Video Link: https://vimeo.com/589925391

For many, the word dyscalculia, will be easy to link with numbers because it is similar sounding to the well known word...calculator.

Both words, dyscalculia and calculator come from the same word, calculus which means small pebble.

• Question: What have pebbles got to do with calculators?

Pebbles were used as an early counting device.

Throughout history there have been many counting devices, including some that pre-date modern systems of numbers and numeric symbols.

There are records of tallies being carved into stone, wood or bone as a method of counting, going back over forty thousand years. So they can be thought of as a type of stone-age calculator.

Counting is something we all need and do. Our stone age ancestors probably used counting to make sure all of their animals were accounted for, for example.

The system of numbers we learn at school in mathematics, are systems that have evolved from counting pebbles, fingers, tallies and using an abacus.

The numbers we learn are represented by numeric symbols.

So, 2 is a numeric symbol representing the number two, or two of something.

This mini-history lesson of numbers is important because hopefully we have separated two different areas:

• 1. The process of counting
• 2. The system of numbers used in mathematics

The reason we have separated these is because difficulties with numbers and mathematics can make it look like the person has difficulty counting. If the difficulty is caused by the numbers system and/or symbols, then there is an opportunity to learn about counting in different ways, just as our ancestors did.

For children with CVI, before explaining what dyscalculia means, it is first important to explain that it isn't necessarily the same as difficulty learning maths.

To explain...

Number / Mathematics Difficulties & CVI
CVI, for many reasons explained in previous lessons, can lead to things not being seen clearly or consistently. For some this can lead to extreme difficulties with learning.

Let us use the simple example of a teacher who has made the image below for their class to teach the children the numbers 1, 2 and 3 using the three frogs. Whilst this example is of a teacher in a classroom, it is relevant wherever the child is being taught, including at home.

How can CVI affect learning numbers?

Early Learning
When numbers are first taught, it is often with fun images like these friendly frogs, but to make sense of this lesson, the child needs to see as others see and hear as others hear.

Seeing Clearly
If the child has reduced visual acuity and / or reduced contrast sensitivity, have you checked how clearly they can see the image?

If you had not seen the above image on the right before, would it make much sense to you?

There is a free programme called sight-sim you can use to take a photo of anything and add the child's measurements, to see what it looks like to them, as compared to how you see the same thing.

One Thing At a Time
How many things can the child see at once? In addition to three different frogs, the image also has a flower, other plants and a pond. How much can the child see? One way to find out is to ask them in an open and non-leading way, for example 'Can you describe everything you can see?' rather than 'Can you see the three frogs?'

If the child can describe only one element of the overall image, that tells you there is too much visual information for them to process everything in the image all at once.

It may also be that when the teacher is talking, the child is unable to look at the same time, as many with CVI struggle to look and listen. Children have repeatedly told us that they try to figure out what the teacher means by what they say alone, and that they do not use anything visual to aid their understanding. If the teacher is relying upon the child to understand the image they are talking about, then they may not be making sense to the child.

Words
At the same time as learning about numbers, the child is also developing their vocabulary. We know that CVI can affect the development of language in children, some so severely that they remain completely non-verbal and profoundly learning delayed.

Has the teacher checked the child definitely knows what a frog is?

The three frogs all look completely different. Has anyone checked the child knows the correct meaning of all the words being used?

This is something that should not be taken for granted, especially in younger children.

In situations in which learning is difficult, whatever the subject, someone needs to check that all the words used are known and correctly understood. At the end of this lesson is a short video, showing how a child mis-learnt the words apple and banana, because the words got mixed up when they were learning, because the child sees in a different way.

Distractions
Take a moment to stop and really look and listen. The environment the child is learning in is as important for many with CVI, as the teaching and books. When the environment is cluttered, or noisy, or there is shuffling, a child chewing gum or tapping their foot, a lawnmower outside or the smell of cooking from the refectory, it can mean that the child can't learn, or is finding learning more difficult. For a further explanation, please see further reading 'Attention & Its Calibrations' at the end of this page.

How is the child feeling?
If the child is worried or anxious, maybe because they find the subject difficult, this will make learning even harder.

Mathematics
Notice we haven't even started on the numbers and mathematics yet!

Is anything learnable this way?

For many children with CVI who struggle with mathematics, the issue is that it is not taught in a way that they can learn.

This is not dyscalculia, but we have explained it here because it is so common.

For children with CVI who struggle with mathematics for these reasons there is a great deal that can be done:

Check the basics
No matter what age the child is, go back and check they are confident with counting, and then see how far their understanding is in relation to addition, subtraction, multiplication and division to check if any of the processes have not been understood correctly, before moving on to more complex topics. Check the ability to see the numeric symbols, and the child's understanding of the words used. Little misunderstandings of these basics will affect everything.

Non-Visual Learning
Use non-visual ways to learn, including what might appear to be the very old fashioned chanting of times tables. Repeating the same information makes memories stronger.

Use songs and rhymes, especially with younger children or where learning may be more severely affected. Make the songs fun, but reinforce the numbers often.

Number songs:

• Ten in the bed
• Five little monkeys jumping on the bed
• Ten green bottles
• One two three four five, once I caught a fish alive
• One two buckle my show

Always check what the child can see, and is looking at if you are using anything visual including a book, television / video show or computer programme. When speaking, we think it is good just to assume the child will struggle to listen and see at the same time, and to talk like you are talking to someone on the telephone, where they can't see what you are talking about. This way you will naturally explain in a way that is more accessible for the child to learn.

Low-Vision Technology
Some of the technology and strategies used to teach mathematics to eye blind children can be effective for children with CVI. Contact your local provider of educational support for visually impaired children for further advice.

Patience
Give the child time, let them ask questions, and be mindful where they may not have understood you. It is not the child's fault if they have not understood.

Teacher Checklist

If you are teaching a child anything, formally in the classroom as a teacher, or at home as a parent, or anyone anywhere else, think and check, every time:

• Can the child see it clearly, consistently and all of it?
• Can they hear me?
• Can they listen to me and see what I am talking about at the same time? For many with CVI that answer is they can't.
• Does the child know what all of the words I am using mean? Might they understand some differently or not at all?
• If I am needing the child to sometimes look at the work in front of them, and sometimes me and sometimes a black board / white board / smart board, and regularly switch between them, can they do that and keep up?
• Have I given them enough time?
• Have they understood fully the basics, what I am teaching relies on.

In relation to all these questions...

• How do you know?
• Have you checked?
• Are you sure?

Because of you have missed any of these points, your teaching may not be accessible for these children.

Finally...to the mathematics!

Next is a very abstract step, involving the adding of a symbol, a numeric symbol to replace the frogs or ducks or other ways of teaching early counting.

So this is what 3 is, is it?

This is one of the reasons children with CVI struggle to learn mathematics. Not because of an inability to understand counting, but because mathematics is taught in a way that is inaccessible for them to learn. Here we have explained just some of the reasons why.

This is not dyscalculia, this is what happens to all children when any teaching is not accessible. They don't learn, and so their learning becomes delayed because learning is difficult. The cause is something we all do, it is called self-referencing, see level 4 lessons.

We are not blaming anyone, it is something we come pre-programmed to do.

But... to make learning, including learning mathematics accessible for children with CVI, we first need to look at how we teach, and 'we' includes everyone at home and at school.

Dyscalculia

The mathematical symbols including numbers, needed for the calculating processes, are stored for most as visual memories in the left temporal lobe, as we explained in lesson 3i (Visual Recognition).

If anything has happened to the area where those memories are stored, it can mean difficulties with numbers. Something seemingly simple, like counting backwards from ten might be very difficult, because to do that correctly, you need to have memories of all the numbers, and so there may be gaps for example.

The underlying left temporal lobe cause can be from birth, possibly where the brain in this area developed atypically or due to an incident a birth. It can also be acquired at any time in life due to an injury, disease or event affecting the left temporal lobe area of the brain.

Evidence is not always going to show on an MRI.

To separate dyscalculia from difficulties with maths associated with the learning challenges we describe in this lesson, go through some of the support suggestions to see if you can find a cause in the way maths is being taught.

If the child is otherwise learning well, and their difficulties with numbers seem out of place with their other learning abilities, they may have a degree of dyscalculia. It can be mild or severe.

The most severe form of dyscalculia is called acalculia where numbers and their meaning are not recognised at all. Acalculia is most common as the result of an acquired brain injury, for example a stroke.

It is possible to have both learning difficulties around numbers associated with CVI and dyscalculia.

Visual Behaviours

If from birth, it may be that the child has particular difficulty with numbers. They may also have difficulties with other areas of learning needing memories in the same part of the brain, particularly letters. Here it can be very difficult to work out the cause, and we suggest going through our learning checklist to rule out or understand if the teaching method and / or environments are creating the difficulties.

If there are some learning challenges but they do not completely explain the number difficulties, then the child could have both dyscalculia and other challenges affecting learning in this area. The child may well be otherwise able and academic and excel at subjects and areas where the left temporal memory requirements are less, for example in art and music.

If dyscalculia is acquired, following a brain injury, the person may feel embarrassed as very simple tasks they could easily do before they struggle with now, like mentally adding up the price of a few shopping items to ensure they have sufficient money to pay, counting out money, or remembering their pin number. In the video tutorial we mention many ways numbers are used in life, and to lose the ability to manage life with numbers must be frustrating and worrying. If identified and understood, there is a great deal you can do.

Targeted Support

Our lives are governed by numbers. Just think about what you have done in the last hour and somewhere there will be numbers - set a microwave, checked the time, paid for something etc.

Think about ways you can help the person without number skills, for example telling the time. Just because a clock is now hard to understand, it does not mean the person has lost the understanding of night and day, so different alarms could be set to indicate different periods during the day as needed. In school a child could learn to remember the bells or buzzers separating the periods.

Where possible, aim for either auditory or tactile prompts and alternatives. There are many provided by low vision services.

Learn numbers differently, or re-learn numbers differently, not relying on the pictures of numbers. In the modern technological age chanting and repeating numbers may seem out dated, but in terms of how your brain learns, simple repeated experiences is how it learns best.

Checklist

Before moving on, please check that you have understood the following:

• What calculia means
• Different devices used for counting
• The difference between counting and the modern numeric symbol system of teaching and understanding mathematics
• Why CVI can cause difficulties learning numbers and mathematics
• The CVI teacher checklist
• The different difficulties with CVI and learning mathematics, and dyscalculia
• The part of the brain responsible for dyscalculia
• That dyscalculia can be from birth or acquired
• That dyscalculia can be mild or severe
• The most severe form of dyscalculia is called acalculia

Next Lesson: Level 12b Visual Processing Disorders affecting Reading & Numbers - Neurological Dyslexia

Further reading is not needed to move on, but if interested you may find the following enjoyable:

Teacher Checklist
A page to explain in more detail, with links, the Teacher Checklist we refer to in this lesson.

This video (below) explains how easy it is for children with CVI to learn words incorrectly, here mixing up apple and banana.

Video Link: https://vimeo.com/504348192

Cool Games Introduction
Learning the names of things can be difficult for children with CVI, meaning the words we use to teach may not make sense. Here we explain in a little more detail with a link to games to help.

Attention and its Calibrations
Explaining the importance of the environment for children with CVI to learn.

Gordon Dutton's Blog 6 Radio Parenting
Explaining the opportunities if we speak like we are on the radio or telephone, where we do not rely upon others to see as we do.

Yellowstone Blog 3 Accessible Teaching
Explaining the difficulties with the complexity of geometry.

CVI Now from Perkins have Maths & CVI resources including many different accounts from parents who have successfully taught their child. Click here to view page.