The Research That Informs Our Work
To maximize our impact on math achievement, we construct our programs on a strong foundation of research. From brain development to effective pedagogy to barriers to learning, we incorporate key findings to continually improve our programs and services, fostering the growth of all types of learners.
Read on to learn about some of the research we find most compelling.
The Power of Developing Early Math Skills
Strong early math skills predict subsequent academic success more reliably than socio-emotional behaviors do.
- Research: School Readiness and Later Achievement, (Developmental Psychology, November 30, 2007)
- Read more: Early Math Skills Predict Later Academic Success, (Phys.org News, April 28, 2011)
The ability of preschoolers to do true counting is a key predictor of later math performance.
- Research: Associations Between Counting Ability in Preschool and Mathematic Performance in First Grade Among a Sample of Ethnically Diverse, Low-Income Children, (Journal of Research in Early Childhood Education, December 13, 2013)
- Read more: Preschoolers’ Counting Abilities Relate to Future Math Performance, Researcher Says, (Science Daily, November 8, 2012)
Counting-on is a refinement of counting-all, and shows that children understand cardinality. It often emerges around age 4, but can be taught if it doesn’t emerge spontaneously.
- Source: Counting all, counting on, counting up, counting down: the role of counting in learning to add and subtract, (International Journal of Primary, Elementary, and Early Years Education, July 30, 2007)
- Read more: The Significance of Counting (Author Q & A with Effie McLellan, 1993)
The more accurately children can estimate where a number should be placed on a number line, the higher they will score on a math achievement exam.
- Research: Development of Numerical Estimation in Young Children, (Child Development, March 23, 2004)
- Read more: Why Guessing is Undervalued, (Time, November 23, 2011)
For children in elementary school, families’ school involvement is a significant predictor of children’s math knowledge. The overall quality of the home learning environment is associated with math achievement.
- Research: Decreasing the SES math achievement gap: Initial math proficiency and home learning environments (Contemporary Educational Psychology, August 2015)
Research-based support for structured math activities and practitioners’ recommendation for embedding math into everyday life can be reconciled.
- Read more: Reviewing the Family Math literature
Science of Learning and Cognitive Development
Brain scans taken at age 8 predict children’s math learning at age 14 better than skills tests and other factors.
- Research: Brain Structural Integrity and Intrinsic Functional Connectivity Forecast 6 Year Longitudinal Growth in Children’s Numerical Abilities, (Journal of Neuroscience, August 19, 2015)
- Read more: Brain scans better forecast math learning in kids than do skill tests, study finds, (Stanford Medicine News Center, August 18, 2015)
The perception-action cycle of the brain shows why math skills are strengthened by handling manipulatives.
- Research: Support of mathematical thinking through embodied cognition: Nondigital and digital approaches, (Cognitive Research, February 20, 2017)
- Read more: What the Perception-Action Cycle Tells Us About How the Brain Learns, (MIND Research Institute blog post, 2017)
Math anxiety triggers the same neural pathways as those triggered when someone experiences physical pain.
- Research: When Math Hurts: Math Anxiety Predicts Pain Network Activation in Anticipation of Doing Math, (PLoS ONE, October 31, 2012)
- Read more: Math Problems Can Trigger Physical Pain, Study Says, (CBC Radio Canada, November 5, 2012)
Math anxiety disrupts cognitive processing by compromising ongoing activity in working memory.
- Research: Math anxiety: Personal, educational, and cognitive consequences, (Current Directions in Psychological Science, October 1, 2002)
- Read more:
Most learned information is forgotten very quickly, unless measures are actively taken to retain it.
- Research: Replication and Analysis of Ebbinghaus’ Forgetting Curve, (PLoS, July 6, 2015)
- Read more:
- Why We Forget Most of the Books We Read, (The Atlantic, January 26, 2018)
- Did That Really Happen? How Our Memories Betray Us, (NPR’s Hidden Brain, December 16, 2019)
The Impact of Emotions and Beliefs on Learning
Growth mindset drives motivation and achievement.
- Research: A National Experiment Reveals Where a Growth Mindset Improves Achievement, (Nature, August 7, 2019)
- Read more: Carol Dweck on How Growth Mindsets Can Bear Fruit in the Classroom, (Association for Psychological Science, October 29, 2019)
Emotion is essential to learning. “It is literally neurobiologically impossible to think deeply about things that you don’t care about.” – Mary Helen Immordino-Yang
- Research: Emotions, Learning and the Brain: Exploring the educational implications of affective neuroscience. (W. W. Norton & Co., 2015)
- Read more:
- To Help Students Learn, Engage the Emotions, (The New York Times, May 4, 2016)
- How to Make Math More Emotionally Engaging for Students, (KQED.org, August 2, 2016)
Positive emotions about math predict subsequent achievement, and positive achievement predicts positive emotions. Similarly, negative emotions about math negatively predict math achievement, and negative achievement predicts negative emotions.
- Research: Achievement Emotions and Academic Performance: Longitudinal Models of Reciprocal Effects, (Child Development, February 8, 2017)
- Read more: Bored Out of Their Minds, (Winter 2017, Harvard Ed. Magazine, Winter 2017)
Having a positive attitude correlates to activation of the hippocampus and predicts math achievement.
- Research: Positive attitude toward math supports early academic success: Behavioral evidence and neurocognitive mechanisms, (Psychological Science, January 24, 2018)
- Read more: Positive attitude towards math predicts math achievement, (Stanford Medicine News Center, January 24, 2018)
Math anxiety is negatively correlated with math performance in young children (1st and 2nd grades) who have strong working memory.
- Research: Math anxiety, working memory and math achievement in early elementary school, (Journal of Cognition and Development, May 8, 2013)
- Read more: Math anxiety causes trouble for students as early as first grade. (UChicago News, September 12, 2012)
Parents with math anxiety can pass it on to their kids when they “help” with homework.
- Research: Intergenerational Effects of Parents’ Math Anxiety on Children’s Math Achievement and Anxiety, (Psychological Science, August 7, 2015)
- Read more: Parents’ math anxiety can ‘infect’ kids, (Science News for Students, September 23, 2015)
Parents who “come to the rescue” and don’t let kids grapple when they’re learning something new can cause them to give up more easily when faced with future challenges.
- Research: Children Persist Less When Adults Take Over, (Child Development, January 23, 2021)
- Read more: A Pre-COVID Education Study with Big Implications for Remote Learning During the Pandemic: When Parents Take Over, Children Give Up Easier, (The 74, February 22, 2021)
High-Impact Instructional Practices
Interleaving multiple skills when practicing results in much better mastery than drilling one skill, then switching to drill another skill.
- Research: Interleaved Practice Improves Mathematics Learning, (Journal of Educational Psychology, 2015)
- Read more: The Interleaving Effect: Mixing It Up Boosts Learning, (Scientific American, August 4, 2015)
Spaced practice (studying information over time) leads to greater retention in the long run.
- Research: Spacing Effects in Learning: A Temporal Ridgeline of Optimal Retention, (Psychological Science, November 1, 2008)
- Read more: “Spacing Effect” calls for an end to last-minute cramming, (The Globe and Mail, February 6, 2011)
The ideal classwork and homework for students is not so easy that it is boring, nor so hard that it is frustrating. This is known as the concept of “flow.”
- Research: Talented Teenagers: The Roots of Success and Failure, (Cambridge University Press, November 13, 1996)
- Read more: Enjoyment of learning crucial for students to excel, (University of Chicago Chronicle, February 3, 1994)
Physically active math lessons improve academic achievement, and the impact persists even after the lessons are ended.
- Physically Active Math and Language Lessons Improve Academic Achievement: A Cluster Randomized Controlled Trial, (Pediatrics, March 2016) and
- Follow-Up Study Investigating the Effects of a Physically Active Academic Intervention, (Early Childhood Education, August 19, 2019)
- Read more:
- Physically Active Math, Spelling Lessons Multiply Academic Success, (CBC Radio Canada, February 24, 2016)
- Why Kids Need to Move, Touch and Experience to Learn, (KQED MindShift, March 26, 2015)
Children’s constructive play and spatial abilities contribute to math word-problem performance.
- Research: The relation between children’s constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students, (Frontiers in Psychology, July 17, 2014)
- Read more: Why Toy Blocks Rock: The Benefits of Construction Play, (Parenting Science blog, 2018)
Best practices for using manipulatives to teach math include: 1) use them consistently, over a long period of time; 2) begin with highly transparent concrete representations and move to more abstract representations over time; 3) avoid manipulatives that resemble everyday objects or have distracting irrelevant features; and 4) explicitly explain the relation between the manipulatives and the math concept.
- Research: What Makes Mathematics Manipulatives Effective? Lessons from Cognitive Science and Montessori Education, (SAGE Open, June 26, 2015)
- Read more: Ask the Cognitive Scientist: Do Manipulatives Help Students Learn? (AFT American Educator, Fall 2017)
Powerful learning often takes place at the periphery, in extracurricular activities and clubs, rather than in core academic classes.
- Research: In Search of Deeper Learning, (Harvard University Press, April 9, 2019)
- Read more:
- Authors Jal Mehta and Sarah Fine on What the Best HS Classrooms Have in Common – Mastery, Identity, and Creativity, (The 74, April 3, 2019)
- Why the Periphery is Often More Powerful Than the Core, (Harvard Ed. Magazine, Winter 2017)
- Investing in Successful Summer Programs: A Review of Evidence Under the Every Student Succeeds Act, (RAND, 2019)