Just read this fantastic quote about Ofsted inspections from Cazzy Pots.
"In preparing for lesson observations, what is actually happening to many teachers in an awful lot of schools is more reminiscent of what Michael Jackson ultimately did to his face. He kept picking and messing to the point of ugly ruin. So obsessed was he with achieving the perfect nose, that the whole thing eventually collapsed onto his face and he had to use tape to hold it together."
To me, a fraction is a specified number of pieces, where the pieces are equal segments of a whole (I'll probably revise this many times during my career).
So the equal segments part of the meaning is represented by this:
But to show the specified number of pieces part, I feel a video might be required. Also the picture, does not define but does imply, that a fraction must be less than one. Hmm.
This morning I went to a fascinating talk by Sue Hall on the Gift of Dyslexia. Three hours of dyslexia lectures, many hours and papers of reading and I hadn't learnt anything. In one hour with Sue, my mind's eye was opened and I'm starting to understand how it all fits together.
"everybody is capable of learning, just not necessarily the way they are being taught"
Sue defines dyslexia as a natural ability to alter perception (which I don't possess to any real degree).
Exercise 1: Picture a dog in your mind, and have it looking at you face on. Now walk around it, so you can see it side on. Now walk behind and look at it from the tail. Finally walk round, looking at the final side and again face the front.
Dyslexic people find this incredibly easy, whereas for myself I was just able to turn the dog around, almost as though it was stood on a lazy susan, but I wasn't able to move myself around the dog. This ability to alter perception is incredibly useful for athletes, for example Wayne Gretzkey is able to view the whole hockey game from above so can easily decide where he needs to be or where to hit the puck.
But out of the 3D real-life world and into the 2D world of print, this gift can be a hindrance. When looking at a lower case d when your mind's eye is wandering around it, there's no guarantee that it will come up as a d, or a p, or even a sticking out tongue. Our education system is established for auditory learners, so phonetic instruction is used for learning to read, which doesn't work for dyslexic learners. Instead they need to visualise the whole word and connect it with an image. Instead, students are often given 'band aid' techniques, such as big elephants can always understand small elephants which helps to spell 'because' , but this doesn't directly relate to the word, it's like third party learning.
Exercise 2: Picture a bicycle in your mind. What colour is it? Now get rid of the bicycle and think of a pencil. Now picture the meaning of tree. Now picture the meaning of the.
In this second exercise, I was surprised by how unimaginative I was when I realised that my image of a bicycle was a pencil sketch in 2D. I used my imagination for the next few, picturing a beautiful oak tree, with the reds and oranges of autumn. But 'the' and I was completely stumped. As was everyone else. For a dyslexic that is creating their own internal film from reading, the screen is suddenly blank. It turns out we have 217 of these 'filler' words.
If the movie screen is blank would you stay in the theatre?
A simplistic image of multiplication.
So for maths we need to come up with images to represent our concepts, our vocabulary, our meaning and our purpose. What's the image for an integer? What's the image for multiplying?
Now initially for multiplying it seemed easy to consider it as bags containing sweets, and having multiple lots of these sweet bags. But what happens when we multiply fractions? It seems that if we are able to come out with a satisfactory image to represent multiplication, we will have completely defined it, not only for dyslexic pupils but for the understanding of all students.
Exercise 3: Imagine the house that you live in. Now get rid of it. Now imagine your house again. And get rid of it. Now imagine it again. And get rid of it. Now imagine it again.
Repetition is dull. Once you have an image in your mind, you don't need to repeat it over and over again. In fact, after a while, I started doubting whether I was truly picturing my house properly. If this is done with a mathematical concept, the student might start doubting whether they truly understood it in the first place.
Exercise 4: Calculate 137 + 19 in your head and write down the answer. Now, without a single word entering your head, and with no internal dialogue of what you are doing, calculate 293 + 18.
I couldn't it. I literally couldn't stop my brain from talking me through what I was doing and what the result was. For some dyslexics at the extreme end of the spectrum, they have never heard a voice inside their head. They must be working in some other way!
Exercise 5: You can only watch the video below once. As it is running, write about it. Stop writing when the video stops.
If you didn't make it to the end don't worry! Most movies are 24 frames per second. Dyslexics think at 32 frames per second. Imagine being asked to write about a concept, when the video is running even faster than what you just watched. I gave up and now I understand why they might too.
Instead, Sue recommends drawing a picture mind map. Once that's done, number the pictures. Then the student has a framework, taking each picture in turn and writing about what each picture means.
Now to begin to find images for all of mathematics... in the world...
Just read this fantastic quote about Ofsted inspections from Cazzy Pots.
But out of the 3D real-life world and into the 2D world of print, this gift can be a hindrance. When looking at a lower case d when your mind's eye is wandering around it, there's no guarantee that it will come up as a d, or a p, or even a sticking out tongue. Our education system is established for auditory learners, so phonetic instruction is used for learning to read, which doesn't work for dyslexic learners. Instead they need to visualise the whole word and connect it with an image. Instead, students are often given 'band aid' techniques, such as big elephants can always understand small elephants which helps to spell 'because' , but this doesn't directly relate to the word, it's like third party learning.