Permutations for Elementary Students
When I was browsing the lovely photos on MathiasQuads.org yesterday for this morning’s post, my daughter M took great care to read the names in each photo caption. She wanted to be sure to match each face to the right name. As an identical multiple herself, she understood how important it was to see Mary Claire, Anna, Grace and Emily as individuals.
M, aged 7, observed that they were rarely in the same order between photos.
M: There’s 16 ways for them to be lined up.
Me: How did you figure that out?
M: Because there’s 4 sisters and 4 spots and 4 times 4 is 16.
Me: That’s a very good deduction, my mathematician girl, but it’s actually 24. Can I show you how?
Is 7 a little young for combinatorics? Sure, but M showed an interest in it, so I dug back into my 8th grade math memories. I drew her a picture to show her how to think of permutations. She picked the colours for each sister.
Me: There are 4 sisters who can go in the first spot. I’m just going to draw one of them. Once she’s in her place, there are only 3 sisters left to go second.
M: Then 2, then 1!
Me: Exactly. So there are 6 orders available for each sister who goes in the first spot.
M: And 6 times 4 is 12 and 12 is 24.
Me: Which is also 4 times 3 times 2 times 1.
M: Well, that was easy.
We’ll probably chat about combinations tonight during bath time.
I’ve always taken this approach to educating my daughters. If one or both of them is interested in something that illustrates a larger pattern or important skill, I explain it to them at a level that is pertinent, interesting, and within their abilities. Later on, when they’re more intellectually mature, I’ll come back to it. In a couple of years, I’ll show M how to use factorial notation.
My teacher friend Kaylan tells me that the eduspeak term for this is “spiral learning.”
What sparks your child’s interest? What’s your approach to teaching?
Sadia (rhymes with Nadia) has been coordinating How Do You Do It? since late 2012. She is the divorced mother of 7-year-old monozygotic twins, M and J. She lives with them and their 3 cats in the Austin, TX suburbs and works full time as a business analyst. She retired her personal blog, Double the Fun, when the girls entered elementary school and also blogs at Adoption.com and Multicultural Mothering.