Spiral Learning: Permutations for Elementary Students

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Categories Development, Education, From the Mouths of Multiples, Higher-Order Multiples, Identical, Parenting, School-AgeTags ,

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.

Explaining permutations for elementary students. Showing them the first quarter of the pattern allows them to derive the pattern themselves. From hdydi.com

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.

Spiral Learning

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.”

Spiral learning is the practice of returning to a topic over time to build an increasingly sophisticated understanding

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.

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Sadia (rhymes with Nadia) has been coordinating How Do You Do It? since late 2012. She is the divorced mother of 10-year-old monozygotic twins, M and J. They live in the Austin, TX suburbs, where Sadia works full time in information technology. She contributes to a number of parenting websites and magazines and also runs The Mommy Blogging Guide, where she answers mommy bloggers' technical questions.

8 thoughts on “Spiral Learning: Permutations for Elementary Students”

  1. I didn’t know the term for this until I learned it from you, but I think this is such a logical – and brilliant! – approach. Instead of saying, “You’ll understand this / study this when you’re older,” explain a question or a concept in age-appropriate terms, and then build on it as curiosity / understanding deepens.

    I was just channeling you a few days ago. 😉 I took a deep breath and explained the female menstrual cycle to my girls. They’ve been a little curious of certain aisles in the grocery store. I finally decided I’d rather introduce them to a top-line overview now, and build on it over time…rather than sitting them down for a “formal” conversation in three or four years.

    I love the insight into your girls’ minds, too!

      1. They were completely unimpressed. Hahaha! Honestly, I didn’t time it perfectly. I psyched myself up to do it…so I did…but I probably should have waited for them to ask another question.

        I’ve been thinking a lot about this, though. I so want to introduce concepts to them in bits, at an age-appropriate level, so they know things aren’t “a big deal”. I do not want to be sitting down at age 12, when they are completely creeped out, to have “The Talk”.

        Thanks for the encouragement a few weeks ago! I borrowed a couple of lines from “Aunt” Sadia!

        1. Being unimpressed is probably the best reaction. They see it as fact rather than something shocking or scary. You’ve planted the seed. And seeing ‘”Aunt” Sadia’ in that comment made me tear up. Love you guys!

    1. Yep. This is the sort of thing where “profoundly gifted” affects our day-to-day lives. I can almost understand why J’s kindergarten teacher just gave up on teaching her. Almost. Not quite, though, since her current teacher is so amazing. She (the girls’ teacher) sent me this note on Facebook last night: “Be ready… we are learning how to use higher level synonyms (we are calling them wonderful words) in class and I gave your kiddos a book full of really fun ones like “periphery” and “predilection.” It should make their conversations at home even more fun!”

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