Individual differences in the development of children’s arithmetic fluency from grades 2 to 3

Individual differences in the development of children’s arithmetic fluency from grades 2 to 3

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Title: Individual differences in the development of children’s arithmetic fluency from grades 2 to 3

Journal: Developmental Psychology, 57(7), 1067-1079.

https://doi.org/10.1037/dev0001220

Authors: Chang Xu, Jo-Anne LeFevre, Sheri-Lynn Skwarchuk, Sabrina Di Lonardo Burr, Anne Lafay, Judith Wylie, Helena P Osana, Heather Douglas, Erin A Maloney, and Victoria Simms (2021).

What did we ask?

Mathematics involves a complex set of numerical and functional associations. How do the relations among symbolic number skills (i.e., addition, multiplication, and subtraction) change for students from grades 2 to 3?

How did we test it?

Students (n = 244) completed cognitive measures (i.e., vocabulary, working memory, reasoning, and inhibitory control) in grade 2 (aged 7-8 years). They also completed addition and subtraction tasks. One year later, they did addition and subtraction tasks again, as well as measures of multiplication, math knowledge, word-problem solving, algebra, and measurement.

What did we find?

Learning arithmetic seems to be a hierarchical process. When students practice a new math skill (i.e., multiplication), individual differences reflect the integration of the new information with their existing knowledge. By grade 3, subtraction uniquely predicts multiplication, whereas addition does not. This indicates that subtraction captures the highest level of associative integration as the ‘best’ predictor of multiplication. Both subtraction and multiplication predict performance on the measures of mathematics knowledge.

Why is it important?

For integration across arithmetic operations to be successful, students need to have acquired strong addition and subtraction skills prior to being introduced to more advanced operations. Novel arithmetic associations should be learned in the context of existing knowledge because each operation is constructed and consolidated in relation to associations that are already present in the mental network.

Brought to you by Dr. Erin Maloney’s Cognition and Emotion Lab at the University of Ottawa and the Language Learning and Math Achievement Project.

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