Understanding Williams Syndrome: Math Instruction

“Breaking the Math Myth for Students with Williams Syndrome”

A summary of a presentation at the Williams Syndrome Association National Convention, 2022

Information in this post is summarized from a presentation with permission from the authors to share:

By Robin Pegg, EdDc, MEd, COTA/L, ATP- WSA Educational Consultant

Dr. Carolyn Mervis, PhD- University of Louisville

Research supported by NIH (National Institute of Health) and Williams Syndrome Association

Often the math gaps for students with Williams Syndrome is due to language.

In IQ DAS-II tests, children with Williams Syndrome test in mild to moderate intellectual disabilities, but when we look at the subscores, we can see that the low IQ is due to their spatial disability. The verbal and nonverbal scores tend to be in low to average ranges but the spatial range shows a moderate disability, pulling the overall IQ score down.

IQ data source: Mervis, Intellectual Assessments

Williams syndrome brain studies have shown that due to genetic code insufficiency, the neuron pathways in the dorsal stream develop abnormally. This pathway of information in the brain greatly limits a person’s ability to reason spatially. This makes mathematics and many motor planning functions difficult. The same brain study found an increase in neural movement in the ventral stream, the pathway that is used in social, musical and auditory functions. Knowing this brain science, we know that students with Williams syndrome activate the ventral (social) pathway during learning.

Source: Mervis, Neural mechanisms (2006)

In the following graph, you can compare a typical developing (TD) child performing math to a child with Williams Syndrome (WS). You can see that students typically activate their visuospatial pathways during a math task but students with WS have higher activity in the social pathway of their brain. Because brain pathways are used differently for students with WS, we need to approach math in a different way to optimize their learning.

Strategies to improve math success in students with Williams syndrome:

Deliberately teach relational language. One weakness for students with WS is that they struggle with spatial vocabulary; making it difficult to interpret instructions in math. The following vocabulary should be practiced in multiple settings including in the math classroom and during speech/language therapy. In order to master these terms, students must know both the word and its antonym. Otherwise, they have not truly mastered the concept.

Dimensional terms: ex- small/large
Quantitative terms: ex- more/less
Spatial terms: ex- under/over
Temporal terms: ex- before/after

Notice in the graph below, that the curve of students that can master relational terms (TRC graph) correlates directly with IQ sub-scores (DAS-II spatial tests). The PPVT graph shows typical developing students for comparison.

Most students with WS are said to “max out” on their math success by 2-3 grades. This overall lack of success is not due to their ability to do math, it has to do with the shift in teaching styles that occur that turn toward representational math.

The CRA approach to math does not work well for students with Williams Syndrome for several reasons:

This teaching is designed as a spiral approach. Students with WS need prolonged practice until mastery. The spiral approach, which leaves a concept and then revisits it later for reinforcement does not give students with WS enough time to master the concept. They do better in a sequential curriculum.
“Draw it out” or representational tasks (which are typically introduced in 2-3 grade) require spatial reasoning and are not likely something a student with WS can do successfully… explaining why many have low success advancing past 3rd grade math!
Concrete and abstract approaches to math work for students with WS. Abstract is best used with accommodations where students have sequences mapped out for the process since they have poor working memory.
Work around representational math- students with WS have spatial deficits that are not curable. They will never think that way. Instead…

Use manipulatives and technology.
Provide cue cards for the process of solving a problem
Use graph or lined paper on its side to help them line up their place values.
Use concrete method of teaching even in higher grades.

Math programs that work well for many students with WS:

Programs designed for dyscalculia- students with dyscalculia have similar problems to kids with WS.
TouchMath
NumberRock- uses music to solve problems
Manipulaties- best if they are designed for low vision students- larger and more tactile work best
Kidspiration maps- virtual math manipulatives for fractions-
EquatIO tool in google- allows students to type their math so they are not limited by their handwriting; can be used for dictation, lines up numbers for the student and suggests equations or gives a limited options in the formula finder which helps students figure out what to use.
Algebra tiles- makes algebra manipulative *really cool program!
Desmos graphing calculator
Geogebra- geometry will be difficult

Math goals should NEVER be centered around time, measurement and money because these are representational tasks.

Teach students to use technology, digital clocks and alarms for time.
Mix functional math with grade level mathematics. Students with WS can perform algebra with support!
Teach students the dollar up method for money.

Counting coins is not a useful skill anymore. Focus on money handling that they will use: calculating tips, adding totals, rounding up to the nearest dollar for payment, counting cash.

Focus math goals on number sense. Push them to higher tasks on Bloom's taxonomy.

Know when they should use math; why; what situations
Work on when to use money, how to manage money, judgment on when and how to use it
Focus on all aspects of number sense

With the right supports and teaching strategies, students with WS have the capacity to learn algebra!

Students with WS have poor working memory. This makes solving problems with multiple steps or sequences very difficult. Typically students with WS will lose the ability to solve a problem due to not knowing the next step. They often get stuck and respond by just sitting there, guessing or relying on a teacher for a verbal cue.

Students with WS do well with routines and with cues that help them remember steps. Use the following methods to accommodate working memory issues:

Use instructional routines to liberate the students to know what to do next. Example- cue cards for the sequence of actions to solve a problem, color code each step with an example problem showing those steps.
Make cue cards in google slides and print like a book with a sequence on how to solve an algebraic problem.
PEMDAS- Pre-algebra instructional routines made for students with WS work as an accommodation (see below).

Because students with WS think with their social pathway, teacher cues can become restrictive. If a student needs to stay on task, the worst cue a teacher can use is verbal instruction. It pulls their attention away from the task and makes it difficult for them to return to the work. Use the prompt hierarchy below to prioritize how you can cue a student with WS in the least restrictive manner. Use that cue routinely to teach them predictable, on task behaviors (conditioned responses) that lead to their success.