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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
Siegler, Robert S.; Lortie-Forgues, Hugues – Grantee Submission, 2017
Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of…
Descriptors: Mathematics Education, Number Concepts, Arithmetic, Fractions
Lortie-Forgues, Hugues; Siegler, Robert S. – Grantee Submission, 2016
In two studies (N's = 55 and 54), we 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, Mathematical Concepts, Knowledge Level, Middle School Students
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
Siegler, Robert; Lortie-Forgues, Hugues – Grantee Submission, 2014
Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…
Descriptors: Numbers, Theories, Individual Development, Cognitive Development
Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S. – Grantee Submission, 2015
Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…
Descriptors: Arithmetic, Fractions, Mathematics Instruction, Mathematical Concepts