Say Anything Blog

Math isn’t as hard as most people think. Developing mathematical skill is actually fairly straight forward (even for a non-mathematical guy like me), and not unlike the study of martial arts. Skills like adding, subtracting, multiplying and dividing are like learning basic moves and stances. Fractions and ratios are like simple combinations. Like the simplest block, all these skills are developed through practice. To become good you must practice at least enough to develop automatacity. If you have to think about a block or about 7x7, you don’t know it. Practice prepares you for more advanced stages such as sparring or Algebra.

With a little common sense, it’s not hard to design a system to train students to master simple mathematical principals, and prepare for more advanced study. Unfortunately common sense is not a quality education professors are known for.

Like most other subjects, mathematics instruction is being assaulted by educational practices based more on social and political beliefs than on proven results.

In the current issue of City Journal, Sandra Stotsky explains how the progressive educational theorists are trying to purge mathematicians from the designing of math curriculum.

The educational trends that led to the NCTM’s approach to math have a long pedigree. During the 1970s and 1980s, educators in reading, English, and history argued that the traditional curriculum needed to be more “engaging” and “relevant” to an increasingly alienated and unmotivated—or so it was claimed—student body. Some influential educators sought to dismiss the traditional curriculum altogether, viewing it as a white, Christian, heterosexual-male product that unjustly valorized rational, abstract, and categorical thinking over the associative, experience-based, and emotion-laden thinking supposedly more congenial to females and certain minorities.

Those trying to overthrow the traditional curriculum found mathematics a hard nut to crack, however, because of the sequential nature of its content through the grades and its relationship to high school chemistry and physics. Nevertheless, education faculty eventually figured out how to reimagine the mathematics curriculum, too, so that it could march under the banner of social justice. As Alan Schoenfeld, the lead author of the high school standards in the 1989 NCTM report, put it, “the traditional curriculum was a vehicle for . . . the perpetuation of privilege.” The new approach would change all that.

Two theories lie behind the educators’ new approach to math teaching: “cultural-historical activity theory” and “constructivism.” According to cultural-historical activity theory, schooling as it exists today reinforces an illegitimate social order. Typical of this mindset is Brian Greer, a mathematics educator at Portland State University, who argues “against the goal of ‘algebra for all’ on the grounds that . . . most individuals in our society do not need to have studied algebra.” According to Greer, the proper approach to teaching math “now questions whether mathematics as a school subject should continue to be dominated by mathematics as an academic discipline or should reflect more fully the range of mathematical activities in which humans engage.” The primary role of math teachers, constructivists say in turn, shouldn’t be to explain or otherwise try to “transfer” their mathematical knowledge to students; that would be ineffective. Instead, they must help the students construct their own understanding of mathematics and find their own math solutions.

Classroom practices follow logically from these theories. Teacher-directed learning goes out the window, despite its demonstrated benefits for students with learning problems; instead, schools should embrace “student-centered” math classrooms.

Imagine going into a karate school and having with no sensei. Instead you get a karate facilitator who tells you construct your own techniques. Do you think you’re likely to, on your own, develop a superior kick or punch, or will you just developt bad habits? Unless you’re a natural Bruce Lee, chances are you’ll simply develop bad habbits that will take months if not years to unlearn.

The same thing happens with mathematics. When every step down the path of learning math requires the student to, figuratively, re-invent the wheel, a lot of kids pick shapes other than round for their wheels.

This is a concept that is understood in the countries where students achieve higher levels of mathematical competence than the average American student.

High-math-achievement countries teach arithmetic in the elementary grades in a coherent curriculum leading, step by step, to formal algebra and geometry in middle school. The progressive educators, by contrast, support “integrated” approaches to teaching math—that is, teaching topics from all areas of mathematics every year, regardless of logical sequence and student mastery of each step—and they downplay basic arithmetic skills and practice, encouraging kids to use calculators from kindergarten on. The educators also neglect the teaching of standard algorithms (mathematical procedures commonly taught everywhere, with only minor variations, because of their general applicability), insisting instead on the value of student-developed algorithms—this despite research by cognitive psychologists strongly supporting a curriculum that simultaneously develops conceptual understanding, computational fluency with standard algorithms, and problem-solving skills as the best way to prepare students for algebra.

The heart of the disagreement between progressive math educators and mathematicians is whether students are acquiring a foundation in arithmetic and other aspects of mathematics in the early grades that prepares them for authentic algebra coursework in grades 7, 8, and 9. If not, they then cannot successfully co