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# Maths Café

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# 'Cool cash' card confusion

richard 09 November 2007 17:35
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'Cool Cash' card confusion

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Chris1974 13 November 2007 13:34
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Heard about this on locacl radio - the DJ's annoyed me by trying to say that the person concerned was right, and that it was confusing.  I appreciate what they say about the warmer / colder thing.  It really does support what they say about functional innumeracy in society.  is it our fault as maths teachers??
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petegriffin 13 November 2007 17:05
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I thought that this bit was interesting:

".......... the card doesn't say to look for a colder or warmer temperature, it says to look for a higher or lower number. Six is a lower number than 8. Imagine how many people have been misled."

Is there a general perception / conception that the "size" of a number is independent of it's positivity/negativity/direction, i.e. magnitude of a vector.

I have come across a number of students (and adults) who want to refer to "a big negative number".

Mmmmmmmm,....... maybe not so straight forward a mistake as it might seem (as with most misconceptions).

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Chris1974 14 November 2007 08:42
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It is a VERY common misconception.  I often use terms like very positive and very negative to talk about extremes of the number line, but we do and there are many questions along the lines of which of these is bigger or put them in order from smalles to biggest or inser the correct symbol (< or >) or stuff like that.

In terms of langauge, if -10000 is very small and 100000 is very big, how do i describe 0.000001, whiuch instinctivly is small, and even harder, -0.000001

Chris

Confused of Calne.

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richard 14 November 2007 11:13
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A debt of £135000 is a very high level of debt

A temperature of -135C is a very low temperature

Is it that the language of positivity and negativity changes in different situations? So maybe students' concept of the size of a number depends on the context in which it's introduced?

I saw a really interesting converation in class the other day about the question 'which is bigger out of 10 and -10?'

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Helene_Huille 15 November 2007 07:49
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I thought it was sad and hilarious... Negative numbers are hard for many students and obviously some get out of school with no understanding... that is the sad part...
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Steve_Humble 17 November 2007 21:11 - Last edited by Steve_Humble on 17 November 2007 21:13
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Standard form is another area of problems with negative powers.

Lots of students have issues with 10-3 say, as a negative number.

I like looking at the pattern of dividing each time by 10 to get round this issue. It also answers the questions about anything to the power zero.

103=10x10x10

102=10x10

101=10

100=1

10-1=$\frac{1}{10}$

10-2=$\frac{1}{10*10}$=$\frac{1}{10^2 }$

p.s. But as you can see from my poor use of "insert equation" notation is never easy!

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Chris1974 17 November 2007 22:07
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I saw a really interesting converation in class the other day about the question 'which is bigger out of 10 and -10?'

I'd love to 'hear' the details of that conversation.

Chris

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richard 19 November 2007 18:44 - Last edited by richard on 19 November 2007 18:46
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The overheard conversation covered what was meant by the word 'bigger', whether it means more positive or whather it means larger and what that would mean in the context of negative numbers.

The students also covered the contexts that I posted earlier in this thread - they agreed that,  in some cases -10 was the same size as 10 but that 10 was always more positive than -10. There was a lot of reasoning, example and counter-examples

What I found really interesting was that there was very little teacher input and that the students spent a lot of time pushing themselves. I've written before about keeping students 'on the edge of their thinking' (a phrase used in some Strategy materials) and what I saw and heard was, I think, a perfect example of that. At the end of the lesson one of the students walked past me and said "that was really confusing - but in a good way"

Let me know if you ask some students - I'd be really interested in hearing what they say.

What do others think - which is 'bigger'?

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