There are times when I grit my teeth when I hear any of my advanced mathematics students exclaim: “I have to teach myself in your class!” They cling to their experiences from earlier mathematics courses where they could nearly sleep through the class and still receive an A+. I believe there are far too many students across America like this who are not challenged enough in secondary mathematics courses leading up to calculus, as the content is taught primarily as procedural methods with little to no emphasis on conceptual understanding, connecting topics, or problem solving. Many of these same students arrive at college suddenly finding that they require remediation in one or more areas before they are able to go ahead with more advanced coursework, such as a first semester calculus course.
There are other times when I am glad when students make a similar declaration, as they reached the point where they accepted their role in learning. These students are much less likely to need remedial mathematics instruction when they arrive at college. This is a brief story of one such student who described the need to teach herself as the single academic accomplishment of which she is most proud.
Susan (a pseudonym), one of my former AP Calculus students, requested that I write a recommendation letter for her. She gave me a copy of her academic resume, which our College and Career Center provides students to help them communicate about themselves beyond what a recommender may know about the student from shared, in-classroom experiences. Susan’s paraphrased response to the prompt below follows.
Describe the single academic accomplishment (major paper, science project or experiment, artistic project or accomplishment) of which you are the most proud. Tell why you take this special pride.
“Math has always come easy to me. But last year, I ran into a roadblock where I needed to work harder than I ever needed to in my life. I spent hours a night on math when in past years I only needed to spend a few minutes. Mr. Math Teacher’s teaching style was dramatically different than every other teacher I ever had. His basic philosophy was that if a student wants to learn material, they should teach it to themselves and the teacher will just be a guide. I had a really rough time adjusting to this new way of learning. Fortunately, my hard work paid off and I was not only able to pass the AP Exam, but I earned a 4. Now, everything else seems so easy!“
While her characterization of my philosophy differs somewhat from how I put it into effect that year, I can see how she would interpret it as written. In truth, I explained any new concept as clearly as possible via an example or two then allowed students to experience, and often struggle, with applying it to various exercises. I find this is the most effective method for calculus students to develop any true understanding of the calculus.
Nonetheless, in my recommendation letter for Susan, I wrote:
Susan performed extremely well in a very challenging course, scoring in the top quartile. Susan learned much more than calculus that year. She discovered fortitude, overcoming the challenge posed by a higher-level mathematics course where the student must take responsibility for their learning, rather than relying solely on the teacher to fill them with knowledge. Many students struggle with this transition in high school; Susan was no exception. However, unlike many classmates, Susan did not abandon all hope, or completely place blame externally. She recognized that success required effort on her part. As such, she dug deep inside tapping into a reservoir of strength that will serve her well as she faces greater challenges in life. From conversations with her AP Calculus BC teacher, it seems Susan continues to benefit from her discovery.
While I had no reservations providing a recommendation letter for Susan, I honestly struggled initially with the written description of her accomplishment. Perhaps it triggered a defensive posture, as I may have allowed myself to perceive her statement as indicting my method, or I may have reacted to her ever so slight mischaracterization of my philosophy. A colleague helped quell these thoughts when he excitedly shared his copy of her academic resume with me pointing out what she wrote as her proudest accomplishment. It still took a while for me to come around to seeing her description as a positive for me. It helped that I was truly proud of her accomplishment, irrespective of whether she agreed with my method or not. It also helped that I believe my approach is the best way forward for my students. So much so that I doubled down in my approach this year, requiring students actually to “teach themselves” before arriving in class: I will write more about this later.
The bottom line: Susan found a way to succeed in my course, which more than readied her for the much more challenging follow-on course: AP Calculus BC.
As a teacher, you cannot ask for more than that from a former student!