tape the sign to their chest. I placed the student inside the triangle at one of the acute angles. Then I chose three other students to take the signs and pin them to the appropriate string. I asked the rest of the class if their placements were correct and to explain why. On their own, they came up with the fact that the opposite side was the one the student could not touch. Now I had another student become the 'degrees' and move to the other acute angle. Three new students now got the clothes pins and signs and moved them around. This was an important part of the activity because the student who went to move the hypotenuse sign said "Hey, doesn't it stay in the same place?" This was a natural way to discuss where the hypotenuse is, why it is always the same, and why we don't use the right angle as our reference angle.

In my first geometry class, we jumped right from there into the measuring sides and angles activity and it flopped due to the fact that students still weren't understanding exactly where the opposite and adjacent sides were and that they had to look from the perspective of both acute angles. So by the time my second period of geometry came around, I remembered Dave Sladkey's post on kinesthetic right triangle trig. Although I do have a Flip cam, I didn't record it. But I did have students create right triangles with their bodies. I took our handy dandy 'degrees' sign and put it on the floor inside their body triangle at an acute angle. I asked for the opposite, adjacent, and hypotenuse and each person raised their hand accordingly. I did the other acute angle and then rotated to every other group to do the same. Then, (yes we spent a lot of time on figuring this out but what is right triangle trig without knowing that?) I had already drawn a bunch of colorful right triangles all over the board with a theta at random angles to represent the reference angle. I called each student up individually and had them choose any triangle and based on theta, label the sides accordingly. This proved to me that every single student now could correctly identify each side of a right triangle.

Hopefully you have checked out the link by now or this lesson is probably making no sense. From this point, students worked in groups measuring different sized triangles with the same angle and then finding the sine, cosine, and tangent ratios without knowing what they were yet. The idea (I think) was that students would realize their ratios were almost the same for each angle even though their triangle legs were different lengths. Then each group would graph their results and we would have what should be the graphs of sine, cosine, and tangent. Enter great discussion on nonlinear graphs that aren't quadratic and discrete vs. continuous. Maybe I misunderstood the objective of the lesson (READ THE LINK) but the graphs didn't turn out.

The instructions said to have the horizontal axis be degrees 0-90 and the vertical axis to be 0-1 by increments of .1. See below one graph each for sine, cosine, tangent.

But when the students plotted the points, it was just a bunch of scattered clusters of points.

If I connect them, is it going to work out? I'm not sure what the problem is. The students don't know what it's supposed to be yet. I though about giving them some more angles and having them use the calculator to find the value and graph some more points. Maybe we don't have enough data? Or do we have the wrong data? Or have I totally misunderstood the point? Please help.


Systems of Equations: Substitution

Keep in mind that we have already done systems by graphing and reviewed finding solutions of equations. I started class with this:

Next, I presented them with this slide and asked them how to solve:

They easily knew what to do and how to write it as an ordered pair. Next I presented them with this slide: 

I think maybe one or two students kind of knew what to do but for the most part, they were stumped. Now that is where the index cards come in. So we took one half (I just had them cut them up so I wouldn't have to use as many) and on one side they wrote y. On the other side, they wrote x - 1 because that is what y equals. Next, I passed out legal size white paper. I had them write the second equation down. Instead of writing the y though, I told them to draw parentheses big enough that your index card would fit inside it. We practiced looking at the equation with the index card showing the y and then flipping it over to see the x - 1. I think this was a good 'kinesthetic' activity because we were literally replacing the variable in the equation with an expression. So now students knew we had to do distributive property and then combine like terms.

From there we did one or two more examples and then they figured it out with out having to use the index card.

The next day, we practiced again.

This time, I had students get a colored pencil to write the substituted parts to make them stand out better. So we started out with a system. I told the students to make a cloud around the equation where the variable is alone. In the example below, we clouded 5y - 1. I asked the students what that equaled and when they answered x, I showed them to then circle the x in the second equation. From there we plugged in (with the colored pencil) the cloud where the x had been. We went through the steps of solving and found that y = 2. Then, with colored pencil, make a cloud around that. Draw an arrow from one cloud to the other. I asked them what happens when two clouds hit? (You know where I'm going right?) Make it rain! Last year my students always forgot to find the second coordinate of the ordered pair but now I know they will always remember to make it rain (if nothing else!).

I found this joke worksheet last year and I really like it because students can self-check using the answers on the right. But beware, students can figure out the joke. Specifically tell them you will be checking their work, not just the answers.

I assigned #1-4 for homework at first because you don't have to solve for a variable to start out.

One student told me she cried because she couldn't figure it out. I think what frustrated them about this was that they knew what to do, they knew that they could do it, but they were just making mistakes. Some students have actually told me that they like this and one girl said it was the easiest thing we've done all year. I've tried to stress to them that this is a new concept but a familiar process. As they practice, they improve. But what I have been impressed by is that they don't give up. They know they can do it.

Right before lunch one girl said I was making her hungry with all of this thinking and hard work. Success!

Those of you that have been reading and responding to my tweets have probably noticed my moody-bitter-I-hate-everybody-what-is-the-point-of-teaching diatribe. I still feel that way. I feel like even though my students are learning at this point, they won't know in two weeks how to do it. Or two months. And definitely not in two years. We have data to back that up.

I feel like my job is pointless. They aren't retaining anything and I don't know how to make them retain it. We've identified that students aren't really doing any critical thinking but I don't know how to fix that. Or teach it better. Or make it stick.

So. I will keep going on but yesterday, I wanted to quit. This job is impossible. If the people before me couldn't do it, what makes me think I can? I think a mark of a good teacher is when you can make the lower level students learn. I'm not doing that. Anyone can teach the top students. How do you reach the rest? 

Even then, our smart kids are not retaining anything. 

What. Is. The. Point.



SBG + PLC = I Finally Get It

This one article assigned in our PLC class has finally cemented how SBG should work FOR ME.

*from Revisiting Professional Learning Communities at Work pg 190-193
Dufour, Dufour, & Eaker, 2008

Diana, Se, Marie, and Amy, the second-grade team at Westlawn Elementary, began their collaborative process for improving  math proficiency for their students by engaging in collective inquiry regarding the current results and practices in second-grade math. Their math achievement data from the previous year's summative district assessment indicated 78% of second graders met or exceeded the district's proficiency target in math. They agree to establish a team SMART goal to improve upon last year's results by at least 10% on that same summative district assessment. The goal was strategic in that it was aligned with the school's goal to increase the percentage of students meeting or exceeding proficiency in math as measured on local, county, state, and national indicators. The team goal was measurable because it asked for a 10% increase over the previous year. The team believed the goal was attainable because improved results (higher levels of student learning) were required to achieve the goal. It was time-bound because the goal was to be accomplished within the course of the school year.

Prior to developing strategies to achieve their goal, Diana, Se, Marie, and Amy had a candid conversation about how they had approached the math curriculum in the previous year. They acknowledged they had followed the same 4-step pattern for each unit:
  • Step 1. Administer the pre-assessment from the textbook.
  • Step 2. Teach the unit.
  • Step 3. Administer the post-assessment from the textbook.
  • Step 4. Move on to the next unit, repeating steps 1 through 3.
They recognized they would only improve student performance in math across second grade by seeking out and implementing new and better practices. They committed to each other to use the team learning process of a PLC to guide their teamwork throughout that year.

What Did They Do?
1. They clarified the 8 to 10 most essential student learning outcomes (skills, concepts, dispositions) in math for each semester by doing the following:
  • Talking with the third-grade team to determine the skills and concepts most essential to student success in math for entering third graders
  • Analyzing and clarifying their state and division second-grade math standards
  • Consulting with school and division math specialists to clarify multiple interpretations of the same standards
  • Analyzing the district assessment, and identifying where their students had struggled in the previous year.
  • Developing a math curriculum map and common pacing guide they all agreed to follow
2. They created a series of common formative assessments aligned to the essential math outcomes by doing the following:

  • Studying the language and format of the district's summative assessment of second-grade math
  • Selecting appropriate items aligned to the essential math skills from math textbooks, individual teacher assessments, and state and national websites providing released math items
  • Creating new items deemed by the members of the team to be valid ways of assessing the essential skills
  • Including at least five items per skill on each common assessment to provide students an adequate opportunity to demonstrate their proficient
  • Increasing the number and frequency of assessments so that only two or three skills were considered on each assessment
3. They established a proficiency target of 80% for each skill on each assessment. For example, if they used five terms to assess a particular skill, students needed to solve four of the five problems correctly to be deemed proficient.

4. They collectively analyzed the results from each common formative assessment, identifying, skill by skill, the individual students throughout second grade whose scores exceeded, met, or fell below the team's proficiency target.

Through this collaborative analysis of common formative assessment data, the team was quickly able to do the following:
  • Identify individual students who were experiencing difficulty on any skill.
  • Identify individual students who were already highly proficient
  • Create flexible groups of students across the grade level for the intervention/enrichment period each day based on skill-by-skill proficiency.
  • Establish a protected block of time each day for the team, resource specialists, and instructional assistants to provide students with coordinated and precise intervention and enrichment based on students' personal needs.
  • Identify the teachers whose students were experiencing the greatest success on each skill.
  • Assign students who were struggling with a particular skill to work with the teachers experiencing the best results in that skill on the common assessments during their intervention/enrichment period.
  • Explore and discuss the strategies being used in individual classrooms
The team also engaged students in the process of monitoring their own learning by requiring each student to maintain simple bar graphs indicating his or her proficiency on each essential math skill. Items on the assessment were arranged by skill, and each item was assigned its own box on the graph. After every common assessment, students would color in the box for each item they answered correctly. As individual students discovered they had not not met the proficiency target on a particular math skill or concept, they knew to report to the corresponding small-group tutorial during the intervention/enrichment period to receive additional support for their learning.

At the completion of this skill-driven cycle, the team administered another form of the common assessment to students who had experienced difficulty on any of the essential skills. At that point, new student learning groups were formed. Students who demonstrated proficiency were moved to enrichment groups, while students who continued to struggle were moved to smaller, more intensive group interventions.

This intervention/enrichment process ensured that any student in second grade who was having difficulty understanding a skill would receive intensive, small-group instruction from the most effective teacher on the team for that particular skill. The process allowed the team to continue with new direct instruction during the regular math period each day, so the difficulties of a few did not adversely impact the opportunity for all students to learn new material. Meanwhile, the team continued to build shared knowledge of the best way to help young students acquire math  skills through  a collective study of the research on the topic. At the same tine, however, members were conducting their own action research on effective math instruction and learning from one another.

Systems of Equations: Substitution

I spent one day on solving systems by graphing which is exactly what I wanted since I know I will need much more time for substitution and elimination.

Before jumping into it, I wanted to review testing ordered pairs to see if they were solutions or not. Here was my thought: I would take four systems from our graphing investigation that weren't parallel and had simple ordered pairs for solutions. I made up a similar worksheet so that students could write the solutions in. Then in the middle box, we substituted the solution into the equation to algebraically prove why the ordered pair was a solution. I wanted to spend the rest of the class period reviewing this concept. So at home I had made up these index cards (I know, I'm obsessed!) of equations and their solutions.

And I said to myself, "Kyle, (That's what I call myself. Just kidding, that's a reference to a Boy Meets World episode. Eric is ridiculous!) how can I use these cards?" My first thought was a scavenger hunt where solutions would be hidden around the room and students would have to search for the correct one. Ok, so that was my only thought. But then what to do with the equations? Well why not hide them too? I had one of my geometry classes hide the cards and they were super sneaky. I should have taken pictures of all the places they hid them. It was insane. So students happily searched high and low, writing down equations and solutions in their nice, neat rows. And then suddenly it dawned on me...everything was written down randomly. We had no idea which solution went with which each equation. It would take forever to plug in every solution to every equation. What to do? Luckily, that was the end of class so I had plenty of time to ponder.

The next day I created another sheet, very similar to the past two. I laid out all of the index cards (there were 9) and had each student (luckily there are 9 of them too- what a coinky dink) take one. They wrote this at the top of the paper. Then, I gave them the first ordered pair which they wrote in the left column. In the middle column, they plugged the ordered pair into their equation. If it worked, they wrote 'yes' in the right column. If not, they wrote 'no'. The beauty of this was that there would only be one yes each time. But since you never know who will be yes, every person has to do every problem. Well technically after you get a yes, you don't need to do anymore, but I wanted them to practice.

This turned out to be a long, drawn out activity to practice nine problems. And they only used one equation! Next year I suppose I should give them one ordered pair and have them test several equations? Or maybe just scrap this entire activity and find something that gives practice with a variety of ordered pairs and equations.

I am proud of myself for making this activity work, even though it floundered on day one.

The students asked me if they could have a quiz over solving systems by graphing and proving solutions of equations because it was so easy, so I take that as a positive sign.

And I might just take them up on that offer.


Systems of Equations: Graphing

It was time to start systems of equations which I like, but starting with the graphing method, I don't. My instructional coach suggested I use graphing calculators since it is practically impossible to do by hand. Light bulb! It's investigation time. :)

I wanted to make something up where students would graph two lines and then find the intersection point. Thanks go to @bbrennan- he suggested that I have the students calculate the intersection instead of just estimating. Which worked out wonderfully by the way!

I typed up step-by-step directions so that students could work individually for once.

I had students read the first three sentences and stop. I had hoped from a previous investigation on parallel and perpendicular lines that students would understand the concept of solution and no solution. Unfortunately, they did not. We kinda scrapped that investigation anyway. So once I explained solution, the students figured out quickly what no solution meant. From there, I had them flip the paper over and go down through each system to decide if the lines were parallel or perpendicular based on their previous knowledge of slope.

Then we flipped back to the front page and I let students work on their own through the example. I circulated the room making sure that everyone got the correct answer before allowing them to move on.

Once everyone had the process under control, I set them loose on the back page. Fingers were flying, buttons were clicking, math was being done! When students came upon systems of equations that were parallel, they still typed it in the calculator and then got an error. When they asked for help I guided them back to their graph and asked what kind of lines they saw. As soon as they noticed the parallelism (te-he), they realized their mistake. Maybe next time I should put more emphasis on actually looking at the graphs before calculating.

The solutions for number 7 and 8 were ugly decimals that students whined about writing down. But once they cried me a river, built a bridge, and got over it, they realized it was only 8 digits of writing.  I think this activity went well. Students thought it was cool to have the calculators doing the work for them and the process became almost a mantra: "Second, trace, 5, enter, enter, enter".

Compared to graphing by hand, I LOVED this method. I think it was a great visual, an actually effective way to incorporate technology, and is a good foundation for understanding the point of systems. Also, I planned for it to take whole period, and only one period, and it did! By golly, I might be getting the hang of this.


Slopes of Parallel and Perpendicular Lines

Previously I had created what I thought was a pretty good investigation of slopes of parallel and perpendicular lines. It reviewed graphing slope-intercept form and point-slope form, plotting points, finding intersections, and comparing/contrasting equations with a nice ending that would smoothly transition into systems of equations. Little did I know, I made an error on one set of equations that made them neither parallel nor perpendicular. Another set of equations ran off of the graph, which made it harder to see that the lines were perpendicular rather than just intersecting. And I gave this to students on a day I was not in class. And weird timing things happened and we skipped a few days before going back to it. Probably not my best idea ever.

So alas, I scrapped it and found this packet on-line. It just seemed like my students were confused and needed the basics without the investigation. We spent two class periods on it and I gave some for homework. It was straightforward and hit the four concepts I wanted to leave them with: using point-slope formula to write an equation in slope-intercept form, use the slope formula and determine if the slopes are parallel/perpendicular/neither, solve two equations for y and compare their slopes, and write the equation of a line parallel/perpendicular to a given equation. After this packet, I did an index card review.

Here is card 1a and 1b.

Same concept, different numbers. Students worked in partners so that they had someone to ask if they struggled. After 4 minutes, the cards rotate. Now the students receive cards 2a and 2b.

But, if they flip it over, the answer to 1a and 1b is on the back. The idea is that students are able to self-check and not spend the whole hour working problems incorrectly. I saw this idea on Amy's blog and also at a ICTM conference.  Create stations and each station has the solution to the previous station. Amy mentioned that her students wanted to rotate cards instead of rotating desks. I thought this would be easier as well and had my students sit in a circle. I made 8 sets of cards (total of 16) and we only had 4 sets of partners (8 students total) so then they were working on sets 1a/1b, 2a/2b, 3a/3b, and 4a/4b. The problem came when we rotated cards. The students with 4a/4b now had 1a/1b when they really needed 5a/5b so that they could flip them over and see the answers. Things got messy quickly and I was juggling index cards all over the place. It took me two classes in a row to figure out how to remedy this. My last class has 16 students so my set of 8 would have worked but they are terrible at transition and we waste too much time and energy of mine trying to complete simple tasks.

Light bulb! I put the two cards under the document camera. The slower students worked to complete one card while faster students could complete two in the same amount of time. (Hello differentiation!) After the timer went off (4 minutes again), I showed the solutions to both cards and then on to the new set of problems. The class was very well-behaved and quiet- most worked diligently.

I liked doing this but I want to make the station idea work too. I think that next time I should make students rotate stations or I should make two sets of 4 cards. My smaller class could do one set and then the other if there was enough time. Then my class of 16 could combine the two sets and use them all. But that won't always work, depending on the class size.

I think that I accomplished what I set out to, even if the method was different than what I imagined. But what fun is building a boat if you aren't carrying your tools while swimming?