# Calculus Victories

Today's the AP Test. What's changed in the last year? Here are three areas of improvement worth celebrating.

### Preparation

There are 35 taking the exam this year, down from 50 a year ago. Though about 65% of the population is in a good state of preparedness. This is based on my observations through how they spent their class time and what comes up when they attended after school sessions. The kinds of questions I'm getting are more focused and we have had some excellent discussions. Last year that number was like, 20% or less. A big factor is some adjustment I made on my end. I tweaked my benchmarking process and rearranged what happened after Spring Break to give my exam takers about 10 days to just sift through stuff and work. Last year it was about 3 days. I demanded more of the kids. These 35 responded to that challenge.

The full list of stuff they were given since late March:

• 8 topic, 50 question Free Response Collection
• 50 multiple choice questions from various practice exams
• reference sheet
• study recommendations
• varied fundamentals (limits, polynomial sketching, trig values, etc)
• 6 released FRQ, 2 calculator, 4 non-calculator, to let them simulate a full set
• access to the 2014 practice exam from the secure teacher portal

The goal is to demonstrate how to prepare for something over a long period of time. Cramming the week before won't aid their long term retention in anyway. Though I can't control it, they were forbidden from doing math yesterday. Their preparation materials were given out slowly over a period of six weeks. We spent two of those weeks finishing the curriculum while they started work on their own time.

### Conceptual

Huge gains in conceptual understanding this year. Primary inspiration drawn from this question:

It's not enough to know the mechanics of calculus with defined functions. You need to be able to apply it in the abstract. We did extensive work throughout the year applying principals using functions defined only in theory. Kids found it strangely simple. I think more of them understand "f prime" as a thing that can be manipulated in a number of ways now.

### Pictures

I also realized last year that curve sketching and function sketching in general is a huge a weakness. I made efforts to improve it in Pre-Cal to help me out for 2017-18. For this group of Calculus students, we took time to review the concepts of polynomial sketching and how it can help us analyze the behavior of a function (specifically spotting things like false critical points). As part of our review weeks, I made a point to mention how a picture can help a situation. Take this question:

A couple years ago I did a horrible job preparing students for something like this. Particle motion is a topic my students feel very confident about, provided they have a picture. The questions are almost trivial with the use of a calculator. But here it's easy to feel screwed. Unless you realize drawing that cosine function jump starts this problem in a huge way. Students also had hang ups with pi-terms as coefficients. We spent some time with it and now it's not a big deal.

There are similar situations where a polynomial is given. Breaking it into binomials and making a sketch gets where you want to go quickly. No tedious quadratic formula required.

### Further Steps

Several students had weak connections between the behavior of a derivative and the impact on the original function. For example, about three weeks ago I got a lot of blank stares about identifying where an object changes direction, or what positive values of the derivative mean. We were successful in clearing up this confusion, but it was a little strange it had to happen in the first place. Other than that, the majority of concerns lie with differential equations. This was expected, given how late it was introduced and the limited time we spent with it (about a week).

There's probably about 10% of the curriculum we didn't address. But I feel good about my students' understanding of the 90% we did cover. In analyzing a practice exam, this group ideally could pick up 10 more questions over last year.

A huge thing I noticed a couple years ago was class time being diverted to in class assessment. I have a gradebook obligation to the kids, but continuing to be creative in this area will help us get more time back. In year 1 I gave 14 in class tests, year 2 had 12, and year 3 only had 8. At the moment I'm not sure what, if any, formal paper tests my Calc kids next year will have.

Posted