Monica Wijers

Patterns and Formulas

The previous chapter sketched out the subtle relationship between numerical calculations and algebraic thinking, and suggested ways of introducing young students to algebraic thinking through the ‘world’ of arithmetic. The present chapter elaborates on this topic and specifically addresses the topic of patterns and formulas. In Chapter 1, the domain of patterns and formulas has been identified as an important strand in algebra education. At the heart of this strand is the ability to recognize patterns and structures in problem situations, to capture and generalize this regularity by using the mathematical language of formulas. The work with these formulas takes place within the abstract world of algebra rather than in the tangible world of the problem situation. In terms of Freudenthal’s proposition quoted above, this strand therefore involves both horizontal and vertical mathematization.