Algebraic generalisation strategies: Factors influencing student strategy selection

Abstract

This study reports on the algebraic generalisation strategies used by two fifth grade students along with the factors that appeared to influence these strategies. These students were examined over 18 instructional sessions using a teaching experiment methodology. The results highlighted the complex factors that appeared to influence student strategy use, which included: (a) input value, (b) mathematical structure of the task, (c) prior strategies, (d) visual image of the situation, and (e) social interactions with the teacher and other student. Particular combinations of these factors appeared to increase the predictability of student strategy use. However, the complex nature of the factors influencing these strategies demonstrates the challenges that exist in encouraging students to move toward more sophisticated strategies.

Elementary school students engaging in making generalisation: a glimpse from a Singapore classroom

“…Three of the seven did not mention cases when not all the numbers could be paired up, for example, in cases such as 1 + 3 + 5 + 7 + 9. They were using the explicit strategy described by Lannin, Barker & Townsend (2006). The students who left out the cases when not all the numbers could be paired up, however, were not comprehensive in their use of the explicit strategy.…”

“…The two students were clearly using 1 + 3 + 5 = 3 9 3 = 9 to do 1 + 3 + 5 + 7 = 4 9 4 = 16. They were using the recursive strategy described by Lannin, Barker & Townsend (2006) that is these students needed 1 + 3 + 5 + 7 + 9 + 11 = 6 9 6 = 36 to do 1 + 3 + 5 + 7 + 9 + 11 + 13.…”

“…When asked for an alternate method, all of them were able to do so. They were also able to articulate in verbal language a general method to find the sum of all odd numbers 1 to n. They were using an explicit strategy described by Lannin, Barker & Townsend (2006). Able to perform the near-transfer task…”

“…Two of the 12 students explained that since 1 + 3 + 5 + 7 + 9 = 25 then 11 + 13 + 15 + 17 + 19 = 25 + 5(10) and 21 + 23 + 25 + 27 + 29 = 25 + 5(20) and so on. They were using the chunking strategy described by Lannin, Barker & Townsend (2006).…”

“…Lannin, Barker and Townsend (2006) also lamented that there has been few studies into the factors that influence strategy use in generalisation. Hence, the second aim of the present study was to investigate factors that influence strategy use in generalisation.…”