Against "Against Algebra"

What Temple Grandin's critique of algebra gets right and wrong.

Temple Grandin:

I’m terrible in areas such as algebra, which rely entirely on abstraction and provide nothing to visualize.

I couldn’t bring myself to title this newsletter “For Algebra.” As it happens, animal scientist Temple Grandin is right about a lot in her essay “Against Algebra,” especially her critique of the gatekeeping role that advanced algebra plays in our society. High school graduation requirements and university admission policies in math prevent too many people from reaching educational goals that have no meaningful connection to their ability to factor third-order polynomials or conjugate radical expressions.

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

For example, Grandin writes, “I value my different way of seeing the world, because it’s made me who I am.” Grandin refers here to her tendency to think visually, but she may as well speak for every student who feels like the ways they see the world—the images and experiences and histories they bring to class every day—have no place in algebra.

Grandin is right that in many versions of algebra instruction, students are offered an abstract idea (an equation, for example) and asked to transform it into another abstract idea (a graph!) with no tangible benefit beyond a grade. Grandin is right that this kind of curriculum and instruction asks students to rush quickly up “the ladder of abstraction,” forsaking ideas they can understand and visualize in favor of ideas that are abstract and alien.

We shouldn’t accept this as an inherent feature of algebra, though. 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.

Very early into the lessons in our curriculum, for example, we ask students to play, sketch, describe, write a story, predict, notice and wonder—all efforts at inviting a student’s concrete, visual, and sensory knowledge.

We ask students to turn that concrete knowledge into algebraic abstractions, but we help students see how the abstract fortifies rather than replaces the concrete. Algebra sharpens our intuition. It makes our predictions more accurate and tedious tasks more efficient. It adds new textures to the ideas and images we bring to class.

Grandin is right that this isn’t often the reality, but it can and should be. Not every student will be “for algebra,” but they should know, at least, that algebra is for them.

What Else?

• Come hang out with me next week and experience one of our lessons as a student in an Amplify Step Ahead webinar.

• Our team over here just released Challenge Creator to the public, a feature of Desmos activities (previously internal only) that lets students create challenges for one another. 

• Our newer, beefier “Free Response” component lets students add images and audio responses to their text responses—all an effort to get technology out of the way of student thinking.

• I’m extremely enthusiastic about Dominic Hill’s context for cooling curves: what should you make the delivery radius of your pizzeria?

• “Split 25” came up on my timeline again last week, bringing to mind the late Malcolm Swan and the fantastic math posters from Xi Yu and Joey Kelly at Play With Your Math.