Elementary School Mathematics Education Mysteries


Since these two problems are really the exact same problem, in two different forms, why not just use “x” to teach it, from the beginning, in elementary school, instead of using the little box? The two symbols have the exact same meaning!

To the possible answer, “We use an ‘x’ for multiplication, instead, so doing this would be confusing,” I have a response: why? Using “x” for multiplication is a bad idea, because then students have to unlearn it later. In algebra, it’s better to write (7)(5) = 35, instead of 7×5 = 35, for obvious reasons — we use “x” as a variable, instead, almost constantly. This wouldn’t be as much trouble for students taking algebra if they had never been taught, in the first place, that “x” means “multiply.” It’s already a letter of the alphabet and a variable, plus it marks spots. It doesn’t need to also mean “multiply.”

Why are we doing things in a way that causes more confusion than is necessary? Should we, as teachers, not try to minimize confusion? We certainly shouldn’t create it, without a good reason for doing so, and these current practices do create it.

These things may not be mysteries to others, but they certainly are to me.

[Note: for those who do not already know, I am a teacher of mathematics. However, I do not have any experience teaching anything at the elementary level. For this particular post, that’s certainly relevant information.]

2 thoughts on “Elementary School Mathematics Education Mysteries

  1. Of course, in the olden days (!) we used to write a cross for multiply and a curly x for the variable (unknown) (call it what you like). Now even the textbooks use the cross in place of curly x. Result; a new symbol for multiply, the fat and often blue dot.
    The question ” What goes in the box?” may not be the correct one – if I put a 5 in the box, who says I can take it out of the box?
    Seriously, the symbols are getting in the way here. The sensible question is ” What do I need to add to 7 to get 12?”. No symbols. Or does this now count as a word problem?
    I despair sometimes.


  2. Although the two examples look similar, the forms of the questions seem suggest diffrent questions. For example the symbol x looks like an abstraction of a number whereas the box just means “what do we need here?” for some reasons.

    Another problem is for those countries which do not use Latin letters. They have to learn a new alphabet letter x.

    In fact what I have expected from the title is what I thought problematic in primary school. If the example be a problem of the 2nd grade, (1) the number in the box is a natural number and (2) more importantly we should not expect students to solve algebracally, like BOX = 12 – 7, that is, the answer should be always guessable. But too “wise” teachers seem sometimes forget it.


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