Constructing paths to multiplicative thinking: breaking down the barriers
Creators: name: Breed, Margarita
Publisher: name: RMIT University
Year: 2024

description: Large scale research on numeracy in Years 5 to 9 identified an 'eight-year' range in student achievement almost entirely due to difficulties with multiplication, division, fractions, decimals and proportional reasoning (Siemon, Virgona &amp; Corneille, 2001). This study was supported by an Australian Post-graduate Award Industry (APAI) scholarship as part of a larger project on the development of multiplicative thinking in Years 4 to 8, the Scaffolding Numeracy in the Middle Years Project (SNMY), that was funded by the Australian Research Council and the Victorian and Tasmanian Departments of Education in 2003-2006.<br><br>The study was designed to explore what it would take to address the learning needs at-risk students in relation to multiplicative thinking. A design experiment methodology was adopted as it accommodated an evolving innovative learning environment and simultaneous evaluation of the innovations (Brown, 1992). The sample comprised ‘performance outliers’, that is, students performing well outside what is generally expected: at-risk intervention (ARI), at-risk non-intervention (ARN), and successful (SC) students. Comparison across and between the groups determined the degree of similarity and difference between the students, as well as the impact of the intervention program. Data was collected over three distinct periods: a Pre-Intervention (Pre-I) Phase, an Intervention Phase, and a Post-intervention (Post-I) Phase. During the Pre-I and Post-I Phases, interviews were administered to determine student beliefs about learning mathematics, and the strategies used to solve multiplicative tasks. The Intervention Phase took place over 18 weeks. Three hour-long sessions were held weekly with all ARI students, focussed on building student confidence, developing procedural fluency, working mathematically, and improving communication skills. <br><br>Beginning and end data from the SNMY project revealed that all nine ARI students, who were assessed at the lowest level of the LAF (Zone 1) in the Pre-I Phase, were assessed at Zones 4 or 5 in the Post-I Phase. They had access to a range of efficient strategies to solve multiplicative tasks. In contrast, the five ARN students and eight SC students made little, if any shift, suggesting that the shift in performance of the ARI students was due to their participation in the intervention. In addition to confirming the critical role of beliefs and attitudes and the importance of experiencing success, the interview data suggests that successful intervention is much more dependent on the depth of teacher knowledge for teaching mathematics and the extent to which he or she is able to engage with the emerging identities of students. In particular, the capacity to create mutually endorsing, productive communities of learners appears to be strongly related to the teacher’s own sense of identity and agency, and the extent to which they actually care about their student’s welfare beyond the classroom.<br>As the overall results of the SNMY project suggest that up to 35% of students in Years 7 and 8 do not have the foundation knowledge, skills and understandings to successfully participate in further school mathematics (Siemon et al., 2006), this study has important implications for addressing the learning needs of students at this level and for the professional learning of teachers.