The difficulties associated with math are complex in nature. You will meet some students with WS who perform very poorly, others perform at grade level and still others only struggle with some areas such as time and money. This unpredictability of math skills is something that psychologists find interesting. It may lead to clues as to what areas of the brain are used for certain types of problem solving. It may also open doors to understanding new teaching methods that could help many students who struggle with math- whether they have WS or not. Due to the unique nature of the WS brain, much can be learned by our little ones. Their unique abilities give psychologists clues to how humans learn.

When compared to other intellectually challenged groups of students - such as those with Downs Syndrome, Turners syndrome and children diagnosed with math learning disabilities, those with WS have unique deficits. The other groups tend to score low in all aspects of mathematics versus WS who have a mixture of high and low scores based on the skills required for each type of math skill assessed.

### Brain science- why is math hard for my child?

There are two theories as to why those with WS struggle in math. One theory is that the grey matter in the parietal lobe of those with WS is known to exist in low amounts. Grey matter is a collection of neurons (or nerve cells) that specialize in thinking and problem solving. In general, the more grey matter in an area of the brain, the greater talent that person has to do those tasks. The brain is covered in ridges called gyri. Each gyri, built from grey matter, has its own job or function in one aspect of thinking. For example, the precentral gyrus (also known as the motor cortex) is used to control when muscles contract in all parts of your body. The post central gyrus (also known as the primary somatosensory cortex) is designed to identify touch and other sensory ques. In between the gyri are narrow dips or grooves called sulci (sulcus). These also contain grey matter and divide the functional regions of the cerebrum. WS brain studies suggest that the intraparietal sulcus of the parietal lobe contains low amounts of grey matter. This affects the intellectual ability of a person with WS to understand some parts of math, especially those that are related to spatial cues. There is a well known link between the amount of grey matter and a person's IQ. Lower IQ and intellectual disability which could explain a lower overall understanding of mathematics.Another theory that explains math disability in those with WS is that their brain just works differently than most. In addition to low amounts of grey matter, there are impairments to the pathways that lead to the parietal lobe. Some psychologists feel that difficulties related to math in kids with WS are more due to the flow of information within the brain rather than the amount of grey matter in the parietal lobe. These pathways are made of white matter, which are made of neurons coated in fat. The fat makes the messages move quickly from one area to another. These pathways are used to link different gyri and sulci together to coordinate a more complex task. There are some pathways that are used more often- like highways of the brain. The dorsal stream pathway runs from the visual area of the brain up to the parietal area. This stream is known to be impaired in WS and may be one reason why mathematics is difficult for kids with WS. You can see in the picture, below, that the dorsal stream is used to figure out where things are in space.

The other stream of information is called the ventral stream. This flow of information is used to identify what things are in your environment. This stream of information is actually used more in the WS brain and has links to short term memories and language. Therefore the cognitive profile of someone with WS involves rich short term memories and language gifts yet they have a high amount of difficulty navigating spatially. Based on these brain studies, there are theories that the spatial tasks involved in mathematics is weak yet verbal aspects of math are strong, giving them a lopsided ability to fully understand mathematics. Due to the quizzical nature of the WS mind there are several research studies that test these two theories. While no definitive answers exist, there are definite findings that the WS mind can learn math, though it must be addressed differently than a typical child would learn.

(Visit this post on my blog to learn more about the brain science associated with WS.)

### Verbal vs. Spatial

When learning mathematics, there are two categories of problems- verbal math and spatial math. Considering the dorsal stream being spatial and ventral stream being language based, anyone with some knowledge of WS could probably predict that kids with WS will score strong in verbal math and perform poorly on the spatial math.Examples of verbal math are language centered- such as naming and identifying numbers and counting including counting by 5 and 10s. These skills use the verbal stream of information and tend to be a relative strength for most kids with WS.

Examples of spatial math would be recognizing relationships between numbers such as using number lines, greater-than versus less-than and estimating amounts. For example, on one test students were given a triangle with two numbers (such as 5 and 9) at the base and one number (such as 6) at the point. The student was asked to choose the base number that is closest in size to the 6. Children with WS performed poorly on this task, most likely due to the spatial disability that is so strong in WS. In addition, if children or adults are given numbers and were asked to estimate which of them are closest together on a mental number line, those with WS had a much harder time identifying the correct answer. They also had increased difficulty the closer those base numbers become. If the outlying numbers are very different, they can usually figure out the answer.. the smaller the numerical gap, the more difficult the task becomes. This ability does not tend to improve with age. Many children with WS struggle with these same spatial tasks as they age and will need to learn how to compensate them with verbal memorization.

### Developing math skills

Studies that focus on WS mathematical disabilities vary greatly in their results. Overall testing tends to show that young children with WS tend to score comparably to those who are typically developing. As they mature and mathematics becomes more conceptual rather than concrete, some students begin to fall behind. Also, as a young child, math tends to focus more on verbal ability- counting, naming numbers and memorizing basic math facts. Children tend to excel in these task that require the ventral nerve stream. As they age, the spatial concepts are introduced such as greater than/less than, money and telling time. This is when parents often find their child struggling to understand mathematics.In some of the mathematics studies, adults with WS performed math facts as expected for a typical adult. Psychologists who studied the active areas of the brain in those participants have found that those with WS use different parts of their brains to solve those math tasks in contrast to the average person, thus suggesting that they are "wired differently". This suggests that mathematics can be learned by those with WS but different methods of learning should be explored. The path to success is different for those with WS because they think differently than the other children in their classroom.

Another theory of why mathematics becomes more difficult for a person with WS is due to developmental aspects of mathematics. As a young learner, children use their frontal lobe to learn and recall mathematics facts and processes. The frontal lobe is used when you have to think about difficult and more complex thoughts. As students practice these mathematics principles they become rote and easy. The task then in stored in areas of the parietal lobe, particularly in the back portion of the brain along that dorsal stream. Therefore, adults can complete simple math that once challenged them mentally but now are more like reflexes. Because the area where those reflexes are stored is atypical in WS, some psychologists think that maybe adults with WS do not store those principles in their parietal lobe but always use their frontal lobes to figure out those types of problems.

### Strategies to help teach math

Because memorization is a strong skill for those with WS, the approach to learning mathematics should be language centered. Also, if a child with WS never really understands spatial math such as cardinality, number lines, etc. they should just move on to other skills that are more attainable. The mathematics instruction should be modified because some kids will never grow to understand those concepts despite the practice. They need to learn how to solve mathematics in other ways that focus on their verbal strengths rather than using spatial skills.The Williams Syndrome association also provides a list of strategies, compiled by Dr. Karen Levine, that can be used to modify a child's curriculum. These suggestions are based on the spatial difficulties that most individuals with WS may never really develop even into adulthood- such as telling time with a analog clock and counting money.

Karen Levine, Ph.D. suggests the following modifications:

- "Digital clocks and watches
- Calculator use
- Teach time concepts by personalizing
- Use wall calendars for daily, weekly and monthly schedules with events sketched or written in
- Encourage the elementary school aged child to have a date book
- Be flexible in curriculum, avoiding a rigid 'prerequisite' curriculum design
- Some children may never learn coin values but should move on to the next curriculum phase which they may be able to more readily understand" (WSA)

Sources:

- Mathematical skill in individuals with Williams Syndrome: Evidence from a standardized mathematics battery
- Mathematical skills in Williams syndrome: insight into the importance of underlying representations; O'Hearn K
- Williams Syndrome Information for Teachers by: Karen Levine, Ph.D.
- Music therapy resources related to academics