Over the course of this past week, fifteen to twenty of next school year’s seventy-five AP Calculus AB and AP Calculus BC students attended a boot camp in my classroom. The boot camp spanned a range of prerequisite mathematical topics.

Each day of the boot camp ran from 8:00 AM to 10:00 AM for AP Calculus. Some students attended another session from 10:30 AM to 12:30 AM. Counting the earlier week, students were able to attend up to four different AP boot camp courses from nine selections which included English Literature, US History, Physics, Economics, Calculus, and etcetera. The major complaint from students throughout the week was the early start of my session. I agreed with them since I am not a morning person, which is not the greatest for a teacher.

## Boot Camp Purpose

I hosted the AP Calculus boot camp to boost students’ prerequisite knowledge, understanding, and skill as well as raise their confidence so that they can succeed this fall. My experience this past fall convinced my admin team and me that it was critical to offer a boot camp to rising AP Calculus students.

The goals for the course were for students to:

- Know more than when they arrived,
- Understand the prerequisites better,
- Enhance their mathematical skills,
- Develop confidence that they will succeed in the fall, and
- Look forward to learning calculus…with Mr. Math Teacher!

## Boot Camp Outcomes

Based on the results from the following brief survey each student completed, I can say the boot camp attained these goals.

With a mean score on question #1 of 4.2 (boot camp helpfulness / unhelpfulness) and a standard deviation of 0.66 for fifteen students, I felt satisfied that my first attempt at running an AP Calculus boot camp was a win-win: a set of students were more ready for the course in the fall, which helps them and me. Interestingly, it seems that of those students who attended, those who scored best and worst on the readiness test rated it highest, while those who scored more towards the mean tended to rate it less helpful.

I only wish more students attended, as at least twenty more need significant help improving their prerequisite skills. One student even wrote that she “recommended it [boot camp] already, but my friends are too lazy to come.” Reflecting back on my summers as a teen, I can empathize with them completely. At the same time, knowing what I experienced as a junior my first few weeks of calculus, come this fall, I believe these students will wish they had attended boot camp.

Several quotes from boot camp students about why they chose their specific rating on question #1 follow.

*“[The boot camp] helped me conceptualize much of my prior knowledge in math, as well as understand the right mindset I need to succeed in calculus next year.” (rated boot camp a 5; AB student) *[1]

*“I found it extremely helpful, but certain days I felt like I wasn’t being very productive. I feel way more prepared than I came in feeling.” (rated boot camp a 4.6; BC student)*

*“I liked the group work we did and presenting the work because I learned from what others did or failed to do.” (rated boot camp a 4; AB student)*

*“I liked meeting some new classmates and the useful handouts because I can better prepared **[sic] *for calculus now.” (rated boot camp a 5; AB student)

*“I’d rate this boot camp as a 4 because I learned more about what I needed to know for BC than what I thought I would by the end of the week. I now know what I need to look over before school starts.” (rated boot camp a 4; BC student)*

*“I didn’t really somewhat benifit *

*[sic] a whole lot, but I really appreciate all the worksheets and the certain problems such as using trigonometry to show that you can find statements through logic and reasoning instead of just memorization. I like your philosophy, but as for reviewing material, I felt like you skipped through explanations at times. I’m not calling you out as a bad teacher in any way or form; however, I expected a little more.” (rated boot camp a 3/4, initially rated it a 1, scratched it out, then a 2/3 and scratched it out; AB student)*[NB: This student missed the first two days of the boot camp.]

Student dislike spanned from the aforementioned earliness of the course to its proximity to next fall saying, “I did learn a little bit, but I feel like I am going to forget because the start of school is so far away.” The student also went on to say that “[AP Calculus] is going to be very hard for me because I’ve struggled in past math classes.” Other dislike comments included a comment that “it is 2 hours long. [*sic*] Maybe an hour a day for 2 weeks [would be better].” The same student mentioned “I was not looking forward to this class but I’m really glad I went.”

As with all things, improvements will make it more effective, however, as a maiden voyage, it accomplished what I had desired. I believe these students will not suffer as significant of a shock come this fall, or perhaps more precisely they will adapt more rapidly to the vastly different course that is AP Calculus as compared to their earlier mathematics coursework. Nonetheless, come mid August, many students will scramble to follow the algebraic and trigonometric concepts embedded in calculus problems.

## A Boot Camp Input: Student Readiness

While I did not have any idea as to my incoming students’ skill levels last fall, I have a detailed view of nearly every student’s ability this time. The following table shows the results of an AP Calculus Readiness test I created and administered to sixty-six incoming students. The test contained fifty multiple choice questions covering algebra, trigonometry, and functions, to name a few domains.

The results of those scores, segmented by whether a student requested AP Calculus AB or AP Calculus BC, show that students will need to be reintroduced to aspects of prerequisite knowledge throughout the course. However, I plan to take a different tack this year and not spend the first few weeks reviewing prerequisites abstracted from the calculus. Instead, I plan to jump right into limits, which they studied in precalculus so it is a slight review of sorts. At the same time, limits are intimately involved in the calculus they will study. [2]

As an added benefit of the readiness test, students’ scores were broken down into major concept categories, which helped drive those areas on which I focused greater attention and effort during the boot camp. Trigonometry leapt out as a key focus area, as did polar coordinates, vectors, and series, albeit the latter were only necessary for students who chose AP Calculus BC.

As the following readiness test score distribution reveals, students who requested the more advanced course, AP Calculus BC, scored higher, on average, than those who requested AP Calculus AB. This bodes well for those students, as rumor had it that one-third of them selected that class so they would not have me as their teacher next year, given the bumpy start last fall.

While that may have played into their decision, which is fine with me, they clearly have not overreached relative to their peers. As an aside, I discussed the rumor with the BC teacher, who made me aware of it in the first place, and hold no ill will towards those students, assuming the rumor is true. I let the BC teacher know that if any student who requested the BC class felt they were in over their head, they would be welcome to take my class. My class will serve as a safety net for them. In fact, they may even come to realize that having me as a teacher is not all bad anyways.

[1] Link added to the quote, as I introduced students to the concept of Mindset (Dweck, 2006)

[2] Note that students’ understanding of limits is not that great given they just finished learning limits in their precalculus classes. Both the BC teacher and I were quite surprised by students’ scores on limits.

Mr. Math Teacher,

How can I get my son to attend this boot camp? I wish I had this during my high school days.

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Hi Arthur. I put this together as a custom one-week course for my incoming students. It finished last week. I can give you some suggestions for your son though, if you’d like, so let me know. If you’re the Arthur Look I think you are, send me an email and we can continue this conversation via email.

Dave

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Well done, Dave!

Russ

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