Three weeks into our 2012-2013 school year, several of my AP Calculus AB students remain deep in the throes of AP angst. Fortunately, there are several that accept the new challenge calculus presents to them, while others are waiting to see if they will attain a state of certainty, knowing they will succeed in the class.

Unlike last year, when student anxieties and concerns took me by surprise in my first foray into AP, I took preemptive efforts over the summer to lower the chances of a repeat this fall. However, in spite of the one-week AP boot camp I ran in June, and the atypical AP summer work assigned, student worries started to increase the second week of school. My principal anticipated this more so than I, which gave me some solace when students started to grumble. Nonetheless, I still worried that a repeat of last year was on the horizon.

With concern rising in my two AP sections, I increased my effort to establish a productive disposition towards calculus in my students. In my earlier attempts, I mentioned that: 1) I dropped calculus as a junior in high school 32 years ago, 2) many students who take AP Calculus AB feel similarly to how my students feel, 3) in time, students will regain familiarity with algebra and trigonometry if they invest time outside of class, and 4) once we complete limits and the definition of a derivative, the focus will shift towards procedural fluency for a while, which students new to calculus believe is the sole focus of mathematics coursework in high school. None of these sunk in with students, mostly due to students’ acculturation to learning through imitation as the primary method of instruction while a few students tortured themselves believing in their worst fears using their present experience as confirmation of last years’ horror stories.

Sadly for many students in our country, an overemphasis on procedure in mathematics instruction renders students ill-prepared to handle problems that differ slightly from what they observed in class, or worse, differ significantly as with true “problems” to be solved versus “exercises” to be worked. As the NRC quoted in Adding It Up: Helping Children Learn Mathematics (2001):

*“…when students are seldom given challenging mathematical problems to solve, they come to expect that memorizing rather than sense making paves the road to learning mathematics…”*

In my case, especially last year, certain segments of students, perhaps in a sense of entitlement, but mostly a result of our nation’s narrow pedagogical and curricular approach to developing mathematical thinking, lost confidence in their teacher: namely, me. I do not want this year to snowball into a similar situation, even though we eventually settled into a routine that worked for everyone last year.

Whether my two sections settle down sooner, rather than later, is still in question. I believe it will be sooner, as I continue to acknowledge their concerns, offer suggestions, explain the benefits of keeping an open mind (similar to Carol Dweck’s growth mindset versus fixed mindset theory), and ensure I offer them ample opportunities to experience success in the class, even if they do not fully grasp the material. In time, as the semester progresses, and material spirals through, I believe most will reach a satisfactory level of understanding for them to receive a grade with which they are happy.

Sadly, too many of my students, and their parents, worry about their GPA more than the course content, which is another sad state of affairs in secondary education today. Hopefully, my liberal grading scale, which uses 15% steps for each letter grade and not the traditional 10%; allowing students to retake quizzes and tests à la a standards-based approach to assessment; and my intense desire to help all students to learn the material will be enough to mitigate additional angst building up. Only time will tell.

Check out Prof. E Mc Squared’s Fantastic Original & Highly Edifying Calculus Primer by Howard Swann and John Johnson 1975 ed pub by William Kaufmann, Inc Los Altos Ca.

It is a graphic novel type of book that explains calculus with cartoons. Must be seen to be believed. Might be hard to find. Just guarantee them an 80 minimum if they show up and do the work.

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You are convincing me that calculus should not be taught in high school. Send the few that are ready off to a junior college as was the case when I went to school. So few will actually use calculus in their real lives in any case.

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Yes and no, and its not really an issue of using calculus in real life, but developing higher order analytical and problem solving skills. A student’s success all depends upon the level of preparation he / she has coming into the course. There are studies (published by the CollegeBoard, which has a conflict of interest, IMO) that state that irrespective of student pass rates on the AP Exam, students who take AP Calculus in high school fare better in a calculus course in college than those who do not. I believe they specifically compared pass rates for Calc II between those who had AP in high school, and those who did not.

So, I’ll take any and all students who wish to take calculus. But if they wish to learn the material at a high level of understanding, they MUST master the algebra and the trigonometry before taking the course, as the College Board states explicitly in its course description.

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I had a 40 year career in the public high school classroom during which I taught AP Calculus AB and BC for the previous 16 years. I still tutor those subjects today. I agree with your comments in response to the previous posts. I did find that most students were weak in their algebra and trigonometry skills, even the BC students. Many times it was not the calculus which stumped them, but rather the ensuing algebra. I found that after the unit on limits things seemed to settle down as you say. The concept of limit exists well before the Calculus class, but many teachers miss the opportunity to develop it in courses prior to Calculus. Good luck this year!

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Thanks, Sue. I totally agree that as math teachers, we are not preparing students adequately for subsequent courses. Much of this is due to the complex nature of teaching to a diverse range of students with vastly different backgrounds, experiences, skills, etc. I hope blended learning via online resources can help those students who are willing to put in the extra effort.

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The thing with GPAs is that colleges admission people don’t look at GPAs. They are too easy to manipulate by just not attempting difficult courses. What admission people look at is whether a student challenged herself or himself by taking the more difficult courses such as AP calculus. Reminding your students of that and or having someone from guidance, or better yet a college, explain that too them may help alleviate at least that problem.

As for algebra problems, that is very common among calculus students. It’s the rare class that doesn’t have problems with algebra skills. Perhaps it’s lack of confidence or just too long since they used the particular algebra skill they need today. Try a brief review of just the skills they need for today’s work before they start. For example, if you are going to ask them to differentiate 1/(3x^2)^3 give a quick review of how to raise products to powers, and what to do with negative exponents before they see the problem.

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Thanks, Lin. Front-loading does help, although there is only so much that can be done for students who never mastered the prerequisites. At those times, the entire day devolves into one on prerequisites, which even then may be inadequate to bootstrap a larger than expected segment of students. Nonetheless, if a large enough group of students still do not understand, I reteach until the vast majority feel confident enough to succeed.

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I had similar issues one starting teaching AP calculus. This is my sixth year now. And a combination of my reputation and results, have assuaged my current students. I holding meeting with my future students in May, and have my current students there. I explained to them that the course is very challenging unlike any math they’ve taken so far…. But that if they’re willing to put forth an honest consistent effort. They will learn calculus and Ace the AP test. To help them feel better about their grades, And to make sure that they learn all the content to my satisfaction – I allowed them retakes on all assessments (Score equals one third of original grade +2/3 of new grade) they can do this as many times as they like. Provided they have completed all class and homework for the assessment and gone over the quiz or test with me ahead of time… This helps too!

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Excellent idea re: having meeting with BOTH upcoming and existing students! I might even make it a panel discussion. Wow, love it!

My students may retake assessments (except final) within one week of return as long as they submit corrections with explanation of their mistake / misunderstanding with their request. They receive higher score but I really like your 1/3 old + 2/3 new approach. Less harsh than an average but some incentive to not blow off initial assessment knowing they can retake.

My students may also resubmit any other assignment any time except for the last week of any marking period.

Appreciate your suggestions!

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I am an AP Calculus teacher for 10 years. I agree with the lack of Algebra/pre-requisite skills…but if you look at our mandatory curriculum guides to follow in Florida, you get about 1 day per section of the textbook to cover. This doesn’t allow ANY deeper level comprehension or understanding, just a basic “get by” understanding. Any solutions? Year long schooling? 😦

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I couldn’t agree more Dave.

Parents can be their kids’ worst enemies. They often put pressure on their children to achieve unrealistic heights and, in the process, create enormous pressures that ultimately lead to a sincere hatred and phobia for math.

This pressure often bubbles over and teachers themselves feel bullied by parents who, because their children “earned” an “honors standing” in junior high, feel that should be maintained at the senior high level as well.

My feeling is that things have gotten far worse in the last 10-15 years.

Changes have to be made.

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It gets worse…the College Board is marketing that more students should take AP, even if they do not obtain college credit, as they have studies that show students who took AP calc perform better in college calculus than non-AP students…so as more and more students who are not prepared are essentially forced into the course, they struggle mightily trying to keep up and not be demoralized by their struggles. Many do not have adequate social or family support re: this level of course, so it is a ton of pressure to place on adolescents. Some break down crying in front of me when I console them by telling them I know that they are doing their best. Humankind’s heavy hand distorts a natural process too often in our desire to right wrongs, perceived or otherwise, especially when one’s ego, or bonus, is involved…

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Heres something I do….have your students write an anonymous letter to next year’s students. I have my students do this every year. Their job is to tell future students what to expect in my class. I even promise not to read this letter (which is admittedly scary). Then, they fold the letter and put it right in front of the textbook. When I ask my new students for their book number the next year, they are greeted with a letter of advice.

I have taught either AB or BC for the past 15 years. I always say: “it’s not the Calculus that will kill you, it’s your Algebra skills”.

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Thanks, Ed. I had students last year write a letter. However, they were a bit too wacky so I nixed them. Last year was veeerrryyy challenging on everyone. I will retry letters this year. And I repeatedly remind students that its the algebra and trig that is diffcult in calculus, hoping that they will study those a tad. One can always dream… 🙂

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