ABSTRACT
This chapter considers shifting and sometimes competing views of mathematical knowledge, including knowledge as a collection of skills, as a set of meaning concepts, and as a process of engaging in a particular way of thinking. It highlights historical and theoretical influences on these views. Procedural knowledge is an important aspect of mathematical knowledge that includes knowledge of symbols, syntax, and algorithms. The notion of relational understanding is similar to that of conceptual knowledge. A counterpart to procedural knowledge, conceptual knowledge "can be thought of as a connected web of knowledge" such that relational understanding is a prominent feature. Psychologists, educators, and mathematicians have long argued for the importance of teaching "meaningful" mathematics, which emphasizes ideas and sense-making over rote memorization. A wide range of instructional strategies have since been forwarded for how to effectively teach mathematics, including the use of concrete representations, games, discourse, investigations, worked examples, and direct instruction.
