Mathematics for Teaching Category: Elementary School Math

Category: Elementary School Math

Why PEMDAS is ‘morally’ wrong

Here’s a video that explains why you need to memorise PEMDAS (or BODMAS, BIDMAS, depending where you are in the world) order of operation and why you don’t need to. Minute Physics who made this video made a mistake in assuming that PEMDAS is taught in schools without emphasising that multiplication and division should be…

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Why do we ‘invert’ the divisor in division of fractions

The easiest (and the most common) way to teach division of fractions is to just give the rule: To divide 5/8 by 2/3, just multiply 5/8 by the reciprocal of the divisor, 2/3. That is, 5/8 ÷ 2/3 = 5/8 × 3/2 = 5×3/8×2 = 15/16. If this is all we want our students to learn why…

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A triangle is a fish

Why is it that students find it easier to calculate the area of triangle ABC but will have difficulty calculating the area of triangle DEF? Middle school students even believe that it’s impossible to find the area of DEF because the triangle has no base and height! That knowing the invariant properties that makes a…

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Bob is learning calculation

Bob is an elementary school student. He is learning to calculate. He just learned about addition and multiplication but there are some things that he doesn’t understand. For example, how come 1+3 = 3 + 1? How can it be the same thought Bob? Every morning I have 1 piece of bread for breakfast while…

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What are fractions and what does it mean to understand them?

Negative numbers, the irrationals, and imaginary numbers are not that easy to make sense of for many students. But this is something understandable. One only needs to check-out the histories of these numbers. The mathematicians themselves took a long time to accept and make sense of them. But fractions? How can something so natural, useful,…

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