To Infinity and Beyond? The Finite Math Elective

October 13, 2016
desmos-mathalicious-pictureThe Finite Math Elective offered to 11th graders is not a new course; it follows the basic outline of a Finite Math class taught to seniors. However, in the few weeks of school that we’ve had, the elective has already diverged into a vastly different place due to the small class size and heightened level of motivation of these students to choose to study an additional math class during their junior year.
After learning the first unit on Exponential Functions and discussing the mathematical implications of exponential growth and decay – in situations like depreciation of a car’s worth, loss of ibuprofen in one’s body over time, and rapid growth of bacteria – I thought it would be neat to expand beyond the “real-world” word problems that we were practicing.

In a two-day mini-unit, we used a pre-made lesson that I discovered on Mathalicious to explore the concept of memory accuracy. In short, according to memory specialists and neuroscientists, the fidelity of a particular memory in fact decreases exponentially with each remembrance. This was mind-boggling to me and the students, but we could not argue with facts that we listened to on podcast interviews and video clips with said scientists. The lesson was embedded with dynamic Desmos graphs as well as accompanying worksheets with graph paper; in this way, the students were able to explore and actually interact with the mathematical ideas of exponential decay using the powerful graphing calculator before sketching graphs on their individual papers. Eventually, the concept began to sink in.

On day two of our lesson, we deepened our understanding of the significance of this new and counter-intuitive idea of memory loss. We thought about eyewitnesses being questioned repeatedly. We posited that this notion may be why therapists ask patients with PTSD to continuously recall an event in the hopes of diminishing the vividness of the memory. We even spoke about Holocaust survivors, and questioned whether the graph behaves the same for a memory of a “regular” event versus a “very traumatic” event.

At the close of the lesson, we watched a clip of “60 Minutes” where a newscast interviewed several people who have super autobiographical memory, a condition in which their memory remains perfectly untainted despite the number of times it is recalled. This was the clincher. A deep discussion ensued, during which time the students argued whether this abnormality was a “curse” or a “gift,” and whether they’d elect to have it if given the choice. During this time of year, when the High Holidays and Days of Judgement are just around the bend, it was especially interesting for us to think about how we would live our lives if we had this condition. Would it debilitate us, or spur us to live that much more mindfully, as an interviewee had said it did? I questioned my students about why G-d did not make this condition the norm, and instead made the default for memory accuracy a model of exponential decay. We agreed that, among other things, if we were to remember everything – including every consequence of our every action – we would lose a bit (if not all) of our temptation to repeat a bad action, thereby robbing us of our characteristically human ability to chose (“bechirah”). Finally, we brainstormed ways to avoid this inevitable loss of accuracy, and decided that writing down an event (in something like a journal) could help us preserve the memory forever.

In reflecting on this past unit, students wrote that “Finite Math [Elective] takes math up ten notches” and that “is a big help in understanding math as whole.” The smaller size of this elective class gave us all a “safe space” to get thoroughly engaged in what became a highly personal application of a math topic. Above all else, I was deeply moved by my students’ level of sophistication in processing such a jarring concept, relating it to themselves, and allowing me to push them to think about it in the context of their religious and interpersonal growth. I am always inspired by math, and am infinitely more inspired by the synthesis of math and daily life; I am glad to see that my students were able to be exposed to this marvelous synthesis, too.