Power of ten math program7/9/2023 ![]() Many recent studies have revealed that U.S. Improving teachers’ mathematical knowledge and their capacity to use it to do the work of teaching is crucial in developing students’ mathematical proficiency. There is a substantial body of research on teachers’ mathematical knowledge, and teachers’ knowledge of mathematics is prominent in discussions of how to improve mathematics instruction. It includes familiarity with the common difficul-īecause knowledge of the content to be taught is the cornerstone of teaching for proficiency, we begin with it. Knowledge of students and how they learn mathematics includes general knowledge of how various mathematical ideas develop in children over time as well as specific knowledge of how to determine where in a developmental trajectory a child might be. The mathematical sensibilities they hold matter in guiding their decisions and interpretations of students’ mathematical efforts. In the course of their work as teachers, they must understand mathematics in ways that allow them to explain and unpack ideas in ways not needed in ordinary adult life. Teachers certainly need to be able to understand concepts correctly and perform procedures accurately, but they also must be able to understand the conceptual foundations of that knowledge. Knowing mathematics for teaching also entails more than knowing mathematics for oneself. In our use of the term, knowledge of mathematics includes consideration of the goals of mathematics instruction and provides a basis for discriminating and prioritizing those goals. Mathematical knowledge includes knowledge of mathematical facts, concepts, procedures, and the relationships among them knowledge of the ways that mathematical ideas can be represented and knowledge of mathematics as a discipline-in particular, how mathematical knowledge is produced, the nature of discourse in mathematics, and the norms and standards of evidence that guide argument and proof. In the last two sections, we discuss four programs for developing proficient teaching and then consider how teachers might develop communities of practice. In the next two sections, we first discuss the knowledge base needed for teaching mathematics and then offer a framework for looking at proficient teaching of mathematics. In short, teachers need to muster and deploy a wide range of resources to support the acquisition of mathematical proficiency. Familiarity with the trajectories along which fundamental mathematical ideas develop is crucial if a teacher is to promote students’ movement along those trajectories. Teaching requires the ability to see the mathematical possibilities in a task, sizing it up and adapting it for a specific group of students. A teacher must interpret students’ written work, analyze their reasoning, and respond to the different methods they might use in solving a problem. Used by permission from Lawrence Erlbaum Associates.Īppropriate ways to respond. ![]() It is easy to be an elementary school teacher, but it is difficult to be a good elementary school teacher. ![]() Believe me, it seems to be simple when I talk about it, but when you really do it, it is very complicated, subtle, and takes a lot of time. If you can interweave the two things together nicely, you will succeed…. One thing is to study whom you are teaching, the other thing is to study the knowledge you are teaching. A Chinese teacher on how a profound understanding of fundamental mathematics is attained
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