3: Enhancing Specialized Content Knowledge for Teaching Mathematics through Authentic Tasks of Teaching in a Professional Learning Environment

Mathematics teacher educators are learning that teaching demands a form of mathematical knowledge identified as specialized content knowledge (Ball et al., 2008). This specialized knowledge is purely mathematical and uniquely used in the work of mathematics teaching. For example, while students commonly solve computation problems, a skilled teacher is able to examine a student’s strategy for solving a problem to determine where the work might be incorrect as well as what the student understands and what the student has yet to learn. Beyond that, he or she can examine a student-invented strategy to determine if the strategy generalizes to all cases within a class of problems.