Research

Members of the Laboratory for Research on Mathematical and Cognitive Development have conducted a wide variety of studies over the years.  In all of our work we try to explore the development of children’s thinking, often in the domain of mathematics.  We try to understand the processes, concepts, and representations children use as they solve problem, we study how thinking develops and how children differ from each other as they acquire knowledge and skill, and we seek insights that contribute to the design of instruction so that learning can be optimized.

These are the projects that our lab is currently involved in. If you have any questions about any of these projects, or are interested in acquiring additional information, please contact Jeff Bisanz at jeff.bisanz@ualberta.ca.

Number-line Estimation in Autism Spectrum Disorders (ASD)

In the 1940s, the first accounts of autism spectrum disorders (ASD) included observations about how children with ASD think about math and numbers. Since then, studying how children with ASD learn to think about math as a lense for understanding how children with ASB learn to think more generally, has been largely ignored. To better understand how children with ASB learn to adapt generally, we are collecting data on how children with and without ASD make estimates on a number-line task and how their strategies for estimation change as the number-line ranges change. For example, do children use the same strategies to estimate targets on a 0 - to-1000 range as on a 0-to-100 range?

Count Me In

Count Me In is a longitudinal study focused on the development of diverse mathematical skills in knowledge from preschool (4 years of age) through Grade 4. Data were collected from over 400 children in Manitoba and Ontario from 2004 through 2007. One goal is to discover how cognitive and math–related skills early in childhood are related to later forms of mathematical competence. The project is directed by Jo–Anne LeFevre at Carleton University and funded primarily by the Social Sciences and Humanities Research Council of Canada. For more information, visit Count Me In.

Mathematical Equivalence

The concept of equality is an important component in developing algebraic reasoning in children and algebra is often referred to as the “gatekeeper” to higher math. Many children, however, develop an operator view of the equal sign, interpreting the symbol as meaning, “put the total next” or “add up all the numbers”, instead of a relational view expressing the equality of both sides of the equation. One test of children’s interpretation of the equal sign is performance on equivalence problems (e.g., 2 + 4 + 5 = 3 + __ ). In Canada and the United States, the majority of children from Grades 2–5 fail to solve equivalence problems despite having the requisite addition and subtraction skills. Our research explores children’s performance on these problems and factors related to improving performance.

Mathematical Inversion

The principle of inversion, that a + b – b must equal a, is a fundamental property of conventional arithmetic. Exploring how children use and understand the principle of inversion provides important insights about the development of mathematical thinking and about ways of optimizing instruction. A summary of work in this area can be found in a recent review article in Mathematical Thinking and Learning.

Autism and Mathematical Development

In the 1940s the first accounts of autism spectrum disorders (ASD) included observations about how children with ASD think about math and numbers. Since then, the method of studying how children with ASD learn to think about math as a lens for understanding how children with ASD learn to think more generally, has been largely ignored. Currently we are collecting data on children with high functioning autism (HFA) from 3 to 16 years of age on a variety of tasks. The goals of this exploration of math and autism are twofold: to establish baseline measures of how children with HFA think about math concepts and skills, and to establish some procedures for how we might best study mathematical thinking in children with autism spectrum disorders.