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Multiplication and Division Facts for the Whole-to-Part, Visual Learner

The program in this book utilizes semantic reasoning strengths, and a combination of whole-to-part processing and gross motor kinesthetic therapies to compensate for deficits in working memory, expressive language mechanisms, and executive function. Multiplication concepts and facts are linked to the student’s existing knowledge base across a broad spectrum of modalities.

Web-based book support files: Printable worksheets and video links

Articles and Position Papers by Chris Woodin

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Demystifying Math Struggles and Identifying Strategies to Help

Read this online article that includes information and examples (including video!) of how to understand then support struggling math learners through diagnostic and prescriptive teaching.

Books that Provide Research-Based Support

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Dyscalculia From Science to Education, 2019 Butterworth, Brian, Routledge, New York, NY

DUAL CODING THEORY AND EDUCATION Allan Paivio University of Western Ontario Draft chapter for the conference on “Pathways to Literacy Achievement for High Poverty Children,” The University of Michigan School of Education, September 29-October 1, 2006.

Campbell, J. I. D. (Ed.). (2005). Handbook of mathematical cognition. Psychology Press. https://doi.org/10.4324/9780203998045

Number Sense and Dyscalculia, Wilson, W., Dehaene, S. 2007 INSERM-CEA Unit 562 « Cognitive Neuroimaging » Service Hospitalier Frédéric Joliot CEA-DRM-DSV Orsay, France appearing in: Human Behavior, Learning, and the Developing Brain: Atypical Development. Edited by Coch D, Dawson G, Fischer K: Guilford Press, New York 2007.

Human Behavior, Learning and the Developing Brain Coch, Dawson, Fischer

Vygotsky on Education Primer. Peter Lang Publishers. Lake, R. (2012). CHAPTER THREE Pgs. 71-114 Vygotsky’s view of the Dialectical Relationship between Thinking and Speech

WoodinMath in Dyslexic Advantage

The BIG PICTURE of Math Referencing this Video Link Dyslexic Advantage Newsletter August 2017 Issue 20 P. 27

"Problem Categorization A great lesson that Chris has posted on YouTube is his approach to problem categorization. A common challenge that dyslexic students face is getting lost in the myriad of different problems that are presented at one time. Like teaching students to categorize written essay prompts, it can be very helpful to teach students to categorize math problems."

This Issue of the Dyslexic Advantage Newsletter now requires a subscription and cannot be linked.

Articles on Cognition, Language, and Dyscalculia

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Dyscalculia-Based Articles And Powerpoint Presentations

• Math Disability and Dyscalculia: One and the Same, or Not? Butterworth, Brian, Powerpoint Presentation, The Dyslexia Foundation, Boston, 2014

•Subitizing and Visual Counting in Children with Problems in Acquiring Basic Arithmetic Skills. Fischer B, Gebhardt C, Hartnegg K.

College of Optometrists in Vision Development. 2008:39(1):24-29.

• Effects of Daily Practice on Subitizing, Visual Counting, and Basic Arithmetic Skills. Fischer B, Köngeter A, Hartnegg K.

College of Optometrists in Vision Development. 2008:39(1):30-34.

• Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia. Wilson, A.J., Dehaene, S., Pinel, P. et al. Behav Brain Funct 2, 19 (2006). https://doi.org/10.1186/1744-9081-2-19

•Foundational Numerical Capacities and the Origins of Dyscalculia. Butterworth, Brian Trends in Cognitive Sciences, Vol 14, pages 534–541, 2010

•Putting a Finger on Numerical Development – Reviewing the Contributions of Kindergarten Finger Gnosis and Fine Motor Skills to Numerical Abilities. Barrocas R, Roesch S, Gawrilow C and Moeller K (2020) Front. Psychol. 11:1012. doi: 10.3389/fpsyg.2020.01012

Gracia-Bafalluy, M., and Noël, M. P. (2008). Does finger-training increase young children’s numerical performance? Cortex 44, 368–375.

• Virginie Crollen, Marie-Pascale NoëL, Xavier Seron, Pierre Mahau, Franco Lepore, Olivier Collignon, Visual experience influences the interactions between fingers and numbers, Cognition, Volume 133, Issue 1,2014,Pages 91-96, ISSN 0010-0277.

• Crollen, V., Seron, X., & Noël, M. P. (2011b). Is finger-counting necessary for the development of arithmetic abilities? Frontiers in Psychology, 2, 242. http://dx.doi.org/10.3389/fpsyg.2011.00242.

•Fayol, M., and Seron, X. (2005). “About numerical representations: insights from neuropsychological, experimental and developmental studies,” in Handbook of Mathematical Cognition, ed. J. I. D. Campbell (New York: Psychology Press), 3–22.

•The Effects of Concrete to Semiconcrete to Abstract Instruction in the Acquisition and Retention of Fraction Concepts and Skills.Jordan, LuAnn; Miller, M. David; Mercer, Cecil D.Learning Disabilities: A Multidisciplinary Journal, v9 n3 p115-22 Fall 1998-Win 1999

•Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016). Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied & Computational Mathematics, 5(5), DOI: 10.4172/2168-9679.1000325.

Dorsal and Ventral Processing Stream Articles

• Role of the dorsal stream in skilled reading. Younger, Jessica Renee Wise, University of Texas, 2018

Retrieved from https://repositories.lib.utexas.edu/handle/2152/69025

•Developmental Differences for Word Processing in the Ventral Stream Olumide, Flowers, Napolielo, Eden, Guinevere F.Brain Lang. Author manuscript; available in PMC 2014 May 1.Published in final edited form as: Brain Lang. 2013 May; 125(2): 134–145. Published online 2012 May 5. doi: 10.1016/j.bandl.2012.04.003PMCID: PMC3426643

•Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic. NeuroImage: Clinical Volume 18, 2018, Pages 663-674

• Stability and change in markers of core numerical competencies. Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012) Journal of Experimental Psychology: General, 141(4), 649-666. doi:10.1037/a0027520

Cognitive Metrics and their Impact on Math

• Bernabini L, Bonifacci P and de Jong PF (2021) The Relationship of Reading Abilities With the Underlying Cognitive Skills of Math: A Dimensional Approach. Front. Psychol. 12:577488. doi: 10.3389/fpsyg.2021.577488

Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., . . . Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33-41. doi:10.1016/j.cognition.2010.03.012

• Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of ‘‘the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral Brain Function, 2, 20

•) Short-Term Memory, Working Memory, and Executive Functioning in Preschoolers: Longitudinal Predictors of Mathematical Achievement at Age 7 Years, Rebecca Bull, Kimberly Andrews Espy & Sandra A. Wiebe (2008 Developmental Neuropsychology, 33:3, 205-228, DOI: 10.1080/87565640801982312

• Phonological processing and arithmetic fact retrieval: Evidence from developmental dyslexia Bert De Smedt, Bart Boets, Neuropsychologia, V48, Issue 14, 2010, 3973-3981,ISSN 0028-3932

•Malone, Stephanie, Delaney, Michelle, Burgoyne, Kelly and Hulme, Charles. (2019). Learning correspondences between magnitudes, symbols and words: Evidence for a triple code model of arithmetic development. Cognition. 187, pp. 1 - 9. https://doi.org/10.1016/j.cognition.2018.11.016 Retrieved 3.1.2023

•Skagenholt M, Träff U, Västfjäll D, Skagerlund K. Examining the Triple Code Model in numerical cognition: An fMRI study. PLoS One. 2018 Jun 28;13(6):e0199247. doi: 10.1371/journal.pone.0199247. PMID: 29953456; PMCID: PMC6023115. Retrieved 3.1.2023

Language Expression Articles.

Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners

•Numerical morphology supports early number word learning- Evidence from a comparison of young Mandarin and English learners

Corre, M. L., Li, P., Huang, B. H., Jia, G., & Carey, S. (2016). Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners. Cognitive Psychology, 88, 162–186. https://doi.org/10.1016/j.cogpsych.2016.06.003

• Mathematics and English, Two Languages

• How Seeing and Using Gestures Make Ideas More Memorable

• The Shape of Things- The Origin of Young Children's Knowledge of the Names and Properties of Geometric Forms.pdf Verdine,B. et.al. ,J Cogn Dev. 2016 January 1;

• What are Executive Functions and Self Regulation and What Do They have to do With Language -Learning Disorders? - Singer and Bashir

• Vygotsky on Education Primer, Lake, Robert. 2012 Peter Lang Publishers, New York, NY, USA, (CHAPTER THREE Pgs. 71-‐‑114)

Decoding Drake's Dream

Decoding Drake's Dream Fall 2015

The micro-uniting of language permeates not just English classes, but every aspect of the [Landmark] program — every class at Landmark is, to some extent, a language class. Chris Woodin's pulley graphs and floor clocks are as much about language as about math since they get students to understand that problems must be sequenced in time in order to be solved — and sequencing, with its semantic emphasis on past, present, and future, is fundamentally the domain of language.