More Than Just Symbols: Mental and Neural Representations Related to Symbolic Number Processing in Mathematics

Abstract

The ability for students to understand numbers and other mathematical symbols is a crucial part of success in mathematics. Accordingly, it is important for researchers to understand the nature of symbolic number processing – the connections between a symbol or collection of symbols that convey numerical information (e.g., Arabic digits, arithmetic facts, literal symbols) and their related mental and neural representations. Research that joins the mind and brain sciences with education, such as educational neuroscience work, provides a powerful way to examine students’ symbolic number processing. Much of the research in this area has focused on processing of Arabic numerals in adults and children, with relatively less work on symbols common in intermediate and higher-level mathematics. This dissertation contributes two studies that focus on number processing for symbols beyond those used in basic numeracy, arithmetic facts and literal symbols. The first study uses neuroimaging meta-analysis to examine whether there are brain regions that support both arithmetic and phonological processing. Results suggest that activity in frontal and temporo-occipital brain regions support both types of processing, and that there is recruitment of left temporoparietal areas for each type of processing, but these areas are regionally differentiated. The second study investigates the connection between literal symbols and their mental representations of quantity. Results suggest that there is a cognitive processing cost associated with connecting literal symbols to numerical referents because literal symbols have extant mental referents related to literacy. Taken together, these studies expand the scope of existing research in educational neuroscience related to mathematics learning, to more fully incorporate notions of symbolic processing in intermediate and higher-level mathematics, and contribute to theory building on the connections between symbols in mathematics and their mental and neural representations. These studies also form the basis of my future work in educational neuroscience related to symbolic number processing, which will build and expand on the studies presented herein. Research on symbolic number processing that spans symbols learned in early numeracy (i.e., Arabic numerals) and in intermediate and higher-level mathematics (e.g., arithmetic facts, literal symbols) can facilitate a more complete picture of student learning, thereby supporting students’ mathematical development from early numeracy through advanced mathematics.