Educational Research AY2015/2016

Students worldwide often face difficulty in generating the functional rule underpinning a linear pattern generalising task. The difficulty can get even more pronounced when the figural pattern depicts a quadratic relationship and is not presented as a sequence of successive configurations. This paper draws on a research study conducted in Singapore that investigated the generalisation of four figural quadratic patterns by 32 Year 8 students (15 boys, 17 girls) from one secondary school. The figural quadratic patterns were presented in two different formats: (i) a sequence of three secessive configurations, or (ii) a single diagram or a sequence of two or three non-successive configurations. The students were distributed into two groups: one assigned to the former format and the other to the latter format. Of the 32 students, 15 of them (7 boys, 8 girls) were given the patterns with successive configurations whilst the remaining 17 (8 boys, 9 girls) worked on patterns with non-successive configurations. This paper focuses on the students’ performance in just one of the four figural quadratic patterns. Specifically, the success rates, the kind of generalising strategies adopted and the kind of rules generated by the two groups of students will be described in greater detail using examples of students’ generalisations. Overall, about 72% of the students in the two groups combined succeeded in generating a correct functional rule, producing a variety of mathematically equivalent rules using a wide spectrum of generalising strategies.