MEC seminar - 13 October 2021

40 mins Presentation + 20 mins Q&A Associate Professor. Natthapoj Vincent Trakulphadetkrai “Developing Children’s Conceptual Understanding of Multiplication by Creating Story Picture Books” (University of Reading)

Abstract: This talk will describe an on-going research project which sets out to measure the extent to which asking Year 4 (8-9 years old) children to create mathematical story picture books (MSPBs) about multiplication can help to develop their conceptual understanding of the topic.

The use of MSPB in mathematics teaching has been well researched over the past three decades (e.g., Jennings, Jennings, Richey, Dixon-Krauss, 1992; Mink & Fraser, 2005; Van den Heuvel-Panhuizen, Elia, & Robitzsch, 2016). However, these existing studies all treated children as the consumers rather than producers of MSPBs. This study is the first empirical study to investigate the effect of treating children as producers of MSPBs.

Underpinned by Papert’s (1993) theory of constructionism and Kilpatrick et al.’s (2001) notion of conceptual understanding, the study believes that through the process of producing MSPBs, children are actively encouraged to understand in which meaningful context a given mathematical concept or skill can be applied, and how to visually represent them through their own mathematical page illustrations – key elements to foster conceptual understanding.

The study adopted a three-week quasi-experimental design where 46 Year 4 classes (approx. 1,150 8-9 years old children) across 23 primary schools in the southeast of England were randomly assigned to one of the three cohorts: 1) the intervention cohort (mathematical story writing); 2) the comparison cohort 1 (mathematical story reading), and 3) the comparison cohort 2 (“business as usual”). The intervention involved teachers teaching different aspects of multiplications in each of the three weeks (i.e., multiplication as groups of objects; multiplication as arrays; multiplication as scaling). For each of the three weeks, children were expected to create a mini story picture book. Pre-test and post-test specially designed for/by this study to measure children’s conceptual understanding of multiplication were administered right before and after the intervention period to children across all three groups.

Depending on the study’s progress on data coding and analysis over the summer, it is hoped that some preliminary findings will be available to share at the talk.

15 mins: Break

40 mins Presentation + 20 mins Q&A: Prof. Daniel Ansari “How do children learn symbolic representations of number?” (Department of Psychology & Brain and Mind Institute, University of Western Ontario)

Abstract: Humans share with animals the ability to process numerical quantities in non-symbolic formats (e.g., collections of objects). Unlike other species, however, over cultural history, humans have developed symbolic representations (such as number words and digits) to represent numerical quantities exactly and abstractly. These symbols and their semantic referents form the foundations for higher-level numerical and mathematical skills. It is commonly assumed that symbols for number acquire their meaning by being mapped onto the pre-existing, phylogenetically ancient system for the approximate representation of non-symbolic number over the course of learning and development. In this talk I will challenge this hypothesis for how numerical symbols acquire their meanings (“the symbol grounding problem”). To do so, I will present a series of behavioral and neuroimaging studies with both children and adults that demonstrate that symbolic and non-symbolic processing of number is dissociated at both the behavioral and brain levels of analysis. I will discuss the implications of these data for theories of the origins of numerical symbol processing.