Current Projects

Procedural and Conceptual abilities in Algebra

Focussing on understanding how knowledge change occurs and how children learn problem solving procedures. This research is concerned with how to improve students learning using basic principles from cognitive and developmental psychology by identifying the role of the interplay between conceptual and procedural knowledge in algebra problem solving among grades 8 and 10.

Embodied Numerical Cognition

Using an individual differences approach to study how cross national and individual differences in finger counting habits - and handedness- correspond to differences in how number quantities are handled by adults. The more recent investigations have ventured into studying situated factors in how we question and test participants about these individual differences. In this project we look at things like number sense, math performance, magnitude judgment, and associations of numbers and space. In terms of the big picture, the more specificity with which we can attach individual differences in finger-counting to real meaningful numerical performance differences, the more evidence that we have that numeracy is embodied by default rather than as a strategic choice made by children.

Children’s Understanding of Word Problems

This project assess the ways in which grade 6 students approach mathematical word problems, specifically problem that require you to use your real world knowledge and whether or not they make use of real world knowledge when completing math questions. We also aim to examine the relation between performance of these realistic word problems and measures of general intelligence, math reasoning, math calculation ability, and reading comprehension.

Math Automaticity and Working Memory

This project explores the correlation between math fact automaticity and working memory capacity in adults. As many schools drift away from teaching elementary school students their basic math facts with the justification that students have access to calculators at all time (joys of cell phones), it explores the added advantage of reaching automaticity. This research attempts to answer the question whether having your math facts memorized are more beneficial than a fun party trick, and can automaticity actually improve complex math skills and working memory capacity.

Mathematics Anxiety

Math anxiety is characterized by feelings of tension surrounding math and has been shown to hinder performance. There is evidence to suggest that math anxiety can impact career choice, and fields of study that have little emphasis on math tend to have the highest prevalence of math anxious individuals. Consequentially, elementary education is one such program, and teachers’ math anxiety has been shown to have negative implications for their students. In an attempt to remediate math anxiety among elementary education students and their future students, our focus is to assess the effects of automatizing basic arithmetic facts on math anxiety among elementary education students.

Individual Differences in Fractions Learning

An ongoing line of research at RCDMC investigates individual differences in how children understand fractions. We build on the assumption that people possess two types of mathematical knowledge: conceptual and procedural. The current study attempts to discover individual differences in how children combine these two types of knowledge, and how this reflects their ability to solve fractions problems.

Children’s Symbolic and Non-Symbolic Representation of Fractions

In conjunction with the subitization study, the RCDMC team is also working on a project that investigates the ability of undergraduate students to represent fractions symbolically. Symbolically-represented fractions are  the operations we all learn in school (e.g., 2/5 + 3/4). They are termed ‘symbolic’ because they use symbols (such as 2/5) to represent a quantity. Non-symbolic fractions equations involve real, tangible objects and events, such as eating 2 of the 5 pieces of pie, or or tiling 3/4 of a floor.

It has been found that young children are capable of symbolic arithmetic with whole numbers, even without training in formal mathematical operations (see Gilmore, McCarthcy, & Spleke, 2007), which suggests that they are doing these operations non-symbolically. Our goal is to determine if undergraduate students use their non-symbolic understanding to solve arithmetic fractions problems, and if there are individual differences in how well students perform these operations.

Automaticity

This project is a collaborative effort with Sherry Mantyka at the Math Learning Centre.  Dr. Mantyka’s previous research has investigated how training adults and children to automatize certain mathematical tasks can lead to better mathematical performance.  Using a computer program designed by Sherry Mantyka and Michael Rabinowitz that helps teach children the rules of exponents, we are designing a randomized control trial experiment that will evaluate the effectiveness of automatized training compared to traditional teaching on children’s mathematical performance regarding exponents.

Children's Understanding of Time

This is a collaborative study with Dr. Christina Thorpe. We are  investigating children’s implicit understanding of time information and their ability to use this information to successfully perform
time-dependent tasks. In other words, when a child learns about a significant event (e.g., when they get to play with a favourite toy, or eat a favourite food), do they associate this event with the time of day? Also, while some event is occurring, do they have a sense of how much time is passing? We are currently starting two studies looking at these two different aspects of time understanding in preschool children. One project will investigate children’s understanding of the time of day, while the other project will study children’s ability to judge short durations of time.