Podcast Ep 4 - Autism and improving understanding of mathematical concepts
Hi there, and welcome to episode 4 of the Stephen’s Evolution podcast. I’m Stephen McHugh, your host. I have Asperger’s, a form of autism. I record, every 2 weeks, an episode where I talk about how I manage to live with the condition. The content and information contained in this episode is for informational purposes only, and not to be used as a substitute for professional teaching advice.
In this episode, I’m going to show you how you can help an autistic child understand mathematical concepts more easily, as they may experience difficulties understanding new concepts. This possibly may be due to the fact that they have language and speech development delays.
Because of my difficulties with processing language, I would find it difficult to understand new mathematical concepts, and apply new knowledge to given problems. This is the second episode of a number of episodes where I talk about what helped me during my education.
There is an earlier episode, where I talk about support measures that were used to help me try and improve my language and communication skills. The episodes may be useful to you if you work in a teaching capacity, or if you’re a parent trying to support their child in their education. Some of the tips that I may include, may inspire ideas of your own, to help a child with autism try and understand mathematical concepts.
I’m going to talk about how my interests helped me, and got me to cooperate better. I’m going to start off by talking about how I progressed with addition and subtraction. One way in getting me to do sums would be having objects. So, for like, 2 + 3, I’d have 2 objects to begin with, add 3, then count them all, which should come to 5.
And with a subtraction for, let’s say, 8 take away 5, you could have 8 objects to begin with, take 5 of them away, and only be left with 3. Stuck on a wall at home, I remember there being a grid showing numbers from 1 to 100, done in rows of 10. For the subtraction of 8 - 5, you could start at 8, and count 5 squares backwards, arriving at 3.
At one point, I only knew numbers from 1 to 59, possibly due to the fact that I have an interest in clocks and time related things, until my mum once introduced me to numbers beyond 59.
Once I got comfortable working with numbers up to 100, I would be given opportunities to pay for items in shops. This would give me opportunities to work out how much items that I wanted to buy would cost, and to see whether or not I had the right amount. In addition, I’d have the chance to work out how much change I would be given, if any.
When I was introduced to multiplication for the first time, I was confused with what I had meant. For times tables tests, I would read the times tables over, over and over before testing myself. I would also have a preoccupation with pressing the equals sign on a calculator many many times. This would give me an insight into number patterns like 5, 10, 15, 20, 25 onwards.
As with multiplication at first, I found division difficult to begin with, especially when it came to understanding remainders. You could try and employ a bit of drama here. Imagine you have 24 sweets to be shared out amongst 5 children, they’re not all going to get 5 each. When you think about this mathematically, once the sweets have been shared out, 4 of the children are going to have 5 sweets, and 1 is only going to have 4.
As you can imagine, the one with only 4 sweets is going to think that it’s not fair on them that they’ve only got 4, and the rest have got 5. In a situation like this, it would be fair for every child to have 4 sweets each, so that every child is happy. Therefore 24 divided by 5 comes to 4 remainder 4.
When it came to long multiplication, one thing that stood out for me there was when multiplying the top number by the tens unit on the bottom number. Here you’d add a zero. Let’s do an example here. When doing 25 times 35, you could do 25 times 3, which is 75. Multiply that by 10, you add zero to 75 to give 750. Then you multiply 25 by 5, giving 125. Adding 125 to 750 should give you 875.
When it came to decimals, what stood out for me here was the number of places you’d move it to the right or the left, depending on the power of 10 you multiplied, or divided by. For example, multiplying it by 10, you’d move it one place to the right, multiplying by 100, you’d move the decimal point 2 places to the right. It depends on the number of zeros involved.
For dividing decimal numbers you move the decimal point to the left, depending on the power of 10 you’re dividing by. So, for instance, if you’re dividing a number by 10, you move the decimal point 1 place to the left, whereas if you’re dividing by 100, the decimal point is moved 2 places to the left. It depends on the number of zeros involved in the power of 10. They are the patterns that stood out for me here.
Looking back, I saw myself as more of a visual learner. When it came to fractions, I liked to see what a number of them looked like compared to each other. You can do this by incorporating a child’s special interests. Let’s say a child has an interest in sticks, you could measure the length of a stick, mark the halfway point to indicate a half, and then mark a quarter of the way along the length to indicate a quarter, and mark at other various points to indicate other fractions.
I also had an interest in clocks. If you draw a line from 12 to 6, you should be able to see that 6 is half of 12. If you then divide it further by drawing from 3 to 9, you should be able to see that 3 over 12 is one quarter, and that 9 over 12 is three quarters. On some clocks, including toy ones, there will be 5 printed with 1, 10 printed with 2, and 15 printed with 3, and all the way up to 12 which will have 60 printed with it. This can give an insight into multiplication, and how it works, especially the 5 times table.
If a child happens to like Lego, then you can use Lego bricks to try and teach multiplication, division and fractions as well, along with other mathematical concepts. There are some Lego bricks that have 4 studs going down and 2 across, giving a total of 8 on top of the brick itself, which is 4 times 2.
There is also another Lego piece which has 4 studs on it, on top (2 by 2). Compared to the Lego brick with 8 studs on it, it should be half its size compared. This is one way to show how Lego can be used to teach fractions. And if you happen to have 2 Lego chairs, which take up 4 studs (2 by 2), and placed beside each other on a brick with 8 studs on it, that should show you that 8 divided by 4 is 2.
Special interests and fun activities can help to increase engagement and cooperation. I had a particular interest in heights and weights, and often wondered how tall and heavy things were. In the case of the driveway, I wondered how much concrete would have been used to build it, and how much it all weighed.
My mum at the time would guide me in this activity. We’d measure the dimensions of the driveway, the length, the width, and its possible depth. It would then be a case of multiplying these values together with the density of the concrete used itself. The value we got was around 3,500 kilograms, which I know to be around three and a half tonnes.
And whenever I had access to a balance, I liked to try and get this to balance by adding up weights for each side. So if, for instance, I had 200 grams on one side, to balance the other side, I could just place 4 x 50 gram weights on the opposite side, which would get it to balance.
One thing I liked to do in relation to heights, was kick balls up into the air, and estimate how high they’d go in metres, and then convert from metres to feet. There were times when I would enjoy doing conversions between various units of measurement.
I had a fascination with speedometers, and mileometers as well. Along with that, I had a particular interest in fast modes of transport, like trains and planes, and wondered how long it would take these to cover certain long distances. And being interested in space, how long it would take a rocket to go to the moon.
I can also recall that we had a height chart displaying the solar system. I would work out my own scale, by dividing the distances of each planet from the sun by their respective heights on the chart.
Anyone with a fascination for telescopes like me could use their range of magnifications to do fraction simplification. That’s another way of increasing engagement here. Along with that, another thing to do here, could be to work out if you’ve got the right magnification to, let’s say, show you the rings of Saturn. Astronomy was, and still is, one of my favourite hobbies.
Being fascinated with time, I had been fascinated by video recorders, and their counters. I often wanted to see how many seconds had elapsed since the start of a particular recording on a television.
When I saw a jug that could hold over 1,000 millilitres, or 1 litre, I quickly became interested in how many litres equalled 1 pint, and how many pints would equal a gallon. Whenever I saw big planes at an airport, I would wonder how many gallons of fuel they must have needed to travel thousands of miles.
At school, I remember there were interesting educational mathematical opportunities for me too, in particular doing calculations in relation to snooker scores. I would pot snooker balls on a snooker table that we had at home, where I would have my own values for the balls, and add up my score each time I potted a particular ball. This was one way for me to improve my mental arithmetic skills.
That’s all there is for this episode. Thank you for listening if you’ve made it this far. If you’ve liked the sound of it, then why not consider signing up to receive news of newly released episodes. You can find a link to this at the footer of my website on the homepage stephensevolution.com.
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Goodbye for now, and I’ll talk to you all again soon, on the next episode, when I shall be talking about the remainder of my time in junior school, and progress in other subjects, including science, physical education, and foreign languages.