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If you're a fan of the Math Wars, you've heard about the question in the first edition of the EVERDAY MATH K-5 curriculum, "If math were a color, it would probably be ______ because ________." This particular question has probably engendered more ridicule and garnered more notoriety than anything associated with the NCTM Standards of 1989 on, and the progressive reform curricula that emerged from NSF grants in the early 1990s. After Googling on the question, I've concluded that no one on the planet has the slightest idea what could possibly be the point of asking this question. It has resulted in so much negative feedback that it has been dropped from revisions and subsequent editions of EVERYDAY MATHMATICS. Indeed, as recently as last week, Andy Isaacs, an author of the program who works at the University of Chicago Mathematics Project (UCSMP) posted on math-teach at the Math Forum: As for the "If math were a color, ..." question, it appeared in our fir...

Ellen & Robert Kaplan and The Math Circle If you only read one book about mathematics teaching and learning this coming season, let me suggest that it should be OUT OF THE LABYRINTH: Setting Mathematics Free by Robert and Ellen Kaplan, founders of The Math Circle in Cambridge, MA. I had the distinct privilege several years ago of attending a session Bob and Ellen led at Northwestern University's Math Club. We were taken through a short series of problems that led to the main question of the day: is it possible to cover a particular rectangle with non-congruent squares? The way things were led was truly masterful, perhaps the best teaching I've ever seen or experienced. The preliminary questions helped scaffold the main one, but once we entered into trying to solve the main problem, for which most in attendance seemed to believe the answer was "No," very few comments or questions were offered to help us. And yet those "hi...

Recently, there's been an on-going conversation/argument on math-teach@mathforum.org, unusual in its frequently bordering on civility and even some degree of agreement among antagonists, regarding the role of teaching/learning/using the Lowest Common Denominator (LCD) or Least Common Multiple (LCM), which are effectively the same thing, when working with, say, addition and subtraction of fractions. It should be noted that similar issues arise later in working with rational algebraic expressions, particularly when there are polynomials in one or more of the numerators or denominators that can be factored in some of the standard ways that students have worked with previously. But my concern is with something else, specifically the arbitrary way in which many K-5 teachers insist that to add/subtract fractions one MUST find the LCD. Failure to do so often results in all sorts of negative consequences, from stern glances to loss of credit on classwork and tests. On my view, this is a cl...

Something that always blows me away is how teachers will follow books blindly in the face of what should be big warnings from what they know about their own students. All too few teachers are immune to book worship, having been led to believe by their own experience as kids and education students: the math textbook (and its magical authors) knows more than any regular old K-6 teacher. Two cases in point: I was coaching upper elementary teachers in math at a low-performing K-6 school in a district near Detroit a few years ago. They were using the Everyday Math program for the first time. I was asked to guest teach some lessons on fractions in a couple of the 4th and 5th grade classrooms. I noticed that in one lesson, involving pattern blocks, there were three problems for classroom discussion. The first one was clearly needed to establish the relationships amongst the smaller shapes (triangles, parallelograms, trapezoids, that could be fit together to make a hexagon (if you have the sta...

A lot of conversation on one of the lists I read about spiraling vs. mastery in mathematics curricula. Nothing new about that. Just another issue that strikes me as adding more confusion than clarity by creating false dichotomies instead of seeing that most of these things go hand in hand. Frankly, I'm hard-pressed to see how it would be possible to teach or study something as enormous as merely the tiny slice of mathematics we want all students to learn and be able to use in K-12 education (which brings us up to pretty much nothing invented in the field as recently as the 17th century and still excludes enormous amounts of what was already known when Newton and Leibniz were inventing the differential and integral calculus), without doing a reasonable amount of "spiraling" (which is to say that we must revisit already-explored ideas again when students have more sets of numbers to look at, say, or have developed sufficient mathematical maturity to delve deeper into things...

Since several related issues are floating around on various math education lists I'm reading these days, I thought the following problem and what I observed recently with some African-American students would be worth sharing. This problem appeared on an actual ACT exam; it should be noted that it was only #5 of 60 questions in a section of a test which allows 60 minutes total time for those problems: The oxygen saturation level of a river is found by dividing the amount of dissolved oxygen the river water currently has per liter by the dissolved oxygen capacity per liter of the water and then converting to a percent. If the river currently 7.3 milligrams of dissolved oxygen per liter of water and the dissolved oxygen capacity is 9.8 milligrams per liter, what is the oxygen saturation level, to the nearest percent? A) 34% B) 70% C) 73% D) 74% E) 98% First, I want to observe that there are quite a lot of words in the above problem, most of which make it difficult to read ...

I am writing to support David Wasserman's decision to refuse to administer a test in which he did not believe and to decry the way in which he was subsequently dealt with by his superiors. I am a mathematics teacher educator, teacher, and expert on standardized test preparation with more than 30 years' experience working with students on various instruments (e.g., SAT, GRE, ACT, LSAT, and GMAT) as well as with grading state tests from Michigan, New York, and Connecticut. With that experience and expertise in mind, I am deeply troubled by the manner in which this nation has been pushed further and further towards accepting an ill-founded religious belief in the power of (for the most part) multiple-choice, multiple-guess tests to measure not only student achievement, a concept which is at best open to question, but teacher, administrator, school, district, and state competency (not to mention national status when viewing similar international tests such as the TIMSS), in total v...