- I have full texts of all my articles at my website: https://mathematizing4all.com/my-research/edit
Abstract Student participation is an issue of equity. Without participation there can be no learning. This study focuses on the participation (and therefore learning) of struggling students (those with individual education plans [IEPs])... more
Abstract Student participation is an issue of equity. Without participation there can be no learning. This study focuses on the participation (and therefore learning) of struggling students (those with individual education plans [IEPs]) during the implementation of a relational thinking routine in a third-grade inclusion classroom. Students with IEPs often initially used direct modeling with linking cubes as a resource for presenting their thinking. In this way, they were able to demonstrate their ability to think relationally. As the year progressed, these students, who had earlier been reluctant to share and had done so only by using several of the resources that the participation structure of the routine provided, often showed a growth in their abilities to explain their thinking verbally.
Engagement in problem-solving and mathematical discussion is critical for learning mathematics. This research review describes a gap in the literature surrounding engagement of students with Learning Disabilities in standards-based... more
Engagement in problem-solving and mathematical discussion is critical for learning mathematics. This research review describes a gap in the literature surrounding engagement of students with Learning Disabilities in standards-based mathematical classrooms. Taking a sociocultural view of engagement as participation in mathematical practices, this review found that students with LD were supported towards equal engagement in standards-based mathematics through multi-modal curriculum, consistent routines for problem-solving, and teachers trained in Mathematical Knowledge for Teaching. Using this small set of studies (7), we identify the need to deepen the engagement of students with LD in mathematical problem-solving and discussion. This review concludes with implications for teaching and learning.
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This paper describes two myths that circulate widely about the potential of students with Learning Disabilities to learn mathematics: (1) that students with Learning Disabilities cannot benefit from inquiry-based instruction in... more
This paper describes two myths that circulate widely about the potential of students with Learning Disabilities to learn mathematics: (1) that students with Learning Disabilities cannot benefit from inquiry-based instruction in mathematics, and only from explicit instruction; and (2) that students with Learning Disabilities cannot construct their own mathematical strategies and do not benefit from engaging with multiple strategies. In this paper, I will describe how these myths have developed, and identify research that counters these myths. I argue that these myths are the unintended consequences of deficit constructions of students with Learning Disabilities in educational research. Using neurodiversity to frame disability as diversity rather than deficit, I assert that students with Learning Disabilities can learn mathematics to the highest levels, and that these limiting mythologies hold them back.
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Educational research undervalues the experiences of people with disabilities, including those with learning disabilities and/or dyslexia, whom we call insiders. In this study, we examined narratives pertaining to schooling from published... more
Educational research undervalues the experiences of people with disabilities, including those with learning disabilities and/or dyslexia, whom we call insiders. In this study, we examined narratives pertaining to schooling from published memoirs and/or interviews with 30 insiders with learning disabilities or dyslexia. First, we describe how these insiders define learning disabilities. We found multiple definitions of learning disabilities (LD), from sharp divisions between "LDness" and "normal, " to conceptions of universal learner variability such as "everyone learns differently. " We also describe how insiders defined their gifts as learners, and the challenges they faced in schools. Insiders identified strengths around creative problem-solving, multimodal thinking, and persistence. Challenges in school involved learning how to read, difficulty memorizing disconnected facts and needing more time. Recommendations include designing instruction that builds on the cognitive gifts of those with learning disabilities and dyslexia while minimizing instruction that focuses on their challenges.
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This study demonstrates the importance of a critical lens on disability in mathematics educational research. This ethnographic and interview study investigated how ability and disability were constructed over one year in a middle school... more
This study demonstrates the importance of a critical lens on disability in mathematics educational research. This ethnographic and interview study investigated how ability and disability were constructed over one year in a middle school mathematics classroom. Children participated in two kinds of mathematical pedagogy that positioned children differently: procedural and discussion-based. These practices shifted over time, as the teacher increasingly focused on memorization of procedures to prepare for state testing. Two Latino/a children with learning disabilities, Ana and Luis, used multiple cultural practices as resources, mixing and remixing their engagement in and identifications with mathematics. Ana, though mastering the procedural performances necessary for success in the second half of the year, authored herself as separate from mathematics, creating distance between herself and those she considered " smarties. " Luis identified as a creative mathematical problem-solver, and was initially positioned as a " top " mathematics student. As the pedagogy shifted towards memorization, Luis resisted the pedagogy of procedures, and continued to identify as a creative thinker in mathematics. Yet his teachers saw him as increasingly disabled, and eventually placed him in a group only for those in special education. This group, which Luis named the " unsmartest group, " was seen as least competent in mathematics by both teachers and students. The narratives of Luis and Ana highlight mathematics classrooms as relational and emotional, and demonstrate different strategies of resistance to the construction of mathematical disability.
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Understanding learning disabilities (LDs) as constructed through multiple cultural practices including discourse, this paper focuses on a Latino middle school student with a LD named Elijah. This study documents both the discourses and... more
Understanding learning disabilities (LDs) as constructed through multiple cultural practices including discourse, this paper focuses on a Latino middle school student with a LD named Elijah. This study documents both the discourses and practices used to position Elijah as a mathematics learner, as well as his use of similar discourses as he constructs a complex set of self-understandings as a mathematics learner. Elijah is positioned by discourses that prioritise speed as an indicator of mathematical ability, as well as discourses that construct students with LD as having both intelligence and differences such as processing speed. An analysis of interview and observational data suggests that Elijah constructed a unique set of self-understandings as a mathematics learner. Like his sixth-grade special education teacher, Elijah seems to differentiate between knowledge and the performance of knowledge in school. He created a unique identity as both ‘fast’ and ‘slow’ in mathematics, rejecting the binary found in many mathematics classrooms. These findings suggest that multiple discourses circulate in schools about ability and disability in mathematics.
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Students with disabilities are often framed as " the problem " and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between... more
Students with disabilities are often framed as " the problem " and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.
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Using design research methodology, we explored changes in experienced educators’ beliefs, knowledge, and practices related to Universal Design for Learning (UDL) following a professional development course for in-service teachers and... more
Using design research methodology, we explored changes in experienced educators’ beliefs, knowledge, and practices related to Universal Design for Learning (UDL) following a professional development course for in-service teachers and teacher leaders on UDL and design thinking. Data included analysis of focus groups 9 months after the summer professional development course. Findings indicated shifts in educators’ beliefs about UDL, moving from conceptions of UDL as a static, inflexible framework to a “way of thinking” – moment-to-moment responsiveness to students’ access needs. Another finding was the importance of empathy interviews as a practice to learn about students and build relationships. Participants stressed the importance of questioning one’s own deficit thinking about students with disabilities. We call for more investigations into teacher knowledge, beliefs, and practices on UDL.
Disabled students have historically been dehumanized in education, generally, and in research and practice related to school mathematics (K–12), particularly. Typically, they are only offered access to low-rigor school mathematics... more
Disabled students have historically been dehumanized in education, generally, and in research and practice related to school mathematics (K–12), particularly. Typically, they are only offered access to low-rigor school mathematics emphasizing rote procedures and narrow skills, often segregated physically and socially from their nondisabled peers. Educators are crucial to the humanization of disabled students via anti-ableist and antiracist work toward systemic transformation. The purpose of this review is to take stock of the current knowledge base of educator and disability research concerning school mathematics, recommending directions for humanizing future research and practice. Through a humanizing mathematics education lens, we analyze 61 articles involving educators, disabilities, and school mathematics published during the decade between 2007 and 2016. Results of our analysis point to not only the continued perpetuation of dehumanizing approaches and positioning but also subs...
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Conversations of educational equity in mathematics necessitate a more deliberate, nuanced look at the mathematical processes of learning for students of color from historically marginalized communities. This paper describes the... more
Conversations of educational equity in mathematics necessitate a more deliberate, nuanced look at the mathematical processes of learning for students of color from historically marginalized communities. This paper describes the theoretical work of a research collaborative that seeks to develop understanding of the experiences around mathematical identity of Latinas labeled with Learning Disabilities in mathematics classrooms. Expanding the theory of Complex Embodiment from Disability Studies, we explore new interdisciplinary theoretical and methodological tools to analyze the emotional, embodied experience of learning mathematics in the social worlds of mathematics classrooms, using emotional discourse. We take up theoretical and methodological practices around intersectionality through analysis of how power and positioning operate in mathematics identity development. We find that the young woman whose narratives we explore in this paper is positioned through deficit discourses arou...
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Within educational research, dyslexia and other disabilities are typically conceptualized as deficits. The theory of neurodiversity encourages researchers to conceptualize cognitive differences as natural forms of human diversity with... more
Within educational research, dyslexia and other disabilities are typically conceptualized as deficits. The theory of neurodiversity encourages researchers to conceptualize cognitive differences as natural forms of human diversity with unique sets of challenges and strengths. Using neurodiversity as our theoretical framework, we analyze the experiences of five research mathematicians with dyslexia as told through personal narratives to find common strengths and challenges for dyslexic thinkers at the highest level of mathematics. We report on 4 themes: (1) highly visual and intuitive ways of mathematical thinking, (2) issues with language and translation between forms, (3) issues with memorization of mathematical facts and procedures, and (4) resilience as a strength of dyslexia that matters in mathematics. We use our participants’ insights to explore how neurodiversity, a theory of cognitive disability developed by and for neurodiverse people, could expand opportunities for research...
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Anticipating and responding to learner variability can make using talk moves complex. The authors fuse Universal Design for Learning (UDL), differentiation, and talk moves into three key planning and pedagogy considerations.
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Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide... more
Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students wi...
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In this exploratory review, we use a disability studies lens to analyze the focus and outcomes of 15 recently published research articles that spotlight the role of educators in the mathematics schooling of students with disabilities. The... more
In this exploratory review, we use a disability studies lens to analyze the focus and outcomes of 15 recently published research articles that spotlight the role of educators in the mathematics schooling of students with disabilities. The results of our review not only point to continuation of problematic positioning and paradigms in research, but also underscore the value in supporting special educators’ mathematics understandings. Moreover, we note advancements in socio-contextual and socio-political research approaches that afford better understanding of the re/construction of disabled students, spaces, and pedagogy phenomena. We assert that outcomes of this review can inform more just research and practices for students with disabilities in mathematics education.
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Using neurodiversity as our theoretical framework, rather than a deficit or medical model, we analyze the narratives of five dyslexic research mathematicians to find common strengths and challenges for dyslexic thinkers at the highest... more
Using neurodiversity as our theoretical framework, rather than a deficit or medical model, we analyze the narratives of five dyslexic research mathematicians to find common strengths and challenges for dyslexic thinkers at the highest level of mathematics. We report on 3 themes: 1) highly visual and intuitive ways of mathematical thinking, 2) pronounced issues with memorization of mathematical facts and procedures, and 3) resilience as a strength of dyslexia that matters in mathematics. We introduce the idea of Neurodiversity for Mathematics, a research agenda to better understand the strengths (as well as challenges) of neurodiverse individuals and to use that knowledge to design better mathematical learning experiences for all.
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How do children develop identifications with mathematics over time, seeing themselves as agents in their math classrooms (or not)? This ethnographic and interview study followed nine Latino/a children with and without learning... more
How do children develop identifications with mathematics over time, seeing themselves as agents in their math classrooms (or not)? This ethnographic and interview study followed nine Latino/a children with and without learning dis/abilities through two years of mathematics in a high-poverty urban school. The children participated in two distinct mathematical pedagogies (discussion-based and procedural-based) that differently constructed ability and dis/ability in mathematics. Individual children constructed unique and dynamic self-understandings as math learners over time, using the cultural resources of the multiple contexts in which they participated, including positioning through language use, ethnicity, gender, and dis/ability. Children made connections between equity and discussion-based mathematics, and between procedural mathematics and fixed conceptions of mathematical ability.
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hile California Common Core State Standards in Mathematics (CA CCSSM) call for rigorous mathematics for all students, students with disabilities have not been provided equal access to instruction that meets these standards. Universal... more
hile California Common Core State Standards in Mathematics (CA CCSSM) call for rigorous mathematics for all students, students with disabilities have not been provided equal access to instruction that meets these standards. Universal Design for Learning (UDL) is a research-based framework to develop strategic, expert learners within classroom settings that maximize engagement of a wide variety of students, including students with disabilities. This brief describes how UDL can provide the foundation of mathematics instruction that provides access to rigorous, standards-based mathematics for all students in California. W Increasing Access to Universally Designed Mathematics Classrooms
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In this article, I propose a mathematical version of Universal Design for Learning called UDL Math. I describe three classrooms that include students with disabilities in meaningful mathematics and explore how the teachers create access... more
In this article, I propose a mathematical version of Universal Design for Learning called UDL Math. I describe three classrooms that include students with disabilities in meaningful mathematics and explore how the teachers create access through multiple means of engagement, representation, and strategic action.
While the COVID-19 pandemic radically changed all aspects of everyone’s life, the closure of schools was one of the most impactful, significantly altering daily life for school personnel, students, and families. The shift to Emergency... more
While the COVID-19 pandemic radically changed all aspects of everyone’s life, the closure of schools was one of the most impactful, significantly altering daily life for school personnel, students, and families. The shift to Emergency Remote Teaching (ERT) presented particular challenges to special educators of students with significant support needs who often benefit from strong interpersonal connections, modeling, and the use of physical manipulatives. This paper details the experiences of two elementary special education teachers as they navigated the transition to ERT. The teachers reported three distinct stages of ERT: making contact, establishing routines, and transitioning to academics. They also discussed the challenges they faced during this period, such as the inequity in resources amongst their students, needing to rely on at-home support in order to meaningfully teach students, and changes in what it meant to be a teacher while having to teach online. While clearly not i...
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This paper presents a case study of the experiences of a highly experienced special educator named Ms. Z teaching standards-based mathematics during Emergency Remote Teaching (ERT) during the spring of 2020.
This paper presents a case study of the experiences of a special educator named Ms. Montes (pseudonym) teaching standards-based mathematics during Emergency Remote Teaching (ERT) during spring 2020. Ms. Montes was interviewed twice during... more
This paper presents a case study of the experiences of a special educator named Ms. Montes (pseudonym) teaching standards-based mathematics during Emergency Remote Teaching (ERT) during spring 2020. Ms. Montes was interviewed twice during this period; data were analyzed through inductive thematic analysis. Pre-COVID, Ms. Montes provided her students daily opportunities to tackle challenging mathematical problems and taught self-regulation strategies for students to better understand themselves as learners. After the shift to ERT, Ms. Montes described “the wall between us” as various barriers that made teaching mathematics online far more challenging. Challenges included supporting students with productive struggle when not physically present with them and supporting student self-regulation during mathematical problem-solving. Supporting students with disabilities to learn mathematics during ERT and distance learning will require considering emotional and affective dimensions of lear...
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One middle school teacher developed classroom routines to make challenging questions accessible to all learners in her class.
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While the COVID-19 pandemic radically changed all aspects of everyone's life, the closure of schools was one of the most impactful, significantly altering daily life for school personnel, students, and families. The shift to Emergency... more
While the COVID-19 pandemic radically changed all aspects of everyone's life, the closure of schools was one of the most impactful, significantly altering daily life for school personnel, students, and families. The shift to Emergency Remote Teaching (ERT) presented particular challenges to special educators of students with significant support needs who often benefit from strong interpersonal connections, modeling, and the use of physical manipulatives. This paper details the experiences of two elementary special education teachers as they navigated the transition to ERT. The teachers reported three distinct stages of ERT: making contact, establishing routines, and transitioning to academics. They also discussed the challenges they faced during this period, such as the inequity in resources amongst their students, needing to rely on at-home support in order to meaningfully teach students, and changes in what it meant to be a teacher while having to teach online. While clearly not in favor of online learning, the teachers do present glimmers of hope, for example, with regards to increased communication between teachers and parents. The challenges and strategies used to overcome these challenges will be of use to educators in the coming months, with implications for distance learning in this population.