Memorization

I've written quite a few times about bell ringers in my classroom. Generally, the smartest student in the group does the bell ringer while the rest of them stare blankly in the general direction of the paper.

In the past couple weeks I have tried something new.

It's called the perfect challenge and it tests students on perfect squares 1-20.



I did not create this file but it is an Excel file with seven tabs. Each tab is two half sheets with numbers 1-20 squared on it and they are in a different order on each tab. I added the eighth tab as a chart of how I record my students progress. We start with a goal of the whole class scoring 100% in under two minutes with a calculator. We work down to eventually the whole class scoring 100% in under one minute without a calculator.

The students have liked it a lot better. Everyone is participating, everyone is engaged, and everyone is working on memorization. Also, since I am timing it, the whole process takes less than 3 minutes compared to 10-12 minutes with the bell ringers. We trade and grade with a student reading the answers out loud. I collect them and record the percent of students who made a 100% and that what goes into my chart. Once they reach 100%, we move to the next category. A lot of students have started competing with themselves, trying to beat their own time.

I've liked it so much that I've decided to do perfect cubes next. There is just something about an entire class flipping their papers at the same time and eagerly writing that a math teacher comes to love.

And of course, being the all or nothing person I am, I've already been thinking about doing this all next year instead of bell ringers.

What are some other things high school students should memorize?

• Perfect squares
• Perfect cubes
• Decimal equivalents of fractions
• Common formulas
• Reducing fractions
• LCM and GCF

This is all I've come up with so far and I would love your input!

Interventions

One of my huge weaknesses as a teacher is letting students fall the crack. I'm going to be real vulnerable here and say that my default feeling is that students who don't try or don't show up or do nothing in my class, do not deserve my extra help.

That sounds bad. But part of that comes from the fact that I don't know what to do for those students. I feel like students who consistently try and show up don't fail. So that leaves me with those who don't try and so I solely place the blame on them. It's easy that way, right?


I have two  students who have been failing my class all year. I keep feeling shocked that no one has done anything about this without ever putting the responsibility on my own shoulders. I've talked to both students' parents one time during this year. Somehow I've convinced myself that that is enough.

I always give students the opportunity to come in and retake tests and very few do. And the ones who need to do it never do. They don't come in for help, they don't come in and retake tests, they don't ask questions in class, and therefore I don't know what to do for them.

Obviously you will fail if you don't try. I have to make myself see beyond that and question why they aren't trying.

What kind of interventions can I do in the classroom?

One elementary teacher mentioned working with a small group within the class that are not understanding. Which I don't do. I feel that if they are too lazy to even ask for help, why would I devote my time to them? Bad, I know.

Another teacher mentioned preferential seating which I don't really do either. I rotate each group to a new group of tables each quarter and that's about it.

How do you get past feeling like they don't deserve help?

What do you do for students who put in no effort? What do you do for students who can't even begin problems or are missing middle school skills like reducing fractions or knowing factors of a number?

What interventions do you use in your classroom?

Update: I asked some more teachers about interventions and here's what they said:

• Parent Contact (early and often)
• Recommend for tutoring (narrow down specific areas that need to be worked on) 
• One-on-one
• Small groups
• Modified tests/quizzes
• Test/quiz retakes
• Break students into groups, send group to library to work and work with struggling learners in classroom

I feel like I need a form to fill out to document student behaviors and easy interventions. Does anyone have something simple? Our old forms are pages and pages long. I'd like something easy to use and easy to read that shows a lot of information at once.

Even More Classroom Routines

Somehow this idea turned into three posts...

Make Up Quiz/Test: If students are absent on the day of a quiz/test, I write their name on the board under the heading Quiz/Test. Then I check the attendance to see if their absence if excused or unexcused. If unexcused, I erase their name and give them a 0 (school policy). If excused, I take their quiz/test and write their name on it and hang it on a clipboard. I remind them the next day to come in and make it up. If they don't come in that day, I put a 0 in the grade book. If they never come in, then the 0 stays and I don't have to worry about a missing grade. Some students see it and then it reminds them that they have something to make up.

Hot Dog Style: I only grade quizzes and tests and I have a green basket that all papers are turned in to. The papers are folded vertically with the white side showing and their name written on the outside. Then I can grade it and write their score on the inside. A student can pass out papers to the class while respecting everyone's privacy.

Seating Arrangements: This year I'm attempting survivor games, which is a year long competition among groups of students. I picked the groups at the beginning of the year and they have stayed together all year. Not my best idea I suppose. Each quarter I rotate the students to a new group of desks. Within those four desks, they get to choose where they sit.

Questioning: I feel like this is one of my best teaching strategies. My most used are: "How do you know?" "Because why?" "Are you sure?" "Can you explain?" "Can you be more specific? "Can you give me an example?" "What would happen if..." "What is the easiest part of...?" "What is the hardest part of...?" "What do you think?"

Some questions that I need to use more often: "Can you explain that in another way?" "Can you draw a diagram that explains this idea?" "What is a common error a student might make on this concept?"

What are some of your favorite classroom routines?

Parent Teacher Conference

What do you do for Parent Teacher Conference?

I print out a progress report for the quarter and highlight any low grades and absences. At the bottom, I write negative behaviors and positive behaviors, making sure I never have more negatives than positives.

I should have written recommendations at the bottom but I just said it out loud instead.

I also make a sign up sheet and ask parents how I can contact them, telling them I prefer email.

Out of 53 students, I had 7 parents show up and I've never had more than 10 show up. And usually it's the parents of kids that have good grades. Imagine that.

Does your school require you to do certain things?

More Classroom Routines

I thought of some more routines and decided to write a new post instead of adding to the last one.

End of Day Routine: It probably seems strange to start with the end of day but I am not a morning person so I don't do as much in the morning. At the end of each day, I clean off my desk so it's clutter free and organized. Random papers on hung on these clipboards so that they all are in a safe place that is NOT my desk.

I copy bell ringers and have them in their page protector and laid out on each desk for the next morning. I set up my powerpoint or notebook file on the computer/SMART board and turn the monitor only off so that it's ready for the next day. I change the date, turn off my digital clock, and erase all boards. I make any copies I need and they go into the correct bin for each class period.

 If there are any activities I need, I have them set out and organized to start right away. Before I leave, I check my school mail box and put away accordingly.

Beginning of Day Routine: I get to school right on time so that means I walk in, turn on the monitor, turn on the Smart board, get my copies for each day, and start my laptop up to take attendance and check my e-mail. I turn the clock on and I'm ready to go, standing at the door to greet my students.

Plan Period: My plan period is second period which means I struggle through first hour and then use second hour to get prepared for the rest of the day/week. But since I make copies after school, I can better use my time to plan. First of all, I take this time to use the bathroom and check my school mailbox as well as email. On Monday plan, I print out the bell ringers I need for the week and have them ready to go. I email my lesson plans to my principal and use that as a guide to see what I need to copy, create, or put together. It's very common for me to internal sub for an absent teacher. That means I bring their students to my room and give them their assignment and I sit and work at my desk. Sucks when I need to leave my room, nice when I get my paycheck. :) I've already wrote about how I plan a lesson, but basically, I look and see what I have, what the book has, and what I've saved online, and do a mash-up of whatever seems easy to understand. Always work out an answer key before copying ANYTHING. I don't know how many times I've had to learn this lesson. Almost every time, I find something I need to fix or want to change. It's always better to be prepared.

Saving My Work: I carry a Western Digital Passport External Hard Drive back and forth  to school where I have everything I've ever done in my five years of teaching. I've tried box.com and Sugar Sync and other programs but if the Internet or server goes down at school, I can't access any of those. So this works best for me. I save things by school year, 2013-2014, then create a folder for each prep that I have. Within those, I create a folder for each unit. Everything I use in a unit is labeled with the prep, the unit, the day within the unit, and the concept.

For example, A2 3 D0 Glossary means Algebra II, Unit 3, Day 0, Glossary. Next comes A2 3 D1 Polynomial Graph Investigation- Algebra II Unit 3, Day 1, concept.

This way I know the difference between what I actually used and stuff I just saved.

I like to know exactly where things are.

Desks: Last year my biggest class was 28 and this year my biggest was 14. The first thing I did over the summer was remove a bunch of desks! I kept 16 and grouped them into fours in a way that no one's back is to the SMART board. This is the best picture I have but I no longer use the bags zip tied to the desk. This is easy to walk around and between, to monitor students, to pass out papers, and to give students nearby resources.

Kleenex: As a high school student, all my teachers only had toilet paper and I was so embarrassed at how red and raw my nose would get. I swore I would always have Kleenex in my classroom. I keep one on my desks that mostly for me and one for students to use. I probably don't even go through 10-12 boxes a year so it's not a big deal for me to buy them myself. I also only use an electric pencil sharpener.

Birthday Candy: At the beginning of the year I give students a calendar that they pass around and write their name, birthday, and favorite candy. I give it to them on their birthday and summer birthday's get theirs on the last day of school. This is something I have always done and will continue to do. I really feel that some students get no presents or specialness on their birthday so I do what I can to show them they are noticed and their birthday matters to me. It costs me $50-60 a year since I only have 50ish students so it's not bad.

Survivor Games: If you noticed in my last post, I mentioned this game a lot. This is the tracking sheet I use. The students picked their own team names and at the top are the categories I'm recoding. I shaded the rows so I can easily see the changes between class periods. I just mark check marks if they did it and x's if they didn't. MMM is Mental Math Monday and I write down their table total. For bell ringers, I record how many they get right through the week. At the end of the week, I put a smiley face next to the group that won that category and over to the left, I write down the number of game pieces they receive. I write the week's date in the top left white corner.



And that's all I have to say about that!

Classroom Routines

Being the slightly OCD, analytical teacher person that I am, I LOVE a good routine. Here's some I've developed so far.

Bell Ringers: 2-5 middle school problems printed on paper inside a page protector. One per group of students. Students used dry erase markers to work problems. I give 2-4 minutes with my timer and collect. I set all four on the board and we compare answers. Students explain what they did. I record how many each group gets correct and the team with the most at the end of the week wins a survivor game piece. I do bell ringers Tuesday-Thursday.

Mental Math Monday: 10 middle school problems that I read out loud to students one a time. They use their dry erase markers to work on the desk and write their answers on a laminated card. At the end we trade and grade. Each group gives me their table totals and I record them. The team with the highest total wins a survivor game piece. If the class has an all time best, we celebrate with a funny youtube video.

Bell to Bell Teaching: I teach all hour, every day. I do not give free time or free days. Students start with a bell ringer and then move on to whatever I have planned. If we finish early and I have nothing else prepared, we get out dry erase markers and either work on the desks or at the board. I make up problems based on whatever we're currently doing or something I think they need to remember. This year I've been better about having the next activity ready in case I need it but I always have the whiteboard as back up. I have found that my discipline problems dropped dramatically and the class environment became a lot more focused on math.

Two Nice Things: Once a student says an insult or rude comment, they have to say two nice things. It doesn't matter if it's about themselves, their mom, a celebrity, a person not in the room, etc. Now the two things are usually made up or insincere, but it's the consistency of making them do it that gets them. It's hard for them to publicly say nice things (sadly) so it slows down some of the verbal diarrhea.

Binders: I gave all of my students three ring binders, sticky labels to put their name on the spine, colored card stock and sticky tabs to create dividers, an empty page protector to hold things, and a concept list of everything I plan to teach during the year.  Tabs are labeled notes, quizzes, and tests. Binders stay in my room at all times except the night before a test. I have a bookshelf with one shelf per period for students to store their binders. Except they normally look like this. How hard is it to stand your binder up?

Miniature Trash Cans: I use these anytime students are cutting. It collects scraps, prevents 80 million people getting up 80 million times, and keeps the floors much cleaner. I leave them there all day if everyone is cutting or if it's just for one hour, I return them to the cart and dump them at the end of the day. Sometimes students will dump them on their own. I got these at the Dollar Tree and they are even our school colors. Love.

Command Center: This hanging file has clothes pin with stickers on them labeling each class period. When a student is absent, I write their name on the paper we did in class and stick it here. The next day, they are responsible for getting it and copying the notes. The hanging file also has a pocket for my dry erase markers which is conveniently right next to my white board.The date is my magnetic numbers that I change at the end of each day. The blue magnetic container below contains the extra numbers. The blue digital clock also acts as timer, random student selector, and thermometer. I use it frequently so that when I say, "I'll give you four more minutes" that I don't waste extra time. The cart below is my supply cart on wheels and each drawer is labeled with a laminated card. Scissors, glue sticks, markers, erasers, paper, protractors, measuring tapes, highlighters, and mini staplers.

Mini Whiteboard: This miniature whiteboard is attached on the outside of my classroom door with sticky strips. I use it to remind students of quizzes and tests, if I take my class to the computer lab etc, and I write bus times for sports on there as well.

Table Tubs: Each table has a tub with fourish calculators, four mini dry erasers, and the mental math Monday cards. At the end of each hour, I record which groups left theirs clean and they earn a survivor game piece. Again, got these from the Dollar Tree.

Unit Tubs: I have a tub for each unit for all three of my preps. I keep all my originals for the unit, any unit manipulatives or activities, and the pacing guide for that unit.

Dry Erase Marker Storage: One member of each group in every period is in charge of holding the markers and the survivor game pieces. I give them a zip up pencil pouch with three rings that stays in their binders. This has severely cut down how quickly I go through markers because they aren't so quick to waste their own. Before, I kept them in tub and every class used the same markers. Wasteful. When their marker runs out, they have to turn in a survivor game piece to get a new one.

Weekend Stories: EVERY Monday I ask students about their weekends. I find it's a pretty good way to get them talking and start the week off on a positive note.

Homework: I don't. The end.

Cheat Sheets vs. Formula Sheet vs. Nothing

What are your opinions on letting students use cheat sheets (of any form) or a formula sheet on a test?

I can see two sides. One, if a student uses a formula sheet (especially one used on an state exam or whatever) then it helps them get used to using it and it only gives them a formula. Using a cheat sheet can give students an example to look at it, which means they are possibly just changing numbers and plugging in without any true understanding of the concept. But then again, you could ask harder questions, such as application so that the formula is only a small part of what you want students to do.

The other side, giving students nothing, means you are assessing both memorization and application of the formula or skill.

Which do you prefer? Does it help or hurt students to use a cheat sheet or formula sheet?

Again, I can see two sides. One, if you're thinking about college, it probably hurts them because not many professors allow that but then again, some do. Two, if you're thinking about real life, if I'm being assessed on the job, I'm going to look up whatever information I need. It seems that in real life, performance matters more than memorization. That's why we have Google, right?

In addition, I seem to remember a lot of standardized tests that give the formula in the problem...again supporting the idea that application and performance are most important.

I guess it's just hard when you think about giving a test that requires several different formulas. If a student can't remember the formula, they have no chance at applying it. If they at least have a formula, they can attempt to apply it.

If using a cheat sheet, is there any merit to the idea that writing out worked examples helps with retention?

Things I Know

Things I Know

• Mental Math Mondays- it's making a difference 
• Semester Reflection- the most meaningful way I've incorporated writing; killing two birds with one stone by writing and getting student feedback
• Staying organized and efficient-makes it a lot easier to multitask and get things done at school
• Plan Period- this is the first year I've actually been able to use it to plan
• That I am 100 times more strict and consistent than I was in year one
• I love miniature trash cans
• I must rid my classroom of even more clutter. 
• I will definitely be adding some more color to my classroom.
• The number of things I accomplish in a school day is amazing
• I don't have a pencil problem this year
• I'm letting students fall through the cracks. 
• I am terrible at parent contact.

Things I Don't Know

• Why I stopped creating fun activities 
• Why I create boring notes instead
• Why students and adults can't follow rules, show up, and do what they're supposed to do
• If my survivor games is a good idea...good theory...keeping students in same groups all year....probably not
• How to do any of the PARCC sample items....and consequently how to teach 
• How to make Algebra II less boring
• What geometry proofs I should be doing other than triangle proofs
• How to get students to work without me hovering or to ask questions and not quit
• What to blog about when I haven't created anything to share :(
• What kind of interventions can I do within the classroom?
• What do I do about a student who does nothing?

Proofs: Cut, Sort, and Paste

One of the other ways I practice proofs is using this activity where students have all the pieces to the proof and are cutting, sorting, and pasting them into the correct order.



This is the first year I've used this idea and in my top two sections, I've used it as a reinforcement activity after students have finished a packet of about 16 proofs that they write on their own.

In my third section, which is a lower group, I plan on using it as a practice activity before students start writing proofs on their own. I'm curious to see if it makes a difference.

I did not create the document, I just wrote out the strips and gave them a table to paste them in. I scanned them in and the second sheet is crooked so I left the blank tables in case you would like to rewrite them yourself. =)

In retrospect, I should have brought students together and discussed the different ways students went about their sorting. But my students were kind of  working on different things at their own pace so I will  attempt that discussion in my third section.

Update in a few days!

Triangle Congruence Proofs

A couple years ago I found this ACT unit for triangle proofs...and LOVED it.

I start the unit with this sheet on labeling parts of triangle and recognizing the opposite side, opposite angle, included side, and included angle. This is the one thing I actually made myself. =)



Next comes this powerpoint. The first slide gets the whole class involved, immediately. Jealous. (By the way the left two cars are mine, the top right is my sister's, and they are all totaled. But save that for the end.)



Next students have to pick which questions need to be answered in order to know if a car is totaled. They usually pick all but 2 or 3. Then I show them the Merriam Webster definition of totaled "to damage so badly that the cost of repairs exceeds the market value of the vehicle". We revisit the questions and they usually narrow it down to 4. I tell them there are exactly 2 and they can figure it out.

From there we go to triangle diagrams with all angles and all sides marked. We match up the congruent sides and angles and then write a congruence statement.

Here's where the connection comes in...this is a lot of information to give. Just like the insurance questions, what is the least amount of information we need to know to decide if two triangles are congruent? And that is the set up for learning our postulates.

Then comes one of my favorite activities (excerpt from the ACT unit).

Print the first two pages on old school transparencies and the third and fourth on paper.



Students have to match a figure on transparency one with the same figure on transparency two. It can be flipped, upside down, or backwards. Using the third page, they write the letters in corresponding order. So clever. After we review correct answers, they work on the fourth page to reinforce the idea that ORDER AND MARKINGS MATTER.

This first pages gets handed out next for students to read and make their predictions of true and false.



We put these away for later and get to another one of my favorite activities. The second and third page of the document above gives students 8 scenarios to create triangles using a variety of angles and side lengths. I created sides from straws and angles from colored paper.

 
Students have to build the triangles as best they can and trace it on to the paper, labeling sides with lowercase letters and opposite angles with capital letters.

When all students are done, I give them eight one-fourth pieces of a transparency (cut ahead of time!), and they number them 1-8 and trace with a dry erase marker, the ENTIRE picture.

Now we bring back our true or false predictions. As a class (with my hints), we create a 'shortcut' name for each sentence. SS, SSS, AAA, etc.

Each number on this page matches up with the number on their transparencies. So each group compares their number one drawings by stacking them on top of each other. Are the triangles congruent? If so we mark True in the Actual column. Repeat for #2-8.

I have to help a lot on these because their drawings are somewhat ridiculous. So...there's that. And we end up seeing that the only true shortcuts are SSS, AAS, ASA, SAS, and HL.

Then I hand out this and students match the correct postulates to the correct markings.



And we work through this next worksheet together, reintroducing concepts like the reflexive property, alternate interior angles, and vertical angles. We practice marking, writing congruence statements, and determining postulates.



And finally, FINALLY, we're ready for real proofs.



The first page from this packet requires them to go back to their vocab notebook or their notes and fill in some definitions. I hope that this makes them notice more things when we start doing proofs. The next couple pages are the actual proofs.

I do algebraic proofs earlier in the year so students know what they look like and that they always start with the given.

From there I really emphasize that they should mark everything on the triangle first before writing anything down. The most common things I see go wrong are they they mark angles or segments that are bisected as congruent but then don't write it out in the proof. I've seen a lot less of that this year though and I've really hit on any time a word is used in the given that definition of that word had to be a reason in their proof.

It has also helped for students to realize that when an angle is bisected, we mark the angles on the letter in the middle. So many students still don't realize the different between bisecting a segment and bisecting an angle. I don't understand...they come with their own symbol, a picture of what it is! Craziness.

From there, I do lots of different activities to practice proofs (I only do congruent triangle proofs) but I just love this setup.

Hope you found something valuable from this looooooooooong post!

How I Plan

I'm really trying to get back in the habit of blogging, but I'm boring this year and either I've created boring guided notes or reused things from the past that are already posted here. =(

A commenter mentioned something about planning so I thought that would make a good post.


How I Plan: Summer Time

• Create a new school year folder on my external hard drive by school year, by class (Alg I, Geo, Alg II) and by the units.
• Go through my pinterest board Teaching Ideas and save lesson ideas to my blogroll pages (see top of this post) separated by class and big ideas
• Read more blogs and also save lesson ideas to my blogroll pages
• From both above ideas, I download the documents and save them into my the correct unit folders on my external hard drive
• Reevaluate my pacing guide (I always rearrange things and I'm really trying to delete things as well) This year I made room in my pacing guide for notes to myself. Some examples of things I've written so far are vocab words that can be cut, concepts that need to be in a different order, concepts that can be cut, or notes of documents that I need to edit (although I try to do those asap)
• Recreate my EOC. This is only our second year of using end of course exams but I find that as soon as my pacing guide changes, my EOC will have to change to reflect that.

How I Plan the Beginning of the Year

• Think about year long themes. We usually start school on a Wednesday so the first three days don't really count. I use this time to find activities that are fun but also reinforce my themes. For example, this year my themes were reading directions, being organized, and team competition. So my activities were a directions quiz, a day of organizing binders (cardstock and sticky tabs for custom dividers labeled Notes, Quizzes, Tests, an empty page protector, syllabus, concept list, and label on the outside of the binder), and a day of team competition (separating my students into teams, creating a group name and a group flag, then the marshmallow challenge)
• I teach in a small school were every student will definitely have me two years in a row, possibly three. I can't just use the same beginning of school activities from year to year. I rotate.

How I Plan a Unit

• My pacing guide is organized into units but from there I guess I create mini-units, where there is a natural break in the concepts. Basically, I am deciding which concepts will go on the same test. I like 4, sometimes 5, and never more than 6.
• I try to give a quiz at least every two concepts but preferably every concepts.
• I already have ideas saved from summer to get me started
• I go through my past years of units and move things I want to use to the current year (I've saved everything I've ever used in my teaching career)
• Look for gaps. What concepts am I teaching this year that I don't already have something for? Is this a concept I understand well enough to create something myself? If not, it's time to google/blog/twitter/pinterest.

How I Plan a Lesson

• Is this a concept I've taught before? If so, do I have anything I can use? If I don't like it, how can I fix it? If I like it, is there anything I can do to make it better, add on, or need to get our for this lesson?
• If this is a new concept, I first use my textbook for ideas. From there I can check my blog rolls to see if I missed any ideas. I can tweet and ask for help. Or I can google.
• Is this lesson boring? Are there any ways I can incorporate an activity to spice it up. My favorites are sorting, rotating stations, pong, concept attainment, or something hands on.
• Make sure practice is involved. After I introduce a concept (usually through an example) am I giving students at least three problems to practice on their own?
• Do I need to include any vocab definitions?
• Did I give students enough space to show their work and a graph if needed?
• Did I include any questions that review an old concept, make them think, make them create their own of something, or ask them to make a prediction?
• Did I include some out of the box problems vs cookie cutter problems?

How I Plan an Activity

• What materials do I need? Do I need to make copies for each student, for pairs, or for each group? Card stock or colored paper? Do they need to be cut ahead of time or can students cut them? If students are cutting, I put mini trash cans on each group of desks to avoid trash on my floors. Do I need glue sticks, rulers, tape?
• Where will I put materials? Can I lay them out for students to pick up, pass them out during class, or assign one group member to get supplies for their group? What is the most efficient way so students aren't crowding, pushing, flowing out the door, or standing in a long line?
• Is this a station activity where students rotate? Do I have directions at each station? How long will students have at each station? How will they know when to rotate? Am I giving students enough time so they don't fell rushed but not so much time that they are doing nothing? (I usually use a timer and tell them to rotate either left or right) Are they writing on something at each station or taking the same paper with them from station to station?
• What is my goal for the activity? Is this an introduction, reinforcement, or practice? Am I going to answer their questions or do they have to rely on classmates? Can they use their notes? Would the best way to reach my goal be individually or group work?
• Am I making them think?
• What parts are potential pitfalls to my students? How can we avoid them? Are my directions clear? Is there a question that every student or group is going to stumble on? Can I give them a hint or a place to look for a hint?
• Is this competitive? Do students know how they earn points? Is there a clear place to keep score? Is there a prize or just for fun? Clear expectations!
• How will I know if the activity achieved my goal? Is there some kind of student feedback? Am I grading or charting results? Quiz? Formative assessment? Exit ticket?

How I Plan a Blog Post

• I don't. I just start typing and it all comes out.

End Behaviors Sort

This activity was not created by me but I don't know the name of the teacher who did create it. I took the questions and created a powerpoint.

Once students have been introduced to end behaviors of polynomial functions, I use this as a reinforcement activity.

There are twelve graphs of polynomials that I print on colored paper and cut (or better yet, have your students cut, and then you get to keep them forever).



I ask students to spread them out at the top of their desks so that they can see each graph.

Then I go from slide to slide on the powerpoint, asking students to choose a select few from the group. It doesn't take long for them to get the hang of it and then I show the answers (immediate feedback).



You can probably make prettier ones with Desmos nowadays but I'm not looking for more work.

This activity could also be used as an alternative assessment or you could use the powerpoint and ask students to create their own graphs for each question.

Before doing this activity, you could give students the graphs and ask them to sort them into any groups they would like. Then have each group compare and contrast for some interesting discussion.

I love a good sorting activity!

Why Do I Blog: Then vs. Now

In response to Dan Meyer's post...

I started blogging five years ago.

The main reason I started was because I was a substitute teacher. That means nothing to plan or create on nights or weekends. Exposure to a variety of teachers, classrooms, and students. And a lot of time to spend on the computer.

I started searching and found this little community of teachers who taught math and liked to talk about. I basically blogged so I could be a cool kid too.

I had no idea what to write about and did a lot of embarrassing, cliche blogger things.

As I started teaching it became more a cry for help when I realized I had NO IDEA what the heck I was doing.

Then it turned it into venting and ranting when I realized just how terrible I was at this thing.

Next it became an outlet for me to share my creations...once I finally felt like I could do some things right.

Currently, I would say it has faded away as one of my priorities and has now become more of a place of reflection and sharing things every once in a while.

When I do read blogs I kind of miss being more involved but then when I'm laying in bed watching netflix, it seems like so much work to even turn the computer on.

So there's that.

A lot of change in the past five years.

What will the next five years of my blog life bring?

Math Class With Less Direct Instruction

In response to @lmhenry9's post...

I've realized that with my smaller class sizes this year, it seems like I am doing less activities than usual. For one reason, direct instruction is a lot easier with 10 students compared to 28. Last year, I knew 100% that lecturing would not hold the attention of my 28 students and so I desperately searched for anything that I could turn into an activity. I was always looking to free myself up to wander the room and put out fires.

This year, that thought hasn't even crossed my mind. Whatever activities I've used in the past I have used again but I can't really think of one new activity that I've created this year. Sad. :(

But I think there are small things that I do that make me feel like I'm not all direct instruction. I guess it depends on how you define direct instruction. I think of it more like a traditional college setting- a professor writes and talks a lot and students write a lot and don't talk. Some people probably define direct instruction as anytime the students are looking at the board or teacher.

If you peeked in my classroom window, it would probably look boring and just like direct instruction. I think it's more the way you arrange, present, scaffold, and question things.

If the paper my students are working on asks them to analyze graphs, write the data in a table, make comparisons, and find a relationship between two categories, is that direct instruction?

If the paper my students are working on asks them to look at two columns of expressions and asks them to explain why the column of expressions on the right can't go in the left column, is that direct instruction?

If the paper my students are working on asks them to write proofs or cut and paste statements and reasons into coherent proofs, is that direct instruction?

If the paper my students are working on asks them to work out various pattern and look for a common end result, is that direct instruction?

Just because I'm at the board and my students are working at their seats, writing on paper, is that direct instruction?

If I am questioning, asking students to try hard problems on their own, asking students what is different about this problem than the last, asking students how they think we should start, asking students what could we do next, asking students to explain another method, asking students to work problems, compare, and discuss with their group; if I am giving students individual think time, asking more questions than I answer, redirecting questions from me to the whole class, and students are writing and talking more than I am, is that direct instruction?

To me, direct instruction is when I am directly instructing students every step of the way; when I say this is the only way to do this, you must copy exactly what I've written; when there is more writing than thinking and more listening than talking; when students have no input; when there is no puzzle, no pattern finding, no analyzing, no comparing, no questions, no discussion.

And to that effect, math class with less direct instruction does not ONLY mean activities, projects, students out of their seats or on the computer, or peeking in my classroom and seeing chaos.

It means my students ask each other for the correct answer before they ask me. It means that they find different patterns and question whose is correct. It means that they can write without listening to me talk. It means they have to look at things, they have to analyze, compare, observe, sort, organize, write definitions, create examples, explain counterexamples. They have to THINK.

I feel that I can accomplish the majority of these things with the way I design and scaffold my guided notes. I have a lot of good activities. I'm not good at projects. I haven't flipped my classroom. I haven't found anything computer based that I like. But I've found a way to present things, to question my students, to scaffold my concepts, that allows my students to do the skills I think real mathematicians need.

I don't feel like a lecturer. I don't feel like a college professor. I don't feel like a public speaker.

I feel like a highlighter. A pointer outer. An offerer. An observer. A questioner.

And I hope my students feel the same.