Integration of EF and Math Training
Project Overview
The Integration of EF and Math Training project developed novel digital games and lessons that focus on exercising the foundation skills, such as relational thinking, working memory, inhibition, and cognitive flexibility, that third grade students need to understand fractions.
The project created games and exercises that simultaneously adaptively challenge math and executive function (EF) skills, adjusting difficulty based on performance as students solve problems. The project addresses critical precursor skills that prepare third grade students for more complex fraction concepts and common challenges they will experience throughout the year. There is a strong focus on gaining comfort with fractions on number lines, as well as combining different representations of fractions and fraction estimation on number lines – topics that third grade teachers most frequently requested support on.
Through the EF+Math Program, the team piloted lessons and games with third graders to explore how these activities could be integrated into existing curriculum. Currently, the activities have been modified to be used within the context of Cignition’s high intensity tutoring, which is conducted in small groups with a skilled tutor and a focus on collaborative learning. The activities have been designed to allow students to demonstrate their thinking through multiple solutions, pathways, and strategies.
Project Approach
The Integration of EF and Math Training project’s approach weaves together math, executive function skills, and equity to help students build the foundational understanding and cognitive skills needed to engage confidently with fractions and future mathematical learning.
Mathematics
Games and lessons that strengthen understanding of fraction number lines and connections among different fraction representations, building a strong foundation for grade 3 learning.
Executive Function Skills
Integrates adaptive EF skill challenges to strengthen working memory, inhibition, cognitive flexibility, and relational reasoning during math learning.
Equitable Learning Experiences
Supports all students in accessing challenging mathematics by targeting conceptual prerequisites for future math learning.
Key Insights and Innovations
Students' conceptual understanding of fractions is deepened through an emphasis on relational thinking
The Integration of EF and Math Training project designs activities that support students in simultaneously using working memory skills, inhibition, cognitive flexibility, and relational thinking to solve puzzles related to a variety of fraction representations. This intentional design creates meaningful links between different representations, establishing a more enriched foundation for conceptualizing fractions. Examining relationships between multiple representations helps diversify the way that fractions are represented in the brain, making the information more flexible, which can help students generalize and apply the information to novel math problems.
Focus on precursor concepts builds a strong foundation for fraction understanding
To strengthen students’ understanding of fractions, the project focused on key precursor concepts—equipartitioning and measurement—as well as teacher identified bottlenecks: understanding fractions on a number line and recognizing relationships between different fraction representations. Drawing on learning sciences research and teacher input, the team designed interactive digital lessons that include scaffolding for students to make these foundational concepts more engaging and accessible.
Engaging games connect mathematics and executive function skills
The Integration of EF and Math Training project developed digital games to complement the lessons that integrate math and executive function practice, helping students strengthen cognitive flexibility, working memory, and inhibition while engaging in math learning. One example, Treetop Treasure, challenges students to map fractions on a number line and play “concentration” with multiple representations of given fractions, all within a fun, adaptive environment. Students capture rewards for making progress in the game, and students and teachers receive actionable data on areas for support and celebration. Co-design with educators and expert reviews helped ensure the games are usable, inclusive, and instructionally meaningful.
Research Highlights
Acknowledgments
We gratefully acknowledge the leadership of Cignition, with collaboration from the University of California, Berkeley.
Explore Our R&D Projects
The EF+Math portfolio of R&D projects developed innovative math learning products and advanced research on mathematics learning, executive function skills, and equitable learning experiences using inclusive R&D methods.