The Science of Learning

“What Neuroscience Can Tell Us About Making Fractions Stick”, Schwartz, MindShift, November 21, 2016.

"What Neuroscience Can Tell Us About Making Fractions Stick", Schwartz, MindShift, November 21, 2016.

  • A review of neuroscientific principles of learning and how they can be applied to the teaching of fractions.

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Neuroscientific Learning Principles

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

Summer Slide Research

“Reviews Before and After Vacation”, White, American Education, pp 185-188, 1906.

"Reviews Before and After Vacation", White, American Education, pp 185-188, 1906.

  • Summary of early research demonstrating the phenomenon of summer slide – the loss of academic progress over the summer vacation.
“Summer Math Loss”, Shafer, Harvard Graduate School of Education Newsletter, June 24, 2016.

"Summer Math Loss", Shafer, Harvard Graduate School of Education Newsletter, June 24, 2016.

  • Three Harvard professors summarize various research about the loss of math learning during the summer.
  • On average, students lose approximately 2.6 months of learning in math over the summer.
  • Teachers have to give up weeks of class time, or more, to make up for that loss.
  • Schools and communities have worked to find ways to partner with low-income families to ensure their children keep reading through the summer, however, summer math loss is bigger than reading loss. It has proven difficult to find ways to exercise math skills over the summer that are engaging to children.

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“All Work and No Play? Listening to What Kids and Parents Really Want from Out of School Time”, Duffet et al. Study sponsored by the Wallace Foundation. 2004.

"All Work and No Play? Listening to What Kids and Parents Really Want from Out of School Time", Duffet et al. Study sponsored by the Wallace Foundation. 2004.

  • Organized activities, outside of school, play a valuable role in kids' learning.
  • Low income and minority families are more likely to be dissatisfied with the quality and affordability of options.
  • Kids prefer not to have academic work over the summer.
  • This suggests an enhanced need, over the summer, to provide engaging activities that are mathematical.
“The Effects of Summer Vacation on Achievement Test Scores: A Narrative and Meta-Analytic Review”, Cooper et al., Review of Educational Research, Fall 1996, no 3, pp 227-268.

"The Effects of Summer Vacation on Achievement Test Scores: A Narrative and Meta-Analytic Review", Cooper et al., Review of Educational Research, Fall 1996, no 3, pp 227-268.

  • This is a meta-analysis of 39 prior research studies of the summer slide.
  • The conclusions include:
    • There is a summer slide in math and reading.
    • The slide is worse for math than reading.
    • The slide most deeply affects math computation and spelling (i.e., less on the conceptual and more on the skill).
    • For math, both lower income and middle income families had roughly equal slides (and greater than reading).
    • For reading, lower income families had bigger slides.
    • The negative effects of summer increased with students’ higher grade levels.
“Summer’s Influence on Teaching and Learning All Year”, National Summer Learning Association.

"Summer’s Influence on Teaching and Learning All Year", National Summer Learning Association.

  • This article includes results of a survey of 500 teachers from 16 school districts around the U.S. Conclusions include:
    • 66% of teachers said it takes them at least 2-3 weeks to teach the previous year’s skills at the beginning of a new school year. Of those, more than a third said it takes them 5 weeks or more.
    • 77% of teachers agreed or strongly agreed that students who have participated in a summer learning program are better prepared for school in the fall.
    • 88% said summer learning is an important part of the overall plan to support student success in school.

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“Learning from Summer: Effects of Voluntary Summer Learning Programs on Low-Income Urban Youth”, Multi-year study sponsored they the Wallace Foundation and conducted by RAND Corporation.

"Learning from Summer: Effects of Voluntary Summer Learning Programs on Low-Income Urban Youth", Multi-year study sponsored by the Wallace Foundation and conducted by RAND Corporation.

  • Assessment of district-led, voluntary summer programs in five school districts and measurement of their effects on more than 3,000 students
  • Some results include:
    • Promising evidence that high attendance in one summer led to mathematics benefits that persisted through the following spring.
    • Promising evidence that high attendance in second summer led to mathematics and language arts benefits that persisted.
    • Promising evidence that students with high levels of academic time on task benefited from the programs and that these benefits persisted in both mathematics and language arts.

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“How School Districts Work to Improve Summer Learning with Ed-Tech Programs and Rapid Cycle Pilots: Summer Ed-Tech Programs”, Digital Promise.

"How School Districts Work to Improve Summer Learning with Ed-Tech Programs and Rapid Cycle Pilots: Summer Ed-Tech Programs", Digital Promise.

  • These reports review trials of ed-tech products across three school districts as part of summer programs to reduce the summer slide in reading and/or math. Conclusions include:
    • In order to get students engaged, it is important to recruit parents and students early.
    • In order to maintain students’ motivation, it is useful to provide ongoing incentives. The educators involved recommended, for the future, selecting ed-tech tools that are highly interactive and fun in order to keep students motivated.

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Learning Research

Learn about the latest pedagogy research that we use to develop the games within Fog Stone Isle, 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.
“Using Neuroscience to Improve Learning Fractions”, Salimpoor, webinar recording, July 28, 2016.

"Using Neuroscience to Improve Learning Fractions", Salimpoor, webinar recording, July 28, 2016.

  • A detailed review of ways neuroscientific principles can be applied to teaching.

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“Lessons from Singapore Math: How to Help Students Think, Reason, and Make Sense of Fractions”, Jalalpour, webinar recording, March 21, 2017.

"Lessons from Singapore Math: How to Help Students Think, Reason, and Make Sense of Fractions", Jalalpour, webinar recording, March 21, 2017.

  • A detailed overview of the principles of Singapore math and ways to apply them in the classroom.

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