On Review and Remembering

Recently, our high school math department met up with the middle school math department to discuss all kinds of things. Part way through the discussion, someone mentioned the need for a magic pill to help students remember what they've learned.

We all agreed. We have all experienced the frustration of believing that our students have mastered a concept, only to discover they can't remember what they've "learned" just days, weeks, and certainly months later. By the next year, we're hearing that they have "never" seen whatever thing we are expecting them to remember.

In the middle of this conversation, it occurred to me that maybe we are teaching students to forget. A traditional math classroom (including mine until I started SBG) looks like this:

1.  Teach a unit
2.  Review the unit
3.  Test over the unit
4.  Move on to next unit
5.  Start forgetting previous unit

The end of each of my units always had a review day, where I would have students practice a bunch of problems that were really similar to the ones they'd see on the test the next day. Only the numbers were changed. The next day, my students would (generally) do pretty well on the test. I would pat myself on the back for my good teaching ability, and away we'd go to the next unit.

Now I'm thinking . . . Do those big-review-days-that-look-just-like-the-test-right-before-the-test-day just train students to stuff in the information, hold it in for 24 hours, and regurgitate it the next day? If our students do very well on such a test immediately following such a review day, does it give us a false representation of what they've actually learned? What if the "forgetting" we see is really just "never learning"?

What should review look like? When do you review? What do you review? WHY do you review?

Fighting Assessment Freak-Out

Our school was asked to present a "high school" perspective on preparing for state assessments. I don't know that we are doing anything all that unusual, but here are some of the things we shared.

1. Teach the standards. I don't want to over-simplify this, but at a time when so much is unknown, it makes sense to focus on what we do know. In the CCSS, we have a document that states what our students need to know. Make sure you're teaching that stuff.

2. Focus on the essentials. While it is our goal to teach every standard, we know that might not be possible. We printed out the standards for each of our classes, one to a page. One at a time, we took the standards for each class and sorted them into "most", "somewhat", and "less" important. Then we took the "most important" stack and narrowed it down to the 8-10 most essential standards for each class. If we don't do anything else, we'll make sure our students don't leave our classes without mastering those standards.

3.  Assess what they've learned. All of our departments are working on regular formative assessment. Data is brought back to weekly PLC meetings where we discuss the teacher side (how can the teacher approach this topic more effectively) and the student side (what interventions can we provide for students who didn't learn).

I am piloting standards-based grading, soon to be joined by the rest of our math department and more. Each skill is based on 1-2 standards from the CCSS.  The difference is the data. Instead of identifying that a student scored a "74% on chapter 3", I can identify exactly which skills each student has mastered, and which ones need more work. If the class doesn't learn a particular skill, I can devote more class time and/or spiral back to that skill as we move forward in the curriculum. If individual students don't do well on a skill, I can provide opportunities for them to continue to work on that skill.

4.  Provide interventions. We have all kinds of interventions.

If a student is deficient in a lot of skills: We provide an extra hour of instruction in addition to their regular math class, called "math lab" or "opportunity room". Here they spend a portion of the time working on skills like math facts and solving equations. The remaining time is spent reinforcing what they are doing in their core math class. Right now this option is only available for math. English will be next.

If a student needs help on a particular concept: They may work with the teacher before or after school, or be assigned to our tutoring center "irish hub" to work with a national honor society student. We could not do this without our NHS students. They are amazing, and they often explain something in a different way that clicks with a student. This intervention is available to all students for all classes.

If a student just refuses to do something: They go through the "non-compliant" side of our intervention plan, which involves a lot of follow-up and administrative assistance to help the student be successful. This is also a school-wide intervention. Here's the flow chart:

I was surprised that standards-based grading was the portion of our talk that received the most questions/responses when we were done. There are so many in the world of blogging and twitter who use SBG that I forget it is actually not that common (in our area, at least, SBG is fairly rare). The room was full of mostly administrators who were very supportive of the idea, but they were meeting resistance. The idea (specifically the unlimited re-assessment) is apparently a tough philosophy for many to embrace. 

Changing Everything, Using Blueprints

My Algebra 2 classes have been textbook-free since 2007. It started when my school purchased a textbook that I eventually came to hate. I started changing the order that things were taught, customizing lessons, re-doing units, adding activities, and so on. Over time I developed an "Amy Gruen" version of Algebra 2.

All was well and good until Common Core. I read the standards and I tweaked things regularly and added a few new units here and there, but I couldn't shake that "re-arranging chairs on a sinking ship" kind of feeling.

The problem is that I was planning for Common Core in the way that I think a lot of teachers are planning.  I started with the hodgepodge that was Amy Gruen's Algebra 2 curriculum on the left, and over there on the right was the pile of CCSSM. I tried to file those in where they fit, but I had some left over. And there were things in my curriculum on the left with no matches in the CCSSM.

So here I am. I am ready to pitch everything in my Algebra 2 classes and start fresh. After much thought and reading about lots of approaches, I keep coming back to a great session I attended at TMC14 . . . Blueprints*.

Blueprints are a joint project by Kate Nowak, Mathalicious, Illustrative Mathematics, and others. The Blueprints include a sequence of CCSSM that makes sense, justification for decisions, and links to activities that coincide with each standard. What draws me here above other approaches is that they have STARTED with the common core standards. None of this taking a thing that's already done and stamping it up with the words "common core".

Now I can reverse the planning process . . . starting with the CCSSM on the left and a pile of resources on the right and filing those in where they fit.

I've decided to go all in. Start from scratch. Possibly planning just a few days ahead. I am the kind of person who usually shows up August 11 with the year (somewhat) planned out, so this is a bit of a stretch for me. But it feels good and right to start each lesson plan with a standard rather than matching the standard to an already-existing lesson.

I am excited for this new adventure.

Update since I started writing this post: So far I've used the Blueprints to plan a few weeks and I am already seeing a lot of positives. I will write about those soon I hope.

*I got a sneak peak at the "almost final" version at TMC14, and I'm using that to get started. The final version is to be published this fall.

A Desmos Challenge for Everything?

Last year, I used the animation feature on Desmos a to assess students' understanding on parent functions and their transformations. This year I expanded the activity by giving students a series of animation challenges (with increasing difficulty), like so.

Desmos Animation

Then I ended the unit with a Desmos question on the assessment. I color-coded the questions from easiest to most challenging. I was so happy that most of my students selected the most difficult level. Here are the cards I used:

Desmos Cards

I still feel like there is so much more that I could do with this. I am thinking of creating a set of Desmos challenges to coincide with every unit.

For example, one of my classes is working on systems right now. I could have them create systems in Desmos with various constraints such as a given solution, a solution in quadrant 1, no solution, and so on.

I am inspired.

Desmos challenges for everything! (Or at least lots of things.)

Scenes From My Classroom

Here are a few this and thats from around my room. I have a lot more to write about, but for now this is all I can muster. I am full-on beginning-of-school exhausted.

Inspired by Glenn Waddell at TMC14, I thought I would use this progression of (h, k) forms. That might be changing (more on that later), but I still love my yellow brick road with ruby slippers to show where we are. I still want an emerald city, but at some point I needed to stop decorating and plan lessons. So that didn't happen.

(I printed a brick pattern on yellow scrapbook paper, then printed the equations on top of that).

My weekly schedule board. I felt really clever when I used a 2 for "two's day".

I downsized my supply baskets this year. Then I noticed that the red/green/yellow cups fit right on the handle. That's handy.

Red/green/yellow posters.

Pretty syllabus inspired by Sarah's post.

On the first day of school, I combined "telling them how awesome I am" with a plicker quiz. I asked the students "Which pet does Mrs. Gruen own?" and such. It turned out to be a yawner. There is nothing worse than boring the children to tears on the first day of school. I managed to make it fun by following up my quiz questions with little stories, but next time I will put the questions in a slide show and follow them up with a picture answer. When it comes to perfectly executing the first day of school, I am not there. YET.

I use an apple TV to project iPad and/or laptop in my classroom. As a security feature, I have to enter a 4-digit code each time I connect wirelessly. A different code is randomly generated by the apple TV every time, and last year I had a few students start to try and guess the code before it popped up. I thought I would start the year by having every student guess a 4-digit number for a fun on-going game. There could be a prize when someone's number comes up. I just set up a google form to collect guesses and students immediately started talking about probability! How many prizes will I need?

Finally, my buddies and I rocking our TMC shirts. Bring on the school year!

TMC14 Take-Aways

Just a few ways TMC14 will influence my classroom in 2014-2015.

1. Re-thinking Algebra 2. I spend most of my day teaching Algebra 2. I really enjoyed our Algebra 2 morning sessions led by Glenn Waddell and Jonathan Claydon. I left with so very much to think about. There will be strong evidence of these sessions in my classes this year. So much that it will need its own post. Or ten.

2. Alex and Mary's session was a game-changer. Inspiring, I'd say. These two teachers pitched everything and teach grade 10 applied math using ONLY activities. Such bravery! Mary blogs about all 85 days of the semester course, starting here. I am not sure what I will do with this information. At the very least, I'll read through Mary's blog and steal some great activities. At the most, I could jump off that proverbial cliff that Alex talked about.

3. Routines. Though not an actual session, I am pondering what routines should take up daily or weekly space in my classroom. There was talk of so many amazing resources and how people were using them. I am thinking of daily warm-ups, estimation 180, visual patterns, talking points, fostering collaboration and growth mindset, giving students time and space to share about their personal lives, and more. There is value in every one of these things. I really want to be purposeful in how I use my class time. I have a few days to figure that out.

4. Oh, the beautiful beautiful notebooks. There were tabs, foldables, colored paper, and highlighters. Did I say tabs? TABS!! I don't know if I can attain this and I am not entirely sure that I want to try, as I am conflicted by the time spent cutting and gluing and such. Oh, but it was nice being in the same room with all of them. They were so pretty, so organized . . . so full of reference materials. The comment that lures me the most? Kids love their notebooks. They OWN them. They protect them and save them for years after your class.

That TMC Post

If you are reading this little ole blog, then chances are you've already read multiple recaps of Twitter Math Camp 2014. I don't have anything to add in the way of expressing how amazing it was, but I'll jump in anyway and share my experience.

First of all, I traveled with my three colleagues. Yep, the entire math department from my little school was in attendance. I didn't think it was a big deal until person after person commented along the lines of "You brought people with you?! How did you do that? I mention twitter math camp and I just get an eye roll." I don't have a good answer. Full disclosure, it was only a four hour drive and our school covered expenses . . . but still. My co-workers gave up five days of summer to go to this "crazy nerd camp", and they all left saying it was the best conference ever. I am excited for all the in-house conversations that will result from this shared experience.

See what a good little MTBoS evangelist I am?

Presenting! This being my second year to attend TMC, I felt like I wanted to contribute by helping with/leading a session. TMC can't exist without people chipping in, right? Problem: I didn't feel like I had anything to share that I haven't learned from others in attendance. I ended up teaming with Jasmine Walker to share about coding projects we'd done in our classrooms, inspired by a "my favorite" she'd shared at TMC13. We spent a lot of time prepping for that session and it felt good to contribute, even in a small way. 

Another advantage to this (again, my second) TMC is that there were more familiar faces. The feeling was  family-reunion-y, in the best way possible. There were also people I knew but I'd never met. We were oddly half-friends and half-strangers. Now full-friends.

I met a few people who recognized me and thanked me for something I'd shared on my blog. (WHAT?!) They might as well have handed me a million bucks. Appreciation is currency around here. I want to remember to be more generous in saying my thank yous to the many who share so freely.

All this and I haven't even talked about the sessions and how they will affect my teaching this year. There are so many things to write about! And here I just talked about the experience, because that's what first came to mind.

What we have here is unique, for sure. 

Dear Genie (A Modest List of Wishes)

Dear Genie, Some days summer prep feels overwhelming. I need your help. Please bring me these things so that I can do a better job incorporating SBG and INBs in all my classes for next school year. I will need everything on this list for each of my classes:

1.  A concise skill list with 10-ish skills per quarter. Connect the list to my state's standards. Format the list to fit in the notebooks, with space for students to record their scores.

For each skill on the list, I need all of the following:

2.  Some good learning activities. These may include lecture, inquiry, projects and such. I'd like a variety, actually. At least a portion of each activity should be formatted to fit in the notebooks. And, if it's not too much to ask, I'd like the notebook portion to be real pretty. Please used colored paper and markers.

3.  A set of differentiated practice problems with a key. Whenever possible, make the practice not look like a worksheet. Kindly make sure each set is structured to encourage cooperation and discussion within groups or between partners.

4.  Four versions of each assessment. When students need to re-assess, I will be prepared.

5.  Additional learning activities and practice (again, with a key) for when my students haven't mastered a skill.

Please deliver by August.

Thanks a bunch, Genie. I am going to bed.

What's For Supper?

One more non-mathy post before I (hopefully) get into full next-year-prep mode.

In case it is helpful to any of my teachery friends out there, I thought I would share a system I set up to help with one of my biggest school-year stresses: Making supper.

While this won't make supper cook itself, it will at least save a ton of time when it comes to menu-planning and grocery-list-making.

First I made a list of 30-ish meals my family likes enough to eat, well, once every 30-ish meals. These are the only things I am going to cook during the school year, usually along with a salad or frozen veggies. Occasionally something might get bumped from the list and something else might get added, but this is pretty much it. There is nothing sophisticated here for sure. They are mostly simple meals with short prep time and minimal ingredients. Cooking isn't really my thing. But it is cheaper and healthier than eating out, so I try.

When it is time to "menu plan", I just need to highlight 5-ish meals on the list. Those are what I'm cooking this week. I cross off the meal once we've eaten it. When we've gone through the entire list, I will print a new one and start over. 

The next problem I've always had is grocery list making. I hate digging around for recipes and putting the ingredients on a list. I also hate trying to remember all the things we use on a regular basis and hoping I don't forget about toothpaste or toilet paper. And then I discovered this app:

You can input your own recipes, or pull them in from a variety of websites. This took me some time, but should pay off with huge time savings later. (Hint, you can skip typing the directions. Its the ingredients that matter). Now I can select the meals that I've already decided to cook, click the grocery cart (see it there in the upper right corner?), and boom! The ingredients are automatically compiled in a list.

I also added a recipe titled "staples" where the ingredients are items we always keep around like milk, bread, breakfast bars, and such so that I can easily add them to the grocery list by clicking on that recipe. And, because I am very thorough, I also created a recipe called "stuff we use" where the ingredients are toothpaste, toilet paper, and such. So I can also add those items to the list with one click. It is very easy to remove items from the list if you already have them on hand. 

Then go shopping. I haven't figured out a way to speed up that process.

I picture myself coming home from a long day of school, looking at what's highlighted on the list, and throwing something together easily since I will already have all the ingredients on hand. So no more worries about supper.

One less thing.

Thank You June

This June I decided not to think about school. It turns out that was an impossible goal, but I did manage to not do any much school-related work for a whole month. Instead I focused on things I wanted to do at home, and on spending time with my family. My husband is also in education, and we end up having six weeks with the whole family home together. So nice.

There were t-ball games, camping trips with hiking, and a dance recital. There were story times, swimming lessons, zoo visits, and play dates. I cleaned out some closets, sewed a Willy Wonka costume (long story), painted a bedroom, trained for and ran a 10k, and made photo books documenting our daughter's (almost) five years of life.

We homed a caterpillar, named her Buttercup, provided her with luxurious living conditions, and watched her do something very unexpected. She died. 

We started this book, loaned from a friend. I am fascinated by the process of helping a little one learn to read. And it works! She's sounding out words like a champ. 

My little learner set up this cute little system for our reading time. The red watermelon means that she is busy chewing a fruit snack or taking a drink and needs a little break. The green peas signify that she's ready to read. It reminded me of red/yellow/green cups from @druinok. And my mind was back to school again . . .

I feel refreshed. And I'm ready to tackle some new challenges in 2014-2015 with a fresh perspective. I'm looking at you, Calculus, cooperative groups, interactive notebooks, formative assessments, SBG, PLC, common core, lions, tigers, and bears, oh my.

Creative Inspiration

I am soooooo looking forward to Monday. We have district wide in-service. I can't wait!

And I'm not even being sarcastic.

We get to spend the entire day with our PLCs. My math-teaching buddies and I have decided to use the whole day to create activities for our classrooms.

No yawn-inducing sessions that don't apply to us. We are going to create stuff that we can use!

I've been compiling supplies, links, and ideas for inspiration.

Beach balls, because summer is soooo close.

I made the pink ice breaker one a while back. It is covered in silly questions. You toss the ball to someone, they answer the question underneath their right thumb and toss it to someone else. Something like that with math facts might be perfect for our intervention teacher?

Plastic eggs I got on clearance after Easter.

I am thinking an egg hunt? Maybe a problem inside the egg leads to an answer written on the outside of another egg which opens up to reveal another problem? There could be a different color for each group.

Or, that same thing in an egg carton. I like these white plastic eggs because they aren't seasonal. It might only be a worksheet in disguise, but its way more fun.

Foam pieces. I've found that writing on pieces of craft foam with a sharpie makes for durable sorting cards & such. No laminating necessary. The strips could work for putting the pieces of a proof in order? I am sure we can find some other uses as well.

I have a bunch of wooden blocks in my cabinet. Perfect for custom-made dice.

Links to my favorite activity structures: Add 'em up, speed dating, solve-crumple-toss, war (all via Kate's blog). Also bucket of lies, math dominoes . . . what else?

Here are some samples of those for everyone to look at.

And some cooperative learning books with tons of great ideas.

Oh, and I am hoping to convince someone to try Barbie bungee.

Hoping for a productive day!

Today's PD Brought To You By . . . Students

My colleague James had the idea to invite students to our PLC for a panel discussion. It was a very interesting/insightful conversation. The students were pretty honest with us.

First we put together a list of questions. We did this rather quickly, so there is nothing special about them. We just wanted to give students some prompts to get them talking.

Next we selected a group of students. We chose all older students, thinking that they would have had most of the teachers in our little department at one time or another. It turns out they mostly commented on their current classes, so next time we will choose students from every class. We also chose a variety of students in terms of ability level and performance. Finally, we looked for kids who wouldn't shy away from speaking up and giving us some constructive criticism. We ended up with six students, and that was just the right amount.

Finally, we gave each student a personal invitation to come to our meeting and share their thoughts about math class. All of them gladly accepted.

Here are the questions we asked and a summary of the responses. We have about 25 minutes for our PLC meetings, and we finished these six questions with just the right amount of time.

1. Name one thing from one of your math classes that you would NOT change. Why?

• Having answer banks on homework
• Activities where we can move like scavenger hunt or quiz/quiz/trade
• Being forced to organize (a binder or composition notebook)
• Spiral review helps us remember stuff from earlier in the year
• Projects/creating things
• Having assignments on paper (versus out of a textbook)

2. Name one thing that you would change. Why?

• The answer banks on homework make us too reliant 
• The paper is too small in the composition notebooks
• Units should not be longer than two weeks

3. When you miss class, how do you usually get help to make up the work?

• Edmodo
• Talk to the teacher
• Get help from friends/other students in class

4. Do you like us using Edmodo? Is there another way you would like us to post work?

• Those who use it do like it
• Only about half of them use it because they don't remember how to log in (!)
• Edmodo needs to be easier for us to access

5. How do you perceive the advanced classes versus the regular classes?

• At first when I found out I was not going to be in the advanced class I felt stupid, but now I like that the class is at a good pace for me and I understand what we are doing.
• I (student in regular) used to cheat a lot last year (love the honesty!). I haven't cheated at all this year because I understand what I'm doing.

6. What would you like to see more of?

• extra credit
• games
• hands-on activities

The hardest part of the whole discussion was NOT responding when students said something negative. When they mentioned a practice they didn't like, my gut instinct was to explain why we do it that way. But that's not what this is about. Listening is key. 

This discussion triggered a few adjustments and more discussions for us. At our next PLC meeting, everyone shared their favorite hands-on type activity or game. Teachers shared specific activities that were mentioned by the students. We also resolved to use Edmodo during class occasionally, just so that everyone knows how to log in and is aware of what resources are available there.

Next time we will get a different set of students and probably write some new questions, but we will definitely do this again.

April Fool's Day, Volume II

Teaching relatives is weird, but also pretty fun. I've be able to see my nephew almost every day of his high school career. Two years ago, he pulled a cute little April Fool's joke.

He's a senior this year and his little brother is a freshman. This year they decided to step up the level of their April Foolin'.

It is a good thing I like them . . . because they recruited assistance and spent an hour and a half of their evening on March 31st prepping this April 1st surprise for me:

I couldn't even walk through the door!

And I was a little proud.

I would send them to the office for a detention, but the Principal OK'd the whole thing in advance. 

And the Assistant Principal unlocked my classroom door for them.

How's that for a conspiracy?

On Peer Coaching, Struggling Students, and Green Pens

Backstory #1: I've mentioned before that this is my first year teaching two levels of Algebra 2. The regular (i.e., not advanced) class has challenged me like no other. When things go well, I must document so I can try to make that happen again.

Backstory #2: In our PLC recently, we resolved to look for ways to increase peer tutoring in our classes. This is something that has been important to me for a long time, but lately I've been looking for ways to be more intentional about it.

We are at the end of a unit in Algebra 2 and for the past two days, my lesson activities have looked like this:

Step 1: Finish yesterday's assignment (rational equations, most had 2-3 problems left).

Step 2: Work on a set of 16 review problems. Get a green star from me on each and every problem. (One of my strategies has been to check every problem. It helps me to locate errors and misconceptions, and students seem to be more confident and make more forward progress when they have immediate feedback.)

Step 3:  If you have any incomplete assignments from this unit, work on these pages in your composition notebooks.

Step 4:  Teacher will assign extra practice or tutoring another student.

On Day 1 all students progressed from Step 1 to Step 2. No one finished step 2 entirely. I roamed from table to table answering questions and placing green stars on papers.

Day 2 was perfect. I was a little frantic for the first 10-15 minutes as I ran around with my clip board answering questions, giving green stars, and double checking to make sure everyone was working on the step they were supposed to be working on. But there was a moment, about 20 minutes into the class, when about half of my students had finished step 4, received a green pen, and been assigned to another student who was working on another step. All of the sudden I became an observer to the learning that was happening. I still monitored progress and answered an occasional question, but the students who were assigned to tutoring were doing a GREAT job! They were sitting there, green pens in hand, talking about greatest common factors and common denominators and reciprocals and exponents. This is what I want my class to look like. 

Things I'm still smiling about:

1. The look on each student's face when they reached step 4 and I handed them a green pen. I have written about green pens before, but I haven't used them a lot in this class. I didn't feel like these students were ready. But on this day I trusted them and they exceeded my expectations. The green pen truly conveys confidence to a student. Students feel honored to receive it.

2. When I borrowed someone's green pen and they said "May I please have the green pen of power back?"

3. Four students who got everything completed and were assigned to extra practice on white boards. They kept asking me for more problems so that they could race. I was using this set of problems from Kate's rational expression speed dating since I already had them printed out. These are not easy, but these "struggling" students were asking for more.

4. Realizing that these students are mastering the exact same content as my advanced algebra 2 classes. We are going more slowly, pausing more for reinforcement and review, but they are doing the same sets of practice problems and the same tests. I was not sure that this would be possible. But maybe it is.

5. My superintendent walked in to visit when the green pen students were all paired up and tutoring away. She is always welcome, of course, but it was nice that she got to see a moment that I was particularly proud of.

And a few reflections:

1. I am wondering if the green pen is so powerful because I use it constantly. I am always walking around, looking at students' work, and giving them green stars when they are good to go. Students might view it as kind of an authority thing. Hence, the way they feel when they receive "the green pen of power". 

2. Using multiple steps for review was a win! I noticed that when students got to step four, they were pumped that I assigned them to tutoring rather than extra practice. And the few who finished up on tutoring were not surprised or upset when I told them they were ready for extra practice. It was right there on the board, so no one was surprised. Truth, I really only cared that everyone made it through step 2. There would have been so many missed opportunities if I had let them stop there!

So, I have plenty of days that don't go as planned, but this was a great day. Here's hoping something in this post will serve to help me re-create it more often. :)

Sketching f' from f

My calculus class recently finished up sketching a derivative, given the graph of a function.

We began with using spaghetti and estimating the slope at each individual point. Among other things, I used this sheet from Math Teacher Mambo.

I told my students that the next step was to be able to sketch the basic shape of the derivative, sans spaghetti. No more estimating the slope at each individual point.

Students were having some trouble with this (they usually do, hmm). And then I thought about using color-coding, like so . . .

First we identified points where the slope was zero. We marked those in green on the original function and transferred the points to the x-axis of the derivative.

Next we identified regions where the function was increasing (positive slope). We shaded them in yellow and then shaded the corresponding region of the derivative ABOVE the x-axis only.

Then we identified regions where the function was decreasing (negative slope). We shaded those in blue and then shaded the corresponding region of the derivative BELOW the x-axis only.

Now, to sketch the basic shape of the derivative, you draw a graph that hits the green points and stays within the shaded regions.

It worked great! Students were all "Oh, now I get it!" Love those words!

We also needed a way to color-code places where the derivative was undefined, such as sharp points and discontinuities, so we added pink. A pink point translated to a vertical line on the graph of the derivative as a "don't touch this" signal.

Then we did a little more practice by matching some function/derivative cards. These are not my creation, but I am not sure where they came from to give credit.

Function and Derivative Cards by sqrt_1

There used to be lots of arguing and discussing during this activity, this time students breezed through it easy-peasy. I was just sitting there going ". . . but aren't you going to discuss . . . and argue and stuff?"

Next time I'll keep the spaghetti for sure. After that I'll have them try the card matching before the color-coding thing, and then back to the cards.

First on the Drop Pile

I wrote about this once before. Go back and read that if you want. Or don't. I'm about to summarize here anyway. :)

Yesterday the math PLC at our school did a "Keep. Drop. Create" activity. Among other things, "questions at the beginning of class" ended up in the drop pile. This is something I have felt strongly about for a while, so I am very happy that our whole department is in agreement.

I am probably preaching to the choir here, but if you give practice assignments on a regular basis and you're using the first ten or fifteen minutes of class to answer questions about yesterday's assignment, you should consider using that time for something else. Here's why:

Low student engagement. During question time, most of our students fit into one of three categories:

1. Students who didn't do much (or any) of the practice. They are now sitting there writing down the problems while you work them out. They're not thinking. They're transcribing.

2. Students who did most of the practice. When they got to a tough problem, they gave up because "I'll just ask that one in class". They learn to wait for help rather than persevering.

3. Students who did all of the practice before coming to class. They are now bored to tears while they watch your performance of math problems they already know how to do. Not learning.

(There may be a fourth category of students who legitimately have a question and are now eagerly anticipating your answer. But there are maybe two students in that category. Also, I would suggest that doing the problem for them while they watch is not the best kind of help.)

They're ready to learn. If there is a portion of the class period that students are most ready to do something, it is at the beginning. Don't lose them here.

Opportunity cost.  Instructional time is precious. Let's use those ten minutes for something else. Something that engages all students. We are working on a list.

In the mean time, we have decided to have little slips of scrap paper cut up and ready to go. At any moment we can do a quick formative assessment by posting a problem, collecting the slips, sorting them into piles, and identifying where students are having trouble.

What will you do with your extra ten minutes?

Or, an even better question, what other "math class traditions" need to go on the drop pile?

So Long, 2013

2013 brought a few firsts to my classroom (and life):

1.  I started SBG in my Calculus class. And I am wondering what took me so long. Students loved it. They liked that they could focus on learning without the stress. I loved that my valdectorian-competing students had complete control over their grades. Want a higher grade? All you need to do is simply demonstrate a higher level of knowledge. Boom. That's it. Next stop, my Algebra 2 classes. In order for SBG to be successful here, I must figure out how to be more efficient with all the paper work and re-assessing.

2.  Two Algebra 2s. This year my school decided to offer two levels of Algebra 2. I teach both. The basic level Algebra 2 was especially challenging. I think every student in that room hated math and everything associated with it. At least it felt that way some days. I put a lot of energy into managing behavior and felt like I didn't do justice to the math. It was just tough. Really tough. I have an opening in my schedule for second semester, so I will be able to split that class into two sections. I am very much looking forward to working with smaller groups. It will be better. I am feeling determined and hopeful.

3. I decided my (non-advanced) Algebra 2 class would be the best place to start Interactive Notebooks. I am pretty sure that what I am doing does not count as a true INB. There are no beautiful foldables or elaborate color-coded notes. (Even though I wish there were). But there is a lot of stuff glued into a notebook. I like that the constraints of the page size forced me to edit content and constantly ask what was really important for students to know/do. All but 1 or 2 students had perfectly completed/organized notebooks at the end of the semester. When it was time to review, everyone could easily locate what they were looking for. There is something about numbering pages and filling out tables of contents and gluing notes or practice into a composition notebook that equals organizational magic. I had my challenges with this group, but locating someone's missing assignment was not one of them.

4. On a personal note, and because I cannot resist writing about it, I ran my first EVER half marathon in 2013. This was a pretty big deal for me. I was the kid who dreaded, every year of my entire life, the day in PE class when we had to run a mile. As an adult I have loved what running has done for me . . . I am healthier, I have found friendships with running buddies, and I've figured out that I am capable of so much more than I ever imagined. I love sharing this story with my students, as many of them experience math the way that I experienced running. I like to think that I understand what they are feeling in some way.

I wish I could hug the guy who took this picture around mile 8 or so because . . . people behind me!

Lastly, because I hate to break tradition, my most-read (or least not-read?) posts from the last year:

How I Taught End Behavior:  This is my goal . . . more lessons like this where students are sorting and looking for patterns and figuring things out. More students doing, less teacher telling.

Trig Hand: Trick alert! My mistake was using this in my Algebra 2 classes. I won't do that again, even after focusing on the conceptual understanding. But I will use this with my Calculus students, and I have used it myself since I discovered it.

Plethora of Practice: I made two sets of cards for evaluating trig ratios, and found a lot of different ways to use them for a variety of practice sessions.

Desmos Test Question: I fell in love with Desmos this year, and I am still discovering all the many ways I can use this tool in my classroom. Here I used it for assessment.

Diving Into Programming: This year I dipped my toes into simple programming on a TI-83/84 calculator. After a few days, I am convinced that programming has a place in every math classroom. My dream is to have a project to go with each unit of the classes I teach. And the entry is so much lower than you think. You can do this, too.

This Lesson Cost $1: My intro to the zero product property.

Unit Circle: This post exemplifies what I love about blogging. I came asking for help, and I received some really helpful comments. I am thankful.

Happy 2014!!