Cake
• As a result of this weekendâ€™s panel here đź‘‡

a question was asked on Twitter by @LilMathGirl on whether the multiplicative inverse of a fraction was a trick.

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As I mentioned to @jlaib earlier this week, Iâ€™m a big fan of Liping Maâ€™s work on elementary math education. Two tweets sum up my feelings on this question:

• This is what I was waiting for. Too many educators, and students I encounter say â€śjust flip the fractionâ€ť and do not know why or the reason for it. (Before flip it there was simply cross (X) multiply it) These foster lack of understanding of the math needed to divide fractions. FLIP IT if not backed up with proper procedure leaves a huge gap in math learning. James Tanton has a great set of videos called â€śFractions Are Hardâ€ť https://m.youtube.com/watch?v=TS3xS1kEFpw

• Too many educators, and students I encounter say â€śjust flip the fractionâ€ť and do not know why or the reason for it.

I think algorithms are so baked into traditional math thinking that teachers can follow the traditions without realizing the self-limiting behavior. Also, the demands on teachers are so great that time for reflection or to ask â€śdoes this make sense?â€ť can be limited. Thatâ€™s why I have the utmost respect for the teachers who wrestle with these issues on Twitter, even if I donâ€™t always agree with their conclusions.

What I like about Lipingâ€™s explanation is that it draws out the idea of multiplying by 1, expressed as a fraction, to create understanding of why you â€śflipâ€ť the second fraction.