The accomplished mathematician on why he thinks the current system is “dysfunctional” and how Reasoning Mind is uniquely positioned to improve it.
Dr. R. James Milgram, professor emeritus of mathematics at Stanford University, is not shy about expressing his opinions on the state of U.S. math education. The accomplished and outspoken mathematician, who recently gained attention for his comments on what he sees as deficiencies in the Common Core math standards, has been a member of the NASA Advisory Council, the National Board for Education Sciences, and the Common Core Validation Committee. In addition, Dr. Milgram has been a main author and national reviewer for several states’ math standards.
Recently, Dr. Milgram sat down with the team at Reasoning Mind to share his thoughts on why he thinks the current U.S. math system is “dysfunctional” and what we can do to fix it. The resulting interview is below.
How did you get involved in mathematics and what sparked your interest in K-12 math education?
Well, my father was a very well-known mathematician. And what your father does, you tend to get interested in. And I think it’s reasonable to want to communicate at a deeper level with your parents as you get older. So there wasn’t a choice. If I was going to do that, I was going to study mathematics.
To your second question—I’m a research mathematician first and foremost. But for family reasons I got very interested in the issues in math education. My colleagues and I, we had our kids in the public school system, so we were in a position to see the damage that was being done to them. For the most part, faculty in the schools of education in this country deny that it is possible to harm K-12 students when they are subject to experimental curricula—but any reasonably aware parent would assure you that it is, indeed, very possible. And we didn’t like it.
Can you summarize your current take on math education in the United States?
It’s hard to imagine any system that works more poorly.
What in particular do you see as the central problem?
An awful lot—maybe even the majority—of the people who are responsible for structuring the math educations that students will receive, and math training for the pre-service teachers intending to teach at the elementary or middle school level in the United States, have a degree from the education schools, typically an Ed.D. with a specialty in mathematics education. Well, the majority of these individuals have never in their entire lives had a course in mathematics at the university level beyond, at most, the level of intermediate algebra. And yet they are the ones that are being tasked with setting up what math is being taught and how it is presented to both the prospective teachers, all the students, and then actually teaching this material to the new teachers. It’s hard to imagine a more dysfunctional system and it’s also unnecessary. The vast majority of these preservice teachers would be glad to fill in their missing backgrounds if only the education school faculty in charge of the math methods courses knew more about the subject so they could teach math at a higher level.
“Typically, a math educator [in a high-achieving country] has a Ph.D. in mathematics, with a specialty in math education. In particular, they have taken the full graduate sequence of math courses that any other math Ph.D. takes … This what’s done in the high-achieving countries. I really don’t see any excuse or any justification for not doing it here.”
How is this approach different from other countries?
Well, do you know what they do in the high-achieving countries? Typically, a math educator there has a Ph.D. in mathematics, with a specialty in math education. In particular, they have taken the full graduate sequence of math courses that any other math Ph.D. takes. Such a person simply has a different level of understanding of the subject and can teach it to a much higher level. This is what’s done in the high-achieving countries. I really don’t see any excuse or any justification for not doing it here.
Why do you think so few U.S. math Ph.D.’s currently want to work or teach in K-12 education?
That’s a misconception, I think. An awful lot of them would be perfectly delighted to do this. In Europe, and in the high-achieving countries, a professor of mathematics at the university level is expected to teach a course at a local high school every two or three years. And so they maintain a high level of coordination between the college level and high school level. And at the same time, the professors at the university know very well what’s going on at the high school level. Well, there’s no reason why we can’t do that.
From a mathematician’s perspective, what are some of your main concerns with how K-12 math is being taught in the U.S.?
In Kindergarten through 8th grade, there are a number of basic—absolutely crucial—parts of mathematics that are introduced which are going to be important all the way through college. Through calculus, and then through differential equations, and then through real statistics and data analysis. So you have certain key topics that you have to carefully teach all the way to real mastery in these early grades. These key subjects include fractions and above all ratios, rates, percentages, and proportions. If students manage to learn these basic topics, and learn them so well that they can use them on-demand and do everything that’s expected of them, this will last them well past calculus. Those items represent the majority of things they really need. Oddly enough, and unfortunately, when you look at the topics that teachers in the U.S. tend to struggle with, guess what they are: fractions, ratios, rates, and proportions.
Are there any strategies or policy efforts in math education reform, past or present, that you see as having been particularly successful?
Whole sequences of strategies have been tried. I don’t think any which have been mandated by legislative action have been successful or even point in a successful direction. But there have been a number of projects where individual groups have succeeded. For example, a small group of mathematicians at the University of Vermont created and developed the Vermont Math Initiative, which re-trained practicing or in-service teachers. And it created a very significant, measurable improvement in the math outcomes for students. But it took a long time—300 contact hours for each participating teacher, and that’s a lot. And nobody has been able to produce such outcomes with less time than that. Now, there are a lot of programs out there funded by the government, and a lot of programs funded by private industry, but they only give you maybe 20, 30, 40 hours of contact which is not nearly enough.
“Okay, so what do we need? We need to have a program that is designed to work with the largest percentage of students that you can manage. Well, Reasoning Mind’s work is based on the programs in the high-achieving countries. In fact it’s really closely based on them.”
You were consulted by our co-founder, Alex Khachatryan, many years ago before he and his family decided to launch Reasoning Mind. Why have you remained interested in Reasoning Mind’s approach to math education and what do you see as the organization’s value?
Here’s the situation. We had a bunch of textbook publishing companies in this country and they tended to get bought up one by the other, so now we have two or three major textbook companies that dominate the market in the United States. Under these circumstances, the textbook companies now really control curriculum. Where are the schools going to get their textbooks except from these two or three companies? And that means the publishers can get away with things that they couldn’t get away with before when there was competition. They can get away with writing programs that have no math content at all, and claiming that these programs are satisfactory and satisfy all the requirements that you’re going to need. The only advantage that such a program has is that it’s going to make life easier for the lowest quartile or quintile of students. It’s going to be a total waste of time for your average, above average, and accelerated students. Just a complete waste. So you have to look around, and you have to say, okay, we can’t really trust the textbook companies anymore—is there anybody who is actually trying to produce programs that will have really good outcomes? And I think at this point, the only one that I’m sure of in the entire country is Reasoning Mind. So what’s going on there is very important.
What is it about Reasoning Mind that makes you confident it can improve math education in the United States?
Okay, so what do we need? We need to have a program that is designed to work with the largest percentage of students that you can manage. Well, Reasoning Mind’s work is based on the programs in the high-achieving countries. In fact it’s really closely based on them. So let’s look at what the outcomes look like in the high-achieving countries. Typically, in the high-achieving countries, over 90% of the populations graduate from high school. And for fully half of these high school graduates, the highest high school math course that they’ve had is calculus. Now, that’s simply a different level of magnitude than what we’re used to in this country. The U.S. doesn’t get anything close to 90% of our students graduating from high school—we get more or less on the order of 65-70%, somewhere in there. And our outcomes are getting progressively weaker and weaker. But the outcomes in the high-achieving countries remain at this high level. And there’s only one program in the U.S. that comes from what they’re actually doing in these high-achieving countries—Reasoning Mind.