Chapter 1: Mathematics—The Science of Patterns: The Importance of Patterns in the Teaching and Learning of Mathematics

Preparing mathematics teachers and teacher educators is a complex, “interdisciplinary enterprise requiring knowledge of teaching and learning as well as knowledge of mathematics” (Conference Board of the Mathematical Sciences [CBMS], 2012, p. xi). The level of mathematics knowledge for teaching teachers¹ required to prepare teachers to enter classrooms in schools and teach mathematics has increased exponentially, not withstanding the level of mathematics knowledge required to successfully teach mathematics to diverse student populations with varied mathematical experiences in learning and seeking to understanding mathematics.

Given that mathematics education places emphasis on a high level of mathematical knowledge, inclusive of the preparation of mathematics teacher educators, mathematics teachers, and the teaching of mathematics situated in the context of schools and universities, one need only reflect on the last five decades forward to recognize that an emphasis on mathematics as a study of numbers and number theory was a driving philosophical force on how mathematics was defined and mathematics curricula and teaching were guided. Importantly, the past three decades or so have witnessed a transition to include an increasing emphasis on mathematics as the study and practice of patterns in problem solving.²Halmos (1980) writes that the work of the mathematician “is to solve problems, and that, therefore, what mathematics really consists of is problems and solutions” (p. 519). Therein, mathematics education, the teaching of mathematics that focuses on solving problems, draws forward the importance of understanding patterns in mathematics problem solving.