Justifications Gallery Walk

As we get closer to the AP Exam, I'm working on helping my kids "play the game" in the way they can benefit themselves most- to be as mathematically precise in their language as possible. Although I've emphasized it all year, students tend to rely on their long term memory once you start review and that tends to be a little less precise than we might hope.

To get students thinking again about technical justifications for curve sketching today, I started with this warm up gallery walk. 

1)  Students did a silent, individual gallery walk to critique justifications (some close, some very off, maybe even some right!?). They left a post it under each one with their feedback on how to make it better.

 

2) Next, I grouped students and had them each work on one particular justification. Students read through the feedback and sorted it, using it to generate a new and improved justification.

3) Each group presented the feedback they'd seen on their problem and their new and improved justification to the class. This gave us an opportunity to talk as a class about what could be improved and to examine some common issues. 

After that, we did a released AP problem that required multiple justifications and I saw a huge difference in the precision of their language. It was a good jump back into more extensive mathematical writing. It could also be applied pretty easily to EVT, MVT, and IVT justifications, among other things! 

What's New for AP Review 2017?

New Year, New Curriculum, New Review! 

I'm revamping my review system this year and trying out some changes with my kids. We have about 15 total 80 minute classes for review (assuming Mother Nature gets her act together and doesn't send us any more huge storms), which is a pretty healthy amount. I'm trying to integrate much more mixed review this year to get my kids thinking wholistically about the curriculum and am also using a standards-based approach to topical review to get them to key in on where they are struggling. Here is my basic outline so far:

Pre-Assessment (2012 Practice Exam)

I am very much against a prescribe approach to review, as every class I've ever taught has varied in their strengths and weaknesses. Moreover, I vary in my strengths and weaknesses in teaching and need to be realistic about where those are. I started this year by giving my kids a full exam right off the bat- something I shielded my kids from until well into our review last year. This is a reality check and a pre-assessment...a confidence builder or a wake up call. I did an analysis of common mistakes and will be going over these with my class when we look at the exam. 

Full Practice Test #dunkinandderivatives

Nothing in schooling really prepares you for the stamina you need during an AP test until you are smacked in the face with a 3 hour marathon and only a set amount of energy with which to work. To get my kids used to the demans and the pacing of the exam, I offered the secure exam during a full session on a Saturday. We made a deal that I'd get them breakfast if they showed up to do it, and so it lovingly became titled Dunkin' and Derivatives. Of the 65 calculus students in the school, we had about 30 show up. The ones who did are already asking if we can do another before the test day, so they have clearly seen a benefit to the experience. I chose a day in the near future and we'll go over it together as a group. I am hoping that this will become a tradition and we can get more kids participating as they years go on.  

Standards-Based Feedback

The problem with offering the secure test as a practice exam is that I can't hand it right back to them to study. I loved during our breaks hearing the kids conversations about what topics they noticed they were having trouble remembering, so while they worked I took the time to put together a topical feedback form for each of them. I left a spot next to each question so I could write my comments there to give general feedback on that particular topic. 

Here's a link to a word version of the file. Feel free to edit/tweak: 

Practice Exam Feedback Form

Standards-Based Review Quizzes

Fom my review grade, I decided to use a Standards Based Grading model. I developed

my AP Calculus Learning Objectives last summer and have been using them throughout the year to help guide students' studying. I have consolidated all those learning targets into the big ideas that students need to know and am going to give small quick checks on each topic. I will use the 0-4 grading scale (at left) to mark each one. Students who get a 4 have demonstrated mastery. Anything below that means we have more room for growth, so after completing corrections on their quiz and demonstrating remediation in some way they will be able to re-assess to mastery. Higher or lower, their final re-assessment grade will be what is used in calculating their score. I will average all of their quick checks on the different topics to get one final average.  I stole the formula to convert this to a percentage from Mrs. Poulsen at Lake Placid High School in NY in a recent presentation she gave on SBG: Percentage=15(Average-3)+85

It may not be the most complex conversion option, but it is easy for my kids to understand:

4 translates to 100%

3 translates to 85%

2 translates to 70%

1 translates to 55%

0 translates to 40%

Here are my ground rules, thanks to lots of feedback from colleagues who are thinking of implementing SBG next year:

SBG Remediation Wall

• Only 1 quick check will be taken in class. All others must be taken by appointment
• I have a QR code in my room that will take kids to a Google sign up for times when I'm available. They must give me a minimum of 24 hours notice. That way I have quizzes ready to go (so NOT running around like a chicken with my head cut off)
• Students may re-assess no more than 2 times per quick check (I have mixed feelings about this one, but it's a compromise for people who don't believe in re-assessment at all and also emphasizes learning it sooner rather than later since we have an AP exam coming shortly)
• Students "ticket" to re-assess is proof of remediation. This can include extra worksheets from my giant Standards Based Remediation Wall (yes, I created this on my bulletin board...like a crazy person), notes from an online video, or extra practice from another resource. I am putting this on them, not me.
• Re-assessments must be completed within one week of the original assessment.

I am giving my kids this tracking sheet to help them organize:

  Standards Based Review Tracking Sheet

Topical vs. Mixed Review

Last year I spent a TON of time on topical review and I know it benefitted my students, especially since they were in a specific course that was built to help some of the students who might never take Calculus succeed. However, I think not starting mixed review with them earlier in the year meant that they struggled more when trying to distinguish what to do when. With that in mind, this year I structured my review this year so that each night has mixed review homework from our practice book. Then, students will have a brief worksheet on whatever we worked on in class that day. The first few days it will be topical review as we go back through the course highlights. Then, we will move more towards AP style application and justification questions. Lastly, I left the final few days of my review unplanned so we can do completely mixed review on what we need the most. I also won't give specific homework those days, since APs will be about to begin and they should be focussing on what they need most. 

Here's the review overview I gave my kids: 

AP Review Overview

Cram Session
This isn't new, but I figured I'd post it again in case anyone didn't grab it off my Twitter last year. Stacey Roshan created this awesome Cram Video for AP Calculus a while back and last year I created a student assignment to accompany it. I make it optional, but it's a great resource for kids that want to do it! 

Cram Video Student Worksheet

We're also doing a giant review tournament and the winners get a WWE Tag Team belt (not a joke, got it in the toy section at Target), so that's keeping their attention pretty successfully. I'll write more about that later in the month. 

I'm sure I'll be tweaking and changing as I go, but I'm interested to see what kind of results this gives! If you so anything that you LOVE for review, please pass it along! 

Area Between Curves Partner Task

We are starting my favorite unit of the year tomorrow....area and volume! 

Not only is it the culminating moment in the course- our very last unit- but it's also just plain FUN! I'm replacing half their test with a performance task, having them build 3D models of anything possible, and just spent way too much money on honeycomb party decorations on Amazon Prime. You'd think by now my husband would just expect weird and seemingly non-math related items to be shipped to our house regularly, but evidently I'm still surprising him. 

To start off tomorrow, I wanted to get the kids working in partners and visualizing what is actually going on when we find area between curves. We can do a lot with technology, but this one time where I want them to develop the idea by hand. Each group will be given a different set of functions and a different interval on which to graph them. They will then develop the formula for area between the curves with their partner. We can hang them all up and compare our methods to determine area. 

Area Between Curves Partner Task

I'm worried about the "big idea" here...once they have that, we can get into the more complicated and interesting things we'll explore this unit. I'm excited to build some models of 3D solids with known cross sections, spend some time playing with honeycomb decor, and revisit my Volumes Performance Task from last year. This will be a unit where I will definitely miss being in a science classroom (I know, I was spoiled), but I'm so excited to get started. Let the fun begin!