Confusing Things For Students 1

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Sometimes a student's understanding is blocked by something that people who have made it past a certain level of maths don't even notice. In this series of posts I will highlight some of these blocks.

The first one has to do with implicit signs. Consider the following expression:

 2(x+1)

There is an implicit multiplication in this expression, which can be made explicit by writing

2\times(x+1)

So far so good, for anyone who has made it past basic algebra. But now consider the fraction:

 2\frac{1}{2}

Once again there is an implicit sign but this time it is different. The fraction can of course be broken up as

 2+ \frac{1}{2}

So this can be extremely confusing for the beginning student of maths, who does not appreciate that implicit signs can be context dependent. Either mistakes can be made thinking that

 2(x+1) = 2+x+1 = x+3

if the student is more used to seeing the implicit sign in fractions, or they can be mistaken in thinking things like

 2\frac{1}{2} = 2\times\frac{1}{2} = 1

if the student has been doing a lot of beginning algebra and is rusty on their fractions.

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