Where to Start

Research indicates that the initial approach often advocated in standard school mathematics textbooks of performing exercises of algebraic manipulation or collecting like terms of the type 2a + 2a + 3a = 7a is counter-productive and can easily lead to pupil algebraic alienation (Lins et al., 2002; Warren, Trigueros and Ursini, 2016). Pupils should have a firm understanding of structure and patterns within arithmetic which they can then use to form generalisations. Therefore, an alternative approach may be to introduce algebra from a familiar arithmetic scenario, and this can be often received more favourably by learners. A more difficult professional aspect for teachers to solve is that not all learners in a class will be cognitively ready at the same instant in their development to move from the concrete world of arithmetic to the abstract world of algebra.