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:


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


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


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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