# Math lacks a fundamental narrative

Mike Thayer says:

Baker’s complaint about math education (NOT MATH!), as I read the article, is that it

lacks a fundamental narrative. That is, we expose our students to “hairy, square-rooted, polynomialed horseradish clumps of mute symbology that irritate them, that stop them in their tracks, that they can’t understand.” We do this for a variety of reasons: it’s on the test, it’s the next unit in the (Common Core) curriculum, it’s what they need to take the next course, etc.We spend no time at all on the great story, which is of math itself and the power we humans have gained by its use. As a result, we produce large numbers of students who (mostly) think of math as that disconnected, irrelevant, annoying, frustrating subject.

via http://hyperbolicguitars.blogspot.com/2013/08/nicholson-baker-algebra-2-and-equity.html

I agree: what’s missing in math is the narrative that connects maths to the individual. But math is not the only subject that fails to make that narrative connection. From my perspective, we should talk about how human beings make sense of the world: we measure it and we communicate with each other, verbally, in writing, and via electronic media. We measure with mathematics and with science and with recorded history. We communicate in poetry, prose, music, art. We study the world and its people, and we share that with each other. Fundamentally, it’s all measuring and communicating to make sense of who we are and why we are and the possibilities that the world holds for us.

It’s hard to construct a narrative out of decontextualized fact nuggets. And it’s hard to communicate a narrative using multiple-choice test responses.

Good one, I wonder if some history of math could be included in the math curriculum to help tell this story?

I agree on the need for narrative, but how people benefit from math is the wrong narrative. the narrative needs to integrate the math that students need to learn. And Scott I agree that anyone who allows test stuff to drive instruction is going to have a bad time.

Math, when properly taught, does have a fundamental narrative: we can, by building tools that start with counting on our fingers and develop in logical (though sometimes hard to intuit) way, deepen our understanding of the world.

This isn’t to say there aren’t problems. Another way of looking at the mathematics curriculum is that it is an intricately plotted narrative, whose many subplots don’t really come together until a course in complex analysis (and graduate level sequels like a course in the algebra of Hermetian matrices or numerical techniques for solving partial differential equations). But since these courses are not generally required even for mathematics majors, the only students for whom this narrative makes sense are those who go to graduate school for mathematics, and the other 999 out of 1000 students see math as a frustrating series of unconnected topics.

In my humble opinion, teaching students about the narrative of math as a collection of useful problem solving techniques would not require any major shifts in curriculum. But it would require much better delivery and pedagogy. In my experience, low performing high school math students _want_ math to be an unconnected series of memorization tasks, because they think they can do this. Somewhere along the way, they have learned that that word problems are some mixture of impossible and irrelevant, and convincing them to even read the problems, let alone attempt a solution, can be a huge challenge. Few textbooks or tests avoid word problems completely, but students and teachers get caught in a feedback loop where students don’t like word problems so teachers teach less of them and then don’t differentiate between relevant and irrelevant (but still possibly interesting) problems, so students don’t have experience solving relevant problems so they fear any math problem with words…

I tried to make it clear that I believe (and I believe that Baker believes) that it’s not math itself that lacks the narrative, but that it’s the way we structure it when it is taught. I’m curious to know from Dr. Willingham what narrative _should_ be used to teach mathematics, if not that of utility? Beauty, alas, will only cut it for <1% of students. And I'm also intrigued by the comment that the narrative needs to integrate math that students need to learn. I'd love to hear a good argument in favor of students "needing" to learn the topics from the Algebra 2 "gecko" book Baker gleefully cites.

Curricula are designed by those who haven't the slightest interest in telling the big story; the same can be said about the vast majority of textbook authors. Both curricula ("big picture" from the perspective of math ed) and textbooks ("little picture") are created by committees of people, all of whom were good at "school math" (including skill at solving lots and lots of pseudocontext-laden word problems), and all of whom see logic in the particular mode of presentation of mathematics to students that Baker decries.

Baker's demand isn't to teach what we currently teach better, in other words; my sense is that he'd prefer a discussion about what it is we actually should teach and how we should go about it. I think this is a discussion that should be happening.

Is this the kind of thing that could help math _education_ find a narrative? The story of numbers? http://www.youtube.com/watch?v=Ar7CNsJUm58