{"ID":775,"title":"Why EFs, Math, and Equity?","altTitle":"Why EFs, Math, and Equity?","subtitle":null,"url":"https:\/\/efmathprogram.org\/why-ef-math-and-equity\/","slug":"why-ef-math-and-equity","content":"<!-- wp:acf\/hero-secondary {\"name\":\"acf\/hero-secondary\",\"data\":{\"hero_secondary_headline\":\"Why EFs, Math, and Equitable Math Learning Experiences?\",\"_hero_secondary_headline\":\"field_hero_secondary_hero_secondary_headline\",\"hero_secondary_overline\":\"\",\"_hero_secondary_overline\":\"field_hero_secondary_hero_secondary_overline\",\"hero_secondary_subheading\":\"EF+Math saw potential in understanding how executive function (EF) skills and equitable math experiences interact to support math learning. Prior research showed strong correlations between EF skills and math achievement, the potential promise of explicitly developing EF skills in math, and the importance of equitable learning experiences for improving math outcomes. Through our work, we contributed new understandings of these intersections and what they mean for improving math learning.  \",\"_hero_secondary_subheading\":\"field_hero_secondary_hero_secondary_subheading\",\"hero_secondary_styles_next_section\":\"1\",\"_hero_secondary_styles_next_section\":\"field_hero_secondary_hero_secondary_styles_next_section\",\"hero_secondary\":\"\",\"_hero_secondary\":\"field_hero_secondary_hero_secondary\"},\"mode\":\"edit\",\"id\":\"acf-block-697d5d79f1e3a\"} \/-->\n\n<!-- wp:acf\/venn-diagram {\"name\":\"acf\/venn-diagram\",\"data\":{\"venn_diagram_headline\":\"Explore Our Research Areas\",\"_venn_diagram_headline\":\"field_venn_diagram_venn_diagram_headline\",\"venn_diagram_content\":\"Our research assessed student learning in three areas: EF skills, math learning outcomes, and students' perceptions of their math learning experiences, as a way to measure our focus on equitable math learning. We note that there are many other pathways to design for and study equitable math learning experiences that are not addressed through our research.\\r\\n\\r\\n\\u003cstrong\\u003eClick on each area below to learn more about each area, how the areas relate to each other, and to access actionable insights for supporting student math learning.\\u003c\/strong\\u003e\",\"_venn_diagram_content\":\"field_venn_diagram_venn_diagram_content\",\"venn_diagram_modal_skills_0_color\":\"cyan\",\"_venn_diagram_modal_skills_0_color\":\"field_venn_diagram_venn_diagram_modal_skills_color\",\"venn_diagram_modal_skills_0_headline\":\" Executive Function Skills (EFs)\",\"_venn_diagram_modal_skills_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_headline\",\"venn_diagram_modal_skills_0_subheading\":\"EFs are cognitive processes that all students have, which they use to manage and direct their learning, attention, and behavior. EF+Math focused on 5 EF skills in the context of mathematics learning: cognitive flexibility, inhibitory control, working memory, planning, and metacognition.\\r\\n\",\"_venn_diagram_modal_skills_0_subheading\":\"field_venn_diagram_venn_diagram_modal_skills_subheading\",\"venn_diagram_modal_skills_0_link_boxes_0_headline\":\"We advanced a vision of EFs as culturally relevant, math-related, and dynamic across our work, enabling a paradigm shift in the field.\",\"_venn_diagram_modal_skills_0_link_boxes_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline\",\"venn_diagram_modal_skills_0_link_boxes_0_link\":{\"title\":\"Learn More\",\"url\":\"https:\/\/osf.io\/preprints\/osf\/stzmk_v1\",\"target\":\"_blank\"},\"_venn_diagram_modal_skills_0_link_boxes_0_link\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link\",\"venn_diagram_modal_skills_0_link_boxes_1_headline\":\"Our teams built measures that provide asset-based data on how students engage their EFs in math learning, and enable new understanding of how contextual and environmental factors influence that engagement.\",\"_venn_diagram_modal_skills_0_link_boxes_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline\",\"venn_diagram_modal_skills_0_link_boxes_1_link\":{\"title\":\"Access Our Measures\",\"url\":\"https:\/\/efmathprogram.org\/measures\/\",\"target\":\"\"},\"_venn_diagram_modal_skills_0_link_boxes_1_link\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link\",\"venn_diagram_modal_skills_0_link_boxes\":2,\"_venn_diagram_modal_skills_0_link_boxes\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes\",\"venn_diagram_modal_skills_0_accordion_0_headline\":\"Cognitive Flexibility\",\"_venn_diagram_modal_skills_0_accordion_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_0_accordion_0_overline\":\"\",\"_venn_diagram_modal_skills_0_accordion_0_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_0_accordion_0_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eCognitive flexibility is demonstrated any time a student adjusts their thinking and behavior in response to their environment. In math class, this may look like switching between operations during an arithmetic problem set, or listening to and trying out a classmate\u2019s strategy.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D project teams built opportunities for students to engage their cognitive flexibility skills within math learning by using different notations, representations, operations, and approaches within mathematical tasks. \\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can engage students\u2019 cognitive flexibility skills through their design of activities, such as facilitating a discussion comparing different ideas about a concept or selecting problems which require students to use different strategies and make connections between problem types.\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eGiving multiple ways to access a mathematical task, as well as switching between multiple goals or methods, allows students to have agency in their own learning by selecting the strategies that make sense to them in each problem situation.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe SparkMath team created a game called \\u003ca href=\\u0022https:\/\/saga.org\/equivacards-the-fun-math-card-game-for-fluency-blog\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eEquivacards\\u003c\/a\\u003e that uses rules similar to those of UNO while engaging students\u2019 algebraic reasoning and flexibility with mathematical expressions and variables. The team studied how students engaged their cognitive flexibility skills and other EFs while playing the game, and determined which game scenarios enabled them to engage these skills effectively. Studies also showed positive benefits for students\u2019 math-related affect and engagement from playing the games (\\u003ca href=\\u0022https:\/\/efmathprogram.org\/resource\/the-role-of-educational-games-as-an-instructional-context-to-promote-executive-function-processes-in-mathematics-education\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eWebb, 2023\\u003c\/a\\u003e). \\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_0_accordion_0_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_0_accordion_1_headline\":\"Inhibitory Control \",\"_venn_diagram_modal_skills_0_accordion_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_0_accordion_1_overline\":\"\",\"_venn_diagram_modal_skills_0_accordion_1_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_0_accordion_1_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eInhibitory control is used to ignore distracting information (and classroom distractions, too!), and focus on relevant information for the task at hand. In math class, this can involve selecting appropriate strategies to solve a problem, choosing which information and context is necessary to interpret an answer, and focusing on key ideas in peers\u2019 thinking.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D Project teams built opportunities for students to engage their inhibitory control skills in multiple ways, such as staying focused when playing games with shifting rules and goals, or when determining which information is relevant to solve open-ended tasks.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can help students engage their inhibitory control by acknowledging distractions and helping students re-focus on the task at hand. Distractions arise at many processing levels: sensory distractions, such as peer behavior; contextual distractions, such as irrelevant information in word problems; and conceptual distractions, such as a previously used strategy that is insufficient for the current problem.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eInhibitory control skills are often celebrated or acknowledged when students exhibit white-normative behaviors, such as being quiet in class. Rather than trying to control students' behavior, build the capacity to recognize student agency in using inhibitory control. For instance, notice how a student chooses to engage in classroom discussions based on their learning goals for the day.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe Mathematical Thinkers Like Me team used a platform in which students work collaboratively on math problems to advance researchers\u2019 understanding of what inhibitory control skills look like during problem solving using qualitative coding of student activity - a previously unexplored approach to research. Participating students demonstrated inhibitory control in complex geometry tasks by ignoring visual cues and using geometric rules instead, ceding control of the tools when asked by a peer, suppressing unsuccessful strategies and trying new ones, and staying engaged in team efforts (\\u003ca href=\\u0022https:\/\/flr.journals.publicknowledgeproject.org\/index.php\/journal\/article\/view\/1371\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eRenninger et al, 2025\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_0_accordion_1_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_0_accordion_2_headline\":\"Working Memory\",\"_venn_diagram_modal_skills_0_accordion_2_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_0_accordion_2_overline\":\"\",\"_venn_diagram_modal_skills_0_accordion_2_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_0_accordion_2_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eWorking memory is the ability to hold and manipulate information in the mind to achieve a task; students\u2019 working memory capacity - the amount of information they can hold in mind - increases naturally with development and also can be improved with practice. In math, students use working memory to hold numbers in mind while performing calculations, remember multiple steps in a problem solving process, or keep track of different pieces of information needed to solve a word problem.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D project teams focused on increasing and supporting working capacity in the context of mathematics, including through: increasing the amount of items students have to hold in their working memory during fluency games; providing scaffolds to offload some information from working memory while managing new information; and using their working memory to listen, understand, and respond to others in discussions while also considering their own ideas.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eStrong working memory skills support current math skills and also enable future math learning, which is why it is so important to provide opportunities for students to practice and improve working memory while doing math (\\u003ca href=\\u0022https:\/\/www.danamillercotto.com\/uploads\/4\/7\/7\/2\/47725475\/zhang_miller-cotto___jordan__2023_.pdf\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eZhang et al, 2023\\u003c\/a\\u003e).\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eStudents are better able to engage their working memory skills when they are more familiar with the materials being used (e.g., \\u003ca href=\\u0022https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC10348702\/pdf\/nihms-1860124.pdf\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eNiebaum \\u0026amp; Munakata, 2023\\u003c\/a\\u003e). To help students increase their working memory during math tasks, teachers can select culturally relevant tasks and ensure students receive ample exposure to the mathematical symbols and notations required in the curriculum.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe MathicSTEAM team found a strong correlation between math-embedded working memory (\\u003ca href=\\u0022https:\/\/efmathprogram.org\/resource\/on-the-relationship-of-math-and-executive-functions\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eBuschkuehl et al., 2024\\u003c\/a\\u003e) and arithmetic fluency, as well as significant improvements on multiple working memory tasks as a result of playing games that simultaneously train EFs and fact fluency (Feng et al, 2022). \\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_0_accordion_2_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_0_accordion_3_headline\":\"Planning \",\"_venn_diagram_modal_skills_0_accordion_3_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_0_accordion_3_overline\":\"\",\"_venn_diagram_modal_skills_0_accordion_3_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_0_accordion_3_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003ePlanning, in both EFs and mathematical terms, is the ability to think several steps ahead while solving a complex problem, and anticipate whether a chosen strategy will lead to a desired solution. In math learning, students use planning skills when they are deciding how to tackle a task or open-ended problem, such as determining what to do first, what information they might need, and how they will know when they have achieved their goal.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D project teams promoted planning by: assigning problems with specific, non-routine goals, such as challenging students to land on a specific score in a game; including an explicit step for students to explore and understand what new problems are asking before starting to solve them; or asking students to reflect on their plans and identified strategies during and after solving problems.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can modify almost any math game to incorporate planning by providing a target score instead of the traditional \u201chighest score wins,\u201d and by making the game collaborative so students jointly plan their strategy. During problem solving practice, teachers can assign tasks that lack clear strategies, so students can exercise their agency to choose and evaluate their own strategies.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe end goal of planning is not necessarily to carry out the plan regardless of shifts in circumstances or new ideas. As in life, plans in math need to adjust based on what students learn along the way! The CueThinkEF+ team \\u003ca href=\\u0022https:\/\/efmathprogram.org\/project\/cuethinkef\/\\u0022 rel=\\u0022noopener\\u0022\\u003ebuilt supports for student planning\\u003c\/a\\u003e into their problem solving platform and encouraged students to modify their plans as they tried strategies and learned more about the problem. Reflecting on how plans changed and why can be just as useful as creating a plan in the first place.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThere are a few tests of planning skills that have been predominantly used in cognitive science research, but these tests may not accurately capture the unique ways planning skills are engaged within a math learning context. To address this, the Fraction Ball team built a new game-based assessment to understand students\u2019 planning skills while solving rational number problems. They found that this new measure can provide insight into planning in a similar way to the traditional tasks, while also gathering information about students\u2019 understanding of the math content knowledge (\\u003ca href=\\u0022https:\/\/scholarspace.manoa.hawaii.edu\/server\/api\/core\/bitstreams\/b6699b64-3087-4e44-997d-a83573b2582a\/content\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eLopez et al., 2025\\u003c\/a\\u003e). \\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_0_accordion_3_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_0_accordion_4_headline\":\"Metacognition\",\"_venn_diagram_modal_skills_0_accordion_4_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_0_accordion_4_overline\":\"\",\"_venn_diagram_modal_skills_0_accordion_4_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_0_accordion_4_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eMetacognition is reflecting on one\u2019s own thinking\u00a0 \u2013 an important skill in and out of the classroom. In mathematics, metacognition allows students to evaluate their own learning, effort, and skills while in the middle of a problem or over the course of a year.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D teams supported students in developing metacognitive skills through opportunities to: set and evaluate their own learning goals; compare problem solving strategies and their relative effectiveness in different contexts; and reflect on and improve their collaboration skills when working with peers.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eHistorically, students have been taught to apply procedures without making sense of the conceptual mathematics behind them. Educators now know that teaching sense-making is key to developing a deep understanding of math content topics (e.g., Rittle-Johnson \\u0026amp; Siegler, 1999; \\u003ca href=\\u0022https:\/\/www.nctm.org\/PtA\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eNCTM 2014\\u003c\/a\\u003e), and EF+Math researchers are going one step further: helping students reflect on and direct their own mathematical learning.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003ePracticing metacognition can build students' agency to understand how they learn best and to advocate for the learning opportunities they need. Teachers can incorporate metacognitive practice into any mathematical activity by asking students to reflect on their approach, how it worked, whether they adjusted it, and what they learned as they worked through the problem (e.g. \\u003ca href=\\u0022https:\/\/www.landmark.edu\/research-and-training\/blog\/combine-executive-function-scaffolds-metacognitive-prompting-and-problem-solving-questions-to-spark-math-learning-for-all-students\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eBryck, 2024\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe CueThink team found that practicing metacognitive reflection can positively impact the extent to which students solve problems correctly and their ability to demonstrate conceptual understanding of content topics. In addition, findings suggest that increasing metacognitive skills can minimize the impact of math anxiety and other math beliefs on student performance (\\u003ca href=\\u0022https:\/\/files.eric.ed.gov\/fulltext\/ED658385.pdf\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eRhodes, et al., 2023)\\u003c\/a\\u003e.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_0_accordion_4_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_0_accordion\":5,\"_venn_diagram_modal_skills_0_accordion\":\"field_venn_diagram_venn_diagram_modal_skills_accordion\",\"venn_diagram_modal_skills_1_color\":\"blue\",\"_venn_diagram_modal_skills_1_color\":\"field_venn_diagram_venn_diagram_modal_skills_color\",\"venn_diagram_modal_skills_1_headline\":\"Math Learning\",\"_venn_diagram_modal_skills_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_headline\",\"venn_diagram_modal_skills_1_subheading\":\"Math learning is a social and cultural activity that involves understanding mathematical content and developing mathematical practices. Success in math learning is assessed through day-to-day engagement in mathematical activities and overall mathematics achievement. EF+Math attended to each of these facets in order to advance more equitable mathematics learning experiences for students. \",\"_venn_diagram_modal_skills_1_subheading\":\"field_venn_diagram_venn_diagram_modal_skills_subheading\",\"venn_diagram_modal_skills_1_link_boxes_0_headline\":\"EF+Math project teams explicitly designed their instructional materials to integrate principles from learning science research that articulate how mathematics learning happens within the brain.\",\"_venn_diagram_modal_skills_1_link_boxes_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline\",\"venn_diagram_modal_skills_1_link_boxes_0_link\":{\"title\":\"See Our Products\",\"url\":\"https:\/\/efmathprogram.org\/projects\/\",\"target\":\"\"},\"_venn_diagram_modal_skills_1_link_boxes_0_link\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link\",\"venn_diagram_modal_skills_1_link_boxes_1_headline\":\"In addition to our individual impact studies, we conducted analyses to explore interactions between the design principles in our portfolio of learning products and how they supported student math learning. \",\"_venn_diagram_modal_skills_1_link_boxes_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline\",\"venn_diagram_modal_skills_1_link_boxes_1_link\":{\"title\":\"Read Our Research\",\"url\":\"https:\/\/efmathprogram.org\/resource\/efmath-competitive-product-analysis\/\",\"target\":\"_blank\"},\"_venn_diagram_modal_skills_1_link_boxes_1_link\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link\",\"venn_diagram_modal_skills_1_link_boxes\":2,\"_venn_diagram_modal_skills_1_link_boxes\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes\",\"venn_diagram_modal_skills_1_accordion_0_headline\":\"Math Practices\",\"_venn_diagram_modal_skills_1_accordion_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_1_accordion_0_overline\":\"\",\"_venn_diagram_modal_skills_1_accordion_0_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_1_accordion_0_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eMathematical practices are the activities and skills that are used to do mathematics; students need opportunities to develop these practices across all content topics and grade levels.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eR\\u0026amp;D Project teams within EF+Math emphasized mathematical practices that have been identified as pivotal for accessing more advanced levels of proficiency, such as: problem solving, discourse, and peer collaboration. Teams studied how these practices were developed and used within their focal content topics and math learning environments.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eWhile specific mathematical practices have been identified as part of national standards over the years (such as \\u003ca href=\\u0022https:\/\/www.thecorestandards.org\/Math\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eCommon Core State Standards, 2010\\u003c\/a\\u003e; NCTM, 2009), research continues to identify and study additional types of mathematical practices. Building more examples of how mathematical practices show up across various mathematics learning environments and contexts allows us to better identify and support student brilliance.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can pair instructional goals for math content topics with goals for developing mathematical practices to ensure they are planning for these practices in their activities. For example, teachers can support students\u2019 development of discourse skills by intentionally designing tasks that can be solved with multiple strategies and having students discuss their strategic approaches with peers.\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eOne R\\u0026amp;D Project team investigated how students' cognitive and collaborative engagement shifted throughout different stages of problem solving. They found that students engaged their EFs more during \u201cexploration\u201d stages compared to later stages of problem solving, and that task structure strongly influences how students engage. Notably, findings demonstrate that student problem solving skills differ when working individually, compared to working collaboratively in groups (\\u003ca href=\\u0022https:\/\/flr.journals.publicknowledgeproject.org\/index.php\/journal\/article\/view\/1371\/1339\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eRenninger, et al., 2025\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_1_accordion_0_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_1_accordion_1_headline\":\"Math Content Topics\",\"_venn_diagram_modal_skills_1_accordion_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_1_accordion_1_overline\":\"\",\"_venn_diagram_modal_skills_1_accordion_1_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_1_accordion_1_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eMath content topics are the specific knowledge, concepts, and skills that students must understand and apply to achieve mathematical proficiency and overall achievement. Content topics are grouped to show how these ideas build upon one another across grades to reach this end goal (e.g., \\u003ca href=\\u0022https:\/\/www.thecorestandards.org\/Math\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eCommon Core State Standards for Mathematics, 2010\\u003c\/a\\u003e; \\u003ca href=\\u0022https:\/\/www.nctm.org\/Publications\/Essentials-Made-Easy\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eNational Council of Teachers of Mathematics, n.d.\\u003c\/a\\u003e).\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D project teams targeted content topic areas critical to unlocking access to advanced mathematics understandings and overall success in mathematics learning: fluency of operations, rational numbers, ratios and proportions, and more. Each team studied key ideas within their focal content topic and designed their interventions to address common challenges students face when learning these concepts.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eGrade-appropriate math topics were identified through years of research, and evidence shows that connecting new math concepts to what students already know helps them build deeper understanding. For example, students learn multiplication more effectively when it's connected to their existing knowledge of addition and grouping. Some content topics are well-studied, with clear implications for how these ideas should be taught to students. For example, understanding rational numbers can be supported through manipulatives and number line representations to engage students in reasoning about magnitude (see our \\u003ca href=\\u0022https:\/\/efmathprogram.org\/resources-for-educator-practice\/\\u0022 rel=\\u0022noopener\\u0022\\u003erepository\\u003c\/a\\u003e for more detail on this content topic and other actionable, research-backed insights for educator practice).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eEF+Math R\\u0026amp;D Project teams studied the role of fact fluency when building proficiency with operations and numbers. This foundational elementary content topic builds into more advanced number systems in later grades, along with algebraic reasoning. One team used clickstream data gathered while students played fluency games to identify challenges students faced in their understanding and \\u003ca href=\\u0022https:\/\/efmathprogram.org\/project\/mathicsteam\/\\u0022 rel=\\u0022noopener\\u0022\\u003etailored the problems they worked on to provide scaffolded practice\\u003c\/a\\u003e through these concepts.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_1_accordion_1_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_1_accordion_2_headline\":\"Math Achievement \",\"_venn_diagram_modal_skills_1_accordion_2_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_1_accordion_2_overline\":\"\",\"_venn_diagram_modal_skills_1_accordion_2_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_1_accordion_2_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eMathematics achievement means how well students perform on tests and other measures of their math knowledge across different topics. It is used to compare student performance across schools, districts, or states, often using standardized tests.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThroughout the studies of learning products in the EF+Math portfolio, mathematics achievement data was gathered as a metric of potential long-term impacts, focusing on math course grades and standardized test scores.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eImproving students\u2019 overall mathematical achievement requires improvements in intermediary mathematics learning outcomes, such as engagement, increased or improved use of mathematical practices, and development of content knowledge or skills within a particular topic. Because of this complexity, research has not yet identified an overarching pathway for systematically improving mathematics achievement for all students.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eMath learning products rarely improve student achievement on their own\u2014and this is especially true for supplemental resources (e.g. \\u003ca href=\\u0022https:\/\/edworkingpapers.com\/sites\/default\/files\/Tutoring%20Meta-Analysis%20Oct%202024_unblinded.pdf\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eKraft, et al., 2020\\u003c\/a\\u003e). However, these products can improve how teachers teach and how students experience learning math. That is why it is crucial for math curricula to be based on research on how students learn and be practical to use in real classrooms (see how we achieved these goals through our \\u003ca href=\\u0022https:\/\/efmathprogram.org\/inclusive-research-development-and-evaluation-toolkit\/\\u0022 rel=\\u0022noopener\\u0022\\u003einclusive R\\u0026amp;D processes\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eWhile improving math test scores is difficult, it is still an important measure of student learning. Some of our teams saw promising results on achievement: schools that used \\u003ca href=\\u0022https:\/\/efmathprogram.org\/project\/fraction-ball\/\\u0022 rel=\\u0022noopener\\u0022\\u003eone learning product\\u003c\/a\\u003e consistently achieved higher scores on a measure of rational number understanding across multiple studies, and schools that used \\u003ca href=\\u0022https:\/\/efmathprogram.org\/project\/cuethinkef\/\\u0022 rel=\\u0022noopener\\u0022\\u003eanother product\\u003c\/a\\u003e achieved higher scores on state standardized tests than schools that did not (see the independent evaluations of EF+Math project teams\u2019 math learning products \\u003ca href=\\u0022https:\/\/efmathprogram.org\/project\/american-institutes-for-research\/\\u0022 rel=\\u0022noopener\\u0022\\u003ehere\\u003c\/a\\u003e). \\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_1_accordion_2_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_1_accordion_3_headline\":\"Math Engagement \",\"_venn_diagram_modal_skills_1_accordion_3_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_1_accordion_3_overline\":\"\",\"_venn_diagram_modal_skills_1_accordion_3_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_1_accordion_3_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eMath engagement refers to how invested a student is, both cognitively and socially, in learning math. This includes visible participation, such as speaking up in class, as well as less visible signs like focused thinking, interest, and motivation.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eStudent engagement is an essential component of creating powerful math learning experiences, including developing students\u2019 abilities to manage their own engagement. Across EF+Math Program efforts, studies gathered qualitative engagement data through logs, surveys, and interviews, emphasizing the importance of educator and student perspectives.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003ePeople may define or measure engagement in different ways, making it challenging to build a shared understanding. Regardless of the measurement approach, it is important to avoid labeling children based on their engagement and instead emphasize descriptive data on \\u003c\/span\\u003e\\u003ci\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003ehow\\u003c\/span\\u003e\\u003c\/i\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003e students engage in math learning.\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can support increased engagement in mathematics learning by incorporating opportunities for students\u2019 individual choice for activities or tasks, authentically connecting the mathematics content and contexts to student interests or cultures, or providing students with routines and strategies to regulate their engagement and have agency over their learning.\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe Our Mathematical World project team found that elementary students were highly engaged in math learning when supported by storybooks depicting mathematics in use in real world scenarios, as well as discussions of \u201cbios\u201d which demonstrate how people use mathematics every day. Teachers reported increases in student questions, enjoyment, and identifying connections between the mathematics content to their own lives (e.g. \\u003ca href=\\u0022https:\/\/efmathprogram.org\/resource\/the-development-of-storybooks-supporting-elementary-students-math-identity-executive-function-and-word-problem-solving\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eHornburg, et al., 2023\\u003c\/a\\u003e)\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_1_accordion_3_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_1_accordion\":4,\"_venn_diagram_modal_skills_1_accordion\":\"field_venn_diagram_venn_diagram_modal_skills_accordion\",\"venn_diagram_modal_skills_2_color\":\"yellow\",\"_venn_diagram_modal_skills_2_color\":\"field_venn_diagram_venn_diagram_modal_skills_color\",\"venn_diagram_modal_skills_2_headline\":\"Math Perceptions\",\"_venn_diagram_modal_skills_2_headline\":\"field_venn_diagram_venn_diagram_modal_skills_headline\",\"venn_diagram_modal_skills_2_subheading\":\"EF+Math aimed to understand students' math-related perceptions about themselves and their learning experiences, including investigating a wide range of interrelated concepts, like affect, beliefs and identity, sense of belonging, and their classroom context and culture.\",\"_venn_diagram_modal_skills_2_subheading\":\"field_venn_diagram_venn_diagram_modal_skills_subheading\",\"venn_diagram_modal_skills_2_link_boxes_0_headline\":\"EF+Math\u2019s insights led to the creation of professional learning resources to help teachers understand how to leverage EFs in their instruction to develop students\u2019 math identities.\",\"_venn_diagram_modal_skills_2_link_boxes_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline\",\"venn_diagram_modal_skills_2_link_boxes_0_link\":{\"title\":\"Build Your Practice\",\"url\":\"https:\/\/efmathprogram.org\/resources-for-educator-practice\/\",\"target\":\"\"},\"_venn_diagram_modal_skills_2_link_boxes_0_link\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link\",\"venn_diagram_modal_skills_2_link_boxes_1_headline\":\"EF+Math R\\u0026D Project teams explicitly designed their instructional materials to incorporate evidence-backed features that increase students\u2019 positive math learning experiences and perceptions.\",\"_venn_diagram_modal_skills_2_link_boxes_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline\",\"venn_diagram_modal_skills_2_link_boxes_1_link\":{\"title\":\"Read Our Research\",\"url\":\"https:\/\/efmathprogram.org\/resource\/efmath-portfolio-analysis-paper\/\",\"target\":\"_blank\"},\"_venn_diagram_modal_skills_2_link_boxes_1_link\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link\",\"venn_diagram_modal_skills_2_link_boxes\":2,\"_venn_diagram_modal_skills_2_link_boxes\":\"field_venn_diagram_venn_diagram_modal_skills_link_boxes\",\"venn_diagram_modal_skills_2_accordion_0_headline\":\"Affect\",\"_venn_diagram_modal_skills_2_accordion_0_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_2_accordion_0_overline\":\"\",\"_venn_diagram_modal_skills_2_accordion_0_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_2_accordion_0_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eAffect refers to a student's emotional state, including their emotions, attitudes, and dispositions toward math. Affect is closely connected to thinking and learning\u2014it shapes how students perceive their learning experiences, how well they can engage, and how effectively they can use their cognitive skills.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eIn the EF+Math Program, project teams focused on various components of affect in the mathematics learning context, such as math anxiety, math confidence, and enjoyment. We aimed to recognize the real impacts that negative affect can have on student learning, while intentionally supporting increased positive affect, underscoring our belief that all math learning experiences should be joyful.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eAffect influences students\u2019 development of mathematical proficiency, which has implications for long term success in mathematics; in particular, having a positive affect can support productive struggle and perseverance, as well as the development of reasoning and problem solving skills (Kilpatrick, et al., 2001).\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eStudent affect can influence the extent to which they can engage in a learning environment or particular experience. Teachers can promote positive affect (such as increasing students\u2019 confidence in their ability to solve a problem) or decrease negative affect (such as math anxiety) in math learning by creating an environment where mistakes are normalized and used to spur growth and future learning (e.g. rough draft thinking, \\u003ca href=\\u0022https:\/\/www.routledge.com\/Rough-Draft-Math-Revising-to-Learn\/Jansen\/p\/book\/9781625312068\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eJansen, et al., 2020)\\u003c\/a\\u003e.\u00a0\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eElementary students who played Fraction Ball, which integrates playful learning and embodied cognition, reported two key changes: increases in positive math-related emotions and decreases in negative emotions like boredom. Importantly, the students whose positive emotions increased the most also showed the greatest improvements in math performance. This connection suggests that intentionally supporting student affect can enhance mathematics learning (\\u003ca href=\\u0022https:\/\/www.uciscienceoflearning.org\/uploads\/1\/1\/7\/8\/117864006\/buckets_of_fun_fraction_ball.pdf\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eAlvarez-Vargas, et al., 2024\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_2_accordion_0_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_2_accordion_1_headline\":\"Beliefs \\u0026 Identity\",\"_venn_diagram_modal_skills_2_accordion_1_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_2_accordion_1_overline\":\"\",\"_venn_diagram_modal_skills_2_accordion_1_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_2_accordion_1_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eBeliefs \\u0026amp; Identity refers to the various beliefs students hold about their own capabilities to do mathematics, their perceptions of how others see their capabilities, and their beliefs about the discipline of mathematics itself.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe EF+Math Program examined multiple aspects of mathematical beliefs throughout our inclusive R\\u0026amp;D work. Different project teams explored specific facets of beliefs, such as mathematical identities, self-efficacy, perseverance, and effort, depending on their learning product's features and how they expected it to work.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can support positive beliefs and mathematical identities by explicitly affirming the identities students bring to math learning. When teachers help students recognize that their identities and behaviors are brilliant and mathematical, it influences how students engage with others and with math content, creating more opportunities for identity affirmation (e.g. \\u003ca href=\\u0022https:\/\/pubs.nctm.org\/display\/book\/9780873538565\/9780873538565.xml\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eAguirre, et al., 2013\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eResearch shows many ways to categorize students' beliefs about math learning. Because individual studies and learning products often focus on specific beliefs, it's difficult to understand how different beliefs relate to each other. Several EF+Math R\\u0026amp;D project teams created new measures that assess multiple types of math beliefs at once. These measures will enable future research on how different beliefs interact and which beliefs are most important for teachers to support. You can access these measures in our repository to learn more about their development and see findings from studies that used them.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_2_accordion_1_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_2_accordion_2_headline\":\"Sense of Belonging \",\"_venn_diagram_modal_skills_2_accordion_2_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_2_accordion_2_overline\":\"\",\"_venn_diagram_modal_skills_2_accordion_2_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_2_accordion_2_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eA student\u2019s sense of belonging refers to their perception of membership in their mathematics classroom learning community, as well as membership in the general community of people capable of doing mathematics. Belonging sits at the intersection of an individual\u2019s beliefs about themselves and their perceptions of their environment or context.\u00a0\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThere are multiple strategies for specifically increasing students\u2019 sense of belonging within the instructional materials developed as part of the EF+Math program, including explicit activities where students can build relationships with their peers, or other activities which model expanded representations of people who \u201cdo\u201d mathematics.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe extent to which environments are culturally relevant to an individual is deeply connected to their sense of belonging within a space or community. Black and Latino students often do not experience culturally relevant mathematics learning experiences, which can inhibit their sense of belonging and impact the ways they engage with their peers in math class (\\u003c\/span\\u003e\\u003ca href=\\u0022https:\/\/jaamejournal.scholasticahq.com\/article\/18411-on-defense-african-american-males-making-sense-of-racialized-narratives-in-mathematics-education\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eNasir \\u0026amp; Shah, 2011\\u003c\/span\\u003e\\u003c\/a\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eTeachers can support students\u2019 sense of belonging in mathematics by creating learning environments that are inviting and safe, and by actively affirming students\u2019 brilliance and empowerment throughout their teaching and other interactions (Belonging-Centered Instruction, \\u003ca href=\\u0022https:\/\/osf.io\/n7bv2_v1\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eMatthews, et al., 2021a\\u003c\/a\\u003e, \\u003ca href=\\u0022https:\/\/studentexperiencenetwork.org\/wp-content\/uploads\/2021\/10\/SERN_Research-Snapshot_Matthews_102721.pdf\\u0022\\u003e2021b\\u003c\/a\\u003e). For example, teachers can support student choice in math tasks or learn about students\u2019 identities and explicitly connect the mathematics content to relatable and relevant components of their identities.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eResearch is needed to understand the extent to which these experiences actually lead students to feel they belong. Further, analyses that investigate the relationships between belonging and other math-related beliefs can inform how instruction can most effectively support students\u2019 positive experiences in math learning. Spark Math and other EF+Math R\\u0026amp;D project teams developed measures that enable such analyses, laying the groundwork for continued innovation and attention to student belonging in math.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_2_accordion_2_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_2_accordion_3_headline\":\"Classroom Context \\u0026 Culture \",\"_venn_diagram_modal_skills_2_accordion_3_headline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_headline\",\"venn_diagram_modal_skills_2_accordion_3_overline\":\"\",\"_venn_diagram_modal_skills_2_accordion_3_overline\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_overline\",\"venn_diagram_modal_skills_2_accordion_3_content\":\"\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eA learner's perception of their classroom context and culture includes the physical setup of the space, the values and norms within that environment, and the broader context surrounding the learning environment.\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eOnly some EF+Math R\\u0026amp;D project teams collected data on student perceptions of classroom culture within their studies. However, each team designed its learning products to foster a culturally relevant, asset-based classroom environment. This included messaging and integrated teacher professional learning resources, as well as tasks and features co-designed with students to ensure they were culturally responsive, engaging, and affirming\\u003c\/span\\u003e\\r\\n\\r\\n\\u003cb\\u003eKey Takeaways:\\u003c\/b\\u003e\\r\\n\\u003cul\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eLearning does not happen within a bubble - the culture of the mathematics classroom influences interactions between teachers and students. It is essential that mathematics learning, engagement of EFs, and student perceptions of their learning are all seen as culturally dependent. When we can accept the role of culture in learning, we can build more effective math learning environments.\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eCreating classrooms that serve as positive contexts for learning can involve normalizing struggle and mistakes, demonstrating a wide range of uses for mathematical processes, skills, and content, and ensuring that instruction leverages cultural knowledge and lived experiences of students as assets in learning mathematics (e.g. \\u003ca href=\\u0022https:\/\/www.nctm.org\/Standards-and-Positions\/Position-Statements\/The-Intersection-of-Culture-and-Mathematics\/\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eNCTM, 2024\\u003c\/a\\u003e).\\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n \\t\\u003cli style=\\u0022font-weight: 400;\\u0022 aria-level=\\u00221\\u0022\\u003e\\u003cspan style=\\u0022font-weight: 400;\\u0022\\u003eThe Our Mathematical World project team validated a tool that measures students' perceptions of whether their math learning experiences also teach values related to collectivism and social connectedness (\\u003ca href=\\u0022https:\/\/osf.io\/k2hz8\/files\/8bfy4\\u0022 target=\\u0022_blank\\u0022 rel=\\u0022noopener\\u0022\\u003eMcElveen, et al., 2022\\u003c\/a\\u003e). This measure enables future systematic investigation of how this aspect of classroom culture influences mathematics learning. \\u003c\/span\\u003e\\u003c\/li\\u003e\\r\\n\\u003c\/ul\\u003e\",\"_venn_diagram_modal_skills_2_accordion_3_content\":\"field_venn_diagram_venn_diagram_modal_skills_accordion_content\",\"venn_diagram_modal_skills_2_accordion\":4,\"_venn_diagram_modal_skills_2_accordion\":\"field_venn_diagram_venn_diagram_modal_skills_accordion\",\"venn_diagram_modal_skills\":3,\"_venn_diagram_modal_skills\":\"field_venn_diagram_venn_diagram_modal_skills\",\"venn_diagram_modal_cta_headline\":\"Research Relationships\",\"_venn_diagram_modal_cta_headline\":\"field_venn_diagram_venn_diagram_modal_cta_headline\",\"venn_diagram_modal_cta_subheading\":\"Dive deeper into each of our three research areas - EFs, Math Learning, and Math Perceptions - and investigate the relationships between them. \",\"_venn_diagram_modal_cta_subheading\":\"field_venn_diagram_venn_diagram_modal_cta_subheading\",\"venn_diagram_modal_cta_buttons_0_button\":{\"title\":\"Explore Research Relationships\",\"url\":\"https:\/\/efmathprogram.org\/research-relationships\/\",\"target\":\"\"},\"_venn_diagram_modal_cta_buttons_0_button\":\"field_venn_diagram_venn_diagram_modal_cta_buttons_button\",\"venn_diagram_modal_cta_buttons_0_button_style\":\"primary\",\"_venn_diagram_modal_cta_buttons_0_button_style\":\"field_venn_diagram_venn_diagram_modal_cta_buttons_button_style\",\"venn_diagram_modal_cta_buttons\":1,\"_venn_diagram_modal_cta_buttons\":\"field_venn_diagram_venn_diagram_modal_cta_buttons\",\"venn_diagram_modal_cta_image\":\"\",\"_venn_diagram_modal_cta_image\":\"field_venn_diagram_venn_diagram_modal_cta_image\",\"venn_diagram_modal_cta\":\"\",\"_venn_diagram_modal_cta\":\"field_venn_diagram_venn_diagram_modal_cta\",\"venn_diagram_modal\":\"\",\"_venn_diagram_modal\":\"field_venn_diagram_venn_diagram_modal\",\"venn_diagram\":\"\",\"_venn_diagram\":\"field_venn_diagram_venn_diagram\"},\"mode\":\"edit\",\"id\":\"acf-block-697d5d79f2a62\"} \/-->","description":"","objectType":"Page","author":"Linda Ziembko","date":"December 16, 2025","pubDate":"2025-12-16 22:36:10","attachment":{"ID":"211","src":"https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder.png","img":"<img width=\"1200\" height=\"800\" src=\"https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder.png\" class=\"block w-full h-full object-cover object-center relative z-10\" alt=\"\" decoding=\"async\" loading=\"lazy\" srcset=\"https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder.png 1200w, https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder-300x200.png 300w, https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder-1024x683.png 1024w, https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder-768x512.png 768w, https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder-320x213.png 320w, https:\/\/efmathprogram.org\/app\/uploads\/2023\/10\/placeholder-640x427.png 640w\" sizes=\"auto, (max-width: 1200px) 100vw, 1200px\" \/>"},"meta":{"blocks":[{"blockName":"acf\/hero-secondary","attrs":{"name":"acf\/hero-secondary","data":{"hero_secondary_headline":"Why EFs, Math, and Equitable Math Learning Experiences?","_hero_secondary_headline":"field_hero_secondary_hero_secondary_headline","hero_secondary_overline":"","_hero_secondary_overline":"field_hero_secondary_hero_secondary_overline","hero_secondary_subheading":"EF+Math saw potential in understanding how executive function (EF) skills and equitable math experiences interact to support math learning. Prior research showed strong correlations between EF skills and math achievement, the potential promise of explicitly developing EF skills in math, and the importance of equitable learning experiences for improving math outcomes. Through our work, we contributed new understandings of these intersections and what they mean for improving math learning.  ","_hero_secondary_subheading":"field_hero_secondary_hero_secondary_subheading","hero_secondary_styles_next_section":"1","_hero_secondary_styles_next_section":"field_hero_secondary_hero_secondary_styles_next_section","hero_secondary":"","_hero_secondary":"field_hero_secondary_hero_secondary"},"mode":"edit","id":"acf-block-697d5d79f1e3a"},"innerBlocks":[],"innerHTML":"","innerContent":[],"name":"hero-secondary","data":{"hero_secondary":{"headline":"Why EFs, Math, and Equitable Math Learning Experiences?","overline":"","subheading":"<p>EF+Math saw potential in understanding how executive function (EF) skills and equitable math experiences interact to support math learning. Prior research showed strong correlations between EF skills and math achievement, the potential promise of explicitly developing EF skills in math, and the importance of equitable learning experiences for improving math outcomes. Through our work, we contributed new understandings of these intersections and what they mean for improving math learning.  <\/p>\n","styles_next_section":true,"advanced_accordion":null,"advanced_block_options":{"message_field_message":null}}}},{"blockName":"acf\/venn-diagram","attrs":{"name":"acf\/venn-diagram","data":{"venn_diagram_headline":"Explore Our Research Areas","_venn_diagram_headline":"field_venn_diagram_venn_diagram_headline","venn_diagram_content":"Our research assessed student learning in three areas: EF skills, math learning outcomes, and students' perceptions of their math learning experiences, as a way to measure our focus on equitable math learning. We note that there are many other pathways to design for and study equitable math learning experiences that are not addressed through our research.\r\n\r\n<strong>Click on each area below to learn more about each area, how the areas relate to each other, and to access actionable insights for supporting student math learning.<\/strong>","_venn_diagram_content":"field_venn_diagram_venn_diagram_content","venn_diagram_modal_skills_0_color":"cyan","_venn_diagram_modal_skills_0_color":"field_venn_diagram_venn_diagram_modal_skills_color","venn_diagram_modal_skills_0_headline":" Executive Function Skills (EFs)","_venn_diagram_modal_skills_0_headline":"field_venn_diagram_venn_diagram_modal_skills_headline","venn_diagram_modal_skills_0_subheading":"EFs are cognitive processes that all students have, which they use to manage and direct their learning, attention, and behavior. EF+Math focused on 5 EF skills in the context of mathematics learning: cognitive flexibility, inhibitory control, working memory, planning, and metacognition.\r\n","_venn_diagram_modal_skills_0_subheading":"field_venn_diagram_venn_diagram_modal_skills_subheading","venn_diagram_modal_skills_0_link_boxes_0_headline":"We advanced a vision of EFs as culturally relevant, math-related, and dynamic across our work, enabling a paradigm shift in the field.","_venn_diagram_modal_skills_0_link_boxes_0_headline":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline","venn_diagram_modal_skills_0_link_boxes_0_link":{"title":"Learn More","url":"https:\/\/osf.io\/preprints\/osf\/stzmk_v1","target":"_blank"},"_venn_diagram_modal_skills_0_link_boxes_0_link":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link","venn_diagram_modal_skills_0_link_boxes_1_headline":"Our teams built measures that provide asset-based data on how students engage their EFs in math learning, and enable new understanding of how contextual and environmental factors influence that engagement.","_venn_diagram_modal_skills_0_link_boxes_1_headline":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline","venn_diagram_modal_skills_0_link_boxes_1_link":{"title":"Access Our Measures","url":"https:\/\/efmathprogram.org\/measures\/","target":""},"_venn_diagram_modal_skills_0_link_boxes_1_link":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link","venn_diagram_modal_skills_0_link_boxes":2,"_venn_diagram_modal_skills_0_link_boxes":"field_venn_diagram_venn_diagram_modal_skills_link_boxes","venn_diagram_modal_skills_0_accordion_0_headline":"Cognitive Flexibility","_venn_diagram_modal_skills_0_accordion_0_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_0_accordion_0_overline":"","_venn_diagram_modal_skills_0_accordion_0_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_0_accordion_0_content":"<span style=\"font-weight: 400;\">Cognitive flexibility is demonstrated any time a student adjusts their thinking and behavior in response to their environment. In math class, this may look like switching between operations during an arithmetic problem set, or listening to and trying out a classmate\u2019s strategy.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">EF+Math R&amp;D project teams built opportunities for students to engage their cognitive flexibility skills within math learning by using different notations, representations, operations, and approaches within mathematical tasks. <\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can engage students\u2019 cognitive flexibility skills through their design of activities, such as facilitating a discussion comparing different ideas about a concept or selecting problems which require students to use different strategies and make connections between problem types.\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Giving multiple ways to access a mathematical task, as well as switching between multiple goals or methods, allows students to have agency in their own learning by selecting the strategies that make sense to them in each problem situation.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The SparkMath team created a game called <a href=\"https:\/\/saga.org\/equivacards-the-fun-math-card-game-for-fluency-blog\/\" target=\"_blank\" rel=\"noopener\">Equivacards<\/a> that uses rules similar to those of UNO while engaging students\u2019 algebraic reasoning and flexibility with mathematical expressions and variables. The team studied how students engaged their cognitive flexibility skills and other EFs while playing the game, and determined which game scenarios enabled them to engage these skills effectively. Studies also showed positive benefits for students\u2019 math-related affect and engagement from playing the games (<a href=\"https:\/\/efmathprogram.org\/resource\/the-role-of-educational-games-as-an-instructional-context-to-promote-executive-function-processes-in-mathematics-education\/\" target=\"_blank\" rel=\"noopener\">Webb, 2023<\/a>). <\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_0_accordion_0_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_0_accordion_1_headline":"Inhibitory Control ","_venn_diagram_modal_skills_0_accordion_1_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_0_accordion_1_overline":"","_venn_diagram_modal_skills_0_accordion_1_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_0_accordion_1_content":"<span style=\"font-weight: 400;\">Inhibitory control is used to ignore distracting information (and classroom distractions, too!), and focus on relevant information for the task at hand. In math class, this can involve selecting appropriate strategies to solve a problem, choosing which information and context is necessary to interpret an answer, and focusing on key ideas in peers\u2019 thinking.\u00a0<\/span>\r\n\r\n<span style=\"font-weight: 400;\">EF+Math R&amp;D Project teams built opportunities for students to engage their inhibitory control skills in multiple ways, such as staying focused when playing games with shifting rules and goals, or when determining which information is relevant to solve open-ended tasks.\u00a0<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can help students engage their inhibitory control by acknowledging distractions and helping students re-focus on the task at hand. Distractions arise at many processing levels: sensory distractions, such as peer behavior; contextual distractions, such as irrelevant information in word problems; and conceptual distractions, such as a previously used strategy that is insufficient for the current problem.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Inhibitory control skills are often celebrated or acknowledged when students exhibit white-normative behaviors, such as being quiet in class. Rather than trying to control students' behavior, build the capacity to recognize student agency in using inhibitory control. For instance, notice how a student chooses to engage in classroom discussions based on their learning goals for the day.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The Mathematical Thinkers Like Me team used a platform in which students work collaboratively on math problems to advance researchers\u2019 understanding of what inhibitory control skills look like during problem solving using qualitative coding of student activity - a previously unexplored approach to research. Participating students demonstrated inhibitory control in complex geometry tasks by ignoring visual cues and using geometric rules instead, ceding control of the tools when asked by a peer, suppressing unsuccessful strategies and trying new ones, and staying engaged in team efforts (<a href=\"https:\/\/flr.journals.publicknowledgeproject.org\/index.php\/journal\/article\/view\/1371\" target=\"_blank\" rel=\"noopener\">Renninger et al, 2025<\/a>).<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_0_accordion_1_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_0_accordion_2_headline":"Working Memory","_venn_diagram_modal_skills_0_accordion_2_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_0_accordion_2_overline":"","_venn_diagram_modal_skills_0_accordion_2_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_0_accordion_2_content":"<span style=\"font-weight: 400;\">Working memory is the ability to hold and manipulate information in the mind to achieve a task; students\u2019 working memory capacity - the amount of information they can hold in mind - increases naturally with development and also can be improved with practice. In math, students use working memory to hold numbers in mind while performing calculations, remember multiple steps in a problem solving process, or keep track of different pieces of information needed to solve a word problem.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">EF+Math R&amp;D project teams focused on increasing and supporting working capacity in the context of mathematics, including through: increasing the amount of items students have to hold in their working memory during fluency games; providing scaffolds to offload some information from working memory while managing new information; and using their working memory to listen, understand, and respond to others in discussions while also considering their own ideas.\u00a0<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Strong working memory skills support current math skills and also enable future math learning, which is why it is so important to provide opportunities for students to practice and improve working memory while doing math (<a href=\"https:\/\/www.danamillercotto.com\/uploads\/4\/7\/7\/2\/47725475\/zhang_miller-cotto___jordan__2023_.pdf\" target=\"_blank\" rel=\"noopener\">Zhang et al, 2023<\/a>).\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Students are better able to engage their working memory skills when they are more familiar with the materials being used (e.g., <a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC10348702\/pdf\/nihms-1860124.pdf\" target=\"_blank\" rel=\"noopener\">Niebaum &amp; Munakata, 2023<\/a>). To help students increase their working memory during math tasks, teachers can select culturally relevant tasks and ensure students receive ample exposure to the mathematical symbols and notations required in the curriculum.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The MathicSTEAM team found a strong correlation between math-embedded working memory (<a href=\"https:\/\/efmathprogram.org\/resource\/on-the-relationship-of-math-and-executive-functions\/\" target=\"_blank\" rel=\"noopener\">Buschkuehl et al., 2024<\/a>) and arithmetic fluency, as well as significant improvements on multiple working memory tasks as a result of playing games that simultaneously train EFs and fact fluency (Feng et al, 2022). <\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_0_accordion_2_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_0_accordion_3_headline":"Planning ","_venn_diagram_modal_skills_0_accordion_3_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_0_accordion_3_overline":"","_venn_diagram_modal_skills_0_accordion_3_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_0_accordion_3_content":"<span style=\"font-weight: 400;\">Planning, in both EFs and mathematical terms, is the ability to think several steps ahead while solving a complex problem, and anticipate whether a chosen strategy will lead to a desired solution. In math learning, students use planning skills when they are deciding how to tackle a task or open-ended problem, such as determining what to do first, what information they might need, and how they will know when they have achieved their goal.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">EF+Math R&amp;D project teams promoted planning by: assigning problems with specific, non-routine goals, such as challenging students to land on a specific score in a game; including an explicit step for students to explore and understand what new problems are asking before starting to solve them; or asking students to reflect on their plans and identified strategies during and after solving problems.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can modify almost any math game to incorporate planning by providing a target score instead of the traditional \u201chighest score wins,\u201d and by making the game collaborative so students jointly plan their strategy. During problem solving practice, teachers can assign tasks that lack clear strategies, so students can exercise their agency to choose and evaluate their own strategies.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The end goal of planning is not necessarily to carry out the plan regardless of shifts in circumstances or new ideas. As in life, plans in math need to adjust based on what students learn along the way! The CueThinkEF+ team <a href=\"https:\/\/efmathprogram.org\/project\/cuethinkef\/\" rel=\"noopener\">built supports for student planning<\/a> into their problem solving platform and encouraged students to modify their plans as they tried strategies and learned more about the problem. Reflecting on how plans changed and why can be just as useful as creating a plan in the first place.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">There are a few tests of planning skills that have been predominantly used in cognitive science research, but these tests may not accurately capture the unique ways planning skills are engaged within a math learning context. To address this, the Fraction Ball team built a new game-based assessment to understand students\u2019 planning skills while solving rational number problems. They found that this new measure can provide insight into planning in a similar way to the traditional tasks, while also gathering information about students\u2019 understanding of the math content knowledge (<a href=\"https:\/\/scholarspace.manoa.hawaii.edu\/server\/api\/core\/bitstreams\/b6699b64-3087-4e44-997d-a83573b2582a\/content\" target=\"_blank\" rel=\"noopener\">Lopez et al., 2025<\/a>). <\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_0_accordion_3_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_0_accordion_4_headline":"Metacognition","_venn_diagram_modal_skills_0_accordion_4_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_0_accordion_4_overline":"","_venn_diagram_modal_skills_0_accordion_4_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_0_accordion_4_content":"<span style=\"font-weight: 400;\">Metacognition is reflecting on one\u2019s own thinking\u00a0 \u2013 an important skill in and out of the classroom. In mathematics, metacognition allows students to evaluate their own learning, effort, and skills while in the middle of a problem or over the course of a year.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">EF+Math R&amp;D teams supported students in developing metacognitive skills through opportunities to: set and evaluate their own learning goals; compare problem solving strategies and their relative effectiveness in different contexts; and reflect on and improve their collaboration skills when working with peers.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Historically, students have been taught to apply procedures without making sense of the conceptual mathematics behind them. Educators now know that teaching sense-making is key to developing a deep understanding of math content topics (e.g., Rittle-Johnson &amp; Siegler, 1999; <a href=\"https:\/\/www.nctm.org\/PtA\/\" target=\"_blank\" rel=\"noopener\">NCTM 2014<\/a>), and EF+Math researchers are going one step further: helping students reflect on and direct their own mathematical learning.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Practicing metacognition can build students' agency to understand how they learn best and to advocate for the learning opportunities they need. Teachers can incorporate metacognitive practice into any mathematical activity by asking students to reflect on their approach, how it worked, whether they adjusted it, and what they learned as they worked through the problem (e.g. <a href=\"https:\/\/www.landmark.edu\/research-and-training\/blog\/combine-executive-function-scaffolds-metacognitive-prompting-and-problem-solving-questions-to-spark-math-learning-for-all-students\" target=\"_blank\" rel=\"noopener\">Bryck, 2024<\/a>).<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The CueThink team found that practicing metacognitive reflection can positively impact the extent to which students solve problems correctly and their ability to demonstrate conceptual understanding of content topics. In addition, findings suggest that increasing metacognitive skills can minimize the impact of math anxiety and other math beliefs on student performance (<a href=\"https:\/\/files.eric.ed.gov\/fulltext\/ED658385.pdf\" target=\"_blank\" rel=\"noopener\">Rhodes, et al., 2023)<\/a>.<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_0_accordion_4_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_0_accordion":5,"_venn_diagram_modal_skills_0_accordion":"field_venn_diagram_venn_diagram_modal_skills_accordion","venn_diagram_modal_skills_1_color":"blue","_venn_diagram_modal_skills_1_color":"field_venn_diagram_venn_diagram_modal_skills_color","venn_diagram_modal_skills_1_headline":"Math Learning","_venn_diagram_modal_skills_1_headline":"field_venn_diagram_venn_diagram_modal_skills_headline","venn_diagram_modal_skills_1_subheading":"Math learning is a social and cultural activity that involves understanding mathematical content and developing mathematical practices. Success in math learning is assessed through day-to-day engagement in mathematical activities and overall mathematics achievement. EF+Math attended to each of these facets in order to advance more equitable mathematics learning experiences for students. ","_venn_diagram_modal_skills_1_subheading":"field_venn_diagram_venn_diagram_modal_skills_subheading","venn_diagram_modal_skills_1_link_boxes_0_headline":"EF+Math project teams explicitly designed their instructional materials to integrate principles from learning science research that articulate how mathematics learning happens within the brain.","_venn_diagram_modal_skills_1_link_boxes_0_headline":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline","venn_diagram_modal_skills_1_link_boxes_0_link":{"title":"See Our Products","url":"https:\/\/efmathprogram.org\/projects\/","target":""},"_venn_diagram_modal_skills_1_link_boxes_0_link":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link","venn_diagram_modal_skills_1_link_boxes_1_headline":"In addition to our individual impact studies, we conducted analyses to explore interactions between the design principles in our portfolio of learning products and how they supported student math learning. ","_venn_diagram_modal_skills_1_link_boxes_1_headline":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline","venn_diagram_modal_skills_1_link_boxes_1_link":{"title":"Read Our Research","url":"https:\/\/efmathprogram.org\/resource\/efmath-competitive-product-analysis\/","target":"_blank"},"_venn_diagram_modal_skills_1_link_boxes_1_link":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link","venn_diagram_modal_skills_1_link_boxes":2,"_venn_diagram_modal_skills_1_link_boxes":"field_venn_diagram_venn_diagram_modal_skills_link_boxes","venn_diagram_modal_skills_1_accordion_0_headline":"Math Practices","_venn_diagram_modal_skills_1_accordion_0_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_1_accordion_0_overline":"","_venn_diagram_modal_skills_1_accordion_0_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_1_accordion_0_content":"<span style=\"font-weight: 400;\">Mathematical practices are the activities and skills that are used to do mathematics; students need opportunities to develop these practices across all content topics and grade levels.\u00a0<\/span>\r\n\r\n<span style=\"font-weight: 400;\">R&amp;D Project teams within EF+Math emphasized mathematical practices that have been identified as pivotal for accessing more advanced levels of proficiency, such as: problem solving, discourse, and peer collaboration. Teams studied how these practices were developed and used within their focal content topics and math learning environments.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">While specific mathematical practices have been identified as part of national standards over the years (such as <a href=\"https:\/\/www.thecorestandards.org\/Math\/\" target=\"_blank\" rel=\"noopener\">Common Core State Standards, 2010<\/a>; NCTM, 2009), research continues to identify and study additional types of mathematical practices. Building more examples of how mathematical practices show up across various mathematics learning environments and contexts allows us to better identify and support student brilliance.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can pair instructional goals for math content topics with goals for developing mathematical practices to ensure they are planning for these practices in their activities. For example, teachers can support students\u2019 development of discourse skills by intentionally designing tasks that can be solved with multiple strategies and having students discuss their strategic approaches with peers.\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">One R&amp;D Project team investigated how students' cognitive and collaborative engagement shifted throughout different stages of problem solving. They found that students engaged their EFs more during \u201cexploration\u201d stages compared to later stages of problem solving, and that task structure strongly influences how students engage. Notably, findings demonstrate that student problem solving skills differ when working individually, compared to working collaboratively in groups (<a href=\"https:\/\/flr.journals.publicknowledgeproject.org\/index.php\/journal\/article\/view\/1371\/1339\" target=\"_blank\" rel=\"noopener\">Renninger, et al., 2025<\/a>).<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_1_accordion_0_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_1_accordion_1_headline":"Math Content Topics","_venn_diagram_modal_skills_1_accordion_1_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_1_accordion_1_overline":"","_venn_diagram_modal_skills_1_accordion_1_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_1_accordion_1_content":"<span style=\"font-weight: 400;\">Math content topics are the specific knowledge, concepts, and skills that students must understand and apply to achieve mathematical proficiency and overall achievement. Content topics are grouped to show how these ideas build upon one another across grades to reach this end goal (e.g., <a href=\"https:\/\/www.thecorestandards.org\/Math\/\" target=\"_blank\" rel=\"noopener\">Common Core State Standards for Mathematics, 2010<\/a>; <a href=\"https:\/\/www.nctm.org\/Publications\/Essentials-Made-Easy\/\" target=\"_blank\" rel=\"noopener\">National Council of Teachers of Mathematics, n.d.<\/a>).<\/span>\r\n\r\n<span style=\"font-weight: 400;\">EF+Math R&amp;D project teams targeted content topic areas critical to unlocking access to advanced mathematics understandings and overall success in mathematics learning: fluency of operations, rational numbers, ratios and proportions, and more. Each team studied key ideas within their focal content topic and designed their interventions to address common challenges students face when learning these concepts.\u00a0<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Grade-appropriate math topics were identified through years of research, and evidence shows that connecting new math concepts to what students already know helps them build deeper understanding. For example, students learn multiplication more effectively when it's connected to their existing knowledge of addition and grouping. Some content topics are well-studied, with clear implications for how these ideas should be taught to students. For example, understanding rational numbers can be supported through manipulatives and number line representations to engage students in reasoning about magnitude (see our <a href=\"https:\/\/efmathprogram.org\/resources-for-educator-practice\/\" rel=\"noopener\">repository<\/a> for more detail on this content topic and other actionable, research-backed insights for educator practice).<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">EF+Math R&amp;D Project teams studied the role of fact fluency when building proficiency with operations and numbers. This foundational elementary content topic builds into more advanced number systems in later grades, along with algebraic reasoning. One team used clickstream data gathered while students played fluency games to identify challenges students faced in their understanding and <a href=\"https:\/\/efmathprogram.org\/project\/mathicsteam\/\" rel=\"noopener\">tailored the problems they worked on to provide scaffolded practice<\/a> through these concepts.<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_1_accordion_1_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_1_accordion_2_headline":"Math Achievement ","_venn_diagram_modal_skills_1_accordion_2_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_1_accordion_2_overline":"","_venn_diagram_modal_skills_1_accordion_2_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_1_accordion_2_content":"<span style=\"font-weight: 400;\">Mathematics achievement means how well students perform on tests and other measures of their math knowledge across different topics. It is used to compare student performance across schools, districts, or states, often using standardized tests.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">Throughout the studies of learning products in the EF+Math portfolio, mathematics achievement data was gathered as a metric of potential long-term impacts, focusing on math course grades and standardized test scores.\u00a0<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li aria-level=\"1\"><span style=\"font-weight: 400;\">Improving students\u2019 overall mathematical achievement requires improvements in intermediary mathematics learning outcomes, such as engagement, increased or improved use of mathematical practices, and development of content knowledge or skills within a particular topic. Because of this complexity, research has not yet identified an overarching pathway for systematically improving mathematics achievement for all students.<\/span><\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li aria-level=\"1\"><span style=\"font-weight: 400;\">Math learning products rarely improve student achievement on their own\u2014and this is especially true for supplemental resources (e.g. <a href=\"https:\/\/edworkingpapers.com\/sites\/default\/files\/Tutoring%20Meta-Analysis%20Oct%202024_unblinded.pdf\" target=\"_blank\" rel=\"noopener\">Kraft, et al., 2020<\/a>). However, these products can improve how teachers teach and how students experience learning math. That is why it is crucial for math curricula to be based on research on how students learn and be practical to use in real classrooms (see how we achieved these goals through our <a href=\"https:\/\/efmathprogram.org\/inclusive-research-development-and-evaluation-toolkit\/\" rel=\"noopener\">inclusive R&amp;D processes<\/a>).<\/span><\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">While improving math test scores is difficult, it is still an important measure of student learning. Some of our teams saw promising results on achievement: schools that used <a href=\"https:\/\/efmathprogram.org\/project\/fraction-ball\/\" rel=\"noopener\">one learning product<\/a> consistently achieved higher scores on a measure of rational number understanding across multiple studies, and schools that used <a href=\"https:\/\/efmathprogram.org\/project\/cuethinkef\/\" rel=\"noopener\">another product<\/a> achieved higher scores on state standardized tests than schools that did not (see the independent evaluations of EF+Math project teams\u2019 math learning products <a href=\"https:\/\/efmathprogram.org\/project\/american-institutes-for-research\/\" rel=\"noopener\">here<\/a>). <\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_1_accordion_2_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_1_accordion_3_headline":"Math Engagement ","_venn_diagram_modal_skills_1_accordion_3_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_1_accordion_3_overline":"","_venn_diagram_modal_skills_1_accordion_3_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_1_accordion_3_content":"<span style=\"font-weight: 400;\">Math engagement refers to how invested a student is, both cognitively and socially, in learning math. This includes visible participation, such as speaking up in class, as well as less visible signs like focused thinking, interest, and motivation.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">Student engagement is an essential component of creating powerful math learning experiences, including developing students\u2019 abilities to manage their own engagement. Across EF+Math Program efforts, studies gathered qualitative engagement data through logs, surveys, and interviews, emphasizing the importance of educator and student perspectives.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">People may define or measure engagement in different ways, making it challenging to build a shared understanding. Regardless of the measurement approach, it is important to avoid labeling children based on their engagement and instead emphasize descriptive data on <\/span><i><span style=\"font-weight: 400;\">how<\/span><\/i><span style=\"font-weight: 400;\"> students engage in math learning.\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can support increased engagement in mathematics learning by incorporating opportunities for students\u2019 individual choice for activities or tasks, authentically connecting the mathematics content and contexts to student interests or cultures, or providing students with routines and strategies to regulate their engagement and have agency over their learning.\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The Our Mathematical World project team found that elementary students were highly engaged in math learning when supported by storybooks depicting mathematics in use in real world scenarios, as well as discussions of \u201cbios\u201d which demonstrate how people use mathematics every day. Teachers reported increases in student questions, enjoyment, and identifying connections between the mathematics content to their own lives (e.g. <a href=\"https:\/\/efmathprogram.org\/resource\/the-development-of-storybooks-supporting-elementary-students-math-identity-executive-function-and-word-problem-solving\/\" target=\"_blank\" rel=\"noopener\">Hornburg, et al., 2023<\/a>)<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_1_accordion_3_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_1_accordion":4,"_venn_diagram_modal_skills_1_accordion":"field_venn_diagram_venn_diagram_modal_skills_accordion","venn_diagram_modal_skills_2_color":"yellow","_venn_diagram_modal_skills_2_color":"field_venn_diagram_venn_diagram_modal_skills_color","venn_diagram_modal_skills_2_headline":"Math Perceptions","_venn_diagram_modal_skills_2_headline":"field_venn_diagram_venn_diagram_modal_skills_headline","venn_diagram_modal_skills_2_subheading":"EF+Math aimed to understand students' math-related perceptions about themselves and their learning experiences, including investigating a wide range of interrelated concepts, like affect, beliefs and identity, sense of belonging, and their classroom context and culture.","_venn_diagram_modal_skills_2_subheading":"field_venn_diagram_venn_diagram_modal_skills_subheading","venn_diagram_modal_skills_2_link_boxes_0_headline":"EF+Math\u2019s insights led to the creation of professional learning resources to help teachers understand how to leverage EFs in their instruction to develop students\u2019 math identities.","_venn_diagram_modal_skills_2_link_boxes_0_headline":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline","venn_diagram_modal_skills_2_link_boxes_0_link":{"title":"Build Your Practice","url":"https:\/\/efmathprogram.org\/resources-for-educator-practice\/","target":""},"_venn_diagram_modal_skills_2_link_boxes_0_link":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link","venn_diagram_modal_skills_2_link_boxes_1_headline":"EF+Math R&D Project teams explicitly designed their instructional materials to incorporate evidence-backed features that increase students\u2019 positive math learning experiences and perceptions.","_venn_diagram_modal_skills_2_link_boxes_1_headline":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_headline","venn_diagram_modal_skills_2_link_boxes_1_link":{"title":"Read Our Research","url":"https:\/\/efmathprogram.org\/resource\/efmath-portfolio-analysis-paper\/","target":"_blank"},"_venn_diagram_modal_skills_2_link_boxes_1_link":"field_venn_diagram_venn_diagram_modal_skills_link_boxes_link","venn_diagram_modal_skills_2_link_boxes":2,"_venn_diagram_modal_skills_2_link_boxes":"field_venn_diagram_venn_diagram_modal_skills_link_boxes","venn_diagram_modal_skills_2_accordion_0_headline":"Affect","_venn_diagram_modal_skills_2_accordion_0_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_2_accordion_0_overline":"","_venn_diagram_modal_skills_2_accordion_0_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_2_accordion_0_content":"<span style=\"font-weight: 400;\">Affect refers to a student's emotional state, including their emotions, attitudes, and dispositions toward math. Affect is closely connected to thinking and learning\u2014it shapes how students perceive their learning experiences, how well they can engage, and how effectively they can use their cognitive skills.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">In the EF+Math Program, project teams focused on various components of affect in the mathematics learning context, such as math anxiety, math confidence, and enjoyment. We aimed to recognize the real impacts that negative affect can have on student learning, while intentionally supporting increased positive affect, underscoring our belief that all math learning experiences should be joyful.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Affect influences students\u2019 development of mathematical proficiency, which has implications for long term success in mathematics; in particular, having a positive affect can support productive struggle and perseverance, as well as the development of reasoning and problem solving skills (Kilpatrick, et al., 2001).\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Student affect can influence the extent to which they can engage in a learning environment or particular experience. Teachers can promote positive affect (such as increasing students\u2019 confidence in their ability to solve a problem) or decrease negative affect (such as math anxiety) in math learning by creating an environment where mistakes are normalized and used to spur growth and future learning (e.g. rough draft thinking, <a href=\"https:\/\/www.routledge.com\/Rough-Draft-Math-Revising-to-Learn\/Jansen\/p\/book\/9781625312068\" target=\"_blank\" rel=\"noopener\">Jansen, et al., 2020)<\/a>.\u00a0<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Elementary students who played Fraction Ball, which integrates playful learning and embodied cognition, reported two key changes: increases in positive math-related emotions and decreases in negative emotions like boredom. Importantly, the students whose positive emotions increased the most also showed the greatest improvements in math performance. This connection suggests that intentionally supporting student affect can enhance mathematics learning (<a href=\"https:\/\/www.uciscienceoflearning.org\/uploads\/1\/1\/7\/8\/117864006\/buckets_of_fun_fraction_ball.pdf\" target=\"_blank\" rel=\"noopener\">Alvarez-Vargas, et al., 2024<\/a>).<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_2_accordion_0_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_2_accordion_1_headline":"Beliefs & Identity","_venn_diagram_modal_skills_2_accordion_1_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_2_accordion_1_overline":"","_venn_diagram_modal_skills_2_accordion_1_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_2_accordion_1_content":"<span style=\"font-weight: 400;\">Beliefs &amp; Identity refers to the various beliefs students hold about their own capabilities to do mathematics, their perceptions of how others see their capabilities, and their beliefs about the discipline of mathematics itself.\u00a0<\/span>\r\n\r\n<span style=\"font-weight: 400;\">The EF+Math Program examined multiple aspects of mathematical beliefs throughout our inclusive R&amp;D work. Different project teams explored specific facets of beliefs, such as mathematical identities, self-efficacy, perseverance, and effort, depending on their learning product's features and how they expected it to work.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can support positive beliefs and mathematical identities by explicitly affirming the identities students bring to math learning. When teachers help students recognize that their identities and behaviors are brilliant and mathematical, it influences how students engage with others and with math content, creating more opportunities for identity affirmation (e.g. <a href=\"https:\/\/pubs.nctm.org\/display\/book\/9780873538565\/9780873538565.xml\" target=\"_blank\" rel=\"noopener\">Aguirre, et al., 2013<\/a>).<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Research shows many ways to categorize students' beliefs about math learning. Because individual studies and learning products often focus on specific beliefs, it's difficult to understand how different beliefs relate to each other. Several EF+Math R&amp;D project teams created new measures that assess multiple types of math beliefs at once. These measures will enable future research on how different beliefs interact and which beliefs are most important for teachers to support. You can access these measures in our repository to learn more about their development and see findings from studies that used them.<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_2_accordion_1_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_2_accordion_2_headline":"Sense of Belonging ","_venn_diagram_modal_skills_2_accordion_2_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_2_accordion_2_overline":"","_venn_diagram_modal_skills_2_accordion_2_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_2_accordion_2_content":"<span style=\"font-weight: 400;\">A student\u2019s sense of belonging refers to their perception of membership in their mathematics classroom learning community, as well as membership in the general community of people capable of doing mathematics. Belonging sits at the intersection of an individual\u2019s beliefs about themselves and their perceptions of their environment or context.\u00a0<\/span>\r\n\r\n<span style=\"font-weight: 400;\">There are multiple strategies for specifically increasing students\u2019 sense of belonging within the instructional materials developed as part of the EF+Math program, including explicit activities where students can build relationships with their peers, or other activities which model expanded representations of people who \u201cdo\u201d mathematics.<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li aria-level=\"1\"><span style=\"font-weight: 400;\">The extent to which environments are culturally relevant to an individual is deeply connected to their sense of belonging within a space or community. Black and Latino students often do not experience culturally relevant mathematics learning experiences, which can inhibit their sense of belonging and impact the ways they engage with their peers in math class (<\/span><a href=\"https:\/\/jaamejournal.scholasticahq.com\/article\/18411-on-defense-african-american-males-making-sense-of-racialized-narratives-in-mathematics-education\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">Nasir &amp; Shah, 2011<\/span><\/a><span style=\"font-weight: 400;\">).<\/span><\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can support students\u2019 sense of belonging in mathematics by creating learning environments that are inviting and safe, and by actively affirming students\u2019 brilliance and empowerment throughout their teaching and other interactions (Belonging-Centered Instruction, <a href=\"https:\/\/osf.io\/n7bv2_v1\" target=\"_blank\" rel=\"noopener\">Matthews, et al., 2021a<\/a>, <a href=\"https:\/\/studentexperiencenetwork.org\/wp-content\/uploads\/2021\/10\/SERN_Research-Snapshot_Matthews_102721.pdf\">2021b<\/a>). For example, teachers can support student choice in math tasks or learn about students\u2019 identities and explicitly connect the mathematics content to relatable and relevant components of their identities.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Research is needed to understand the extent to which these experiences actually lead students to feel they belong. Further, analyses that investigate the relationships between belonging and other math-related beliefs can inform how instruction can most effectively support students\u2019 positive experiences in math learning. Spark Math and other EF+Math R&amp;D project teams developed measures that enable such analyses, laying the groundwork for continued innovation and attention to student belonging in math.<\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_2_accordion_2_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_2_accordion_3_headline":"Classroom Context & Culture ","_venn_diagram_modal_skills_2_accordion_3_headline":"field_venn_diagram_venn_diagram_modal_skills_accordion_headline","venn_diagram_modal_skills_2_accordion_3_overline":"","_venn_diagram_modal_skills_2_accordion_3_overline":"field_venn_diagram_venn_diagram_modal_skills_accordion_overline","venn_diagram_modal_skills_2_accordion_3_content":"<span style=\"font-weight: 400;\">A learner's perception of their classroom context and culture includes the physical setup of the space, the values and norms within that environment, and the broader context surrounding the learning environment.<\/span>\r\n\r\n<span style=\"font-weight: 400;\">Only some EF+Math R&amp;D project teams collected data on student perceptions of classroom culture within their studies. However, each team designed its learning products to foster a culturally relevant, asset-based classroom environment. This included messaging and integrated teacher professional learning resources, as well as tasks and features co-designed with students to ensure they were culturally responsive, engaging, and affirming<\/span>\r\n\r\n<b>Key Takeaways:<\/b>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Learning does not happen within a bubble - the culture of the mathematics classroom influences interactions between teachers and students. It is essential that mathematics learning, engagement of EFs, and student perceptions of their learning are all seen as culturally dependent. When we can accept the role of culture in learning, we can build more effective math learning environments.<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Creating classrooms that serve as positive contexts for learning can involve normalizing struggle and mistakes, demonstrating a wide range of uses for mathematical processes, skills, and content, and ensuring that instruction leverages cultural knowledge and lived experiences of students as assets in learning mathematics (e.g. <a href=\"https:\/\/www.nctm.org\/Standards-and-Positions\/Position-Statements\/The-Intersection-of-Culture-and-Mathematics\/\" target=\"_blank\" rel=\"noopener\">NCTM, 2024<\/a>).<\/span><\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The Our Mathematical World project team validated a tool that measures students' perceptions of whether their math learning experiences also teach values related to collectivism and social connectedness (<a href=\"https:\/\/osf.io\/k2hz8\/files\/8bfy4\" target=\"_blank\" rel=\"noopener\">McElveen, et al., 2022<\/a>). This measure enables future systematic investigation of how this aspect of classroom culture influences mathematics learning. <\/span><\/li>\r\n<\/ul>","_venn_diagram_modal_skills_2_accordion_3_content":"field_venn_diagram_venn_diagram_modal_skills_accordion_content","venn_diagram_modal_skills_2_accordion":4,"_venn_diagram_modal_skills_2_accordion":"field_venn_diagram_venn_diagram_modal_skills_accordion","venn_diagram_modal_skills":3,"_venn_diagram_modal_skills":"field_venn_diagram_venn_diagram_modal_skills","venn_diagram_modal_cta_headline":"Research Relationships","_venn_diagram_modal_cta_headline":"field_venn_diagram_venn_diagram_modal_cta_headline","venn_diagram_modal_cta_subheading":"Dive deeper into each of our three research areas - EFs, Math Learning, and Math Perceptions - and investigate the relationships between them. ","_venn_diagram_modal_cta_subheading":"field_venn_diagram_venn_diagram_modal_cta_subheading","venn_diagram_modal_cta_buttons_0_button":{"title":"Explore Research Relationships","url":"https:\/\/efmathprogram.org\/research-relationships\/","target":""},"_venn_diagram_modal_cta_buttons_0_button":"field_venn_diagram_venn_diagram_modal_cta_buttons_button","venn_diagram_modal_cta_buttons_0_button_style":"primary","_venn_diagram_modal_cta_buttons_0_button_style":"field_venn_diagram_venn_diagram_modal_cta_buttons_button_style","venn_diagram_modal_cta_buttons":1,"_venn_diagram_modal_cta_buttons":"field_venn_diagram_venn_diagram_modal_cta_buttons","venn_diagram_modal_cta_image":"","_venn_diagram_modal_cta_image":"field_venn_diagram_venn_diagram_modal_cta_image","venn_diagram_modal_cta":"","_venn_diagram_modal_cta":"field_venn_diagram_venn_diagram_modal_cta","venn_diagram_modal":"","_venn_diagram_modal":"field_venn_diagram_venn_diagram_modal","venn_diagram":"","_venn_diagram":"field_venn_diagram_venn_diagram"},"mode":"edit","id":"acf-block-697d5d79f2a62"},"innerBlocks":[],"innerHTML":"","innerContent":[],"name":"venn-diagram","data":{"venn_diagram":{"headline":"Explore Our Research Areas","content":"<p>Our research assessed student learning in three areas: EF skills, math learning outcomes, and students&#8217; perceptions of their math learning experiences, as a way to measure our focus on equitable math learning. We note that there are many other pathways to design for and study equitable math learning experiences that are not addressed through our research.<\/p>\n<p><strong>Click on each area below to learn more about each area, how the areas relate to each other, and to access actionable insights for supporting student math learning.<\/strong><\/p>\n","modal":{"skills":[{"color":"cyan","headline":" Executive Function Skills (EFs)","subheading":"<p>EFs are cognitive processes that all students have, which they use to manage and direct their learning, attention, and behavior. EF+Math focused on 5 EF skills in the context of mathematics learning: cognitive flexibility, inhibitory control, working memory, planning, and metacognition.<\/p>\n","link_boxes":[{"headline":"We advanced a vision of EFs as culturally relevant, math-related, and dynamic across our work, enabling a paradigm shift in the field.","link":{"title":"Learn More","url":"https:\/\/osf.io\/preprints\/osf\/stzmk_v1","target":"_blank"}},{"headline":"Our teams built measures that provide asset-based data on how students engage their EFs in math learning, and enable new understanding of how contextual and environmental factors influence that engagement.","link":{"title":"Access Our Measures","url":"https:\/\/efmathprogram.org\/measures\/","target":""}}],"accordion":[{"headline":"Cognitive Flexibility","overline":"","content":"<p><span style=\"font-weight: 400;\">Cognitive flexibility is demonstrated any time a student adjusts their thinking and behavior in response to their environment. In math class, this may look like switching between operations during an arithmetic problem set, or listening to and trying out a classmate\u2019s strategy.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">EF+Math R&amp;D project teams built opportunities for students to engage their cognitive flexibility skills within math learning by using different notations, representations, operations, and approaches within mathematical tasks. <\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can engage students\u2019 cognitive flexibility skills through their design of activities, such as facilitating a discussion comparing different ideas about a concept or selecting problems which require students to use different strategies and make connections between problem types.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Giving multiple ways to access a mathematical task, as well as switching between multiple goals or methods, allows students to have agency in their own learning by selecting the strategies that make sense to them in each problem situation.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The SparkMath team created a game called <a href=\"https:\/\/saga.org\/equivacards-the-fun-math-card-game-for-fluency-blog\/\" target=\"_blank\" rel=\"noopener\">Equivacards<\/a> that uses rules similar to those of UNO while engaging students\u2019 algebraic reasoning and flexibility with mathematical expressions and variables. The team studied how students engaged their cognitive flexibility skills and other EFs while playing the game, and determined which game scenarios enabled them to engage these skills effectively. Studies also showed positive benefits for students\u2019 math-related affect and engagement from playing the games (<a href=\"https:\/\/efmathprogram.org\/resource\/the-role-of-educational-games-as-an-instructional-context-to-promote-executive-function-processes-in-mathematics-education\/\" target=\"_blank\" rel=\"noopener\">Webb, 2023<\/a>). <\/span><\/li>\n<\/ul>\n"},{"headline":"Inhibitory Control ","overline":"","content":"<p><span style=\"font-weight: 400;\">Inhibitory control is used to ignore distracting information (and classroom distractions, too!), and focus on relevant information for the task at hand. In math class, this can involve selecting appropriate strategies to solve a problem, choosing which information and context is necessary to interpret an answer, and focusing on key ideas in peers\u2019 thinking.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">EF+Math R&amp;D Project teams built opportunities for students to engage their inhibitory control skills in multiple ways, such as staying focused when playing games with shifting rules and goals, or when determining which information is relevant to solve open-ended tasks.\u00a0<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can help students engage their inhibitory control by acknowledging distractions and helping students re-focus on the task at hand. Distractions arise at many processing levels: sensory distractions, such as peer behavior; contextual distractions, such as irrelevant information in word problems; and conceptual distractions, such as a previously used strategy that is insufficient for the current problem.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Inhibitory control skills are often celebrated or acknowledged when students exhibit white-normative behaviors, such as being quiet in class. Rather than trying to control students&#8217; behavior, build the capacity to recognize student agency in using inhibitory control. For instance, notice how a student chooses to engage in classroom discussions based on their learning goals for the day.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The Mathematical Thinkers Like Me team used a platform in which students work collaboratively on math problems to advance researchers\u2019 understanding of what inhibitory control skills look like during problem solving using qualitative coding of student activity &#8211; a previously unexplored approach to research. Participating students demonstrated inhibitory control in complex geometry tasks by ignoring visual cues and using geometric rules instead, ceding control of the tools when asked by a peer, suppressing unsuccessful strategies and trying new ones, and staying engaged in team efforts (<a href=\"https:\/\/flr.journals.publicknowledgeproject.org\/index.php\/journal\/article\/view\/1371\" target=\"_blank\" rel=\"noopener\">Renninger et al, 2025<\/a>).<\/span><\/li>\n<\/ul>\n"},{"headline":"Working Memory","overline":"","content":"<p><span style=\"font-weight: 400;\">Working memory is the ability to hold and manipulate information in the mind to achieve a task; students\u2019 working memory capacity &#8211; the amount of information they can hold in mind &#8211; increases naturally with development and also can be improved with practice. In math, students use working memory to hold numbers in mind while performing calculations, remember multiple steps in a problem solving process, or keep track of different pieces of information needed to solve a word problem.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">EF+Math R&amp;D project teams focused on increasing and supporting working capacity in the context of mathematics, including through: increasing the amount of items students have to hold in their working memory during fluency games; providing scaffolds to offload some information from working memory while managing new information; and using their working memory to listen, understand, and respond to others in discussions while also considering their own ideas.\u00a0<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Strong working memory skills support current math skills and also enable future math learning, which is why it is so important to provide opportunities for students to practice and improve working memory while doing math (<a href=\"https:\/\/www.danamillercotto.com\/uploads\/4\/7\/7\/2\/47725475\/zhang_miller-cotto___jordan__2023_.pdf\" target=\"_blank\" rel=\"noopener\">Zhang et al, 2023<\/a>).\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Students are better able to engage their working memory skills when they are more familiar with the materials being used (e.g., <a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC10348702\/pdf\/nihms-1860124.pdf\" target=\"_blank\" rel=\"noopener\">Niebaum &amp; Munakata, 2023<\/a>). To help students increase their working memory during math tasks, teachers can select culturally relevant tasks and ensure students receive ample exposure to the mathematical symbols and notations required in the curriculum.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The MathicSTEAM team found a strong correlation between math-embedded working memory (<a href=\"https:\/\/efmathprogram.org\/resource\/on-the-relationship-of-math-and-executive-functions\/\" target=\"_blank\" rel=\"noopener\">Buschkuehl et al., 2024<\/a>) and arithmetic fluency, as well as significant improvements on multiple working memory tasks as a result of playing games that simultaneously train EFs and fact fluency (Feng et al, 2022). <\/span><\/li>\n<\/ul>\n"},{"headline":"Planning ","overline":"","content":"<p><span style=\"font-weight: 400;\">Planning, in both EFs and mathematical terms, is the ability to think several steps ahead while solving a complex problem, and anticipate whether a chosen strategy will lead to a desired solution. In math learning, students use planning skills when they are deciding how to tackle a task or open-ended problem, such as determining what to do first, what information they might need, and how they will know when they have achieved their goal.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">EF+Math R&amp;D project teams promoted planning by: assigning problems with specific, non-routine goals, such as challenging students to land on a specific score in a game; including an explicit step for students to explore and understand what new problems are asking before starting to solve them; or asking students to reflect on their plans and identified strategies during and after solving problems.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can modify almost any math game to incorporate planning by providing a target score instead of the traditional \u201chighest score wins,\u201d and by making the game collaborative so students jointly plan their strategy. During problem solving practice, teachers can assign tasks that lack clear strategies, so students can exercise their agency to choose and evaluate their own strategies.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The end goal of planning is not necessarily to carry out the plan regardless of shifts in circumstances or new ideas. As in life, plans in math need to adjust based on what students learn along the way! The CueThinkEF+ team <a href=\"https:\/\/efmathprogram.org\/project\/cuethinkef\/\" rel=\"noopener\">built supports for student planning<\/a> into their problem solving platform and encouraged students to modify their plans as they tried strategies and learned more about the problem. Reflecting on how plans changed and why can be just as useful as creating a plan in the first place.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">There are a few tests of planning skills that have been predominantly used in cognitive science research, but these tests may not accurately capture the unique ways planning skills are engaged within a math learning context. To address this, the Fraction Ball team built a new game-based assessment to understand students\u2019 planning skills while solving rational number problems. They found that this new measure can provide insight into planning in a similar way to the traditional tasks, while also gathering information about students\u2019 understanding of the math content knowledge (<a href=\"https:\/\/scholarspace.manoa.hawaii.edu\/server\/api\/core\/bitstreams\/b6699b64-3087-4e44-997d-a83573b2582a\/content\" target=\"_blank\" rel=\"noopener\">Lopez et al., 2025<\/a>). <\/span><\/li>\n<\/ul>\n"},{"headline":"Metacognition","overline":"","content":"<p><span style=\"font-weight: 400;\">Metacognition is reflecting on one\u2019s own thinking\u00a0 \u2013 an important skill in and out of the classroom. In mathematics, metacognition allows students to evaluate their own learning, effort, and skills while in the middle of a problem or over the course of a year.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">EF+Math R&amp;D teams supported students in developing metacognitive skills through opportunities to: set and evaluate their own learning goals; compare problem solving strategies and their relative effectiveness in different contexts; and reflect on and improve their collaboration skills when working with peers.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Historically, students have been taught to apply procedures without making sense of the conceptual mathematics behind them. Educators now know that teaching sense-making is key to developing a deep understanding of math content topics (e.g., Rittle-Johnson &amp; Siegler, 1999; <a href=\"https:\/\/www.nctm.org\/PtA\/\" target=\"_blank\" rel=\"noopener\">NCTM 2014<\/a>), and EF+Math researchers are going one step further: helping students reflect on and direct their own mathematical learning.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Practicing metacognition can build students&#8217; agency to understand how they learn best and to advocate for the learning opportunities they need. Teachers can incorporate metacognitive practice into any mathematical activity by asking students to reflect on their approach, how it worked, whether they adjusted it, and what they learned as they worked through the problem (e.g. <a href=\"https:\/\/www.landmark.edu\/research-and-training\/blog\/combine-executive-function-scaffolds-metacognitive-prompting-and-problem-solving-questions-to-spark-math-learning-for-all-students\" target=\"_blank\" rel=\"noopener\">Bryck, 2024<\/a>).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The CueThink team found that practicing metacognitive reflection can positively impact the extent to which students solve problems correctly and their ability to demonstrate conceptual understanding of content topics. In addition, findings suggest that increasing metacognitive skills can minimize the impact of math anxiety and other math beliefs on student performance (<a href=\"https:\/\/files.eric.ed.gov\/fulltext\/ED658385.pdf\" target=\"_blank\" rel=\"noopener\">Rhodes, et al., 2023)<\/a>.<\/span><\/li>\n<\/ul>\n"}]},{"color":"blue","headline":"Math Learning","subheading":"<p>Math learning is a social and cultural activity that involves understanding mathematical content and developing mathematical practices. Success in math learning is assessed through day-to-day engagement in mathematical activities and overall mathematics achievement. EF+Math attended to each of these facets in order to advance more equitable mathematics learning experiences for students. <\/p>\n","link_boxes":[{"headline":"EF+Math project teams explicitly designed their instructional materials to integrate principles from learning science research that articulate how mathematics learning happens within the brain.","link":{"title":"See Our Products","url":"https:\/\/efmathprogram.org\/projects\/","target":""}},{"headline":"In addition to our individual impact studies, we conducted analyses to explore interactions between the design principles in our portfolio of learning products and how they supported student math learning. ","link":{"title":"Read Our Research","url":"https:\/\/efmathprogram.org\/resource\/efmath-competitive-product-analysis\/","target":"_blank"}}],"accordion":[{"headline":"Math Practices","overline":"","content":"<p><span style=\"font-weight: 400;\">Mathematical practices are the activities and skills that are used to do mathematics; students need opportunities to develop these practices across all content topics and grade levels.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">R&amp;D Project teams within EF+Math emphasized mathematical practices that have been identified as pivotal for accessing more advanced levels of proficiency, such as: problem solving, discourse, and peer collaboration. Teams studied how these practices were developed and used within their focal content topics and math learning environments.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">While specific mathematical practices have been identified as part of national standards over the years (such as <a href=\"https:\/\/www.thecorestandards.org\/Math\/\" target=\"_blank\" rel=\"noopener\">Common Core State Standards, 2010<\/a>; NCTM, 2009), research continues to identify and study additional types of mathematical practices. Building more examples of how mathematical practices show up across various mathematics learning environments and contexts allows us to better identify and support student brilliance.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can pair instructional goals for math content topics with goals for developing mathematical practices to ensure they are planning for these practices in their activities. For example, teachers can support students\u2019 development of discourse skills by intentionally designing tasks that can be solved with multiple strategies and having students discuss their strategic approaches with peers.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">One R&amp;D Project team investigated how students&#8217; cognitive and collaborative engagement shifted throughout different stages of problem solving. They found that students engaged their EFs more during \u201cexploration\u201d stages compared to later stages of problem solving, and that task structure strongly influences how students engage. Notably, findings demonstrate that student problem solving skills differ when working individually, compared to working collaboratively in groups (<a href=\"https:\/\/flr.journals.publicknowledgeproject.org\/index.php\/journal\/article\/view\/1371\/1339\" target=\"_blank\" rel=\"noopener\">Renninger, et al., 2025<\/a>).<\/span><\/li>\n<\/ul>\n"},{"headline":"Math Content Topics","overline":"","content":"<p><span style=\"font-weight: 400;\">Math content topics are the specific knowledge, concepts, and skills that students must understand and apply to achieve mathematical proficiency and overall achievement. Content topics are grouped to show how these ideas build upon one another across grades to reach this end goal (e.g., <a href=\"https:\/\/www.thecorestandards.org\/Math\/\" target=\"_blank\" rel=\"noopener\">Common Core State Standards for Mathematics, 2010<\/a>; <a href=\"https:\/\/www.nctm.org\/Publications\/Essentials-Made-Easy\/\" target=\"_blank\" rel=\"noopener\">National Council of Teachers of Mathematics, n.d.<\/a>).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">EF+Math R&amp;D project teams targeted content topic areas critical to unlocking access to advanced mathematics understandings and overall success in mathematics learning: fluency of operations, rational numbers, ratios and proportions, and more. Each team studied key ideas within their focal content topic and designed their interventions to address common challenges students face when learning these concepts.\u00a0<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Grade-appropriate math topics were identified through years of research, and evidence shows that connecting new math concepts to what students already know helps them build deeper understanding. For example, students learn multiplication more effectively when it&#8217;s connected to their existing knowledge of addition and grouping. Some content topics are well-studied, with clear implications for how these ideas should be taught to students. For example, understanding rational numbers can be supported through manipulatives and number line representations to engage students in reasoning about magnitude (see our <a href=\"https:\/\/efmathprogram.org\/resources-for-educator-practice\/\" rel=\"noopener\">repository<\/a> for more detail on this content topic and other actionable, research-backed insights for educator practice).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">EF+Math R&amp;D Project teams studied the role of fact fluency when building proficiency with operations and numbers. This foundational elementary content topic builds into more advanced number systems in later grades, along with algebraic reasoning. One team used clickstream data gathered while students played fluency games to identify challenges students faced in their understanding and <a href=\"https:\/\/efmathprogram.org\/project\/mathicsteam\/\" rel=\"noopener\">tailored the problems they worked on to provide scaffolded practice<\/a> through these concepts.<\/span><\/li>\n<\/ul>\n"},{"headline":"Math Achievement ","overline":"","content":"<p><span style=\"font-weight: 400;\">Mathematics achievement means how well students perform on tests and other measures of their math knowledge across different topics. It is used to compare student performance across schools, districts, or states, often using standardized tests.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Throughout the studies of learning products in the EF+Math portfolio, mathematics achievement data was gathered as a metric of potential long-term impacts, focusing on math course grades and standardized test scores.\u00a0<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">Improving students\u2019 overall mathematical achievement requires improvements in intermediary mathematics learning outcomes, such as engagement, increased or improved use of mathematical practices, and development of content knowledge or skills within a particular topic. Because of this complexity, research has not yet identified an overarching pathway for systematically improving mathematics achievement for all students.<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">Math learning products rarely improve student achievement on their own\u2014and this is especially true for supplemental resources (e.g. <a href=\"https:\/\/edworkingpapers.com\/sites\/default\/files\/Tutoring%20Meta-Analysis%20Oct%202024_unblinded.pdf\" target=\"_blank\" rel=\"noopener\">Kraft, et al., 2020<\/a>). However, these products can improve how teachers teach and how students experience learning math. That is why it is crucial for math curricula to be based on research on how students learn and be practical to use in real classrooms (see how we achieved these goals through our <a href=\"https:\/\/efmathprogram.org\/inclusive-research-development-and-evaluation-toolkit\/\" rel=\"noopener\">inclusive R&amp;D processes<\/a>).<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">While improving math test scores is difficult, it is still an important measure of student learning. Some of our teams saw promising results on achievement: schools that used <a href=\"https:\/\/efmathprogram.org\/project\/fraction-ball\/\" rel=\"noopener\">one learning product<\/a> consistently achieved higher scores on a measure of rational number understanding across multiple studies, and schools that used <a href=\"https:\/\/efmathprogram.org\/project\/cuethinkef\/\" rel=\"noopener\">another product<\/a> achieved higher scores on state standardized tests than schools that did not (see the independent evaluations of EF+Math project teams\u2019 math learning products <a href=\"https:\/\/efmathprogram.org\/project\/american-institutes-for-research\/\" rel=\"noopener\">here<\/a>). <\/span><\/li>\n<\/ul>\n"},{"headline":"Math Engagement ","overline":"","content":"<p><span style=\"font-weight: 400;\">Math engagement refers to how invested a student is, both cognitively and socially, in learning math. This includes visible participation, such as speaking up in class, as well as less visible signs like focused thinking, interest, and motivation.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Student engagement is an essential component of creating powerful math learning experiences, including developing students\u2019 abilities to manage their own engagement. Across EF+Math Program efforts, studies gathered qualitative engagement data through logs, surveys, and interviews, emphasizing the importance of educator and student perspectives.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">People may define or measure engagement in different ways, making it challenging to build a shared understanding. Regardless of the measurement approach, it is important to avoid labeling children based on their engagement and instead emphasize descriptive data on <\/span><i><span style=\"font-weight: 400;\">how<\/span><\/i><span style=\"font-weight: 400;\"> students engage in math learning.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can support increased engagement in mathematics learning by incorporating opportunities for students\u2019 individual choice for activities or tasks, authentically connecting the mathematics content and contexts to student interests or cultures, or providing students with routines and strategies to regulate their engagement and have agency over their learning.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The Our Mathematical World project team found that elementary students were highly engaged in math learning when supported by storybooks depicting mathematics in use in real world scenarios, as well as discussions of \u201cbios\u201d which demonstrate how people use mathematics every day. Teachers reported increases in student questions, enjoyment, and identifying connections between the mathematics content to their own lives (e.g. <a href=\"https:\/\/efmathprogram.org\/resource\/the-development-of-storybooks-supporting-elementary-students-math-identity-executive-function-and-word-problem-solving\/\" target=\"_blank\" rel=\"noopener\">Hornburg, et al., 2023<\/a>)<\/span><\/li>\n<\/ul>\n"}]},{"color":"yellow","headline":"Math Perceptions","subheading":"<p>EF+Math aimed to understand students' math-related perceptions about themselves and their learning experiences, including investigating a wide range of interrelated concepts, like affect, beliefs and identity, sense of belonging, and their classroom context and culture.<\/p>\n","link_boxes":[{"headline":"EF+Math\u2019s insights led to the creation of professional learning resources to help teachers understand how to leverage EFs in their instruction to develop students\u2019 math identities.","link":{"title":"Build Your Practice","url":"https:\/\/efmathprogram.org\/resources-for-educator-practice\/","target":""}},{"headline":"EF+Math R&D Project teams explicitly designed their instructional materials to incorporate evidence-backed features that increase students\u2019 positive math learning experiences and perceptions.","link":{"title":"Read Our Research","url":"https:\/\/efmathprogram.org\/resource\/efmath-portfolio-analysis-paper\/","target":"_blank"}}],"accordion":[{"headline":"Affect","overline":"","content":"<p><span style=\"font-weight: 400;\">Affect refers to a student&#8217;s emotional state, including their emotions, attitudes, and dispositions toward math. Affect is closely connected to thinking and learning\u2014it shapes how students perceive their learning experiences, how well they can engage, and how effectively they can use their cognitive skills.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In the EF+Math Program, project teams focused on various components of affect in the mathematics learning context, such as math anxiety, math confidence, and enjoyment. We aimed to recognize the real impacts that negative affect can have on student learning, while intentionally supporting increased positive affect, underscoring our belief that all math learning experiences should be joyful.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Affect influences students\u2019 development of mathematical proficiency, which has implications for long term success in mathematics; in particular, having a positive affect can support productive struggle and perseverance, as well as the development of reasoning and problem solving skills (Kilpatrick, et al., 2001).\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Student affect can influence the extent to which they can engage in a learning environment or particular experience. Teachers can promote positive affect (such as increasing students\u2019 confidence in their ability to solve a problem) or decrease negative affect (such as math anxiety) in math learning by creating an environment where mistakes are normalized and used to spur growth and future learning (e.g. rough draft thinking, <a href=\"https:\/\/www.routledge.com\/Rough-Draft-Math-Revising-to-Learn\/Jansen\/p\/book\/9781625312068\" target=\"_blank\" rel=\"noopener\">Jansen, et al., 2020)<\/a>.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Elementary students who played Fraction Ball, which integrates playful learning and embodied cognition, reported two key changes: increases in positive math-related emotions and decreases in negative emotions like boredom. Importantly, the students whose positive emotions increased the most also showed the greatest improvements in math performance. This connection suggests that intentionally supporting student affect can enhance mathematics learning (<a href=\"https:\/\/www.uciscienceoflearning.org\/uploads\/1\/1\/7\/8\/117864006\/buckets_of_fun_fraction_ball.pdf\" target=\"_blank\" rel=\"noopener\">Alvarez-Vargas, et al., 2024<\/a>).<\/span><\/li>\n<\/ul>\n"},{"headline":"Beliefs & Identity","overline":"","content":"<p><span style=\"font-weight: 400;\">Beliefs &amp; Identity refers to the various beliefs students hold about their own capabilities to do mathematics, their perceptions of how others see their capabilities, and their beliefs about the discipline of mathematics itself.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The EF+Math Program examined multiple aspects of mathematical beliefs throughout our inclusive R&amp;D work. Different project teams explored specific facets of beliefs, such as mathematical identities, self-efficacy, perseverance, and effort, depending on their learning product&#8217;s features and how they expected it to work.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can support positive beliefs and mathematical identities by explicitly affirming the identities students bring to math learning. When teachers help students recognize that their identities and behaviors are brilliant and mathematical, it influences how students engage with others and with math content, creating more opportunities for identity affirmation (e.g. <a href=\"https:\/\/pubs.nctm.org\/display\/book\/9780873538565\/9780873538565.xml\" target=\"_blank\" rel=\"noopener\">Aguirre, et al., 2013<\/a>).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Research shows many ways to categorize students&#8217; beliefs about math learning. Because individual studies and learning products often focus on specific beliefs, it&#8217;s difficult to understand how different beliefs relate to each other. Several EF+Math R&amp;D project teams created new measures that assess multiple types of math beliefs at once. These measures will enable future research on how different beliefs interact and which beliefs are most important for teachers to support. You can access these measures in our repository to learn more about their development and see findings from studies that used them.<\/span><\/li>\n<\/ul>\n"},{"headline":"Sense of Belonging ","overline":"","content":"<p><span style=\"font-weight: 400;\">A student\u2019s sense of belonging refers to their perception of membership in their mathematics classroom learning community, as well as membership in the general community of people capable of doing mathematics. Belonging sits at the intersection of an individual\u2019s beliefs about themselves and their perceptions of their environment or context.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">There are multiple strategies for specifically increasing students\u2019 sense of belonging within the instructional materials developed as part of the EF+Math program, including explicit activities where students can build relationships with their peers, or other activities which model expanded representations of people who \u201cdo\u201d mathematics.<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">The extent to which environments are culturally relevant to an individual is deeply connected to their sense of belonging within a space or community. Black and Latino students often do not experience culturally relevant mathematics learning experiences, which can inhibit their sense of belonging and impact the ways they engage with their peers in math class (<\/span><a href=\"https:\/\/jaamejournal.scholasticahq.com\/article\/18411-on-defense-african-american-males-making-sense-of-racialized-narratives-in-mathematics-education\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">Nasir &amp; Shah, 2011<\/span><\/a><span style=\"font-weight: 400;\">).<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Teachers can support students\u2019 sense of belonging in mathematics by creating learning environments that are inviting and safe, and by actively affirming students\u2019 brilliance and empowerment throughout their teaching and other interactions (Belonging-Centered Instruction, <a href=\"https:\/\/osf.io\/n7bv2_v1\" target=\"_blank\" rel=\"noopener\">Matthews, et al., 2021a<\/a>, <a href=\"https:\/\/studentexperiencenetwork.org\/wp-content\/uploads\/2021\/10\/SERN_Research-Snapshot_Matthews_102721.pdf\">2021b<\/a>). For example, teachers can support student choice in math tasks or learn about students\u2019 identities and explicitly connect the mathematics content to relatable and relevant components of their identities.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Research is needed to understand the extent to which these experiences actually lead students to feel they belong. Further, analyses that investigate the relationships between belonging and other math-related beliefs can inform how instruction can most effectively support students\u2019 positive experiences in math learning. Spark Math and other EF+Math R&amp;D project teams developed measures that enable such analyses, laying the groundwork for continued innovation and attention to student belonging in math.<\/span><\/li>\n<\/ul>\n"},{"headline":"Classroom Context & Culture ","overline":"","content":"<p><span style=\"font-weight: 400;\">A learner&#8217;s perception of their classroom context and culture includes the physical setup of the space, the values and norms within that environment, and the broader context surrounding the learning environment.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Only some EF+Math R&amp;D project teams collected data on student perceptions of classroom culture within their studies. However, each team designed its learning products to foster a culturally relevant, asset-based classroom environment. This included messaging and integrated teacher professional learning resources, as well as tasks and features co-designed with students to ensure they were culturally responsive, engaging, and affirming<\/span><\/p>\n<p><b>Key Takeaways:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Learning does not happen within a bubble &#8211; the culture of the mathematics classroom influences interactions between teachers and students. It is essential that mathematics learning, engagement of EFs, and student perceptions of their learning are all seen as culturally dependent. When we can accept the role of culture in learning, we can build more effective math learning environments.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Creating classrooms that serve as positive contexts for learning can involve normalizing struggle and mistakes, demonstrating a wide range of uses for mathematical processes, skills, and content, and ensuring that instruction leverages cultural knowledge and lived experiences of students as assets in learning mathematics (e.g. <a href=\"https:\/\/www.nctm.org\/Standards-and-Positions\/Position-Statements\/The-Intersection-of-Culture-and-Mathematics\/\" target=\"_blank\" rel=\"noopener\">NCTM, 2024<\/a>).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The Our Mathematical World project team validated a tool that measures students&#8217; perceptions of whether their math learning experiences also teach values related to collectivism and social connectedness (<a href=\"https:\/\/osf.io\/k2hz8\/files\/8bfy4\" target=\"_blank\" rel=\"noopener\">McElveen, et al., 2022<\/a>). This measure enables future systematic investigation of how this aspect of classroom culture influences mathematics learning. <\/span><\/li>\n<\/ul>\n"}]}],"cta":{"headline":"Research Relationships","subheading":"<p>Dive deeper into each of our three research areas - EFs, Math Learning, and Math Perceptions - and investigate the relationships between them. <\/p>\n","buttons":[{"button":{"title":"Explore Research Relationships","url":"https:\/\/efmathprogram.org\/research-relationships\/","target":""},"button_style":"primary"}],"image":false}},"advanced_accordion":null,"advanced_block_options":{"message_field_message":null}}}}]}}