The Science of Learning

Neuroscientific Learning Principles

Learn more about the neuroscientific approach to optimizing mathematical learning that we have incorporated into our virtual world.

NMAP (National Mathematics Advisory Panel) – Final Report
  • The focus is on the preparation of students for success in algebra.
  • They performed an extensive overview of mathematics teaching in the United States, based on thorough review of pedagogy research literature and surveying of teachers of algebra. In their review of the education research literature, they applied rigorous standards in evaluating experimental designs.
  • A key finding is “Difficulty with the learning of fractions is pervasive and is an obstacle to further progress in mathematics and other domains dependent on mathematics, including algebra.” p. 28

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“Early Predictors of High School Mathematics Achievement”, Siegler et al.

"Early Predictors of High School Mathematics Achievement", Siegler et al. Psychological Science 2012;23(7):691-697.

  • Reviews the British Cohort Study and a similar U.S. study. The British Cohort Study is a longitudinal study involving 3677 children, demonstrating that the best predictor of overall mathematical achievement at the age of 16 is knowledge of fractions at the age of 10.
  • Similar results were found with kids in the U.S., where knowledge of division and fractions best predicted overall mathematics abilities at the age of 16
“Moving Beyond Brownies and Pizza”, Freeman and Jorgensen.

"Moving Beyond Brownies and Pizza", Freeman and Jorgensen. Teaching Children Mathematics, Vol. 21, No. 7. March 2015.

  • Discussion and examples of moving kids from a purely part-whole view of fractions to a view of fractions as numbers. Examples of multiple ways to take advantage of number line representation.
“Unfolding Fraction Multiplication”, Wyberg, Whitney, Cramer, Monson, and Leavitt.

"Unfolding Fraction Multiplication", Wyberg, Whitney, Cramer, Monson, and Leavitt. Mathematics Teaching in the Middle School, Vol 17, No. 5, December 2011/January 2012, pp 289-294.

  • Comparison of teaching fraction multiplication using number lines and area models. Showed evidence for effectiveness of area model in helping students understand why the fraction multiplication algorithm works.
“Multiplication of Fractions and Decimals”, Chapter 17 of “Understanding Numbers in Elementary School Mathematics”, Wu.

"Multiplication of Fractions and Decimals", Chapter 17 of "Understanding Numbers in Elementary School Mathematics", Wu, American Mathematical Society, 2011.

  • Rigorous description of fraction multiplication, with area-model based examples of how to illustrate the concepts.


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