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• Author or Editor: Mark Driscoll
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## What Research Says

When the recent National Assessment of Educational Progress (NAEP) showed that “only about 40 percent of the 17-year-olds appear to have mastered basic fraction computation” (Carpenter et al. 1981). it underscored a problem that is very familiar to teachers of mathematics at all school levels: learning fractions and teaching fractions are two very difficult tasks. Another NAEP conclusion may also be familiar to teachers, but it merits their constant attention: when computational skills with fractions have been mastered by age 13, students have little understanding of them. Once they have forgotten procedures for computing fractions, few teenagers can reconstruct them

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## Implementing the “Professional Standards for Teaching Mathematics”: “The Farther Out You Go…”: Assessment in the Classroom

I can thank a student named Billy for teaching me about the importance of integrating assessment with instruction. It was the early 1970s, and I was teaching in an alternative high school that I had helped found the year before, in a converted warehouse in central St. Louis. Our students were drawn from the city's school-dropout population, and many had not been in a mathematics classroom for years. Luckily, our classes were relatively small, which permitted me on this day to reflect on what Billy had done on a task. I had put five decimals, all between 0 and 1, on the chalkboard and asked the class to rank them in order of number size—a list something Like .06, .607, .6, .6707, .067. Billy anayed them in descending order of length, longest to shortest. I asked, “Which is the number with the smallest value, Billy?” He pointed without hesitation to .6707. “How come?” I asked. This time, Billy thought a bit and seemed to be looking at what he had done through the mists of school memory. “I don“t know. I sort of remember one of my teachers saying, ‘The farther out you go in a decimal, the smaller the number.’”

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## Using Students' Work as a Lens on Algebraic Thinking

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## Research Report: Effective Teaching

In any field, one way to plan for a program's excellence is to study those programs that have been recognized for their excellence and to try to isolate the influential factors. During 1983 and 1984, the Northeast Regional Exchange (NEREX) engaged in “A Study of Exemplary Mathematics Programs.” The study, funded by the National Institute of Education, sought to “identify and describe factors and conditions associated with excellence in precollege mathematics.” Excellence was defined by student outcomes—test scores, awards, consistently high course enrollments, and so on.

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## Principles For Principals: Change in the Mathematics Curriculum

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## Developing Teachers' Knowledge of a Transformations-Based Approach to Geometric Similarity

U.S. students' poor performance in the domain of geometric transformations is well documented, as are their diffi culties applying transformations to similarity tasks. At the same time, a transformations-based approach to similarity underlies the Common Core State Standards for middle and high school geometry. We argue that engaging teachers in this topic represents an urgent but largely unmet need. The article considers what a transformations-based approach to similarity looks like by contrasting it with a traditional, static approach and by providing classroom examples of students using these different methods. In addition, we highlight existing professional development opportunities for teachers in this area.