For Algebra

The Atlantic published an excerpt from Temple Grandin’s latest book (Visual Thinking). They titled it “Against Algebra”, which puts it in a tradition of anti-algebra pieces in various magazines and radio programs (!). Alas, anti-algebra ideas are also present among some math educators. I have written about this repeatedly:

I return to this topic yet again, this time with a specific focus on Grandin’s article. I’ll try to minimize the overlap with those previous posts, so if you’re interested, you might click those links.

Grandin grounds her argument in many facts about education in the US, and many views I agree with.

  • She acknowledges the catastrophic impact of No Child Left Behind and its successors. The standardized test mania has been wielded in the name of accountability and equity, but it has resulted in decades of bipartisan undermining of public education. This has resulted in the narrowing of curriculum and instruction to what can be measured in those tests — disastrous for students, lucrative for the test makers, and yet another way to harass teachers.
  • She points out that we are teaching algebra “too early and too fast”. In broad strokes, that is true, though it is possible to select age-appropriate topics and develop effective strategies to teach them.
  • She understands that you should not and cannot teach abstract ideas without any grounding in the concrete and visual. As she puts it, “abstract reasoning is also developed through experience”.
  • She highlights the fact that the current system is failing a huge part of the population, as evidenced by the fact that so many college students need to take remedial math courses.

While all this is true, it does not necessarily lead to the conclusion that we should not teach algebra to all students. As Grandin says in the final paragraph of this article: “We need future generations that can build and repair infrastructure, overhaul energy and agriculture, develop robotics and AI. We need kids who grow up with the imagination to invent the solutions to pandemics and climate change.” Many of these fields actually involve the use of statistics, computer science, and mathematical modeling. And those disciplines, in turn, require algebra. All that would happen if we did not try to teach algebra to all students is a continuation and reinforcement of current inequities. Children of the well-off would have access to algebra and STEM majors and careers. Children of the working class and the poor would be frozen out.

So, you ask, how should we address all the valid points Grandin makes in her article? Dan Meyer’s response is a good start. He writes:

Grandin frequently attributes to “algebra” what we should really attribute to “ineffective algebra curriculum and instruction.”

He adds:

Effective instruction of any kind in any discipline means teachers are inviting and taking seriously the knowledge students already have–the ideas students can readily and concretely visualize.

He illustrates his brief post with images that suggest ways to base algebra in students’ intuitions.

As it turns out, I have spent much of my career as a teacher and curriculum developer in an effort to ground algebra instruction in the experiential. The textbook I co-authored in the 1990’s (Algebra: Themes, Tools, Concepts) has some weaknesses, but it’s all about laying a concrete foundation for algebraic abstractions. In its title, “Themes” refers to so-called real world problems — a good place to start a lesson. “Tools” refers not only to the increasingly fashionable electronic tools, but also to the manipulative materials beloved by “object visualizers”, including pattern blocks, the geoboard, and the Lab Gear. (These would likely have been appreciated by Grandin when she was in high school! As one of my students put it: “The Lab Gear saved my butt!”) Finally, “Concepts” means that we are not giving up on students’ understanding. (See a visual representation of the “themes, tools, concepts” approach here.)

Grandin opens her article with a suggestion that we ask students “What are you good at?” I worry that this may reinforce a fixed mindset. Very few students start out being “good at” algebra. Almost all can get better — if taught properly.

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