History and MathsIf you have ever read the book ' What is History?' by E. H. Carr you may have come across the idea that 'History stops here.' What this mans is that some historians in the past believed that the History that they wrote was the definitive view; there was no other interpretation. Of course History is constantly being rewritten in the light of current ideas, attitudes and data.
The way I was taught is the only way, 'numeracy stops here'. This is the view of many parents and teachers. They believe how they learnt to add, subtract, multiply and divide is the only correct method to use, anything else is ‘strange’, not ‘proper’ or at worst some kind of trick being played upon their child. None of this is true of course. Each child has his or her own way of learning and remembering things and once confidence is gained using their own method they should continue using it.
Jim, like many pupils could happily subtract when the sum which looks like this.
However as soon as we introduce something more complicated anxiety sets in, he had convinced himself that he couldn’t and never would be able to remember how to in his own words ‘do it when the number on top was smaller’. Such as in the example below. We have all been there as teachers or parents with our pupils or children wanting to subtract 7 from 3 because they can’t remember or don’t know why they have to do in effect 13 minus 7.
A succession of teachers had tried and failed to teach Jim how to do subtract using the traditional method and failed, his parents despaired also having failed to teach Jim how to subtract. He was now 16. Jim is a bright lad, a visual learner, he wanted to subtract so that he could pass his exams.
Open number line
Jim was very comfortable with the open number line, so I decided to show him how to use it to subtract. First I drew the line like the one below and explained that we were at going to go from 17 to 43. I marked on the two numbers.
Now I asked Jim to jump to the nearest 10 from 17, he happily drew a line from 17 to 20.
How about jumping to the nearest 10 to 43 I asked. ‘What 40?’ he queried. He then drew the next jump and without prompting he then drew the final leap.
So how far have you jumped I asked him to which he replied 26. It was then only a small step to make the connection between this method and the subtraction su set out in the traditional way. Jim was thrilled at being able to do subtraction with, as he termed it, ‘difficult take aways’. He successfully continued to use this method with ease and success, passed his exams and reduced his fear and anxiety when tackiling Maths.
Many of you may dismiss using this method as not being correct but it worked for Jim. It may not work for everyone but he was successful and solved problems so who is to deny him, or anyone that but adherence to other methods just because that was how they were taught.
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