Why Math Textbooks Don’t Work and Never Will

I am looking at the very first lesson in a popular and widely-used 7th grade online math textbook right now. The lesson involves ordering rational numbers and is spread out over 6 pages.

The introductory section includes an open-ended activity in which students make number lines on the floor to solve numerous self-generated math problems with a partner. This follows an introductory activity for the chapter that requires students to plot 41 points on a coordinate grid and then create a “dot-to-dot drawing” of their own design with an additional 20 points.

There are 51 problems in the actual lesson, ranging from basic tasks involving absolute values to extremely difficult word problems involving scientific tests on the moon, measuring the corrective powers of contact lenses (in diopters, whatever they are), summit elevations of volcanoes, and the freezing points of various liquids. This does not include the 27 problems of various difficulty levels on the workbook pages designed to accompany the lesson. There are answers to none of this in the text itself; there are answers to the odd-numbered problems in the back of the book, but even then there are no explanations of how the individual problems were solved. Instead, there are two “self-assessments,” one for “skills and concepts” and one for “problem-solving.” Both of the self-assessments invite students to rate their own understanding of the “success criteria” in their “journals,” but include no correct answers or explanations to help them do so. The three “success criteria” are listed in small type back on page one - I know because I searched. They are, “I can graph rational numbers on a number line,” “I can find the absolute value of a rational number,” and “I can use a number line to compare rational numbers.” None of the practice problems in the lesson explicitly involve graphing rational numbers on a number line or using a number line to compare rational numbers. It would be interesting to see how students rate their ability to do something they haven’t been explicitly asked to do.

There are only four examples provided over the course of this 6-page lesson (!), one of which requires reading three full paragraphs of text (you know, because none of our kids have reading difficulties). There is a one-line definition of rational numbers on page one of the lesson, but there are no explicit examples or non-examples to indicate what a rational number is or isn’t.

This is day one of seventh grade math.

There will be roughly 179 more days this year just like it.

This explains math anxiety.

The sad truth is that math textbooks don’t teach math: they assault you with it. Unexplained, uncheckable, unrelenting math, math, math.

This shouldn’t be surprising, though. Textbook publishers aren’t rewarded for teaching math; they’re rewarded for selling textbooks. Who cares if the kids are learning anything so long as sales are up? Can we all just finally admit that textbook publishing is a racket? We should be throwing the book at these snake oil salesmen, not buying books from them. To appeal to as many teachers, administrators, and school boards as possible, publishers fill textbooks (and supplementary materials) with truckloads of content – despite the fact that this produces cognitive overload on the part of the students. That they still do this in 2023 is inexcusable. We’ve known about the very real limits of human cognition since at least 1956, when Harvard’s George A. Miller famously published The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information, one of the most cited papers in the history of psychology. The fact that the limits of attention span and working memory haven’t been baked into instructional design since then is a failure of positively epic proportions.

And then, to add insult to injury, textbook authors don’t lift a finger to help the students learn the content they’ve dumped between the covers. Almost no examples. Very few answers. Almost no explanations.

It. Is. Literally. Insane.

And most of us know it. If you’re like me, you remember writing down any-old-answers during textbook lessons or in workbooks because you had no idea what you were supposed to be doing (not enough examples) and no way of knowing if you were doing the work correctly anyway (no keys to check your work, and no explanations to help you learn from your mistakes).

And if you’re like most of us teachers, you long ago gave up trying to check all of the students’ textbook and workbook work yourself because 1) it’s mathematically impossible, and 2) it’s too depressing. There’s no worse feeling than checking long division worksheets and realizing that, with no examples or key to refer to, most of the students got most of the problems wrong - and just practiced how not to do long division.

And all of this will never change, because textbook publishing is Big Business. The publisher of the book I just referred to, Cengage Learning, has $1.5 billion in annual revenues, and is one of the five publishing companies that control 80% of the $13.9 billion textbook market and is accused of being a cartel. No publisher is ever going to come close to admitting that all of their expensive books, and workbooks, and worksheets, and supplemental games, and e-games, and e-resources, and e-whatever are a complete and total waste of precious educational funds (i.e., your tax dollars).

But they are.

Because they don’t work. As you can see in the 2018 PISA performance rankings below, the US is in the bottom third for industrialized nations despite our extensive textbook use.

Because they unnecessarily complicate a subject that ought to be a pleasure to learn.

Because they cause kids undue anxiety.

But it’s even worse than that. Textbooks make kids feel stupid, and kids who feel stupid in math class start giving up on math itself.

We are literally teaching our kids to hate math, and spending a fortune doing so.

Now this would be an absolute tragedy if we didn’t have alternatives.

But we do.

Math is learned one problem at a time – and only one problem at a time. Contrast that with the 119+ problems students are barraged with in the very first lesson of the year in the example above. All you need is an example problem (which can involve manipulatives, drawings, or symbols depending on the age or level of the student), a similar problem to try, and access to the worked-out solution or solutions to the problem you tried. Once you’ve finished your work and checked it, you need a related and slightly more complex example and practice problem to try, along with the worked-out solution or solutions to that problem. Then it’s just keep ‘em coming.

This “see it, do it, check it” strategy is actually how kids learn. It’s how all of us learn. It’s low-stress, devastatingly effective, and as simple as Lego instructions.

And it’s cheap.

It’s how math should actually be taught.

Anybody who tells you differently doesn’t understand how kids learn - or is trying to sell you something.

Steve Hare

Math-Whisperer. Humanist.
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