Curosity (1996)

**Curiosity (1996)**
Feynman Learning TASKs John Pais There is a PBS videotape on Richard Feynman that begins with a 1965 CAL TECH lecture in which Feynman is trying to explain to his audience how one goes about finding a new physical law. He writes schematically on the board that the process for doing this is to: guess -> compute the consequences -> compare with nature, experience, experiment. In an interview a little further into the tape he describes his personal motivation and explains that his purpose as a scientist is "to find out about the world." He says that nature is configured in a certain way and that he simply is curious to find out what this configuration is. He says that he does not bring an agenda to his quest to understand nature, he does not prejudge it, he simply wants to know interesting things about the world. I suspect that this kind of intellectual curosity and drive to know and understand things about the world is shared by all of us who have chosen a career in teaching and/or research. I also suspect that our common interest to improve the teaching and learning of mathematics stems from a desire to foster and develop this perspective in our students. For those prospective mathematicians, scientists, and engineers that come to us already equipped with this imagination and burning desire to know things about the world, our work is easier and often much more rewarding. However, for those students (the great majority) we serve that wish only to become intelligent users of mathematics, our work is much more challenging and has lead us to devise various "reform" approaches to the teaching and learning of mathematics. Most of us are still struggling with this extremely difficult pedagogical and cultural problem. The key components that I have been developing in order to address student motivation, interest, and engagement include: (1) 75% student-active learning, (2) an applications-oriented, interactive, computer text (Maple V R3), (3) partitioning the course content into what I call "Mastery TASKs", and (4) basing the grade on attaining (or surpassing) a minimum mastery level on a 1/2 hour mini-test for each of 12 TASKs. Each TASK has a minimum mastery level and a variation must be repeated until this level is attained. So, each of these TASKs is like a "gateway" test. However, in order to really stimulate student curiosity, I think the real question that is emerging is how we identify and package a new basic unit of purposeful mathematical activity. I will call this a "Feynman Learning TASK (FLT)." What are the features of an FLT? An FLT is a problem context that includes an "interesting/useful" (small) question about (a piece of) the world. An FLT usually has several components that must be performed/understood in order to answer this question. An FLT is a complete problem, and so the learner sees the point of the TASK. In contrast, the performance of an isolated, mindless activity that disconnects the learner from understanding something "interesting/useful" is not an FLT. However, one of these narrow, isolated activities can be and often is a necessary component of an FLT.