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Lortie-Forgues, Hugues; Siegler, Robert S. – Journal of Educational Psychology, 2017
In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…
Descriptors: Arithmetic, Middle School Students, Knowledge Level, Computation
Fuchs, Lynn S.; Malone, Amelia S.; Schumacher, Robin F.; Namkung, Jessica; Hamlett, Carol L.; Jordan, Nancy C.; Siegler, Robert S.; Gersten, Russell; Changas, Paul – Journal of Educational Psychology, 2016
The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multicomponent fraction…
Descriptors: Grade 4, Elementary School Mathematics, Elementary School Students, Cognitive Processes
Siegler, Robert S.; Lortie-Forgues, Hugues – Journal of Educational Psychology, 2015
Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…
Descriptors: Arithmetic, Mathematics Education, Knowledge Level, Hypothesis Testing