Proficiency in mathematics across the United States has become an area of concern as performance on state accountability tests continues to demonstrate that less than 50% of students in 4th and 8th grade are proficient in mathematics (NCES, 2013). With such large numbers of students lacking proficiency in mathematics, systematic interventions that…

This paper presents the results of a study of the structural development of young students' drawings of arrays, and in particular, the significance of using lines instead of drawing individual squares. Students' array drawings were classified on basis of numerical properties, and perceived structural similarities that reflected the spatial…

Using R. S. Siegler's retrieval-required task, 19 male and 22 female third graders were examined before they had been introduced to multiplication in school. Examination of error patterns suggests that the basic assumptions of the distribution-of-associations model need to be tested directly and that the retrieval-required task confounds retrieved…

Third-graders showing negligible mastery of multiplication combinations were randomly assigned to two groups which practiced different subsets of combinations. Retest results were inconsistent with Siegler's (1988) proposal that item-specific computational practice is necessary to change error patterns and promote mastery. Results suggested that…

In one experiment, subjects from third grade through college relied on memory retrieval rather than on counting to solve multiplication problems. An effect of confusing problems on error rates and reaction times indicated the activation of related information. In a second experiment, subjects demonstrated automaticity of fact retrieval on simple…

This paper studies the difficulties children have solving word problems that correspond to one of the situations modeled by multiplication; that of a ratio (e.g. "candies per box"), multiplied by an extensive quantity (e.g. "boxes") (I x E). Sixty children were individually observed solving and repeating I x E problems. Various…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…