High school students are on a journey. They probably don’t realize it, but they are. They travel a road that is littered with long monotone lectures that put them to sleep, mounds of homework that they ignore until five minutes before the bell, and tests that they are not prepared to take. As they navigate the tricky landscape, they encounter many roadblocks, most of which they roll right over. But there is no roadblock that is more feared than the dreaded math class.
For the last 3 years, I have taught math classes in a private high school in the metro Detroit area. Our students are “tracked,” meaning that they are placed in math classes at one of three levels; honors level, average level, or low level. During my short tenure, I have taught all three levels of students. And at all three levels, my goal as a teacher is the same – teach students how to persevere through problems by engaging in the productive struggle. Though all of my students are walking the same road, their perception of the journey is skewed by their previous experiences in math.
My AP Calculus class consists of the most accomplished (academically) students in the school. I generally have most of the top ten, including the valedictorian and the salutatorian in my class. They have been in honors math classes since middle school. They have breezed through honors level Geometry, Algebra 2, and PreCalculus. They have mastered the art of parroting back our “repeat after me” procedures on quizzes and tests with little difficulty. Their success has made them confident, capable math students; but our failures have made them weak problem solvers.
Enter: AP Calculus. I am extremely hard on these students. On purpose. From the moment they walk in the door, they are pummeled with a big fat reality check. It starts when I give them each a packet of letters written to them at the conclusion of the school year by the previous AP Calc class. The letters usually describe horrors that these honors students have never dreamed they might experience. Last year’s students discuss their first failures, lowest grades ever, and how they might not ever understand math again. They talk about how Russo doesn’t grade (or check) homework and they fell into the trap of not doing it – even though they knew they probably should have. It is not uncommon for me to have several Calc students cry in my classroom because of their grades. They feel like they are rolling downhill with no brakes; and they have no control over where they are headed.
My low level Algebra 2 class is the exact opposite. These students took two years to complete a 9th grade Algebra 1 class. They struggled through every second of every math class they’ve ever had. Many of them are still making up credits for previously failed math classes. They are students with IEPs, behavior issues, and rock bottom self esteem. They walk into my room referring to themselves as “the dumb class.” They have allowed themselves to be defined by failure.
I spend every second of every Algebra 2 class reminding these students that they are quite capable of doing the same work as the higher level classes. We ban words like dumb, stupid, and slow. Rather than referring to their cohorts as “the smart class,” I convinced them to come up with another name – they settled on “the Romans,” since the average level class is labeled with a Roman numeral two (Algebra II) rather than the number two (Algebra 2). These students feel like they are climbing a steep hill – every step is difficult for them.
How you fail is just as important as how you succeed.
My Calc students and my Algebra 2 students are traveling the same road. They are learning how to connect seemingly unrelated mathematical concepts to solve problems that they have never seen before. My Calc students must learn how to fail – and they ultimately figure out that how you fail is just as important as how you succeed. For them, improvement is a direct result of meaningful reflection and analysis. My Algebra 2 students, on the other hand, must learn how to succeed. They begin to see small gains throughout the year that add up to their first passing grade in a high school math class. For them, improvement is a direct result of hard work, persistence, and self confidence.
If I have done my job well, then at the end of the school year, all of my students leave my class knowing that they have accomplished great things. They have learned how to proceed when they don’t know how to proceed. And when they look back at their journey, they find that what they thought was an uphill climb or an out of control drop was made level by their own hard work and dedication.
This post was written for The Virtual Conference of Mathematical Flavors.
2 thoughts on “The Road (not) Less Traveled”
Ditto. The only un-enjoyable part of my AP Calculus classes is reminding students that they volunteered to take the class and grades don’t reflect my opinion of them as a person. I now start every year trying to preempt it all with a speech about how, for some of them, this will be the first time they get a C and if they aren’t comfortable with that possibility then they should take another class.
I also don’t grade homework, but it stings bad if they don’t do it.
I’m curious if you have any suggestions for AP Calc resources! This past year I assigned the new Khan Academy AP Calculus mission and let them work on it independently all year, in the background and in addition to our regular assignments. I would comment each week on the progress and encourage them to stay on target to complete it before the AP Exam. I think it was really helpful and they got excited about making progress toward 100%.
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It’s nice to hear that there is someone else out there having the same experience…the funny thing is they complain all year but their end-of-the-year letters always reveal that they have learned so much more than just math. Looking back, they are always grateful for the experience.
As far as resources, most of what I use comes from the college board (old FR and MC questions or modules that they have put together). When I introduce the fundamental theorem, I use Better Explained (https://betterexplained.com/calculus/lesson-1) to give them a different perspective. I usually give them a print copy of the article and have them read it when we first introduce FTC; then, I wait a few weeks, and when they are much more comfortable with it, I give them the article again. Comparing their “before and after” observations is often quite telling.
I move very quickly through the course (I am usually finished with the entire AB course in February), and then I use the remaining months to do projects and practice with application. Near the end of the 4th quarter, I give them what I call “the 4-day test.” This is an entire AP practice exam broken into 4 class periods. I count those 4 parts as their final 4 test grades in the class. It’s brutal. However, they are always well prepared for the AP exam by the time it comes around.