How Calculators Inhibit Learning the Distributive Property in Algebra

;Adler 81S calculator from the later 1970's :M...
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Do you wonder if your children should be using a calculator “at their age”? Are you a fan of calculators, but have friends who aren’t? Are your friends “into” calculators while you oppose them?

I often hear people say that children 50 years ago understood math concepts more quickly. Although our parents weren’t taking classes called algebra in the 7th grade, they were doing algebra in the 7th grade.

Algebra is arithmetic.

There are two fundamental and rarely understood facts about algebra:

  1. Algebra is arithmetic with one or more numbers in disguise.
  2. Algebra has exactly the same  rules as arithmetic.

Which means if you can do arithmetic you already know how to do algebra!

Our parents or grandparents, 50 or even 30 years ago, weren’t using calculators. They had to apply all the rules of arithmetic to get the job done. Which means that they had to apply all the rules of algebra.

Teaching them a class called “Algebra” was much easier because of this.

What are the rules?

The basic rules that non-calculator users must apply are the distributive property and the order of operations. The distributive property is the thing that calculator use eliminates.

Children could get practice mentally multiplying things like 3 x 86 and do 3(80+6) = 240+18=268. With this practice, they are ready for 4x(3y+2z) = 12xy+8xz.

If they never have to multiply 3 x 86 in their head, they never get the experience of the distributive property. Which means teaching them 4x(3y+2z) = 12xy+8xz will cause anxiety and frustration. They see it as “magic” or “something you made up just to confuse me.”

Give them the tools they need.

Refuse to let students have the calculator. Let them have the tool of the distributive property for algebra before you teach them “Algebra”. Give them the benefit our parents and grandparents had!

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5 Responses to How Calculators Inhibit Learning the Distributive Property in Algebra

    • Playing is okay – provided he is really playing. The thing that our folks let us do (“check our work”) was the harmful thing. If he wants to fiddle around with it, that’s okay.

      In fact, I’m presenting a talk at this conference about teaching creativity with the calculator:

      Thanks for the comment, Betsy!

    • Playing with a calculator is one thing. As long as it remains a source of play, kids can experiment and discover all sorts of neat things.

      But when they stop playing and start using it as a crutch, that’s when to be cautious.

      Thanks for popping in, Betsy. I miss you! #xoxo

  1. Hi — I thought you might like to know that you have a small typo above. 3 x 86 is 258 (not 268), which I arrived at by mentally starting with 3 x 90 (270) then subtracting 3 x 4 (12). Since I don’t “picture” the numbers in my mind very well I generally go for an approximate (270 in this case) then fine tune from there (for some reason only having to subtract 12 seemed easier to me, rather than adding 18 to 240). Thanks for all of the great information!

    • Thanks, Janet!

      I was talking to my friend about how different we all do arithmetic. Isn’t it fascinating how our great minds think differently!

      I appreciate your catch of the error. I’d like to say I did it intentionally, but I’m pretty sure I didn’t. 😀

      However, I’ll leave it in for the enjoyment of others.

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