Countering Deficit Mythologies about the Mathematical Potential of

Countering Deficit Mythologies about the Mathematical Potential of Students with Learning Disabilities Rachel Lambert UC Santa Barbara mathematizing 4 all@gmail. com @mathematize 4 all mathematizing 4 all. wordpress. co m

Rachel Lambert • Taught for 10 years as a general ed. classroom teacher, special ed. co-teacher, resource room teacher, preschool intervention specialist in New York City, San Francisco and Los Angeles. • MA in Learning Dis/Abilities from Teachers College • Ph. D in Urban Education (focus on Mathematics, Science and Technology) from CUNY Grad Center Slides by Rachel Lambert @mathematize 4 all

In Groups • What myths have you heard about the math potential of students with Learning Disabilities (LD, dyslexia, etc. )? • Have you seen deficit thinking used to understand these students? What does that look like, sound like? Slides by Rachel Lambert @mathematize 4 all

Myths about Sw. LD learning math • Sw. LD can ONLY learn from direct instruction • Sw. LD cannot create their own strategies and should not be taught using multiple strategies • Sw. LD are best left to special education experts • Inquiry math has too high a “cognitive load” for Sw. LD • Creativity and real problem. Slides solving is for by Rachel Lambert @mathematize 4 all

My counter argument: Kids Elijah: 5 th grader, African-American and Puerto Rican, IEP for a learning disability (dyslexia), difficulty with writing and memorizing math facts. Who is your counter argument to deficit myths? Your puzzle?

These myths still exist. . . Slides by Rachel Lambert @mathematize 4 all

Agenda • LD- medical model • LD- NEURODIVERSITY • Myths – Low kids need a certain kind of math Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Image search for “learning disability” Slides by Rachel Lambert @mathematize 4 all

Anxiety and Depressio n Mental Illness Behavior Disabilities Emotional Disabilities Mobility Impairment s Deafness Blindness Physical Disabilities Intellectual Disabilities Reading (Dyslexia) Writing (Dysgraphia) Cerebral Palsy Specific Learning Disabilities Math (Dyscalculia) Disabilit y Autism Attention Deficit Hyperactivity Disorder Speech and Language Impairments Slides by Rachel Lambert @mathematize 4 all

LD/Dyslexia Challenges • Phonological processing • Memory for disconnected facts and procedures • Working memory • Executive functioning (planning, self-regulation) How might this matter in mathematics? Slides by Rachel Lambert @mathematize 4 all

Our society is on the cusp of a revolution in how we see disability

From objects of PITY. . .

To the Disability Rights Movement Disability Rights are Human Rights Disability Justice Access is Love

What I hear. . • Don’t all students with disabilities NEED explicit instruction in math? • I don’t know how to teach those kids. I wasn’t trained. • He has so many gaps. • My low kids need direct instruction. • Those students don’t belong in our classes. • She’s not ready for the math in my classroom. She doesn’t know her numbers! • He can’t handle multiple strategies. Medical/Deficit Model of Disability Slides by Rachel Lambert @mathematize 4 all

Neurodiversity • Biological fact: neurological diversity is part of humanity • A social justice movement created by autistic self-advocates (Robertson & Ne’eman, 2008; Boundy, 2008; Robison, 2017) • Differences exist, not as deficits, but part of natural human diversity • Extended to dyslexia/learning disabilities, ADHD, mental illness (“mad pride”) and others Slides by Rachel Lambert @mathematize 4 all

MIND strengths (Eide & Eide, 2011) Material Reasoning Threedimensional spatial reasoning mechanical ability. Interconnected Reasoning perceive relationships and patterns (intuition) Narrative Reasoning remember important personal experiences, understand abstract information in terms of narrative Dynamic Reasoning the ability to perceive and take advantage of Slides by Rachel Lambert @mathematize 4 all subtle patterns in complex and

A dyslexic research mathematician “As a dyslexic, I’ve never been good at calculations or recalling rote facts like times tables. Here’s the thing: beyond a certain point in mathematics, it’s not really about calculations. ” “Geometry class was when math became interesting, and easier for me. Suddenly I was in a world, not of strands of symbols to be processed, but of shape, space, lines, angles, concepts, and narrative-like proofs. Suddenly What does it mean to be “good at math”? everything made sense. ” Slides by Rachel Lambert https: //toomai. wordpress. com/2014/09/17/dyslexic-mathematician/ @mathematize 4 all

Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Neurodiversity + Dyslexia Challenges Strengths • Phonological processing • Memory for disconnected facts and procedures • Working memory • Executive functioning (planning, self-regulation) • • Visual spatial processing Creativity Pattern findings Seeing the “big picture” How might this matter in mathematics? For Elijah? Slides by Rachel Lambert @mathematize 4 all

Myths about Sw. LD learning math • Sw. LD (“my low kids”) can ONLY learn from direct instruction • Sw. LD (“my low kids”) cannot create their own strategies and should not be taught using multiple strategies • Sw. LD are best left to special education experts • Inquiry math has too high a “cognitive load” for Sw. LD (“my low kids”) • Creativity and problem solving is for “high kids” Slides by Rachel Lambert @mathematize 4 all

Slide where there is a picture of me taking a hammer to the concept of “my low kids” (work in progress)

Myth: There are such a thing as “low kids” 1. Scientifically inaccurate • Neuroplasticity (Jo Boaler) • Neurodiversity as scientific fact (all brains are different) • Learner Variability (CAST, UDL) There is no “normal” or “average” brain. We all have varied profiles across multiple dimensions of “intelligence” (Rose)

Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Myth: There are such a thing as “low kids” 1. Scientifically inaccurate (con’t) • Mathematical learning is complex, and not linear • Algebraic thinking vs. geometry thinking

Myth: Sorting our kids into high and low is good for them • They know what you are doing • They take up the labels you offer them • The practice of ability grouping generally is inequitable for students in the “low” groups (so not effective).

The False Deficit Binary Binds our Thinking “my low kids” Explicit “my high kids” Inquiry Instruction Procedures Instruction Concepts Where does it come from? Is there evidence to refute this?

It comes from research. . . “The premise that secondary students with LD will construct their own knowledge about important mathematical concepts, skills, and relationships. . . is indefensible, illogical, and unsupported by empirical investigations. " (Jones et al. , 1998, p. 161). Slides by Rachel Lambert @mathematize 4 all

History of the two fields Clinical Studies Experimental Psychology Behaviorism Information Processing Cognitive Constructivism MATHEMATICS EDUCATION Sociocultural Sociopolitical Critical Slides by Rachel Lambert @mathematize 4 all

History of the two fields Clinical Studies SPECIAL EDUCATION Experimental Psychology Behaviorism Information Processing Cognitive Constructivism MATHEMATICS EDUCATION Sociocultural Sociopolitical Critical Slides by Rachel Lambert @mathematize 4 all

Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Problem solving (Lambert & Tan, 2017) Students without disabilities • “Problem-posing” • Using authentic situations, students craft their own problems • Researchers connected problem-posing to “gifted” or “high-ability” students Students with disabilities • “Word problems” • Uses explicit/direct instruction to teach procedures for solving word problems Slides by Rachel Lambert @mathematize 4 all

Research tells us teachers (and kids) what to do

Myth One: Students with LD can ONLY learn from direct instruction "Although these findings confirm that explicit instruction is an important tool for teaching mathematics to students with LD, it is important to note that there is no evidence supporting explicit instruction as the only mode of instruction for these students"(National Mathematics Advisory Panel, 2008, p. 1229). Slides by Rachel Lambert @mathematize 4 all

Why inquiry-based math is important for Students with Disabilities (+ “low kids”) • • • Increase achievement Increase non routine problem solving Access to mathematics that is meaningful Access to identities as mathematicians Access to future STEM careers Enjoyment and joy in mathematics Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Students with LD can learn from Inquiry-based instruction Enhanced Anchored Instruction • Multi-modal algebra curriculum. Deep investigative problems, including video. Focused on training teachers to equalize small group work, and teacher MKT. Participation equalized and strong achievement gains by LD students. (Bottge et al. , 2001; Bottge et al. , 2007; Bottge et al. 2010; Bottge et al. , 2015) Slides by Rachel Lambert @mathematize 4 all

Students with LD can learn from Inquiry-based instruction Cognitively Guided Instruction (CGI) • CGI algebra routine in 3 rd grade class over 1 year, participation of students with IEPs initially low, but equalized over the year through strong teacher support. Sw. D able to solve algebraic problems without direct instruction (Foote & Lambert, 2011) • Behrend (2003) documented unique strategies of Sw. LD. • CGI problem solving with students with disabilities, found that students with LD were supported in solving open-ended problems through teacher scaffolds and MKT. Also found that teachers reported being better able to understand their students with disabilities. (Moscardini, 2007, 2011) Slides by Rachel Lambert @mathematize 4 all

Myth Two: Students with LD cannot create their own strategies and should not be taught using multiple strategies • Peltenburg, Heuvel-Panhuizen & Robitzsch (2012). Sw. D using the add-on strategy spontaneously. 91 – 78 • Peters et al. (2014), Sw. D moved between multiple strategies for mult-digit subtraction. • Behrend (2003) Sw. LD constructed strategies in fractions • Hunt & Empson (2014); Hunt & Tzur (2017) Sw. LD constructed their own strategies in equal sharing problems Slides by Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Deficit thinking in research • “To expect students who have a history of problems with automaticity, metacognitive strategies, memory, attention, generalization, proactive learning, and motivation to engage in efficient self-discovery learning. . . is not plausible. ” (Mercer, Jordan, 1994, p. 296) • Sw. D will be “confused, ” inquiry “places substantial demands on metacognitive skills, which may not be adequately developed in children with MLD” (Desoete, Roeyers, & de Clercq, 2004, p. 52) Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

Scottish Attainment Challenge Cognitively Guided Instruction Project 2016 -2018 Final Report (Moscardini & Sadler, 2018) After 1 -3 years of sustained PD in CGI: • a significant rise in attainment • growth in teachers' confidence and knowledge about children's mathematics • End to ability groupings in math in the 3 schools • “Perhaps even more powerful evidence was presented by the teachers across all three schools, who stated that over the duration of the project not a single child was deemed to require additional support for numeracy outside the classroom. This does not mean that no child needed support with numeracy, but rather, where individual children were identified as requiring support this was dealt with through restructuring classroom practice. ” (p. 63)

Insider Narrative: Lynn Pelkey On the playground, in gym, and in art classes, or playing games, I was the same as any other child, but academically I could not achieve what other children could. As academics took on more important role in my daily life, being with playmates became less than pleasurable. We were no longer equal. At times, I was physically separated from my classmates. During these times, I was brought to the "special" room where I would receive help with my school work in hopes of bringing me "up to my class level. " No one ever said this to me directly; it was what I overheard: "She is not doing as well as the other children, " "She is having difficulty", "Scoring low", "Not trying, " "Lazy. "

Insider Narrative: Lynn Pelkey I felt humiliated going in and out of [the Resource Room]. The teachers were very kind, but I believe now that they underestimated me. I would do what they told me to do, recite what they told me to recite, but I was rarely asked to really think, and I almost never experienced those moments when something I was learning came together and made sense. I think I did a lot of memorizing, but not much understanding.

Insider Narrative: Lynn Pelkey I said, "Yes, " and grabbed a seat next to my friend. I did not have any paper or a book, I just sat and listened. I was in a "real" class with normal students. I just started skipping whatever class I was supposed to be in during that period and started attending Paul's algebra class on a regular basis. As I sat in that class, something magical happened to me. I could understand what he was teaching. I was learning. I even started participating in the class, raising my hand answering questions. I was LD. But then again I wasn't. I still couldn't multiply or divide very well, and I had to use elaborate ways to come up with the answer. But I wasn't memorizing, I was thinking, and I was figuring out the answer. I was learning. This was one of the experiences that shot a pinhole in the bubble that trapped me in my LDness.

The False Deficit Binary Binds our Thinking “my low kids” Explicit Instruction “my high kids” Inquiry Procedures Cannot think on their own Basics first Instruction Concepts Can think Where does it come from? Is there evidence to refute

How to shift mindset • Educate yourself about neurodiversity, Disability Rights Movement, and the perspective of people with disabilities. Challenge your own internalized ableism. • Narratives (read disability memoirs, interview students, tell stories about students you know) • Experience – Teach a lesson in the special ed class – Do a child study on a Sw. D, to uncover understanding, complexity • Explore the mathematical thinking of children (PD in CGI) • Challenge deficit thinking IRL (“what do you mean by low? ” • Challenge deficit thinking in the system (IEP goals that are procedural, tracking, static ability grouping, segregated classes, RTI, MTSS)

Playlist • Lambert, R. (2018). “Indefensible, Illogical, and Unsupported”; Countering Deficit Mythologies about the Potential of Students with Learning Disabilities in Mathematics. Education Sciences, 8(2), 72. https: //doi. org/10. 3390/educsci 8020072 • Lambert, R. , & Tan, P. (2017). Conceptualizations of students with and without disabilities as mathematical problem solvers in educational research: A critical review. Education Sciences, 7(2), 51. https: //doi. org/10. 3390/educsci 7020051 • Pelkey, L. (2001). In the LD bubble. In P. Rodis, A. Garrod, & M. L. Boscardin (Eds. ), Learning disabilities and life stories. Boston, MA: Allyn and Bacon. • Final report Scottish Attainment Challenge Cognitively Guided Instruction Project (Moscardini & Sadler, 2018)

Extra Slides

Models of Disability Medica l • A defect/deficit • Individual • Fix the deficit, remediate the individual • Find weak math skills, focus on those skills Social Impairment- • Society, cognitive and cultural contexts physical DISABLE differences • Fix the context: classrooms, curriculum Slides by Rachel Lambert

Insider Perspective: Shamus Young What I fail to understand is that the "harder" classes are where math becomes far more interesting. Instead of forty dull problems, they give you five interesting ones. Instead of pointless drills, you can begin to see how to use math as a tool. They finally give you a pile of two-by-fours and let you start nailing things together. Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

“More often than not, we see that [dyslexic] students have a flexibility with numbers and a strong enough working memory that allows them to keep the numbers being worked on ‘in mind’. Flexibility with numbers means being able to see the number 18 as 10 + 8 or 9 x 2 or 20 – 2, all the while proceeding to the solution of a math problems. These are kids who sometimes arrive at an answer before anyone else, but then get bogged down if they are required to ‘show their work. ’” F. Eide Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

What is the problem? • Cognitive deficits in Sw. D (Geary, 2011) • Achievement gap in math for Sw. D (Wei, Lenz, & Blackorby, 2013) • Sw. D not offered access to standards-based math instruction (Kurz, Elliott, Wehby, & Smithson, 2010; Jackson & Neel, 2008) • Sw. D not placed in algebra at the same rate as non-disabled peers, even when controlling for achievement (Faulkner et al. , 2013) • Sw. D not participating deeply in standardsbased mathematics classrooms (Baxter, Olsen & Woodward, 2001; Bottge et al. 2001) • Despite talent, Sw. D not represented in STEM fields (Dunn, Rabren, Taylor, & Dotson, 2012) Slides by Rachel Lambert @mathematize 4 all

Word Problems age 7 - 17 (Wei, Lenz, & Blackorby, Slides by Rachel Lambert 2013) @mathematize 4 all

Jackson & Neel, 2006 [SERIES NAME], [VALUE] 80% Percent of Instruction 70% Conceptual Instruction 60% 50% 40% Procedural Instruction 30% 20% [SERIES NAME], [VALUE] 10% 0% GE class Slides by Rachel Lambert @mathematize 4 all

NORMAL NOT NORMAL • General Education Teachers • General Education Teacher Training • Mathematics Education Research • Special Education Teachers • Special Education Teacher Training • Special Education Mathematics Research Rachel Lambert @mathematize 4 all mathematizing 4 all. wordpress. com

The ultimate goal is that students develop a disposition towards their mathematical learning which involves a sense of themselves as learners who construct mathematical meaning through engaging in mathematical activity, rather than experiencing mathematical instruction as the acquisition of isolated facts and procedures. This study has shown that for the participating pupils with learning difficulties this is a realistic and reasonable expectation, but the realization of this expectations is fundamentally dependent on the knowledge and beliefs of the teacher (Moscardini, 2010, p. 136). Slides by Rachel Lambert @mathematize

“. . . by learning about children’s mathematical understanding the teachers felt more equipped to support particular children in the context of the classroom rather than using this knowledge as a mechanism for their removal” (Moscardini, 2014, p. 76) Slides by Rachel Lambert @mathematize