>> A colleague told me of vainly trying to persuade a college student that .015 was less than .05; the student insisted “but 15 is more than five.”
>> To [students], [the equals sign] doesn’t signify equality, but instead means “put the answer here.” Imagine their confusion when, in algebra, they first encounter problems with numbers on both sides of the equal sign.
Is this really true? I'm sure I and my children (in the UK) were presented with fill in the box questions like:
7 + [ ] = 10
at the very earliest stages of arithmetic.
7 + x = 12
"The 'x' represents the answer, so we have to get it on the 'put the answer here side'; lets write 12 = x + 7 ; now we just need to take 7 from the 'put the answer here side' and we're done. But whatever we do on one side we have to do on the other. Take 7 off. 12 - 7 = x + 7 - 7 => 5 = x ... bingo".