What is the Play Math Program at Wellington-Alexander Center?
Play Math is a neurocognitive approach to teaching the foundational concepts in numeracy that underlie the ability to think mathematically. Play Math is a therapeutic intervention for students with neurodevelopmental uniquenesses that prevent children from learning math using traditional methods of mathematical memorization.
Integrating theory and practice from Thomas Carpenter, Liping Ma, Alexander Luria, and Lev Vygotsky alongside neuroscience research, we help children with dyslexia, dyscalculia, ADHD, and dyspraxia develop foundational numeracy skills through play.
Approximately 5-6% of students have neurobiologically based dyscalculia, yet as many as 50% of students have difficulty with foundational numeracy and math skills. The reasons are broad: Brain differences in visual-spatial skills, working memory, phonological processing, attention, and imagery; co-existing diagnoses, problems with the "language of math", the variations in curriculum, and inconsistencies in teaching philosophies and methodologies.
Our focus is working with children ages 5-14 who have not acquired a foundational understanding of the relationships between numbers. Our most frequent students are referred in grades 3rd-8th when they have been unable to learn and apply their math facts (addition, subtraction, multiplication, and division).
Challenges we often observe include difficulty with:
understanding magnitude & quantity
understanding how quantities fit together and can be taken apart
understanding mathematical symbols & operations
confusion over the meaning of the equal sign
confusing over the meaning on ONE (digit, number, set, thing)
understanding how operations are “the same yet, different”
developing strategies to solve mathematical problems
tempo, rhythm & timing
fluency & automaticity
attention & working memory
The treatment of dyscalculia requires a developmental-cognitive-motor approach to facilitate learning.
Using cognitive-motor play strategies we help children discover numerical relationships to help them develop strategies to compose and decompose quantities represented by numbers.
In a step-wise developmental progression, we build number sense, counting strategies, constructing and deconstructing numbers, problem-solving, and mathematical thinking so that children can apply their skills and knowledge to move beyond counting on their fingers, relying on math fact charts, and guessing.
Large Balls for Rhythmic Counting, and Dice For Estimation and Factoring
Metacognition Builds Confidence
Fundamentally, mathematics is the cognitive processing of patterns and sequences with a coded language of symbols that communicate operations and rules. When we talk through what the students are thinking as they take action mathematically, they become more skillful in problem-solving. Raising metacognition with proactive thinking skills and reliable numeracy strategies builds confidence in children while making math more transparent and students less anxious.
We use metacognitive messaging, Socratic questioning, and executive function skills coaching to help students who feel like math “is not my thing” transform into experiencing that math is pretty fun and super cool. The Play Math developmental cognitive approach is based on cognitive psychology, kinesiology, and applied neuroscience, leveraging what humans know naturally, tempo, rhythm, timing, patterns, and sequences to help them make sense of what was once confusing.
Play Math engages thinking skills, that require the use of imagery, imagination, and language. For many children, imagery is fundamental to the process of thinking with numbers. Sequential and simultaneous processing are both necessary cognitive processes for math as are attention, inhibition, encoding, retrieval, problem-solving, and decision making. For students with dyscalculia, understanding quantity and number relationships is a foundational skill that often requires systematic, patient, and creative instruction.
Children with Dyscalculia Often have Difficulty with:
Number sense
Ordinality
Cardinality
Counting
Understanding quantity and magnitude
Combining and portioning numbers
Understanding the meaning of one digit, one number, and one whole object (separated into parts)
Constructing and deconstructing numbers
Processing numerical order
Encoding and retrieving math facts with fluency and automaticity
Problem-solving
Discriminating the key language context in word problems
Understanding the structure of the base 10 system
Mathematical organization (properly setting up problems and solving them step by step)
Consolidating mathematical concepts in long-term memory (this puts a large burden on short-term memory)
Visual-spatial deficits in graphing, drawing, and problem layout
Mathematical Proficiency has Five Strands (NRC):
Conceptual understanding – understanding mathematical ideas and making connections to previously learned math concepts
Procedural fluency – carrying out effectively and efficiently procedures, such as addition, subtraction, division, when solving problems, not limited to written but including mental and hands-on strategies
Strategic competence – being able to formulate, represent and solve math problems (often referred to as problem-solving) using various strategies;
Adaptive reasoning – reflecting on, justifying, and explaining mathematical ideas; being able to think logically and reason; and
Productive disposition – seeing oneself as a successful learner of mathematics and its application to one’s own life situations.
Source: The National Research Council’s Adding It Up: Helping Children Learn Mathematics describes mathematical proficiency as five interconnected strands (Kilpatrick, Swafford, and Findell 2001).
What We Do in Play Math
We Build Foundational Numeracy Skills - Slowly and Concretely with Intention
We apply the teachings of Das, Dienes, Carpenter, Ma, Montessori, and Vygotsky, to develop children who Think Mathematically. We play math rather than “do math”. This allows for the exploration of quantities and numerical relationships. The development of imagery in numeracy and the confidence to explore, discover and create mathematical solutions are central to our students’ “good work”.
LEVEL I:
We teach students how to count…Not only forward but backward.
We begin with imagery and concrete conceptualization by “seeing” what numbers represent.
We talk about the importance of thinking rather than guessing.
We explore number relationships.
We “leap” to see what numbers we can build and how those numbers are related to one another.
We incorporate multi-sensory-kinesthetic and cognitive-motor activities such as drumming, rapid neural activation, counting activities, block building, and thinking games to build patterning, sequencing, and visualization skills in our learners.
LEVEL II:
We build math facts by “seeing” them and manipulating them, not by memorizing them. This takes time and yields long-term memory gains valuable for a lifetime of applied math.
We use “Magic Tens” and “Fives to Thrive” to facilitate math decomposition and subsequent recomposition.
We teach “the language of math” – that math has words (vocabulary), symbols, and rules that are purposeful, intentional, and meaningful.
LEVEL III:
We develop a personalized toolkit of research-based cognitive strategies to help each student compose and decompose math problems.
We introduce a modification of Touch Math to facilitate math strategy development once the students move from blocks, imagery, and kinesthetic learning to numerical equations.
We play with number relationships, which children find fascinating. As an example, if a student builds 8, 6 times and sees that the sum is 48 we then look at all the numbers we could decompose 48 into. This is an exercise in thinking not memorizing. It involves many “AH-HA” moments which enhance a child’s sense of motivation and connections with math.
Once they can compose and decompose numbers, use Magic 10’s and 5 Alives to understand numerical relationships and work through the similarities and differences in operations, we use Tang Math and a game I call, “Mathish” to build problem-solving, calculation, and extrapolation skills.
Imagine when a student who previously did not understand the similarities between addition and multiplication can now use the Tang Math cards to build relational math problems.
The one word that comes to mind is Thrilling!
Identification of Dyscalculia often entails neurological or cognitive assessment. Clinicians choose from a range of assessments, it's important any diagnosis is based on an evidence-based assessment.
Asking your school learning team or medical provider for a referral for assessment is helpful, screening can be a first step.
Here is the Feifer Assessment of Mathematics
Additional Screeners Dyscalculia.Org
Citations:
Bonacina, S., Cancer, A., Lanzi, P. L., Lorusso, M. L., & Antonietti, A. (2015). Improving reading skills in students with dyslexia: the efficacy of a sublexical training with rhythmic background. Frontiers in psychology, 6, 1510. https://doi.org/10.3389/fpsyg.2015.01510 LINK
Caccia, M., & Lorusso, M. L. (2021). The processing of rhythmic structures in music and prosody by children with developmental dyslexia and developmental language disorder. Developmental Science, 24(1), e12981. https://doi.org/10.1111/desc.12981 LINK
Cheng, D., Xiao, Q., Chen, Q., Cui, J., & Zhou, X. (2018). Dyslexia and dyscalculia are characterized by common visual perception deficits. Developmental neuropsychology, 43(6), 497–507. https://doi.org/10.1080/87565641.2018.1481068
Chu, F. W., Vanmarle, K., & Geary, D. C. (2013). Quantitative deficits of preschool children at risk for mathematical learning disability. Frontiers in psychology, 4, 195. https://doi.org/10.3389/fpsyg.2013.00195 LINK
Gashaj, V., Oberer, N., Mast, F. W., & Roebers, C. M. (2019). Individual differences in basic numerical skills: The role of executive functions and motor skills. Journal of experimental child psychology, 182, 187–195. https://doi.org/10.1016/j.jecp.2019.01.021 LINK
Haberstroh, S., & Schulte-Körne, G. (2019). The Diagnosis and Treatment of Dyscalculia. Deutsches Arzteblatt international, 116(7), 107–114. https://doi.org/10.3238/arztebl.2019.0107 LINK
Peters, L., Bulthé, J., Daniels, N., Op de Beeck, H., & De Smedt, B. (2018). Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic. NeuroImage. Clinical, 18, 663–674. https://doi.org/10.1016/j.nicl.2018.03.003 LINK
Price, G. R., & Ansari, D. (2013). Developmental dyscalculia. Handbook of clinical neurology, 111, 241–244. https://doi.org/10.1016/B978-0-444-52891-9.00025-7
Rosenberg-Lee M, Ashkenazi S, Chen T, Young CB, Geary DC, Menon V. Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia. Dev Sci. 2015 May;18(3):351-72. doi: 10.1111/desc.12216. Epub 2014 Aug 6. PMID: 25098903; PMCID: PMC4320038. LINK
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