Language has such an impact on the way we understand the world around us. Learning any allied language, such as French, shows us that there are many false friends or

(there are plenty more here: http://french.about.com/od/vocabulary/a/fauxamis.htm)

Our learning of Mathematics is fraught with such dangers too, and these dangers catch us unawares because we expect the same word in our everyday language to have the same meaning when we do Maths in English. My daughter once came home confused because from group of pictured objects (scalene triangle, rectangle and regular hexagon) she had identified the rectangle as the regular shape, because she had seen it more

Enlargements can make objects smaller. Differentiation is not about choosing. Conversion is not a religious experience.

And if this wasn't problematical enough, we compound the difficulties by using our language wrongly, in a counter-intuitive way.

Considering the common (but fundamentally flawed) mantra 'Two negatives make a positive', we immediately have problems. How is this? If I have two negative experiences I don't suddenly feel better, I feel worse. In fact this is an example where there are no

I know where it comes from but it sadly is not a universal truth.

The subtraction of a negative number becomes an addition of that number, with its negativeness strangely disappearing. Two negative numbers multiplied or divided become positive. All well and good. The problem comes when we have:

(-3) + (-2)

Does this equal 5? Two negatives make a positive surely!?

The mantra needs changing, and it is not a hard fix either.

'The negative of a negative is a positive'

That works.

(-5) BTW

*les faux amis*, words which sound the same in both languages but may have different nuances at best, or completely different meanings - try bras in French and English.(there are plenty more here: http://french.about.com/od/vocabulary/a/fauxamis.htm)

Our learning of Mathematics is fraught with such dangers too, and these dangers catch us unawares because we expect the same word in our everyday language to have the same meaning when we do Maths in English. My daughter once came home confused because from group of pictured objects (scalene triangle, rectangle and regular hexagon) she had identified the rectangle as the regular shape, because she had seen it more

*regularly*. It was marked wrong but I had sympathy.Enlargements can make objects smaller. Differentiation is not about choosing. Conversion is not a religious experience.

And if this wasn't problematical enough, we compound the difficulties by using our language wrongly, in a counter-intuitive way.

Considering the common (but fundamentally flawed) mantra 'Two negatives make a positive', we immediately have problems. How is this? If I have two negative experiences I don't suddenly feel better, I feel worse. In fact this is an example where there are no

*faux amis*; it's not only wrong, it just doesn't make sense.I know where it comes from but it sadly is not a universal truth.

The subtraction of a negative number becomes an addition of that number, with its negativeness strangely disappearing. Two negative numbers multiplied or divided become positive. All well and good. The problem comes when we have:

(-3) + (-2)

Does this equal 5? Two negatives make a positive surely!?

The mantra needs changing, and it is not a hard fix either.

'The negative of a negative is a positive'

That works.

(-5) BTW