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>Traditional Math Means Never Having to Say You’re Sorry (Barry Garelick)

>Last year at a meeting of the National Mathematics Advisory Panel (a Presidential appointed panel charged with drafting recommendations on how best to prepare students for algebra), a woman named Sherry Fraser read a statement into the public record which began as follows:

“How many of you remember your high school algebra? Close your eyes and imagine your algebra class. Do you see students sitting in rows, listening to a teacher at the front of the room, writing on the chalkboard and demonstrating how to solve problems? Do you remember how boring and mindless it was? Research has shown this type of instruction to be largely ineffective.” (Fraser, 2006).

Such statement falls in the category of “Traditional math doesn’t work” or “The old way of teaching math was a mass failure,” heard early and often at school board meetings or other forums. I am always puzzled by these statements but Sherry’s was particularly vexing given that 1) I was not bored in my algebra classes, and 2) Sherry, like me, ended up majoring in math. So I contacted Sherry and asked what the research was that showed such methods to be “largely ineffective”. Sherry is co-director of a high school math text/curricula called IMP, developed in the early 90’s through grants from the NSF, totaling $11.6 million, to San Francisco State University. She replied to me in an email that she is a “firm believer in people doing their own research” and added that I wouldn’t have any trouble finding sources to confirm her statements. I have assumed she is just trying to be helpful by having me discover the answer myself, rather than just tell me the answer to my question. I have been a good student; here’s what my research shows:

From the 1940’s to the mid 1960’s, at a time when math and other subjects were taught in the traditional manner, scores in all subjects on the Iowa Tests of Basic Skills increased steadily. From 1965 to the mid-70’s there was a dramatic decline, and then scores increased again until 1990 when they reached an all-time high. Scores stayed relatively stable in the 90’s.

Conclusion No. 1: During the 40’s through the mid 60’s, something was working. And whatever was working, certainly wasn’t failing.

Those who decry traditional math generally advocate its reform, and promote the concept of discovery learning. Students supposedly discover what they need to know by being given “real life” problems, frequently without being given the procedures or the mastery of skills necessary to solve them. The reform approach is at the heart of a series of math texts funded through grants from the Education and Human Resources Division of National Science Foundation and based on standards developed by the National Council of Teachers of Mathematics (NCTM).

Long before NCTM’s release of its standards in 1989, math reformers of the 1920’s through the 1950’s had their say in how math should be taught. William A. Brownell, spoken well of by NCTM and various luminaries in today’s reform movement, was one of the key reformers of the early twentieth century and promoted what he called meaningful learning; i.e., teaching mathematics as a process, rather than a series of end products of isolated facts and procedures to be committed to memory.

If the above sounds like what the reformers are talking about today, it is because – like the complaints about education in general through the years – the complaints levied against how mathematics is taught have been perennial. What is often not mentioned when these complaints are replayed is 1) that there have also been perennial solutions and 2) some of these solutions have actually been effective.

The traditional math from the 40’s to mid-60’s was certainly not perfect. Also, it cannot be denied that in spite of the effort made in the texts to provide meaning to the student, some teachers did not follow the texts and insisted on a Thorndike-like approach that relied on rote memorization and math problems isolated from word problems. But neither the reformers nor the mathematicians of those times asked the teachers to teach math that way. Bad teaching was incidental to and independent of the textbooks used and the philosophy put forth by that era’s reformers.

Conclusion Number 2: Yesterday’s reformers sought the same goals as today’s reformers, except their textbooks actually contained explanations.

During the era of test score decline, many social issues emerged which may account for the downslide, such as increased drug use in the mid-60’s, permissiveness, increase in divorces and single family homes, and changes in the demographics of schools. Also, starting in the mid-60’s, many of the teachers of the older generation retired, making way for the newer cadre of reinvented John Deweys from the education schools.

The difference between traditional and present-day teaching is striking.

The emphasis is now on big concepts. These come at the expense of learning and mastering the basics.
Getting the right answer no longer matters.
In theory, it is student-centered inquiry-based learning. In practice it has become teacher-centered omission of instruction.
With the educational zeitgeist having been planted and taken root, the development of the NCTM standards in 1989 were an extension of a long progression. To top it all off, the reform approach to teaching math is being taught in education schools, thus providing future teachers with “work-arounds” to those few math textbooks that actually have merit.
Conclusion No. 3: While bad teaching was incidental to the traditional method in earlier days, it has now become an inherent part of how most math is taught today.

I hope my efforts provide something that Sherry Fraser can cite.

The above is taken from a 3-part article entitled “It Works for Me: An Exploration of Traditional Math,” published here at

Barry Garelick is an analyst for the U.S. Environmental Protection Agency in Washington, D.C. He is a national advisor to NYC HOLD (, an education advocacy organization that addresses mathematics education in schools throughout the United States.

There’s an excellent point here:

Conclusion Number 2: Yesterday’s reformers sought the same goals as today’s reformers, except their textbooks actually contained explanations.

By and large, the goal of educators throughout history has probably been the same. We all want our students to achieve at their fullest potential. We must be careful not to “throw the baby out with the bath water” as we implement new “research” based strategies.

I haven’t conducted formal research, but I’ve noticed a trend in my student population over the past few years. The students who struggle with Algebra almost all struggle with basic mathematical concepts. Many of these early teens cannot multiply one-digit numbers without a calculator. I think that these students have developed too much reliance on calculators to solve math problems. When they reach Algebra, the calculator can no longer replace mathematical reasoning.

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