High school math classes should be broadened to focus on goals beyond college and careers, including teaching the math students will need to be literate participants in civic life. Educators should ensure that all students master a core set of "essential concepts" through four years of math coursetaking. And the classes should be detracked, to prevent students of color from winding up in dead-end math pathways, says an expansive new report from the National Council of Teachers of Mathematics.

The report, unveiled today at NCTM's annual conference, is the product of a task force the group's board of directors created back in 2016. Part vision-setting document and part stock-taking, the report aims to stimulate conversations on how to improve teaching of the subject in high school.

The Algebra-Geometry-Algebra 2 trifecta that has shaped high school math since the late 19th century remains firmly in place without enough evolution, it says. And while 4th grade students have progressed in math on the National Assessment of Educational Progress since the 1990s, scores have been stagnant for decades at grade 12.

The document is also a corrective of sorts to the high school math section of the Common Core State Standards. Some critics and even some of those standards' developers have said the common core's high school standards weren't as lean and polished as those in the K-8 grades. The NCTM's document attempts to identify areas of focus, as the common core's K-8 standards do.

Purpose and Essential Concepts in Math

In a nutshell, the report says that the goal of math coursework shouldn't be just to prepare students for college classes or work, but so they are better able to understand and critique the world. That includes being able to identify, interpet, and critique math in social, scientific, and political systems; to understand math in polls, the media, and other communications; and to make good financial decisions and interpet research.

As part of this effort, the publication gives a list of essential concepts in math that all students should master. Rather than a new set of standards, they should be thought of as "distillations" that will help bring focus to high school curricula, the report states. It breaks them down into the areas of essential concepts in number; algebra and functions; statistics and probability; and geometry and measurement.

For example, for statistics, it says, all high school students should be able to understand the differences in research methods that use sample surveys, experiments, and observational studies, and the problems of bias and validity, among other things.

As part of this, it recommends that some practices should be scaled back. Too much focus in algebra is put on solving equations and inequalities, rather than on learning how to use math techniques to produce a certain outcome, solve a problem, or provide proofs of why algebraic statements are true, the report says.

"There is a lot of what we might refer to as legacy content, particularly in second-year algebra where students spend a great deal of time on symbolic manipulations—factoring equations, solving equations," said Matt Larson, the outgoing president of the NCTM. "Today the emphasis has to move to students understanding, here's a problem situation that can be modeled by using a quandratic equation and then solved. And when you think you have the solution, understanding the math enough to say, 'Yeah, my solution seems reasonable,' or 'No, that doesn't seem to make sense in this particular situation.'"

Equity and Access in Mathematics

Of course, those key shifts will also require new thinking about who takes the classes. On this front, the NCTM says mathematics classes should no longer track teachers or students into different levels (like "remedial" versus "honors" versions of the same course).

"Tracking ... in some cases puts students into terminal mathematics course pathways that are not mathematically meaningful and do not prepare them for any continued study of fundamental mathematics concepts," the report says.

As if on cue, the U.S. Department of Education released data yesterday showing that a disproportionate number of students of color don't take Algebra 1 until the 11th grade, all but ruling out the possibility of higher-level math attainment.

While acknowledging that detracking poses challenges, it can be supported by having schools begin to examine data patterns and assignments, Larson said. That includes which teachers are typically assigned to teach which course levels.

"Often it's the case that those teachers who are the most experienced or perceived to be the most capable are assigned the upper-level math classes. An initial action we recommend is, again, to examine the data," Larson said. "Who is teaching whom in your high school math department?"

And teachers should focus on equitable instruction that focuses on reasoning, problem solving, using mathematical representations, and facilitating mathematical discourse, in which where students and teachers feel comfortable discussing and critiquing one another's reasoning, rather than focusing on "getting the right answer."

Finally, the report calls on rethinking math pathways: All students should take four years of classes that "maintan the integrity" of the mathematical standards, require clarity and precision, and don't allow for substitutions, such as computer science, to stand in for math.

I'll be interested in hearing how the larger math community responds to this report. Any talk about the balance of procedural and conceptual math is bound to raise passionate discussion. Our comments section is open for your feedback!

Image: Thomas Hesse. Licensed under Flickr/Creative Commons