Just posted the following at a fellow blogger’s site after reading his latest post: Wolfram’s Teachings. Natural Language.

“Timely post. As an aspiring mathematics teacher, and current teacher candidate, approaching my half century mark, I reflected last night on how to engage all students in math, especially the underserved, since much of today’s mathematics curricula and pedagogy is BORING, especially to me. So, the thought came to me that math is inside of everything…to some degree, however small, or large, math shaped the creation, existence, and demise of all things. I won’t make the next logical connection for fear of angering too many, but think about it…makes sense, doesn’t it? So the synchronicity of your posting, which I found via a friend’s fb post, is wonderful, indeed.”

I look forward to creating a mathematics curricula, standards-aligned, of course, that catches students’ attention, maybe not captivatingly every time, but hopefully more so than the rampant, ridiculous, rote, repetition required relegating ‘rithmetic resoundingly rejected. Not sure I adhered to proper grammar in that last bit, but I enjoy trying…

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## About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.

I think that part of the problem is that at the elementary level, math is taught as if every student were an aspiring pure mathematician. That implies drill, lots and lots of drill. Like scales at the piano. It’s easy to get sick of it. I got sick of it. It was only as a much older man that I came to appreciate the logic of this approach. The point is that the actual computational procedures involved become second-nature to the extent that they become part of the student’s mathematical intuition, as it were. By this time, the student has probably begun to notice there are patterns in the drill, and that some of the patterns resemble other patterns from seemingly unrelated areas. At this point, advanced work can begin. The student is taught how to connect the dots, so to speak. He/she begins to explore the interconnectedness of mathematics, to answer the question: why does this thing here look a lot like that other thing over there? This sort of thing continues right up to current research. Examples: Extensions of Alexander Grothendieck’s work in algebraic geometry tend to indicate that logic and geometry are connected at a deep level. The Hrushovski construction of Ehud Hrushovski also tends to show that logic, model theory, and algebraic number theory are deeply interconnected.

The problem, of course, is that the aspiring engineer or medical doctor or what have you is rightly unconcerned with such things and has no overriding need for piles of drill.

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I also believe “drill baby drill” is neither effective, nor appropriate for all math students. However, most “high stakes” standardized tests essentially force that modality since it yields the biggest bang for the buck re: short term retention, and it has been the gold standard of mathematics pedagogy for a century, or more. When I was at the academy, we called it “spec and dump” spec and dump. Personally, I believe the math standards should be modified to allow parents to sign their children up for a “non-technical” track which does not require certain levels of math, or even certain concepts such as logarithms, hyperbolic equations, etc. These just serve to frustrate many students, parents, teachers, administrators, etc., specifically for the student who may not desire to attend college, of if so, may not even follow a technical track, and most definitely has no aspirations to be a math major. Many would argue with my position saying “this will preclude students from certain career paths” or “students do not know at this point in their life what they want to study in college,” both of which could be true if the system were maliciously implemented. However, not all students will pass these courses at this early stage in their life. They may need to wait until community college to learn this material. Perhaps the masses of remedial instruction in community colleges is more than an indicator of failed instruction at the high school level. It could be an indicator that students were not ready, for a myriad of reasons, to learn the material in high school. I want all students to have the opportunity to learn, as much as they can, as quickly as they can. However, forcing those who are unable to digest material at the required pacing schedule is not an effective solution. It simply frustrates the entire educational system. I’m rambling now so will stop, go to class, and edit this later… 🙂

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