MATHS VERSUS MATH

THE ENGLISH CALL IT “MATHS,” WHEREAS we ’Mericans call it “math.” And in a sense, this monolithic view of math’s many elements is reflected in math instruction in the U.S. failing to adopt a modular approach that has evolved in other aspects of science education. 

“More Math, Less ‘Math War’” is the title of a Policy Forum offered by Alan Schoenfeld and Phil Daro in Science, March 22, 2024. Schoenfeld is at the School of Education, University of California, Berkeley; Daro, at the Strategic Education Research Partnership Institute, Oakland, California. Here are tidbits gleaned from their article.

Modularity. Schoenfeld and Daro write in their Abstract, “Owing to scientific advances, high-school and college science curricula in the US today barely resemble those of 50 years ago. Most science curricula are ‘modular’: Topics of emerging interest can be inserted as units, without major impact on the broader curriculum.”

To pick two distinctly different examples, units of climate change and of Covid are easily incorporated into appropriate levels of science education.

“Mathematics instruction, by contrast,” Schoenfeld and Daro say, “is much the same as it was a half century ago—hierarchically organized and inflexible, with each building block taking up a semester or an entire year.” 

K-12 mathematical education begins with basic numeration, arithmetic, followed by middle-school/high-school courses in Algebra I, Geometry, Algebra II, Trigonometry, Precalculus, and Calculus. 

A False “Equity Versus Excellence.” Schoenfeld and Daro describe “a false ‘equity versus excellence’ dichotomy that has fueled recent flare-ups of decades-long ‘math wars’ over curricula and instruction.” 

On one side, “equity” favored changes in math instruction to mitigate the higher attrition rates of underrepresented ethnic and socioeconomic groups who are disproportionately filtered out of mathematics and science. On the other, “excellence” feared a “dumbing down” of the subject and sought a status quo.  

Math Wars. “Given the inflexibility of the traditional mathematics course sequence,” the researchers say, “the tension between equity and excellence has seemed intractable. It was a major cause of the math wars that roiled the K-12 educational enterprise for much of the 1990s, stymieing curriculum implementation for more than a decade.”

The researchers say, “We believe that the curricular issues discussed here, though not simple, are amenable to progress if approached carefully and with appropriate scientific rigor. Once curricular issues are politicized, careful and nuanced discussion is nearly impossible. That is the risk for mathematics if the math wars are rekindled.”

Three Principles. Schoenfeld and Daro “propose three simple principles for implementing mathematics curricular reform.” Here’s the essence of these three: First, pathways of maths (I purposely prefer the English word) should be preserved for all students for as long as possible in their education. Second, modularity is the key to successful evolution of these paths. And third, courses should be geared to student requirements, and prior courses should provide robust foundations.

Modularity the Key. Modular units can be employed for insertion in some paths, but not required of others. For example, the STEM (Science Technology Engineering Mathematics) path requires calculus as a goal. By contrast, a non-STEM career might emphasize data science or mathematical modeling.

The researchers note, “For example, everyone should know the basic ideas of exponential growth and decay and the core concepts of trigonometry. However, few students need to be able to solve complex exponential or logarithmic equations or to manipulate trigonometric identities. Some such work can be done with technological tools, and some can be learned once the students who need it have specialized.”

This reminds me of basic arithmetic: We all learned how to add, subtract, multiply, and divide, even the non-trivial process of long division. Somewhere along the way, I also learned the process of extracting square roots. But for the life of me, I’ve long forgotten this algorithm and seem to be no less a person because of it.  

Schoenfeld and Daro continue, “Many students aspire to careers in fields such as nursing, construction, business, and law that require postsecondary certification. Which mathematics serves them and their future clients best? They won’t be factoring polynomials, but they will be making decisions based on measurement and data.”

Conclusions. “There is potential for progress,” the researchers say. “We know a great deal more about teaching, learning, and equitable and ambitious learning environments than we did even a decade ago, and there are tools for making progress along the lines suggested. Yet there is much more to learn about development, about students’ identities and how they affect and are affected by schooling, and about the ways in which the social environment plays out in classrooms.”

Gee, it’s quite enough to make me wanna be a maths professor. ds 

© Dennis Simanaitis, SimanaitisSays.com, 2024