Inclusive Mathematics Education

Developing mathematical knowledge, skills, and literacy is critical not just for pursuing higher education and STEM careers, but also for empowering all students to use mathematics to reason about and contribute to their lives, interests, and communities. Historically, however, mathematics teaching, learning, and assessment has devalued, inadequately supported, and further marginalized populations that are underrepresented and underserved in STEM education. 

In this Spotlight, we feature ten DRK-12 projects focused on approaches, practices, environments, and tools that support equitable and inclusive mathematics education for all learners. CADRE also partnered with TERC to organize this month’s STEM for All Multiplex Theme of the Month on inclusive mathematics education. We invite you to read a perspective piece by Salvador Huitzilopochtli, watch the webinar recording, view the video playlist, and participate in the online discussion that continues this week.

In this Spotlight:


Featured Projects

Precision Math LogoBroadening Participation in Mathematics for English Learners with Mathematics Difficulties: A Multi-Site Impact Study

PI: Christian Doabler | Co-PIs: Benjamin Clarke, Derek Kosty, Leticia Martinez, Megan Rojo
Math Disciplines: The Precision Mathematics intervention was designed to increase student performance in the areas of mathematical measurement and statistical data by building conceptual understanding and problem-solving skills. The scope and sequence of the intervention is based on the Common Core State Standards in Mathematics (2010) and includes lessons on: (a) ordering objects by length, (b) comparing the lengths of two objects using a third object, (c) using standardized and unstandardized length units to measure the length of an object from endpoint to endpoint, (d) organizing, representing, and interpreting data using pictographs and bar graphs, and (e) asking and answering questions about the represented data. In addition to the measurement and statistical objectives of the intervention, each lesson includes whole number operation instruction and fact fluency practice for addition and subtraction combinations within 20.
Grade: 1
Target Audience: First-grade students with or at risk of mathematics difficulties and students who are emergent bilingual/English learners

Description: There has been a recent push in the U.S. to increase representation of traditionally marginalized populations in the STEM workforce. Underrepresented populations in STEM (e.g., students with learning difficulties, emergent bilingual/English learners) often face systemic barriers to accessing high-quality STEM education, which in turn puts these populations at a disadvantage when competing for STEM careers. Thus, the Precision Mathematics First Grade intervention was designed to provide high-quality STEM instruction to first-grade students who are experiencing mathematics difficulties. The intervention is centered on evidence-based practices for struggling learners, such as the use of explicit instruction and visual representations. The intervention also provides supports for emergent bilingual / English learners, including targeted vocabulary instruction and frequent opportunities to use mathematical language. Precision Mathematics-First Grade focuses on the measurement and data domains within the first-grade Common Core State Standards (2010). To build students’ knowledge of statistical investigation, the intervention utilizes components of statistical investigation outlined in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report (Franklin et al., 2007): (1) ask a question, (2) collect data, (3) represent data, and (4) interpret the data. Precision Mathematics is taught in small-group formats, for 30 minutes, four times a week.

Successes and/or Challenges: Students who are struggling in mathematics often have underdeveloped number sense capabilities, including number identification, magnitude comparisons, and fact fluency. Poor fluency in these areas hinders their ability to solve problems and build conceptual understanding of mathematics. Students who continuously demonstrate mathematics difficulties typically require intensified mathematics interventions in these core areas (i.e., number identification, magnitude comparisons, fact fluency) to demonstrate adequate mathematics progress. The Precision Mathematics intervention uses a backdrop of early number sense to prepare students mathematics problems in the areas of measurement and early statistical investigation. Additionally, students with mathematics difficulties benefit from the type of specialized instruction embedded into Precision Mathematics, including teacher modeling; multiple, visual representations; opportunities to respond; and immediate feedback.

Strategies for Reducing Barriers: To reduce barriers to STEM education, schools can implement a multi-tiered system of support model to support all learners within a school system. In this model, students are provided with varying levels of academic or behavioral supports, with the flexibility to receive more intensified and individualized instruction based on need. To reap the most benefit from this model, all students should be screened for academic difficulties at the beginning of the school year. Those scoring below levels of proficiency in a domain should receive targeted interventions in that area (e.g., reading, mathematics, science), such as the Precision Mathematics intervention for students struggling with mathematics. In addition, teachers should use instructional practices that have demonstrated positive outcomes for students from traditionally marginalized and underrepresented populations, such as those used in the Precision Mathematics intervention (i.e., explicit and systematic instruction, targeted vocabulary instruction, opportunities to respond, immediate teacher feedback).

Findings: Currently, we do not have data available for dissemination for the first grade Precision Mathematics project. The results for the 2021-2022 year are being analyzed and will be available soon. We did, however, have promising results for the Precision Mathematics intervention with second grade students on a proximal assessment of early measurement skills (Hedges’ g = .50; See Doabler et al., 2022).

Products: 


PLANAR LogoCAREER: Black and Latinx Parents Leading Reform and Advancing Racial Justice in Elementary Mathematics

PI: Frances Harper
Grades: PreK-5
Target Audience: Parents and caregivers of Black and Latinx children, teachers of Black and Latinx children, community organizations, Black and Latinx students

Description: Decades of reform efforts in mathematics education continue to fail Black and Latinx children, in part, because parents are excluded from decisions about school mathematics. Accordingly, this project explores possibilities for localized change in mathematics education lead by parents and caregivers of Black and Latinx children. We – university researchers, families, teachers, and community organizations – leverage principles of critical, community engaged scholarship to co-design and co-study two educational programs aimed at advancing racial justice in elementary mathematics. The first program, Parents as Leaders (PAL), seeks to build parents’ and caregivers’ capacity to catalyze change in mathematics education within classrooms and local schools. The second program, Teachers as Partners (TAP), will provide teacher professional development that supports elementary teachers of mathematics to learn with and from Black and Latinx families. Research findings have potential to extend our understanding of community-initiated and community-led change in school mathematics, with TAP and PAL serving as model for teacher and family co-learning that increase access and opportunity for Black and Latinx students in mathematics education.

Successes and/or Challenges: 

  • Challenges: The biggest challenge in the original development of the PAL program has been learning about parents' and caregivers' unique needs. The university team needed to "unlearn" some of the strategies that we used for supporting professional learning opportunities for teachers of mathematics. For example, we learned that parents and caregivers, unlike teachers, tended to be less available in the summer months due to disruptions in child care, work schedules, and travel. Thus, we had to revise our schedule for professional learning opportunities accordingly.
  • Successes: In year one of our project, we met monthly with our partners for two community organizations, one that serves the local Latinx communities and another that serves the local Black communities. Through these collaborations, we learned together about racial justice in mathematics education as it relates to the local Black and Latinx communities, and we co-designed the first PAL sessions. Together, we were also successful in recruiting 10 parents and caregivers to participate in PAL, with sessions beginning in October. 

Strategies for Reducing Barriers: We have found that the following strategies have reduced barriers for parents and caregivers of Black and Latinx children to participate in opportunities to learn about racial justice in mathematics education: (1) direct invitations to participate from community partners trusted by parents and caregivers; (2) meetings scheduled at convenient times (e.g., evenings) and familiar locations (e.g., community organizations); (3) stipends for participation in the PAL sessions, which recognize the valuable contributions parents and caregivers make to imagining and advancing racial justice in mathematics education (note: this stipend is in addition to stipends for research participation); (4) available STEM enrichment and homework help for children during PAL meetings to make participation possible and to address parental concerns about their individual child's success in mathematics.

Products: We will post materials for our PAL sessions as they are piloted in this academic year.


mELd LogoCAREER: Designing Learning Environments to Foster Productive and Powerful Discussions among Linguistically Diverse Students in Secondary Mathematics

PI: William Zahner
Math Disciplines: High school mathematics, primarily 9th grade/Algebra 1
Grades: 6-10
Target Audience: Math teachers, Curriculum designers, professional developers, researchers

Description: We know from classroom research that students can learn mathematics through participating in classroom discussions. Yet, many math teachers who work with linguistically diverse groups of students resort to "teaching by telling." In this project, we are working with ninth grade mathematics teachers to redesign their classroom learning environments to promote students' participation in productive and powerful discussions. Our goal is to create classroom learning environments in which multilingual students, including those who are designated as "English Learners," can benefit from participating in discussions. 

Over the past six years we have built on a university-school partnership to work closely, and over an extended period of time, with a group of teachers from linguistically diverse schools serving students from minoritized communities. Using an approach rooted in design based research, we have done multiple iterations of planning, co-design, teaching, and assessing the effects of our design efforts. As a product of this process, we have created model instructional materials as well as design principles for this work.

Successes and/or Challenges: We successfully completed three design cycles refining a unit of lessons that introduces slope as rate of change. The revised unit builds on existing research in mathematics education and it follows the project-specific design principles that we developed throughout this project. We have collected evidence that shows the redesigned lessons resulted in larger learning gains for students classified as English Learners, and that the redesigned lessons resulted in transformed patterns of classroom discourse. We have encountered problems along the way. Perhaps the most obvious was the disruption in our research plan caused by the abrupt transition to remote teaching in spring 2020. 

Strategies for Reducing Barriers: One important strategy for reducing barriers that hinder inclusivity in mathematics is developing robust designs that account for the real world conditions under which the design is to be used. We intentionally created lessons with entry points for students with widely varying background knowledge. We also included structures and lesson features that matched the structures that were in place at the schools where we were working. This made us realize that developing inclusive lessons requires very thoughtful responsiveness to the users--the students and teachers in the local environment. Such lessons may not work "off the shelf."

Products: 


Developing and Researching K-12 Teacher Leaders Enacting Anti-bias Mathematics Education (Collaborative Research: Elliott, Heaton, Thanheiser, Yeh)

PIs: Rebekah Elliott, Ruth Heaton, Eva Thanheiser, Cathery Yeh
Grades: K-12
Target Audience: Teacher leaders, teachers, administrators, mathematics teacher educators, education researchers, families, and parents

Description: The DREAM Project builds on the resiliency and brilliance of Black, Indigenous, Latinx, multilingual students, and students whose communities are impacted by structural inequities, denying them full access to mathematics. We act from an understanding that profound systemic changes in our educational systems, classrooms, and teaching are needed so each and every student thrives and learns mathematics in ways that are authentic to them and the discipline. The DREAM Project explicitly attends to contributors that result in inequities – the bias teachers hold about students, the ways instruction may embody and perpetuate bias through students’ differential opportunity to engage and develop subject matter interest, and disconnects between schools and communities. The DREAM project develops and studies a community-centered, job-embedded professional development model that helps to preemptively reduce bias among classroom teachers through teacher leaders’ engagement with families, colleagues, school community leaders, and administrators, allowing all stakeholders to come together to engage in dialogue to address bias and develop plans for change.

Successes and/or Challenges: During the first year of the project, we explored the leadership experiences of three African American and one Latinx mathematics teacher educators to understand how they explicitly attend to issues of race, racism, and (in)justice in mathematics teacher professional development.  Through the interviews, their podcasts/workshops, and their published materials, we are growing our understanding of the importance of: 1) challenging persistent master narratives about what is considered mathematics and mathematics ability; 2) engaging in community-based pedagogies during professional learning that highlight the cultural identities and mathematics understanding of students of Color; and 3) explicitly attending to how ideologies of whiteness within professional development and research design can still disenfranchise educators,students, and communities of Color.

Strategies for Reducing Barriers: Mathematics education often positions outside others as experts. Education leaders, policymakers, and researchers decide what is best for children and how classrooms and schools can become more culturally responsive and more equitable. However, those most impacted have the greatest insight to create change. We need to bring in teachers, families, and community leaders to collectively identify barriers and develop policies and practices that hinder inclusivity and rich mathematics engagement. What happens if we shift from a model of training and fixing students, parents, and teachers to fit into standardized spaces and instead embrace an approach that recognizes their expertise and prioritizes the collective well-being, self-determination and dignity? 

Products:

  • STEM for All Showcase Video: Developing, Enacting, Researching Anti-Bias Math Education
  • Feature Article in 2022 AMTE Connections
  • Conference Papers & Presentations
    • Yeh, C., Bianco, K., Asato, K., Thanheiser, E., Breana, V., Roady, N., Elliott, R., & Heaton, R. (2022). Navigating the white space of mathematics: Lessons learned from mathematics teacher educators of color. In Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Nashville, TN: Middle Tennessee State University.
    • Elliott, R.,Thanheiser, E., Yeh, C., Heaton, R., Bianco, K., & Asato, K. (accepted). Codesigning tools for justice focused research and mathematics teacher leader development. Presentation at the annual meeting of the Association of Mathematics Teacher Educators 2023.
    • Elliott, R. Thanheiser, E.,Yeh, C., & Heaton, R. (accepted). Centering equity in professional development. Presentation at the annual meeting of the Association of Mathematics Teacher Educators 2023.
       


Teach SIM LogoLeveraging Simulations in Preservice Preparation to Improve Mathematics Teaching for Students with Disabilities (Collaborative Research: Cohen, Jones)

PIs: Julie Cohen, Nathan Jones | Co-PIs: Lynsey Gibbons, Vivian Wong
Grades: Upper elementary
Target Audience: Preservice educators, teacher educators

Description: The focus of our project is on better preparing elementary candidates to support students with disabilities (SWDs) in mathematics lessons. General education teachers typically lack preparation to work with students with disabilities, especially in elementary mathematics. Our study aims to meet this challenge by integrating high-leverage practices for SWDs—and corresponding simulated practice — into elementary mathematics methods courses. Specifically, we are developing a suite of portable and scalable curricular materials, simulations, and coaching supports, which we are currently testing in randomized control trials across several teacher education programs.

A central part of our theory of change is that such low-stakes practice opportunities, when coupled with immediate, targeted feedback, will increase the likelihood that candidates are equipped to meet the needs of students with disabilities. If the materials prove to be effective, it could provide a model for integrating special education methods and content into general education courses in mathematics. Such efforts could pay dividends for teacher preparation programs looking to enhance candidates’ skills without adding additional coursework. Given the brief duration of teacher preparation and the high number of courses required for elementary licensure in most states, this approach could be helpful in developing a wide range of needed skills.

Successes and/or Challenges: Preparing general education teachers to better support SWDs necessitates coordinated supports from general and special educators. However, the fields of mathematics education and special education have historically worked from distinct, often contradictory epistemological and pedagogical approaches. Part of the tension stems from the fact that general mathematics education privileges student-centered approaches that foreground student sense-making and inductive approaches to learning. In contrast, special education methods are often characterized as teacher-centered, with demonstration of step-by-step routines and consistent teacher feedback. Unfortunately, perhaps as a result of these tensions, the two fields are rarely in conversation with each other. This contributes to teachers being ill prepared to support SWDs in mathematics instruction. 

We cannot ignore the need to equip teachers with tools to support students with disabilities in ways that: 1) recognize the intersectional identities of students with disabilities and the structural and systemic inequities special education can perpetuate; 2) capitalize on the assets of learners identified as having disabilities; and 3) scaffold their learning in powerful ways. With the population of students with disabilities growing, it is imperative that we leverage educational systems to disrupt patterns of oppression and help teachers position all students as capable and competent. At the same time, part of positioning students for success is ensuring that teachers are equipped with instructional practices that have a demonstrated track record of supporting students with disabilities. 

Strategies for Reducing Barriers: As part of this work, we convened an expert panel of both general and special educators to meet over a year and a half. The focus of the conversations was what it would look like to prepare teachers to engage in instruction that is both ambitious and accessible. Though there were certainly disagreements among panelists, there were also many places of intersection and shared goals. This suggests that an important first step in promoting inclusive mathematics education is fostering spaces for discussion among these two communities. 

Along the same lines, two of the panelists—a general and special mathematics teacher educator—had previously co-taught a mathematics methods course when they worked at the same institution. Both had a very positive experience and suggested candidates benefited from the collaboration and cross-field discourse. It may be that teacher education needs to move to the same kind of co-teaching model we advocate in K-12 so that beginning teachers: 1) see effective collaboration modeled, 2) understand that supporting SWD’s is the responsibility of all educators, and 3) develop a repertoire of instructional practices that promotes inclusive and ambitious mathematics teaching.

Findings: It is too early to share findings related to our randomized control trial, but we have completed two additional sets of data analysis related to the project. In one paper, we summarize findings from a landscape analysis of nearly 200 mathematics methods syllabi, focusing on whether course syllabi reflect a focus on tools and strategies for supporting students with disabilities. We found that only 38% of the syllabi had references to SWDs. References to SWDs were the most common in the course objectives (23% of syllabi with objective sections). References to SWDs were quite rare in sections of the syllabi detailing specific course activities (9% of syllabi with outlines), or specific readings (6% of syllabi with listed readings). 

Many of the references to SWDs in syllabi were aspirational, part of the broad goals about “meeting the needs of all learners,” rather than tied to specific activities, assignments, or readings. For example, one syllabus had an objective of, “Adapt and enact instruction and content for diverse students, including SWDs and English language learners.” Another syllabus had a lesson plan assignment with a requirement of a “Plan for addressing needs of diverse learners (ESE, ESOL, special needs children, etc.) throughout the lesson.” Most specific readings, assignments, objectives, or activities grouped SWDs with other groups of students, including English Learners. Few assignments or activities focused solely on the specific instructional needs of SWDs. 

Our findings suggest that elementary candidates are receiving limited training on how to meet the specialized needs of SWDs in mathematics in their methods courses. As policy makers look for strategies to ensure that all students, including SWDs, receive effective mathematics instruction, our findings imply that teacher education may be an important site for additional reforms. If we want the next generation of elementary-aged SWDs to receive instruction tailored to their needs, we will need to support mathematics teacher educators in developing foundational knowledge and skills in their pre-service coursework.

In a second paper, we present findings from interviews conducted with 25 leading special education researchers and mathematics education researchers to examine sources of consensus and dissensus in the scholars’ conceptions of the goals of mathematics teaching. Special educators, in general, foregrounded proximal instructional goals, including developing students’ mathematics knowledge, helping students’ complete tasks successfully, and performing well on standardized assessments. General mathematics educators prioritized more distal goals such as developing students’ identities as mathematical sense makers, who use mathematics to engage with the world. Mathematics educators described using instruction to re-envision school-based mathematics, and special educators privileged instructional supports to maximize student success in the current landscape of K-12 mathematics teaching. Special educators talked more often about “efficiency” and the “tyranny of time” in elementary mathematics classrooms, while general educators spoke in more aspirational terms about the potential for “an entirely different” model of mathematics teaching.
 
Both general and special educators emphasized that effective instruction is predicated on deep understanding of students and the fostering of flexible, conceptual understanding, rather than rule-bound, procedural understandings. This suggests possible areas of convergence that could be leveraged in building bridges across these discourse communities.

By engaging leaders in both fields in a focused conversation around a shared problem-- SWDs struggling in general education mathematics classrooms--we hope to better understand barriers and ultimately to improve the connection between two fields, which have often operated in isolation from one another. Our longer-term aim is to develop an instructional framework that reflects the epistemological beliefs of both fields and articulate conceptions of teaching and learning that serve to connect these two communities.

Methodology: Following the development of our curricular materials, we will assess the impact of these resources on candidates’ knowledge, skills, and dispositions related to supporting students with disabilities in mathematics. Specifically, we just launched a randomized control trial (RCT) across three large teacher preparation programs. In two of those programs, nearly 200 teacher candidates have been randomly assigned to either our treatment condition (the curricular modules coupled with simulations and coaching) or a control condition, wherein candidates gain access to readings related to supporting students with disabilities in mathematics but without the focus on practicing instructional methods and receiving feedback on their developing skills.

Products: Read about the simulation research at teachsim.org and in a blog post on AAAS ARISE.


Image of parents and teachers working together.Parents, Teachers, and Multilingual Children Collaborating on Mathematics Together (Collaborative Research, Civil, Pinnow, Quintos)

PIs: Marta Civil, Rachel Pinnow, Beatriz QuintosCo-PIs: Claudia Galindo, Melinda Martin-Beltran, Carolina Napp-Avelli, Samuel Otten, Erin Turner
Grades: 3-5
Target Audience: Teachers, parents and children in grades 3-5

Description: We are developing and researching an innovative mathematical partnership that engages teachers, parents, and multilingual children in grades 3-5, from schools in underserved communities. At the center of this innovation is the integration of two approaches to advancing equity in mathematics education—the funds of knowledge framework (González, Moll, & Amanti, 2005) and positioning theory (Davies & Harré, 1990; Van Langenhove & Harré, 1994). This integrated framework will deepen our understanding of how mathematics learning opportunities are created, sustained, expanded, or limited for particular students. The mathematical partnership will: 1) reorganize spaces and roles to transform school-home power differentials around mathematics learning; 2) leverage children’s and families’ knowledge and expertise as a resource in teaching and learning mathematics with a focus on problem-solving; and 3) build teacher and parent understanding of the role of positioning in supporting mathematics learning.

Successes and/or Challenges: The main successes are: a) parents and teachers have reported enjoying learning from each other and having the opportunity to get to know each other as partners beyond the parent-teacher conferences that often perpetuate the power differential between home and school; b) parents have reported enjoying learning mathematics as adult learners and being able to interact with their children around mathematics in a relaxed environment; c) teacher have reported being able to implement some of the strategies in the study groups in their classroom, with a focus on language and opening up the participation patterns; d) Teachers and parents have connected to how positioning influences multilingual learners’ access to mathematics and to classroom participation with peers. Parents have connected with concepts of positioning such as the role of their child’s narrative in the school and the classroom.   

The main challenges were: a) COVID limited some of the planned activities (e.g., teacher home visits) and impacted some of the study group sessions (e.g., online format for some of them when the Omicron surge); b) recruitment and regular participation of parents and teachers. 

Strategies for Reducing Barriers:

  • Creating mathematical partnerships that restructure power dynamics and build relationships among parents and teachers has an impact on how parents and teachers see the assets that each brings in the learning of mathematics.
  • Joint conversations about funds of knowledge supports establishing relationships of trust between parents and teachers.
  • Conversations that provide a platform for parents to address concerns about supporting their children in mathematics at home.
  • Open-ended mathematics tasks that are grounded in the communities’ funds of knowledge facilitate collaborative and equitable participation between teachers and parents. 

Findings: When caregivers and teachers engage in funds of knowledge conversations they are able to explore the assets that each brings. Parents and teachers made connections and noticed similarities as they shared personal experiences in general and with mathematics learning. For example, in one case some teachers had grown up in Mexico, like most of the mothers in the study group. This led to their noticing that they had similar experiences in terms of their funds of knowledge and how they learned mathematics when they were in school. We provide here one snippet that is representative of the power of bringing teachers and parents together. From a teacher, “I got to know the mother of one of my students better and I was surprised that she knew quite a bit [of mathematics].” This points to the need for opportunities for teachers to see parents as doers of mathematics, which is what the study group sessions provide. In the parents’ focus group, all the mothers agreed that working with the teachers gave them an opportunity to learn more about them and to see them as human beings.

Our study of parent-teacher positioning has focused on the interactions around carefully designed tasks that were open ended and grounded in a meaningful cultural context (e.g., finding out how much of each ingredient to make sugar skulls of different size in connection to the día de los muertos (day of the dead); or a paper flower activity that we had used before with a group of mothers (Civil, et al., 2021). This kind of task provides different entry points for all participants, as they can bring their expertise with the context and with the mathematics. In traditional school tasks that were more familiar to the teachers , they were more likely to guide the discussion. This moved the discourse away from collaboration and towards asymmetrical positionings. We are currently analyzing the data from those different scenarios for mathematical tasks. 

Parents and teachers have noted that understanding how multilingual learners are positioned in the math classroom significantly impacts these learners’ access to equitable math instruction, thinking, and practice. 

Findings from preliminary analyses were shared at the AERA 2022 (Title: Multilingual Children Positioning for Learning: Parents and Children Working Together on Mathematics). The data included selected multilingual children from one site (Arizona) in two different contexts, in interaction with their mother during a parent/child mathematics workshop, and in a mathematics lesson in their classroom. Preliminary analyses suggest that some multilingual learners exhibited agency in these spaces by suggesting alternate paths forward, by resisting others’ attempts to frame their participation in particular ways, and by shifting previously established patterns of interaction. These analyses also revealed interesting similarities in positioning of multilingual youth in interactions across spaces. 

Methodology: We use Design-Based Implementation Research (DBIR) to guide iterative cycles of systematic inquiry as we develop, test and refine our study group model. This collaborative approach to organizing research and development activities supports effective implementation and sustainability (Penuel & Martin, 2015; Roschelle, Knudsen, Hegedus, 2010). A central aim of DBIR is to address potential implementation challenges via close partnerships and ongoing collaborations. Principles of Social Design Experiments guide refinements (i.e., activities to restructure interactions between school and home) and analysis (i.e., a focus on advancing equitable learning opportunities) (Gutiérrez & Jurow, 2016). Social Design Experiments use design-based research methods, but with the explicit goal of reorganizing systems of activity (e.g., interactions among teachers and parents) for the purpose of advancing equitable learning opportunities (e.g., participation and learning of multilingual mathematics learners). A guiding principle of this approach is that the knowledge and expertise of historically marginalized communities is a key resource for understanding issues and conceptualizing solutions.

Products:

  • Presentations
    • Civil, M., Quintos, B., & Salazar, F. (2022, February 10-12). Three spaces for teachers and parents to dialogue about mathematics teaching and learning [Conference session], Twenty-Sixth Annual Conference of the Association of Mathematics Teacher Educators, Henderson, NV, United States. 
    • Civil, M., Quintos, B., Salazar, F., Napp-Avelli, C., Cardenas-Guzman, M. (2022, April 21-26). "Juntos" to support multilingual students' mathematics learning: Bringing families' funds of knowledge into the classroom [Conference session], 2022 American Educational Research Association Annual Meeting, San Diego, CA, United States.
    • Napp-Avelli, C., & Quintos, B. (2022, February 21-25). 1205 Ciclo: Enseñar matemática en contextos culturales diversos: Argentinos en el exterior. Juntos: Padres, maestros y niños multilingües haciendo matemática [Virtual session], Semana UNIPE virtual 2022. Universidad Pedagógica Nacional, Buenos Aires, Argentina. 
    • Martin-Beltrán, M, Pinnow, R., Lindfors-Navarro, H., Salazar, F., Buli, T., Krell, M., Turner, E., Galindo, C., Civil, M., Chval, K, Quintos, B. (April, 2022) Multilingual children positioning for learning: Parents and children working together on mathematics, [Round table presentation]. American Educational Research Association Annual Meeting, San Diego, CA
  • Project Website: Our website includes an overview of our research plan as well as the professional development model created and now updated through the work done with our first Cohort. In addition to our team and contact information, we have listed all the presentations given so far, as well as relevant resources. 
  • ResearchGate Project Website: The ResearchGate project website allows us to share research updates frequently with the research community that follows the project. It also allows for a conversation to happen with interested scholars internationally. We currently have included an overview of the model, our goals, and current presentations. 

Paving the Way for Fractions: Exploring Foundational Concepts in First Grade (Collaborative Research: Jordan, Newcombe)

PIs: Nancy Jordan, Nora Newcombe | Co-PI: Christina Barbieri
Math Discipline: Early fractions knowledge
Grades: 1-2
Target Audience: Results from our project are (and will be) of interest to researchers, math curriculum developers, early elementary school educators, and parents.

Description: Fractions are a crucial part of the formal number system and vital to everyday life. However, fractions are challenging for many students, and there is already wide variation in what children know about fractional quantities by the time they start formal learning in 3rd or 4th grade. Our project aims to understand the roots of these differences in first graders. We’ve been measuring the early, informal ways that first graders think about fractional quantity in contexts such as equal sharing, proportions, and words like “half.” Our goal is to develop playful learning tools to build early fraction skills that position all learners for later success, including children at risk. These play-based activities will build important fraction ideas in fun, meaningful, and developmentally appropriate ways. Through our activities, first graders are learning about fractional quantity and words like “halves”, “thirds”, and “fourths” as they help monsters build roads and dinosaurs find hidden treasures. Children’s familiarity with these simple ideas may help prevent common misunderstandings in fraction learning, such as thinking 1/3 is smaller than 1/4. We hope to help all children develop key conceptual foundations in fractions and to build their confidence to help them stay motivated as they learn about this challenging but important area of mathematics. 

Successes and/or Challenges:

  • Successes: In our project so far, we have learned that almost all first graders have some early knowledge of fraction ideas like equal sharing and recognizing equal proportions. We think that building on these informal ideas will support better understanding and engagement with fraction learning and math in general. A good start is especially important because research shows that students’ motivation may decrease when they struggle with fractions.
  • Challenges: It is always challenging to do research in schools, and the pandemic and teacher shortages have complicated those challenges in many of our partner schools. Schools with fewer resources (or who serve populations of students with fewer resources) are less likely to have time and space to allow our research team to work with their students, and students from families with fewer resources are often less likely to return their consent forms allowing them to participate. Due to these issues, students from higher-income backgrounds or more well-resourced schools are overrepresented in our research. However, we continue to work to broaden the diversity of our sample through partnerships with a variety of public and private schools.

Strategies for Reducing Barriers: Evidence shows that students (and adults) tend to hold more negative views of fractions than of whole numbers (Sidney et al., 2019). However, our preliminary work suggests that children can have fun building early fraction skills in playful ways. By incorporating language about fractions into everyday activities, parents and teachers can help children build on their informal knowledge to start understanding key foundations of symbolic fractions. Below are some specific examples of how parents and teachers can support early fraction learning:

  • Talk to children using fraction words (e.g., “we’re halfway across the bridge!”, “we need four cups and so far we put one in, so we’re one-fourth of the way there!”, “we shared this bag of grapes equally among three people, so each of us got one-third of the whole bag”, etc.).
  • Help children connect fraction symbols with intuitions about equal sharing. For example, one-fourth of a candy bar is one piece when the candy bar is divided into four equal parts. 
  • Always encourage children to think about what the whole is when engaging in fraction activities. (e.g., the candy bar or one inch on a ruler). 
  • Include number lines and other linear models in fraction learning. Children can play a “number race”, measure with a ruler, or build a path using fractional parts. 
  • Research from our project and others shows that early whole number skills are crucial for building fraction understanding. 

Findings: In our first year of working with first graders, we documented their understanding of early fraction ideas with two kinds of representations: visual (e.g., bars, circles, etc.) and symbolic (e.g., “one-half”, ¾, etc.). Our preliminary findings suggest that almost all children showed some knowledge of early fraction concepts at the beginning of first grade. First-graders were best at questions that involved visual representations and the fraction word “one-half”, and they had a hard time answering questions that used other fraction words (e.g., “one-third”) or fraction symbols (e.g., ½). Encouragingly, when we returned to assess the same students at the end of first grade, we found that most students improved in their fraction understanding. This finding suggests that even though children aren’t formally learning about symbolic fractions in school in first grade, they may still be ready to learn some of these early ideas through informal experiences.

Methodology: Part one of our project is using a longitudinal observational approach to track what first graders know about fractions at the beginning and end of the year. We’re also measuring other math skills and cognitive skills like working memory to see how early fraction knowledge relates to these skills. Part two, which we are still developing, will test whether play-based learning about early fractions concepts can improve children’s fraction understanding and math achievement. We will randomly assign students to either play our training games about fractions or a control game involving other kinds of learning games.

Products:

Fractions sample item 1Fractions sample item 2
Fractions sample item 3


Storytelling for Mathematics Learning and Engagement

PI: Erica Walker | Co-PI: Robin Wilson
Math Disciplines: Varied
Grades: 3-8
Target Audience: Students and teachers

Description: Everyone loves a good story! Through this project, we seek to share engaging, inspiring stories about mathematics with teachers and students, as told by mathematicians. Although storytelling is a natural part of human activity, and is used extensively in school subjects like social studies and language arts, it is not typically found in mathematics.  In addition, representations of mathematics and mathematicians in schools, classrooms, and curricular materials—and indeed, in the broader popular culture—often reflect very narrow conceptions of mathematics and mathematicians. To highlight the diversity of mathematics and mathematicians, we have collected rich stories from Black mathematicians of all ages, who reflect on their own learning of math within school and in out-of-school spaces. These short videos cover a range of mathematical topics and provide ideas for teachers and students alike about the places and ways people learn and do mathematics.  They will be available as embedded in units and lessons within a mathematics curriculum package from our curriculum development partner as well as publicly available in a digital database for use by teachers, parents, and students everywhere. The research component of this project will explore the impact of the stories on students’ conceptions of mathematics and sense of belonging and teachers’ instructional practice and beliefs about mathematics.

Successes & Challenges: To date, we have interviewed 30 Black mathematicians to explore their formative, educational, and professional experiences with mathematics. From each hour-long video interview, the team (in collaboration with our curriculum partner, Amplify) carefully identified multiple rich stories  and produced three or four vignettes wherein mathematicians share a story that includes engaging graphics and animations added in post-production. Thus far, 80 vignettes have been produced for dissemination and integration into Amplify’s mathematics curriculum. Vignettes undergo an iterative process of review and revision (ongoing) before they will be included in the curriculum.

Our team of graduate students, mathematics and mathematics education faculty, and curriculum and production partners, along with our advisory board members who include experts in mathematics, mathematics education, curriculum development, research methods, and digital media literacy, have reviewed vignettes for accuracy, engagement potential for teachers and students, especially students who are underrepresented in mathematics, and possibilities for use in K-8 mathematics classrooms. 

The research team has also conducted focus groups with students and teachers to gauge the vignettes’ potential for student engagement and use in classroom instruction (over the next year, selected vignettes will be integrated into mathematics lessons within the Amplify curriculum and we will collect data related to the lessons and teachers’ and students’ engagement with them). 

Responses from teachers and students to the vignettes on their own–without seeing them embedded in a curricular lesson or unit–have been favorable, with students reporting that the videos are interesting and provide new ways of thinking about mathematics. Students noted that the videos would be fun to see in school as part of math class. Most teachers were enthusiastic about the potential of using the video vignettes in their classrooms. Overall, teachers thought that the vignettes

  • made both the mathematics and the people doing the mathematics more relatable and interesting;
  • captured stories and examples from the mathematicians that could potentially provide entry points for students to ask questions and have conversations about mathematics, making mathematics more engaging and accessible;
  • exposed students to more representative STEM role models;
  • could be integrated throughout their mathematics curriculum; and
  • stimulated new ideas for classroom activities related to the stories.

This suggests great potential for both the curriculum and our planned publicly available database of interviews and vignettes, given teacher and student interest in and use of the vignettes, both within and beyond classrooms. 

One challenge for potential curriculum integration in schools is that some teachers described concerns with featuring diverse mathematicians in classrooms, given their local political context and climate. A few teachers wondered how interested their students would be in the vignettes or the experiences shared by the mathematicians, given that their students’ demographic backgrounds largely do not match those of the mathematicians. We will explore these questions further as we begin piloting the curriculum with embedded mathematician vignettes in schools this year.  

Strategies for Reducing Barriers: The dominant view of mathematics in society, purported by popular culture, is that it is a static body of knowledge that only certain groups of people can do and learn. These limited conceptions of mathematics further perpetuate barriers that hinder engagement and a sense of belonging to the discipline. Though people across all gendered and racialized groups continue to succeed in mathematics, those images and stories are not widely publicized. Storytelling for Mathematics Learning and Engagement addresses these issues by leveraging human interest in stories and storytelling to counter narrow conceptions about mathematics and mathematics practitioners.

The collection of videos from the project showcases authentic mathematical narratives about learning elementary school topics in accessible ways. The mathematicians connect the mathematics they learned in school to the mathematics they use in their careers—for instance, using algebraic equations to model efficient mail delivery routes. We hope that by engaging with interesting applications and ways of conceptualizing specific mathematics topics, students and teachers will view mathematics as a creative, dynamic, and purposeful discipline that everyone can do and learn.

In addition to covering mathematics content, the mathematicians discuss their challenges throughout their schooling and how developing critical thinking skills, asking questions, and making and learning from mistakes enabled them to persevere. By detailing their challenges and advice for surmounting them, the mathematicians encourage students to persist. In doing so, they also foster conceptions of mathematics as a process of productive struggle and growth. 

The project also aims to address the gendered and racialized views of who can do and learn mathematics. To that end, we invited a diverse group of mathematicians to share stories about their lived experiences with mathematics in and out of school, with friends and family, and in their current careers. We hope that students will identify with the role models in these videos and perceive themselves as similarly capable of learning mathematics.

Finally, we expect the mathematicians’ stories of their own classroom experiences will impact teachers’ views about their students’ abilities to do and learn mathematics, their conceptions of mathematics as a discipline, and their awareness about careers in mathematics. The mathematicians’ accounts of their own teachers’ practices offer pedagogical recommendations. Not only will teachers have access to these videos to help students grapple with complex ideas, but they can also build activities that motivate early interest in mathematics careers. The mathematicians’ stories provide opportunities for teachers to facilitate mathematics learning and foster belongingness. 

With this initiative, we invite students and teachers to engage with these audiovisual representations of successful mathematicians from diverse backgrounds, their personal and contextualized experiences, and their journeys with mathematics. We hope this database of rich narratives will improve students’ engagement, participation, and performance in mathematics, especially among underrepresented groups.

Products: Project website coming soon!


Supporting Teachers to Develop Equitable Mathematics Instruction Through Rubric-based Coaching (Collaborative Research: Hill, Litke, Wilson)

PIs: Heather Hill, Erica Litke, Jonee Wilson 
Grades: 5-8
Target Audience: Mathematics instructional coaches and middle grades mathematics teachers

Description: HEAR-MI Coaching, a mathematics instructional coaching model, aims to improve middle school mathematics instruction by supporting teachers as they work to develop practices that aim for equity. HEAR-MI Coaching leverages a video-based coaching model and a set of equity-focused, mathematics-specific classroom observation rubrics (Equity and Access Rubrics for Mathematics Instruction [EAR-MI]). The EAR-MI rubrics attend to a set of research-based instructional practices that support historically marginalized students to be successful in mathematics classrooms. Participating coaches and teachers work together through coaching cycles in which they first set goals related to the EAR-MI rubrics. Next, they reflect on video clips of mathematics instruction from the project library as well as clips of the teacher’s own classroom. After reflecting on these clips through the lens of the EAR-MI, coaches guide teachers to identify concrete ways they might elevate their instruction in relation to particular practices. Based on this conversation, teachers identify a specific goal for the next coaching cycle. Through this project, we seek to understand how and in what ways this coaching model can support improvements in instruction aiming for equity and in student empowerment, identity development, achievement, and participation. 

Successes and/or Challenges: We are in the early stages of this work, having spent the first year of the project working in tandem with mathematics coaches to develop the coaching model and adapt the rubrics for use with teachers. Through this collaboration, we have discussed the possibility for tensions that may arise as coaches work with teachers related to two key areas. The first may arise when teachers encounter particular EAR-MI practices that may—on the surface—seemingly conflict with mainstream messages they have received around “good” teaching practices in mathematics education. For example, one EAR-MI practice, positioning students as competent, may challenge teachers to reconsider messages they have received on how to develop a growth mindset with their students. A second tension relates to helping coaches navigate supporting teachers who may demonstrate resistance to various EAR-MI practices, particularly as they relate to disrupting traditional racial and status hierarchies in classrooms.

Strategies for Reducing Barriers: We are working directly with coaches and teachers to surface tensions such as those described above in our development and pilot work. We have designed HEAR-MI Coaching training and ongoing support to address these tensions as they arise. In our pilot year, we are collecting and analyzing data that will allow us to better understand these tensions and resistance that may manifest, and will document strategies coaches use to successfully navigate these spaces of growth. 

Methodology: The goal of the project is to develop and pilot HEAR-MI Coaching, to understand its implementation and the conditions under which it is successful, and to investigate the effects of the intervention on instructional practices and teachers' beliefs, as well as on students' math achievement and sense of belonging in math. We also investigate how teachers' attitudes and beliefs impact their participation and what teachers take away from the coaching. To do this, we are piloting HEAR-MI Coaching with a small group of coaches and teachers from two districts, learning from their experiences and the experiences of their students to refine the model and provide additional support for implementation. Through interviews, surveys, and focus groups, we seek to understand what aspects of the EAR-MI best support teachers in developing instructional practices that aim for equity and what aspects of the EAR-MI students report as supporting their success. We are also interested in the ways in which teachers’ and coaches’ contexts support or constrain their adoption and use of the intervention and how features of the program engage or discourage teachers’ participation. Next, we will expand to a larger group of coaches and teachers and, using a cluster randomized delayed-treatment design, will draw on multiple sources of data to investigate the effects of the coaching model on teachers' beliefs and instructional practices and on students' mathematical achievement and sense of belonging.  

Products: We are in our pilot year of work. Products to come!


Young Mathematicians LogoYoung Mathematicians: Expanding an Innovative and Promising Model Across Learning Environments to Promote Preschoolers' Mathematics Knowledge

PI: Jessica Young | Co-PIs: Kristen Reed, Deborah Schifter
Math Disciplines: Early childhood mathematics
Grades: Preschool/PreK
Target Audience: Teachers and families/parents

Description: In partnership with Head Start programs, teachers, and families, we are connecting preschoolers’ mathematics learning environments—at home and at school—through fun, intentionally designed, early math games and resources.

Successes and/or Challenges: We have been fortunate to partner with Head Start programs and families with a diversity of language and backgrounds to develop materials that are meaningful across a home and school contexts.

Strategies for Overcoming Barriers: Communication across contexts has been a key factor in our project.

Products: We developed 50+ games in partnership with teachers and families with videos and written directions in English, Spanish and Portuguese. These are available on ym.edc.org. For an overview of the project see the 2021 NSF STEM Showcase video.


Additional Projects

We invite you to explore a sample of the other recently awarded and active work that focuses on inclusive mathematics education in the DRK-12 portfolio.


Related Resources

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