Polite Agreement or Something We Can Use? (Barry Garelick)
Education Secretary Spellings recently announced the formation of a presidentially appointed panel that was formed to address math teaching. According to the charter of this panel, one of its purposes is “to foster greater knowledge of and improved performance in mathematics among American students.” The panel is charged with producing a report in two years, which must contain recommendations pertaining to how math instruction can be improved in the U.S. In particular, the report must address the skills necessary for students to acquire competence in algebra and to prepare them for higher levels of mathematics.
The workings of the panel are not the type of thing that makes the front page of newspapers, the top story on TV news, or what is talked about in the local cafes. To hear about this you need to drop in to the blogs (like Edspresso), or the various list serves on the internet devoted to math education. There you will notice some discomfort among those who think that the way math is currently taught and the present crop of math texts being used in the U.S. is just fine. They have openly expressed dismay at the inclusion on the panel of people who have been vocal critics of reform math, stating “This panel is filled with hacks, toadies and stooges. Can you say ‘show trial’, children? Have you ever seen the old reels of the Communist Party Congresses in Moscow?” Allegations of pre-conceived conclusions then follow.
The rancor of the above comment is not unusual to those familiar with the never-ending debate between the mathematics and education communities in what has come to be known as the “math wars”. The debate revolves around on state math standards, math texts and how math should be taught. Reformers advocate the concept of “discovery learning” in which students discover what they need to know by being given “real life” problems, frequently without providing the information and skills necessary to solve them. Such 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). NCTM has had enormous influence over the math standards and texts used by most states and districts in the United States—standards and texts that, in the view of the mathematics community have resulted in dumbed-down, or “skills-lite” curricula.
The formation of the panel comes at an unusual time in the long and storied history of the math wars. Some see the formation of the panel as a possible end to the math wars, at a time when there has been some communication between the mathematics community and the NCTM. Yet at the same time, school districts are continuing to adopt the controversial texts, school boards are continuing to tell parents to “trust us”, and protests from mathematicians and others that the math texts are not doing the job are labeled as ideological arguments—and are ignored.
The real issue is about math content, but few people get that yet. Instead, the arguments center around pedagogy and how the brain works—anything except what are the basic facts, skills and concepts of math that students must master (like they do in Asian countries). Maybe that’s why the panel has five psychologists but only two mathematicians. It doesn’t take a PhD in cognitive science to know that to teach students how to think you need to teach them things to think about. Nevertheless, the panel’s discussions about content may be eclipsed by discussions about learning and teaching theory.
One hopes that the traditional backlash will stop and real dialogue will begin. If it were about how to teach dancing, there would be little argument that you have to teach basic dance steps. What I hope does not happen is that the panel ends up in polite agreement that it’s important to learn facts but then publishes a report recommending that students continue to discover what they haven’t been taught.
Barry Garelick is an analyst for the federal government and lives in the Washington DC area. He is a national advisor to NYC HOLD, an education advocacy organization that addresses mathematics education in schools throughout the United States.
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I teach decision sciences — applied math — in a business school. I have seen over the years students’ math knowledge shrink to the point that I have not a few, but many students who don’t understand they have to mutiply the tax rate by the price to get the total sale, and can’t just add the tax rate.
Frankly, I’m sick of “education experts” running social experiments on high school students, and to hell with what they need to know when they get to the university. Something badly needs to be done.
Chris C said: “if you read the rest of section 4 you will see a number of other goals that require the expertise of people other than mathematicians, including accomplished psychologists and policy-makers.”
This is correct. The question is the degree of emphasis between content and theories of learning.
As someone who has taught a variety of college level courses in subjects other than mathematics, I’ve discovered, by discussing life-problem subjects like compound interest and even just grade computations, that many of my students have no grasp of basic mathematical operations. Based on their own reports, this is because they never memorized rote operations like multiplication tables nor did they ever actually have to perform long division: the result of the NCTM curriculum or possibly the blowback from very poorly instructed teachers who are then handed NCTM texts.
It seems to me that mathematics is a language and certain operations are the vocabularies by which the language is “spoken.” I memorized vocabulary lists in school, and so I can write and speak fairly fluently. I also memorized basic math operations, so when it came time in Algebra, I discovered how to derive the quadratic equation. An experience I would reckon denied about 99% of today’s college students because of poor training, but an experience performed annually by most high school freshmen in Singapore.
“The real issue is about math content, but few people get that yet. Instead, the arguments center around pedagogy and how the brain works—anything except what are the basic facts, skills and concepts of math that students must master (like they do in Asian countries).”
I agree. Most people talk about a child-centered, discovery process that focuses on “understanding”. In fact, the Everyday Math my 4th grade son is taking does no such thing. It just slows down the pace of coverage and provides a much lower level of mastery for the basics. Look at the EM “HomeLinks” pages. There are typically under 10 simple problems to do. I got angry with my son one night because I thought he was wandering away from his homework before he finished. He had finished it in less than 5 minutes. This is not unusual. EM does not lead to a proper course in algebra in 8th grade without a lot of supplementing. This has nothing to do with how it’s taught. The panel will not get very far unless they first agree upon specific grade-level content and skills goals.
“It’s time to stop cheating this nation’s children out of a first rate math education and own up to the failures of the NCTM standards based programs.”
What NCTM calls “standards” are not standards at all but a set of visions. Real standards are focused, specific, coherent and linked to grades. Real standards are disliked intensely by educationists. NCTM had the bright idea of appropriating the term in order to neutralize it.
I wish I had a nickel for every time administrators have argued that graduates of education colleges understand far more about teaching math than the prominent mathematicians who voice concern over the lack of content in NCTM constructivist math programs.
An important objective for the psychologists on the Mathematics Advisory Panel would be to identify constructivism as “second best” when compared to direct methods of instruction. Requiring students to “discover” knowledge takes far more time, money and effort than public education has to invest.
The results from the conversion to constructivist math are plain – our nation now scores near the bottom instead of at the top. It’s time to stop cheating this nation’s children out of a first rate math education and own up to the failures of the NCTM standards based programs.
Policy makers should give parents the right to choose which method works best for their children.
“…if you read the rest of section 4 you will see a number of other goals that require the expertise of people other than mathematicians, including accomplished psychologists and policy-makers.”
This is correct, but the value placed on issues other than content seems to outweigh it. I’m hoping it doesn’t diminish its importance.
It’s overly simplistic to assume the “real” or only issue at play here is “about math content”.
It’s true that one of the goals of this panel is to make recommendations regarding how students “aquire competence in algebra and to prepare them for higher levels of mathematics”, but if you read the rest of section 4 you will see a number of other goals that require the expertise of people other than mathematicians, including accomplished psychologists and policy-makers.
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