Students, teachers, and schools are in urgent need of bold, rigorous mathematics learning approaches that are developed and tested in real classrooms—and are proven to get results. EF+Math is hard at work developing such learning approaches and has reached a significant moment in our program. We are excited to share what the research & development project teams (“project teams”) in the EF+Math portfolio have learned and announce which teams will continue into the next two years of our program to continue the development of their promising math learning approaches and conduct evaluations in collaboration with our independent evaluator.
At EF+Math, we are working to understand the promise of mathematics learning approaches in grades 3–8 that combine executive function (EF) skills, conceptual understanding and multi-step problem solving, and equity. We are launching this blog series to share what we are learning about how equity-centered education experiences, based on learning science, and co-designed by educators, researchers, and developers, can dramatically improve mathematics outcomes for Black and Latinx students and all students experiencing poverty.
Our funded EF+Math project teams base their work and hypothesis on existing research and a strengths-based approach that assumes that students from all backgrounds are equally capable of success in mathematics and focuses on the foundational skills that all students have and that underlie learning: specifically, the ability to hold and work with information in one’s mind, the ability to focus attention on what a student deems important and ignore what she deems unimportant, and to be flexible in her thinking. These abilities are referred to as ‘executive functions,’ and are essential assets every student possesses. Executive functions allow students to have agency over their attention, emotions, and behavior to achieve the learning goals they set for themselves.
By examining the intersection of mathematics, executive function, and equity, we are deepening our understanding of what happens when students have opportunities to develop their math-relevant executive function skills. We build more equitable opportunities for students to develop agency and to use that agency to learn anything. We view executive function skills as a path to student agency, such that students can direct their executive function skills toward learning what they deem important to learn.
This blog series will share learnings and profile the project teams continuing to advance their math learning approaches through EF+Math. Our work builds on existing research which demonstrates that because there are no inherent differences in abilities in students from different races/ethnicities or household income levels, observed performance differences are instead likely driven by differences in opportunities to build math abilities given to students from different races/ethnicities or household income levels. We see students of color and students experiencing poverty are not often offered challenging math learning experiences or opportunities to problem solve and reason, both of which are paramount for student learning (e.g., Chunn, 1989; Oakes, 1995; Sorhagen, 2013). Thus, a core and yet addressable issue in mathematics education is the need to reduce inequalities between students’ opportunities to learn and to be given opportunities to be challenged in mathematics. We support project teams that tackle these challenges head-on and aim to provide opportunities for all students to develop their EF skills to learn challenging math. Our portfolio of advancing project teams is well-poised to continue developing math learning approaches which will advance our understanding of these relationships, evaluate what can positively impact student math learning outcomes, and take those that can to sustainably scale their impact.
ANNOUNCEMENT OF EF+MATH ADVANCING PROJECT TEAMS
Throughout Phases 1-3 of EF+Math’s work, we engaged with project teams regularly to understand their progress towards carefully defined prototype and research milestones, and actively directed the work not only towards individual project goals but also towards our overall program goals – bringing our EF+Math team’s perspectives from and expertise in engineering, research, evaluation, and practice.
In Phases 4-5, we will narrow our focus and collaboration to a smaller set of projects. And we will continue to actively direct the work, bringing into this collaborative inclusive R&D effort our evaluation partners at AIR to lead innovative, iterative, inclusive, and equitable evaluation studies. These studies will allow for both continued R&D of prototypes while also gathering stronger evidence of impact on math outcomes and explanatory evidence on the role of EF and student equity experiences. Going forward, this will be a collective effort across our EF+Math program team, AIR, the advancing R&D project teams, and our district partners to reach our program goals.
We are pleased to announce the three project teams continuing as part of EF+Math’s portfolio:
- Fraction Ball:
- A series of movement-based games that make meaningful connections between math learning in the classroom and the schoolyard and provide a playful context for students to engage in embodied rational number learning while strengthening executive function skills (grades 4-5).
- CueThinkEF+ with Pennesota:
- A web-based learning system for facilitating collaborative mathematical discourse and problem-solving with embedded executive function scaffolds to create safe spaces for historically marginalized students to express their ideas and share their thinking and reasonings (grades 6-8).
- An individualized app that combines math fact fluency with executive function skill training through games, offering adaptive pathways and responsive feedback that honors students’ strengths and supports productive struggle (grades 4-5).
The power of this combination of project teams is in (a) the critically important mathematics being targeted by each of the three teams and (b) the different mechanistic approaches they are taking in the design and study of their learning approaches that allow us to maximize our understanding of the role of EFs and equity in mathematics learning. Through multiple rounds of R&D in their first three years of work, these project teams tested their approaches for improving math learning, strengthening and/or supporting EF skills, and also investigated specific hypotheses on the relationships between EF skills and critically important facets of mathematical proficiency. Importantly, they each demonstrated early evidence of the promise of these approaches, an ability to develop and maintain strong district relationships, and simultaneously develop tools and resources for real-world classrooms while generating generalizable knowledge in a truly inclusive and equity-centered way. In future pieces, we will provide more in-depth profiles of each continuing project team. We are excited about each team’s work and the combined collective potential of the total portfolio.
OUR LEARNINGS IN PHASES 1-3
We arrived at our advancement decisions through three years of Inclusive Research and Development and project team progress. Our Insights Report shared findings from the first two years of research and development earlier this year, but our work continues to build on our body of evidence toward impact for Black and Latinx students, and all students experiencing poverty. We aim to highlight some of the exciting work that is continuing to come out of our program.
- Our project teams found improvements in student mathematics and executive functioning skills through participating in the programThe Fraction Ball team showed that students who participated in their approach to fraction learning through movement improved on math assessments compared to students who did not participate (Bustamante, et al., 2022). The most recent version of their approach built on their previous research findings to improve students’ reasoning when using multiple denominators.Further, the MathicSTEAM team found that along with improvements on math scores, students demonstrated improvements on executive function tasks in a math context. These tasks involved flexible thinking, classifying objects into categories, using their working memory, and strengthening their sustained attention.
- Our teams explored the relationships between mathematical identity and belonging for students and their engagement and achievement in math class, finding new ways to incorporate cultural relevance into math learning materials:
The Our Mathematical World team’s approach includes storybooks for 3rd – 5th graders where diverse characters engage with mathematics throughout their everyday lives. After reading the books, students reported that they related to the book characters and could see multiple ways of solving problems represented, which made them feel more comfortable in solving problems themselves (Hornburg, et al., 2023)
- We are learning more about prototype features and effective teaching moves that support how students engage their executive function skills.
Students working within the CueThinkEF+ platform may receive different pop-up messages providing prompts and scaffolds throughout their problem-solving process, based on the team’s research on the role of metacognition and EFs in problem-solving success (Rhodes, et al., 2023).
Another project, Mathematical Thinkers Like Me, found that when students are provided opportunities to work in groups on non-routine tasks, different stages of the problem-solving process may require the use of different executive function skills. Collaboration in problem-solving is associated with strengthened executive function skills, which generates implications for how collaboration is structured and scaffolded during learning (Renninger, et al., 2023).
The Spark Math team’s approach involves several games that recruit executive functions as students play; they worked to define what executive functions look like and sound like in use during these games (Zengilowski, et al., 2023)
These examples showcase that students can benefit from learning about what EFs are, and how they show up in math learning environments. Further, if teachers can understand how executive functions show up in classroom activity, they can notice when and how students are engaging, and provide more targeted support for learning.
While the research findings thus far are promising and exciting, they also serve tangible purposes in informing the next phases of iterative, equitable, and inclusive research and development. The FractionBall, CueThinkEF+, and MathicSTEAM teams will continue to iterate on their approaches while also engaging in larger evaluation studies with our partners from the American Institutes for Research (AIR).
We are proud of the work our entire portfolio and EF+Math community accomplished over the last several years and are optimistic that what emerges from our next phases of work will have the ability to significantly impact students in becoming proficient in math and seeing themselves as mathematicians. Stay tuned for the next blog in our series.
Bustamante, A. S., Begolli, K. N., Alvarez-Vargas, D., Bailey, D. H., & Richland, L. E. (2022). Fraction ball: Playful and physically active fraction and decimal learning. Journal of Educational Psychology, 114(6), 1307–1320. https://doi.org/10.1037/edu0000714v
Chunn, E.W. (1989). Sorting black students for success and failure: The inequity of ability grouping and tracking. In W.D. Smith & E.W. Chunn (Eds.), Black education: A quest for equity and excellence. Routledge
Hornburg, C. B., Mayes, A. S., McElveen, T. L., Powell, S. R., Melzi, G., Prishker, N., Asad, N., Valdivia, I., Andres-Salgarino, M. B., Tran, L. M., Eiland, M. D., Eason, S. H., Schmitt, S. A., & Purpura, D. J. (2023, November). The development of storybooks supporting elementary students’ math identity, executive function, and word problem solving [Poster presentation]. Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Reno, NV.
Oakes, J. (2005). Keeping track: How schools structure inequality. Yale University Press.
Renninger, K. A., Boehim, R., De Dios, M. C., Hogan, M.R., Kyaw, M. H., Michels, A.G., Nakayama, M., Torres, P.E., & Werneck de Souza Dias, H. (2023, August). Exploring collaboration and executive functions in open-ended problem-solving in mathematics [Paper presentation]. The 20th Biennial EARLI Conference for Research on Learning and Instruction, Thessaloniki, Greece. https://www.earli.org/assets/files/EARLI2023-BOA-280823.pdf
Rhodes, S., Bryck, R., Gutierrez de Blume, A. (2023). Exploring factors influencing success in mathematical problem solving. In T. Lamberg & D. Moss (Eds.), Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2) (pp.95-105). University of Nevada, Reno.
Sorhagen, N. S. (2013). Early teacher expectations disproportionately affect poor children’s high school performance. Journal of Educational Psychology, 105(2), 465-477.
Zengilowski, A., Geng, J., Boudaie, S., Katz, B., Shah, P., & Munakata, Y. (2023, August). Making math fun: Developing executive function strategies and math-positivity through gameplay [Poster presentation]. Annual Meeting of the American Psychological Association, Washington, DC.