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.