Barry Garelick - November 5, 2007
Columnist EducationNews.org

Part 1 of 3

Anyone who has been involved in the debates surrounding math education (and there are more than a few such people) have come across the arguments that "Traditional math doesn't work" or "The old way of teaching math was a mass failure". These are generally heard early and often at school board meetings or other forums at which math textbooks and programs representing a math reform philosophy are being debated. To refresh everyone's memory, I offer some quotes below that are illustrative of these sentiments and come from various luminaries on the side of "reform math":

• "For most students, school mathematics is an endless sequence of memorizing and forgetting facts and procedures that make little sense to them. … Numerous scientific studies have shown that traditional methods of teaching mathematics not only are ineffective but also seriously stunt the growth of students' mathematical reasoning and problem-solving skills. "From Michael Battista who is associated with Investigations in Number, Data and Space, a math program for K-5, developed through grants made by the Education and Human Resource Division of the National Science Foundation (NSF) in the early 90's for $11.4 million. 
• "One would not have to look far to find decades worth of evidence that traditional US mathematics programs have not worked well for the vast majority of students." From Dr. Ruth Parker, who has authored books on mathematics teaching stated in an open letter dated May, 2007, in response to parents' questions about a talk she gave in the Seattle Washington area.
• "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." From Sherry Fraser, co-director of a high school math text/curricula called IMP, (developed through grants from the NSF in the early 90's to San Francisco State University, totaling $11.6 million) recently made a public statement before the National Mathematics Advisory Panel—a Presidential appointed panel charged with drafting recommendations on how best to prepare students for algebra. (Fraser, 2006).

I am continually amazed and perplexed by statements like those above. Despite having been taught facts and procedures that I committed to memory, in classrooms with seats in a row and teacher in front, I and others like me have benefited from the math education we received in the 50's and 60's. Sherry's statement was particularly puzzling given that 1) I was not bored in my algebra classes, and 2) Sherry, like me, ended up majoring in math. So I contacted her and asked what the research was that showed such methods to be "largely ineffective". She replied 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 will resist the temptation to point out that the approach used by IMP to teach what it calls algebra is to remove all semblance of logical sequencing of topics and content and say they've solved the boredom problem. I will also resist concluding that she has no sources to cite. Instead, I have assumed she is just trying to be helpful by using the discovery approach rather than just tell me the answer to my question. What I found is below. How Ms. Fraser will assess my efforts, I will leave to the reader to decide.

"Education has always been bad" and the Rise in Test Scores

Figure 1: Grade-Equivalent Scores on ITBS from 1955 through 2000 for Math (Composite)

Note: Although the increase in scores for math (and other subjects) is documented as starting in the 1940's, the report from which these data were obtained contains scores only from 1955 through 2000. Source: Hoover, et. al, 2003

Complaints about math education as well as education in general are nothing new. Richard Rothstein in his book "The Way We Were" (Rothstein, 1998) provides examples of specific complaints about education in various eras all the way to the 1800's. He states that "It is important to learn, if possible, how school performance today compares with that of the past, and to strive to go beyond anecdotes in order to do so. Unfortunately, however, almost nothing that is statistically reliable can be gathered about the history of student achievement. "Interestingly, two years later after he said this, Rothstein revisits this concept in a slightly different light, in an article he wrote for the NY Times (Rothstein, 2000) pointing to a trend reflected in tests given in Iowa (the Iowa Tests of Basic Skills or ITBS and the Iowa Tests of Educational Development, or ITED). Noting that the State of Iowa is essentially a laboratory for the nation by virtue of having long-term test data from the mid 30's to the present, he notes a general increase in all subject areas from 1940 to about 1965, and then a dramatic decline from 1965 to the mid-70's. Scores increase again until 1990 when they reached an all-time high. (Hoover, et al, 2003). (See Figure 1).

Figure 2

:

SOURCES FOR FIG 2: “Trends in Educational Achievement”; Congressional Budget Office (1986). CBO calculations based on "Iowa Basic Skills Testing Programs, Achievement Trends in Iowa: 1955-1985" (Iowa Testing Programs, unpublished and undated material); A. N. Hieronymus, E. F. Lindquist, and H. D. Hoover, Iowa Tests of Basic Skills: Manual For School Administrators (Chicago: Riverside, 1982); "Mean ITED Test Scores by Grade and Subtest for the State of Iowa, 1962 to Present" (Iowa Testing Programs, unpublished and undated tabulations); and Robert Forsyth, Iowa Testing Programs, personal communication, August 1984.

Since then, scores stayed relatively stable in the 90's, although as discussed later there was a sharp drop in computation skills starting in 1990 into the 2000's.

It turns out Rothstein wasn't the only one looking at the rise and fall of Iowa test scores, many others were also, and apparently, not only the Iowa tests showed these patterns. (Hoover, et. al, 2003; Hernishfeger, et. al, 1976; Nibbelink et al., 1986; Congressional Budget Office, 1986). I may be going out on a limb here in light of the quotes above, but it seems to me that during the 40's through the mid 60's, something was working.And whatever was working, certainly wasn't failing.

What is Traditional Math?

What "traditional math" means can vary depending on what era you're talking about.In general, it means topics covered in a logical sequence with information presented in a straightforward direct manner, and requiring memorization of key facts. Mastery of key concepts and skills are then built upon.The assertion by those who believe this type of math is a failure is that the teaching and/or textbooks rely entirely on rote memorization and excessive drill with no understanding of the procedures and underlying concepts. The reformists generally embrace programs embodying the standards the National Council of Teachers of Mathematics (NCTM) released in 1989 and revised in 2000.NCTM is a large organization based in Reston, Virginia.Since the late 80's they have exerted considerable influence over how math is taught in this country through their standards. In the view of many mathematicians, parents and (alas) some teachers, such standards de-emphasize learning basic skills, relying instead on "strategies for learning". They are informed by a dubious educational theory and philosophy that holds that understanding the big picture concepts of math builds the foundation upon which students learn math facts and develop skills.

The standards have been copied or otherwise incorporated by many states despite protests from mathematicians and others. The Education and Human Resources Division of the National Science Foundation (NSF) in the early 90's started funding the development of math programs and textbooks that embodied the NCTM standards and philosophy. The results were books and programs representing a "reformist" approach to math that began to be adopted in school districts across the country. Such programs also embraced a "constructivist" philosophy of learning in which students learn by constructing their own knowledge through "discovery", rather than being given specific pieces of information directly. In addition, multiple procedures (or algorithms) are presented, most of them inefficient, for the standard operations of addition, subtractions, multiplication and division, (along with the "standard" method as a caboose) and students allowed to pick the method that suits what is believed to be their innate knowledge of mathematics. Such alternative algorithms are presented in the hopes that it explains the theory, but amounts to no more than requiring multiple rote methods to learn, and usually with no understanding of what one is doing when operating with it.

Barry Garelickis 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.

Published November 5, 2007

It Works for Me: An Exploration of Traditional Math Part II
It Works for Me: An Exploration of Traditional Math Part III