Rachel Lambert UC Santa Barbara mathematizing4all@gmail @mathematize4all

1. Countering Deficit Mythologies about the Mathematical Potential of Students with Learning Disabilities Rachel Lambert UC Santa Barbara mathematizing4all@gmail.com @mathematize4all mathematizing4all.wordpress.com

2. Rachel Lambert Slides by Rachel Lambert @mathematize4all 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 PhD in Urban Education (focus on Mathematics, Science and Technology) from CUNY Grad Center Assistant Professor at UC Santa Barbara

3. In Groups Slides by Rachel Lambert @mathematize4all 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?

4. Myths about SwLD learning math SwLD can ONLY learn from direct instruction SwLD cannot create their own strategies and should not be taught using multiple strategies SwLD are best left to special education experts Inquiry math has too high a “cognitive load” for SwLD Creativity and real problem solving is for “high ability” students Slides by Rachel Lambert @mathematize4all

5. My counter argument: Kids Elijah: 5th 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?

6. These myths still exist . . . Slides by Rachel Lambert @mathematize4all

7. Agenda Rachel Lambert @mathematize4all mathematizing4all.wordpress.com • LD- medical model • LD- NEURODIVERSITY • Myths • Low kids • Low kids need a certain kind of math

8. Image search for “learning disability” Slides by Rachel Lambert @mathematize4all

9. Image search for “learning disability” Slides by Rachel Lambert @mathematize4all

10. Slides by Rachel Lambert @mathematize4all

11. 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 @mathematize4all

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

13. From objects ofPITY . . .

14. To the Disability Rights MovementDisability Rights are Human RightsDisability JusticeAccess is Love

15. 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 @mathematize4all

16. Neurodiversity Slides by Rachel Lambert @mathematize4all 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

17. MIND strengths (Eide & Eide, 2011) Slides by Rachel Lambert @mathematize4all Material Reasoning Three-dimensional 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 subtle patterns in complex and constantly shifting systems or data sets

18. A dyslexic research mathematician What does it mean to be “good at math”? Slides by Rachel Lambert @mathematize4all “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 everything made sense.” https://toomai.wordpress.com/2014/09/17/dyslexic-mathematician/

19. Rachel Lambert @mathematize4all mathematizing4all.wordpress.com

20. Neurodiversity + Dyslexia Challenges Strengths Visual spatial processing Creativity Pattern findings Seeing the “big picture” • Phonological processing • Memory for disconnected facts and procedures • Working memory • Executive functioning (planning, self-regulation) How might this matter in mathematics? For Elijah? Slides by Rachel Lambert @mathematize4all

21. Myths about SwLD learning math SwLD (“my low kids”) can ONLY learn from direct instruction SwLD (“my low kids”) cannot create their own strategies and should not be taught using multiple strategies SwLD are best left to special education experts Inquiry math has too high a “cognitive load” for SwLD (“my low kids”) Creativity and problem solving is for “high kids” Slides by Rachel Lambert @mathematize4all

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

23. 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)

24. Rachel Lambert @mathematize4all mathematizing4all.wordpress.com

25. 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

27. 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).

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

29. 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 @mathematize4all

30. History of the two fields Clinical Studies Experimental Psychology Behaviorism Information Processing Cognitive Constructivism Sociocultural MATHEMATICS EDUCATION Sociopolitical Critical Slides by Rachel Lambert @mathematize4all

31. History of the two fields Clinical Studies SPECIAL EDUCATION Experimental Psychology Behaviorism Information Processing Cognitive Constructivism Sociocultural MATHEMATICS EDUCATION Sociopolitical Critical Slides by Rachel Lambert @mathematize4all

32. Rachel Lambert @mathematize4all mathematizing4all.wordpress.com

33. Rachel Lambert @mathematize4all mathematizing4all.wordpress.com

34. Rachel Lambert @mathematize4all mathematizing4all.wordpress.com

35. Problem solving (Lambert & Tan, 2017) Students without disabilities Students with disabilities “Word problems” Uses explicit/direct instruction to teach procedures for solving word problems • “Problem-posing” • Using authentic situations, students craft their own problems • Researchers connected problem-posing to “gifted” or “high-ability” students Slides by Rachel Lambert @mathematize4all

36. Research tells us teachers (and kids) what to do

37. Myth One: Students with LD can ONLY learn from direct instruction Slides by Rachel Lambert @mathematize4all "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).

38. Why inquiry-based math is important for Students with Disabilities (+ “low kids”) Rachel Lambert @mathematize4all mathematizing4all.wordpress.com 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

39. Students with LD can learn from Inquiry-based instruction Slides by Rachel Lambert @mathematize4all 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)

40. Students with LD can learn from Inquiry-based instruction Slides by Rachel Lambert @mathematize4all Cognitively Guided Instruction (CGI) CGI algebra routine in 3rd grade class over 1 year, participation of students with IEPs initially low, but equalized over the year through strong teacher support. SwD able to solve algebraic problems without direct instruction (Foote & Lambert, 2011) Behrend (2003) documented unique strategies of SwLD. 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)

41. Myth Two: Students with LD cannot create their own strategies and should not be taught using multiple strategies Slides by Rachel Lambert @mathematize4all Rachel Lambert @mathematize4all mathematizing4all.wordpress.com Peltenburg, Heuvel-Panhuizen & Robitzsch (2012). SwD using the add-on strategy spontaneously. 91 – 78 Peters et al. (2014), SwD moved between multiple strategies for mult-digit subtraction. Behrend (2003) SwLD constructed strategies in fractions Hunt & Empson (2014); Hunt & Tzur (2017) SwLD constructed their own strategies in equal sharing problems

42. Deficit thinking in research Rachel Lambert @mathematize4all mathematizing4all.wordpress.com “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) SwD 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)

43. 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)

44. 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."

45. 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.

46. 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 and 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.

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

48. 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 SwD, 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)

49. 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/educsci8020072 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/educsci7020051 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)

50. Extra Slides