By David C. Geary, Daniel B. Berch, Robert Ochsendorf, Kathleen Mann Koepke

Acquisition of advanced mathematics abilities and Higher-Order arithmetic Concepts specializes in regular and strange studying of complicated mathematics abilities and higher-order math innovations. As a part of the sequence Mathematical Cognition and Learning, this quantity covers contemporary advances within the realizing of children’s constructing skills with whole-number mathematics, fractions, and rational numbers. each one bankruptcy covers those subject matters from a number of views, together with genetic problems, cognition, guideline, and neural networks.

  • Covers cutting edge measures and up to date methodological advances in mathematical considering and learning
  • Contains contributions that increase guide and schooling in those domains
  • Informs coverage geared toward expanding the extent of mathematical talent within the normal public

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Extra info for Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts, Volume 3 (Mathematical Cognition and Learning

Sample text

S (2011) integrated theory of number development to explicitly emphasize the magnitude representation of fractions and regularly provides students the opportunity to experience and compare rational numbers situated on a number line, just as whole numbers are commonly represented. This approach to fractions instruction has proven to be quite effective, with students consistently outperforming students in business-as-usual conditions. , fractions magnitude understanding), struggling students’ performance improves on complex curricular content beyond what is achieved for matched control group students who receive school-based classroom and more traditional interventions.

Across a series of studies there is a clear pattern that emerges: both children and adults are less likely to use inversion shortcuts on multiplication and division inversion problems. Two studies provide further insights into the difference in conceptual knowledge of inversion between additive and multiplicative versions of the concept. Siegler and Stern (1998) conducted a microgenetic study in which 2nd graders who did not spontaneously use the inversion shortcut on addition and subtraction problems were presented with a set of inversion problems once a week for several weeks.

Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14, 445–451. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Neurodevelopmental Disorders as Model Systems for Understanding Typical and Atypical Mathematical Development 67 Page left intentionally blank Chapter 2 The Understanding of Additive and Multiplicative Arithmetic Concepts Katherine M. S. National Research Council on the state of research and knowledge on children’s mathematics learning, Kilpatrick, Swafford, and Findell (2001) concluded that: “The more mathematical concepts they understand, the more sensible mathematics becomes” (p.

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