Approaching algebra through sequence problems: exploring children's strategies

Algebraic thinking is regarded as a high level of mathematical thinking in numbers. In general, the teaching of algebra starts at the end of the primary school or beginning of secondary schools, but it is widely recognised that children often find difficulties in algebra. Here the authors examined 11-years-old children’s pre-algebraic thinking. The authors first discussed their theoretical framework of their study. They particularly used the ‘roots algebra as‘”Strands or ideas which underlie algebraic thinking’ defined by Mason et al who identified four roots of algebra; expressing generality; rearranging and manipulating; possibilities and constraints; generalised arithmetic (Houssart and Evens, 2003, p. 198; Mason et al, 1985). They concluded however that it is difficult to determine the best strategy’ to solve the task (ibid, p. 210), because children’s solutions have both strengths and weaknesses. In general, this study provides us with rich information how children solve patterns and sequences in mathematics. A suggestion for teachers from this study is that they should take opportunities to work alongside children while drawing diagrams or building models in order to observe whether this informs understanding of the structure. …’ (ibid, pp. 212-3)