Our high school principal explains the centrality of modeling to high school math:
55:23 This is a very important slide and one that you’ll hear me talk about a number of times.This strikes me as fundamentally wrong, but if you guys tell me it's sound, I'll have to revise my view.
Because modeling, we really look at modeling as the way to really permeate through all of the different levels of mathematics at the high school level. And we really look at it from a standpoint of pedagogy. When we talk about modeling, what we’re really talking about is the conceptual side of mathematics. Recently, and there’s been a shift to a very computational format for teaching mathematics, especially at the high school level. And that’s where we would start to break things down and scaffold them into very fine points. But what we have found is mathematics teachers over the last 10, 15, 20 years, when this pattern was happening, was that students were starting to learn their broader understandings of mathematics. 56:19 There was a big need to pull back and get back to the point of teaching to deeper understanding and to the conceptualization of math, not just about being able to compute the correct answer. So modeling we really look at as the link to be able to do that. It’s the opportunity to create real-life problem-solving situations where students need to understand the conceptualization of what’s going on in the math as well as how it relates to the real world.
Geometry, obviously, is when we start talking about shapes and sizes and the relative position of objects, and statistics and probability gives us the opportunity to start looking at mathematics and creating analysis and really looking into the chances of opportunity and things occurring.
57:07 So again, as I mentioned, modeling becomes a real important focal point for us. And the phrase that we’ve been talking about is it becomes this umbrella for us. It’s the umbrella that brings the whole mathematics curriculum at the high school level together, and a way for us to keep progressing through and thinking about how it matches up. So when we think about constantly naming and reinforcing the work that the students are doing we want to constantly bring them back as well to these broader-scale concepts. 57:39 So this slide and the next slide starts to talk about that even within those conceptual designs that I mentioned before, even within algebra, there’s an aspect of modeling that’s critical and important for them to understand in the algebra as well as the other mathematical concepts within.
Similarly you have functions here, and again, there are pieces of it that we pull out and we understand how do we create real-life conceptualization and contextualization for our students so that when they’re working through this, they understand again not just the specific calculation of an equation or formula but what it really relates to.
Similarly we do the same things in geometry and we do the same things in statistics and probability. Again, for me, this is about teaching to big ideas and perspective. We’ve been talking at the school about deep understanding and I said that would be one of those shifts that we keep coming back to, and I think that that’s really one of the most important messages that we can deliver about the mathematics instruction and how the Common Core starts to create a shift for us.
Irvington UFSD School Board Meeting - February 11th, 2014
My understanding of math, of what math is, is that …. mathematics is not essentially, or even first and foremost, a system for representing empirical reality. The fact that math so powerfully -- and so eternally -- does capture many aspects of empirical reality is, in my view, either a) beside the point, or b) creepy.
Math, as I think of math, has a mathiness that cannot be reduced to modeling; math is a thing unto itself and should be taught as a thing unto itself -- or, at least, students should be made aware of the fact that to a mathematician math is not just a code-writing tool.
(Again, setting aside the possibility that math is just a code-writing tool.)