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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...

In a 2006 article for the Hoover Institution, Barry Garelick wrote: "It was another body blow to education. In December 2004, media outlets across the country were abuzz with the news of the just-released results of the latest Trends in International Mathematics and Science Study (TIMSS) tests. Once again despite highly publicized efforts to reform American math education(some might say BECAUSE of the reform efforts) over the past two decades, the United States did little better than average." [" Miracle Math " by Barry Garelick, EDUCATION NEXT, Fall 2006 (vol. 6, no. 4)]. This example of Mr. Garelick's purple prose, replete with "body blows," and the laughable image of media outlets buzzing over ANY education-related item, is a masterful piece of conservative propagandizing in which he clearly sets the groundwork for a classic Hoover Institution tactic: having it both ways. You see, in 2006, Mr. Garelick was all abuzz, if no one else was, about the sh...