Materials count: Linear-spatial materials improve young children's addition strategies and accuracy, irregular arrays don't. 2018

Joanna Schiffman, and Elida V Laski
Department of Counseling, Developmental, and Educational Psychology, Boston College, Chestnut Hill, Massachusetts, United States of America.

Children who use advanced arithmetic strategies, such as count-on and decomposition, are more accurate when solving arithmetic problems and are more likely to later have higher levels of math achievement. The present study tested the hypothesis that instruction using linear-spatial representations would activate children's knowledge necessary for use of mental addition strategies and, thus, lead to greater accuracy on addition problems, than instruction using irregular representations of magnitude. As predicted, low-income kindergartners (n = 29) randomly assigned to practice sums up to 10 using materials that instantiated the linear-spatial features of a mental number line (i.e., discrete squares arranged in rows) demonstrated substantially more improvement in solving unpracticed addition problems than children who practiced with irregular materials (i.e., pictures of stars arranged in random arrays). This was particularly true for children with better initial numerical knowledge, which provided support for the idea that existing knowledge was activated. The use of count-on more than doubled from pretest to posttest among children in the linear-spatial condition and this mediated the difference in improvement between conditions. The importance of aligning instructional materials to relevant mental representations-consistent with the Cognitive Alignment Framework for instructional design-is discussed.

UI MeSH Term Description Entries
D008297 Male Males
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D002648 Child A person 6 to 12 years of age. An individual 2 to 5 years old is CHILD, PRESCHOOL. Children
D002657 Child Development The continuous sequential physiological and psychological maturing of an individual from birth up to but not including ADOLESCENCE. Infant Development,Development, Child,Development, Infant
D002675 Child, Preschool A child between the ages of 2 and 5. Children, Preschool,Preschool Child,Preschool Children
D003071 Cognition Intellectual or mental process whereby an organism obtains knowledge. Cognitive Function,Cognitions,Cognitive Functions,Function, Cognitive,Functions, Cognitive
D005260 Female Females
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D017145 Models, Educational Theoretical models which propose methods of learning or teaching as a basis or adjunct to changes in attitude or behavior. These educational interventions are usually applied in the fields of health and patient education but are not restricted to patient care. Educational Models,Instructional Models,Educational Model,Instructional Model,Model, Educational,Model, Instructional,Models, Instructional
D019359 Knowledge The body of truths or facts accumulated in the course of time, the cumulated sum of information, its volume and nature, in any civilization, period, or country. Epistemology

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