Tag: calculator

How Calculators Inhibit Learning the Distributive Property in Algebra
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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June 1, 2011
How to Use Flashcards when Teaching Math
Siggi over at Turkeydoodles wrote a post about her preference of calculators over flashcards. It’s her preference, but her arguments seem to be founded on the misuse of of flashcards. Furthermore, it seems she’s not seen the detrimental effects of early calculator use, yet.

When you should give a kid a calculator is a topic for another article. In the meantime, here are some tips on good flash card usage.

Flashcards are educational toys.

Flashcards shouldn’t be used as testing devices. They’re educational toys. They’re exploratory devices. Let them “peek” as much as they want.

As a first introduction, use them to build houses of cards. They should be fun and comfortable.

They are limited in scope.

The 6 x 8 = 48 card will never be able to give the cosine of 60 degrees. This makes the flashcards so beautiful. Once you understand what happens when you create a calculator addict, and see how that works as the kid enters college, you’ll know how important this limitation is.

Encourage variation to limit boredom.

I distinctly remember using flashcards in my dining room, sitting next to the sliding glass door. I was reading them. But because they would get boring, I would chant them. It became sing-songy and fun. I could go through them quickly this way.

And I looked forward to the ones that rhymed.

Let the flashcards be rejected.

If a kid really hates them, let it go. There are other ways to get that information across. Schoolhouse Rock’s Multiplication Rock is a fabulous tool for this.

And you can sing or chant multiplication facts yourself. My mother learned the most common prepositions by saying them as she jumped rope. You can vary some skip counting with jumping rope to learn multiplication facts:
- 3 x 1 = 3
- 3 x 2 = 6
- 3 x 3 = 9
- and so on…
Allow the flashcards to be the context in and of itself.

It is not necessary that math be learned in context. So many people keep pushing this. Sometimes it’s just fun to know random stuff – including some quick and nifty facts.

Don’t push math for math’s sake, but offer it. There are kids, lots of them, who just like to do puzzles. Plain math – arithmetic and facts – is a great puzzler.

What do you think? Is this a better use of flashcards than the ones you’ve seen? Share your thoughts in the comments.
April 12, 2011
When to Give a Kid A Calculator

When we teach kids how to drive, we give them a few months in the classroom so they can learn the basics of driving and the rules of the road. Nobody in their right mind puts a teenager behind the wheel and says, while flying down the road, “Now, the brake pedal is the one on the left.”

Not only is it safer, but it makes more sense to teach them outside of the car first. After they pass a competency test then they’re allowed to use the technology (car).

We drop a calculator into the hands of teenagers and ask them to learn math at the same time. There isn’t a safety factor here, but the principle is the same.

There’s a different challenge in learning which buttons to press than learning the reasons behind why you press those buttons. We bring technology into the classroom thinking we’re in service of the children, and instead do them a disservice. We double the concepts and think that one is helping the other. It isn’t.

Begin by teaching user’s manuals.

The use of a calculator, a program or web-based application can be easily taught by teaching children how to read a user’s manual or follow instructions. It’s a device, a tool.

Before they start up their new John Deere riding lawnmower, they should read the user’s manual. Likewise, before they turn on their Hewlett-Packard 32sII, they should bend the spine of its little book.

Math classes and home schools can incorporate user’s manual reading in their curriculum. It will prepare students to learn and understand technology, including calculators and applications.

Introduce the calculator after they have mastered the concept.

Teaching children to do math through calculator use can destroy their sense of confidence in doing it themselves and also make them uncomfortable with the tool. Allow them to fully understand an entire concept in mathematics before giving them technology.

If you want them to learn to graph on a calculator, make sure they can do it with pencil and paper first. Allow a few years between the initial introduction of a concept and learning to make it work on a calculator. This should provide ample time for them to practice it and build their confidence that they can do it without the crutch.

When they are ready, give them the user’s manual to the calculator. Have them do problems by hand on one side of their paper. Have them write the page numbers from the user’s manual and keystrokes for the calculator in a column next to it.

When they have completed this, let them confirm their keystrokes are correct by doing it in the tool. This reinforces the connection between what they have learned, and can do on paper, with what’s being done in the machine.

Do you give your kids a calculator to learn on? Will you continue to do so? Share your thoughts and ideas in the comments.

March 19, 2011
Confessions of a Calculator Addict

I remember being allowed in Jr. High to use the calculator to “check my work.” Soon after I learned that the books in High School had the answers in the back! It was like condoned cheating!

How could I go wrong with the magic box and the answers given to me straight from the publisher?

And then I became addicted.

Sometime after Geometry I lost my multiplication facts. I wasn’t just checking my work on the calculator.

Subconsciously I figured there was no reason to trust my potentially faulty memory of math facts if I had the absolute sure thing right there next to me.

For years I stopped doing arithmetic.

And my dad chastised me. Every time some quick calculation came up in the kitchen, garage or grocery store, I would stare at him blankly. Then I would reach for my calculator.

The way he looked at me, you’d think I had reached for a bong, ripped off my bra, sang Kumbaya and spat on the pope.

I ignored him.

For years.

Until one day I realized that I had absolutely no memory of $8 \times 7$ . Yep – $8 \times 7$ was what did it. I started watching myself. I always did simple arithmetic (even addition of single digits) on the calculator!

Then I watched other people. I saw the clerks in the grocery store reach for the magic box to figure out 10% off something. I saw an older man at McDonald’s send the girl into a tizzy because he modified his cash payment after the girl had already typed it in.

“There’s a problem here,” I thought. Maybe Paps was right.

I put down the magic box. Cold turkey.

I started using prime factors to help me remember my old multiplication facts. I re-engineered subtraction so I could actually do it. I read Dead Reckoning: Calculating Without Instruments. And then I refused to allow students to use the “devil box.”

I put it on my syllabi that calculators were strictly prohibited (unless expressly invited by me – in the case of probability and statistics). I growled at anyone who reached for one.

And I taught them arithmetic.

And we were all better off.

Are you a calculator addict? Share your story in the comments.

March 10, 2011