One thing that most of us remember best about school is our teachers. Thus, when solutions are proposed for reforming American schools in response to critical reports or disappointing test results, teachers are always among the first to be singled out, Scientific American reports. Proposals often turn first to improving the teaching force by focusing on higher quality. For example, in the NCLB [No Child Left Behind] era, considerable emphasis has been placed on a highly qualified teaching force. Districts must certify what percentage of their teachers is highly qualified. However, the states and school districts define what they consider highly qualified, resulting in a great deal of ambiguity. What does it mean to be a highly qualified teacher? The definition of a high-quality mathematics teacher has never been standardized. Therefore, although improving the quality of teachers and teaching is a common cry when we seek to improve schools, there is little agreement and scant empirical evidence that indicates what characteristics define a high-quality mathematics teacher…

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