UDL Math and Inclusive Practices

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Rachel Lambert

University of California, Santa Barbara

Slides by Rachel Lambert mathematizing4all.com

Rachel Lambert

• Taught for over 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.
• Associate Professor in Mathematics Education and Special Education at UC Santa Barbara
• Author of a book!

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My website�www.mathematizing4all.com

Facebook Group- UDL Math

Today we will . . .

• Revisit inclusive practices in the context of disability and mathematics
• Continue to explore dyslexia (learning disabilities in reading) and math
• Designing from the Margins in Mathematics

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Slides by Rachel Lambert mathematizing4all.com

5 statements about Inclusive Practice in Mathematics

1. Inclusive Education is not a place or a placement or a service model or coteaching, but a “a continuing struggle against the processes and practices of schooling that erect barriers which compromise the participation of some students”(Slee & Allen, 2001).
2. Inclusive education is never a recipe book, because students and contexts are complex. So teachers need to tap into their creative problemsolving and ingenuity.
3. Creating truly inclusive mathematics classrooms will mean opening up our understanding about what math is (beyond memorization and procedures)
4. Inclusive practice requires rethinking and rejecting deficit thinking about disability and neurodiversity.
5. If we truly included all kids in our schools, it would transform our schools for the better (Naraiam 2017).

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Slides by Rachel Lambert mathematizing4all.com

Teachers as designers towards inclusive practices

In the math lesson

In the classroom

In the systems

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In our beliefs about students

What barriers have you noticed in your work?

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What change are you inspired to make? (big change, small change, all matter!)

Slides by Rachel Lambert mathematizing4all.com

So how to redesign mathematics from the margins?

Universal Design for Learning is often presented as a checklist

But many of us think of it as a mindset, as a process, as a “way of thinking”, as a “way to move”, as creative work by teachers!

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Teachers as designers towards more accessibility

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Slides by Rachel Lambert UCSB mathematizing4all.com

1. Math class is too narrow

3. Strategic Supports

2. Open up math class

Slides by Rachel Lambert mathematizing4all.com

Does this image of an undergrad math class prompt any memories for you? Emotions?

What barriers do you identify in this undergraduate math classroom?

Neurodiversity

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• Scientific truth that our brains are all different, that variability is the norm
• Social movement led by neurodiverse people that sees cognitive diversity as natural and beneficial to humankind
• Neurodiverse people seen as experts in their own learning and cognition
• Recognizes both strengths and challenges of different neurodiversities

Slides by Rachel Lambert UCSB mathematizing4all.com

Neurodiversity: Dyslexia/LD

Challenges may include:

Strengths may include:

Phonological processing

Language

Memory for facts and procedures

Working memory

Executive functioning

Visual spatial processing

Creativity

Pattern finding, seeing connections

Seeing the “big picture”

Narrative thinking

Slides by Rachel Lambert UCSB mathematizing4all.com

Dyslexia/LD and math

Other kids had known I was struggling in primary school. It was quite obvious when it came to doing maths. We would stand in a line with the teacher facing the front of the queue. The teacher would ask, "What's 9 x 12?" If you got it wrong you would go to the back of the queue and I was always there. I still can't remember my times tables. I can't quite place the information together. (Elliot, 17)

I actually like maths. I like getting through it slowly and problem-solving. What I like is that there is more than one way to answer a question. If I can't do something I can get there another way (Fiona, 15)

In Maths I didn't know my times tables. I couldn't take them in. I only know my twos, threes, and tens. (Freddie, 10)

I'm very good at 3D, the hands-on stuff, and I'm quite good at science and the geometry side of Maths. (Max, 17)

I solve maths problems in a different way. I visualise them. (Molly, 13)

In Maths they were really quick at sums the took me ages. (Elijah, 12)

I was always labelled 'not good at maths' when this shouldn't have been the case. Schools put you in boxes and leave you there. (Charlie, 17)

Slides by Rachel Lambert UCSB mathematizing4all.com

What barriers exist for these learners?�What supports learning?

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Other kids had known I was struggling in primary school. It was quite obvious when it came to doing maths. We would stand in a line with the teacher facing the front of the queue. The teacher would ask, "What's 9 x 12?" If you got it wrong you would go to the back of the queue and I was always there. I still can't remember my times tables. I can't quite place the information together. (Elliot, 17)

I actually like maths. I like getting through it slowly and problem-solving. What I like is that there is more than one way to answer a question. If I can't do something I can get there another way (Fiona, 15)

In Maths I didn't know my times tables. I couldn't take them in. I only know my twos, threes, and tens. (Freddie, 10)

I'm very good at 3D, the hands-on stuff, and I'm quite good at science and the geometry side of Maths. (Max, 17)

I solve maths problems in a different way. I visualise them. (Molly, 13)

In Maths they were really quick at sums the took me ages. (Elijah, 12)

I was always labelled 'not good at maths' when this shouldn't have been the case. Schools put you in boxes and leave you there. (Charlie, 17)

Slides by Rachel Lambert UCSB mathematizing4all.com

If you had a magic wand what would you change about math class that would help more than one of these students?

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Other kids had known I was struggling in primary school. It was quite obvious when it came to doing maths. We would stand in a line with the teacher facing the front of the queue. The teacher would ask, "What's 9 x 12?" If you got it wrong you would go to the back of the queue and I was always there. I still can't remember my times tables. I can't quite place the information together. (Elliot, 17)

I actually like maths. I like getting through it slowly and problem-solving. What I like is that there is more than one way to answer a question. If I can't do something I can get there another way (Fiona, 15)

In Maths I didn't know my times tables. I couldn't take them in. I only know my twos, threes, and tens. (Freddie, 10)

I'm very good at 3D, the hands-on stuff, and I'm quite good at science and the geometry side of Maths. (Max, 17)

I solve maths problems in a different way. I visualise them. (Molly, 13)

In Maths they were really quick at sums the took me ages. (Elijah, 12)

I was always labelled 'not good at maths' when this shouldn't have been the case. Schools put you in boxes and leave you there. (Charlie, 17)

Slides by Rachel Lambert UCSB mathematizing4all.com

What supports learning?

• Going slowly
• Problem solving
• Choice in strategy
• 3D math/geometry/visualization

What are the barriers?

• Remembering math facts
• Focus on speed
• Being labeled, stigmatized

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Slides by Rachel Lambert mathematizing4all.com

Neurodiversity: Dyslexia/LD

Challenges may include:

Strengths may include:

Phonological processing

Language

Memory for facts and procedures

Working memory

Executive functioning

Visual spatial processing

Creativity

Pattern finding, seeing connections

Seeing the “big picture”

Narrative thinking

Slides by Rachel Lambert UCSB mathematizing4all.com

We need to move away from deficit thinking and deficit pedagogies . . .

“my low kids”

“IEP kids

strugglers”

All kids

Explicit Instruction alone

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Guided Inquiry

Grade Level Challenge

Concepts and Procedures

Slides by Rachel Lambert UCSB mathematizing4all.com

Developing our tool kit as inclusive designers . . .

In the math lesson

In the classroom

In the systems

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In our beliefs about students

What barriers have you noticed in your work?

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What change are you inspired to make? (big change, small change, all matter!)

Slides by Rachel Lambert mathematizing4all.com

Empathy Interviews

What barriers have you noticed in your work?

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Who could you ask to learn more about that?

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Slides by Rachel Lambert mathematizing4all.com

Empathy Interview

Pick a few students whose perspective would be particularly useful- often those at the margins or for whom the system is not working

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Slides by Rachel Lambert mathematizing4all.com

Empathy Interview

Pick a few students whose perspective would be particularly useful- often those at the margins or for whom the system is not working

Design an Empathy Interview with 3-6 questions that will help you understand their experience with this barrier.

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Slides by Rachel Lambert mathematizing4all.com

Empathy Interview

Pick a few students whose perspective would be particularly useful- often those at the margins or for whom the system is not working

Design an Empathy Interview with 3-6 questions that will help you understand their experience with this barrier.

Conduct interviews

Debrief with colleagues, developing your understanding of the problem of practice from the perspective of the users . . .

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THEN ReDESIGN!

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Slides by Rachel Lambert mathematizing4all.com

5 statements about Inclusive Practice in Mathematics

1. Inclusive Education is not a place or a placement or a service model or coteaching, but a “a continuing struggle against the processes and practices of schooling that erect barriers which compromise the participation of some students”(Slee & Allen, 2001).
2. Inclusive education is never a recipe book, because students and contexts are complex. So teachers need to tap into their creative problemsolving and ingenuity (UDL!).
3. Creating truly inclusive mathematics classrooms will mean opening up our understanding about what math is (beyond memorization and procedures)
4. Inclusive practice requires rethinking and rejecting deficit thinking about disability and neurodiversity.
5. If we truly included all kids in our schools, it would transform our schools for the better (Naraiam 2017).

​

Slides by Rachel Lambert mathematizing4all.com

“When we as teachers trust in the thinking of our students, especially our students with disabilities, we create the conditions our students need to trust themselves as mathematical thinkers. When we, their teachers, believe that our students can and will solve complex problems, they will be able to.”

Rethinking Disability and Mathematics

Slides by Rachel Lambert UCSB mathematizing4all.com

Resources (more at mathematizing4all.com)�

Resources (many at mathematizing4all.com)

• Lambert, R. (2021). The Magic Is in the Margins: UDL Math. Mathematics Teacher: Learning and Teaching PK-12, 114(9), 660–669. https://doi.org/10.5951/MTLT.2020.0282
• Lambert, R., Imm, K., Schuck, R., Choi, S., & McNiff, A. (2021). “UDL Is the What, Design Thinking Is the How:” Designing for Differentiation in Mathematics. Mathematics Teacher Education and Development, 23(3), 54–77.
• Lambert, R., & Harriss, E. (2022). Insider accounts of dyslexia from research mathematicians. Educational Studies in Mathematics, 111(1), 89–107. https://doi.org/10.1007/s10649-021-10140-2
• Lambert, R. (2023) Webinar: Evaluating Research Claims in Mathematics https://www.nctm.org/online-learning/Webinars/Details/686
• Rooke, M. (2017). Dyslexia is My Superpower. Jessica Kingsley Publishers.
• Brown, L., Brown, L. X. Z., Ashkenazy, E., & Onaiwu, M. G. (2017). All the Weight of Our Dreams: On Living Racialized Autism. Autism Women’s Network.
• Eide, B., & Eide, F. (2012). The dyslexic advantage: Unlocking the hidden potential of the dyslexic brain (Reprint edition). Plume.
• Edmund Harriss’s blog https://maxwelldemon.com/edmund-harriss/
• Empson, S. B., & Levi, L. (2011). Extending children’s mathematics: Fractions & decimals: Innovations in cognitively guided instruction. Heinemann.
• Silberman, S. (2016). Neurotribes: The Legacy of Autism and the Future of Neurodiversity (Reprint edition). Avery.
• Slee, R., & Allan, J. (2001). Excluding the included: A reconsideration of inclusive education. International Studies in Sociology of Education, 11(2), 173–192. https://doi.org/10.1080/09620210100200073
• Blog on defining neurodiversity: https://neuroqueer.com/neurodiversity-terms-and-definitions/
• Fritzgerald, A. (2020). Antiracism and Universal Design for Learning. CAST, Inc.
• Hamraie, A. (2016). Universal Design and the Problem of “Post-Disability” Ideology. Design and Culture, 8(3), 285–309. https://doi.org/10.1080/17547075.2016.1218714
• Meyer, A., Rose, D. H., & Gordon, D. T. (2014). Universal design for learning: Theory and practice. CAST Professional Publishing. http://udltheorypractice.cast.org/
• https://udlguidelines.cast.org/

Slides by Rachel Lambert mathematizing4all.com