Foundational Research

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.

The ability of preschoolers to do true counting is a key predictor of later math performance.

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.

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.

Parental Involvement

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-based support for structured math activities and practitioners’ recommendation for embedding math into everyday life can be reconciled.

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.

The perception-action cycle of the brain shows why math skills are strengthened by handling manipulatives.

Math anxiety triggers the same neural pathways as those triggered when someone experiences physical pain.

Math anxiety disrupts cognitive processing by compromising ongoing activity in working memory.

Most learned information is forgotten very quickly, unless measures are actively taken to retain it.

The Impact of Emotions and Beliefs on Learning

Growth mindset drives motivation and achievement.

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

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.

Having a positive attitude correlates to activation of the hippocampus and predicts math achievement.

Math anxiety is negatively correlated with math performance in young children (1st and 2nd grades) who have strong working memory.

Parents with math anxiety can pass it on to their kids when they “help” with homework.

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.

High-Impact Instructional Practices

Interleaving multiple skills when practicing results in much better mastery than drilling one skill, then switching to drill another skill.

Spaced practice (studying information over time) leads to greater retention in the long run.

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.”

Physically active math lessons improve academic achievement, and the impact persists even after the lessons are ended.

Children’s constructive play and spatial abilities contribute to math word-problem performance.

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.

Powerful learning often takes place at the periphery, in extracurricular activities and clubs, rather than in core academic classes.