2009-04-10 / Columnists

Ken's Math Korner

Why Can't/Won't Johnny Do 4 x 3 Without a Calculator?

As I begin to write this column, I'm reminded of a quote from The Simpsons.

Mrs. Krabappel asks her class, "Whose calculator can tell me what 7 times 8 is?" The students take a moment, and Milhouse excitedly raises his hand and says, "Oh! Oh! Low Battery!"

We've become a society of people who, for the most part, cannot do any mental calculations. If we're asked to multiply 7 times 8, we might know what it is, but we somehow doubt ourselves, and will reach for a calculator if one is handy.

One could ask why it matters.

One reason is that we're often asked to do mental calculations, even when we don't realize it. There are countless times in our personal lives and on the job when we need to do mental math calculations.

Very often after a test, I will have a student argue with me as to why I marked a particular question wrong. Of course I will simply explain that his answer was wrong, and the student would often say, "But I wrote down what my calculator said." I will try to explain that he entered the incorrect numbers into his calculator.

The student at that point would typically just be furious, perhaps partially at me, and partially at his fancy calculator that he had to save up several weeks of allowance money for, which was supposed to be capable of all sorts of advanced functionality.

Why does all this matter? Students are not forced to do any thinking, and exams are now such that they test a student's ability to think, and to reason mathematically. Sure they are allowed to use a calculator in high school. The logic is that the student should have already learned basic arithmetic, and the point of math is not to see if you know what 4 times 3 is, but if you are able to solve a complex problem correctly, determining all of the necessary steps. The problem is that in many cases, no partial credit is given.

A student could do the problem flawlessly, but if the final computation comes down to 4 times 3, and the student's calculator somehow gives him 7, the entire problem is marked wrong.

If you are the parent of a student, you need to somehow convince your child to always check his calculator result for reasonableness. If we're adding 9 + 7, and the calculator says 42, then something is wrong.

How could it possibly be that?

Most students couldn't care less. They'll just write it down, and then stare daggers at you, saying that their calculator told them so.

In some cases they will simply thrust the calculator with the displayed answer in the face of the teacher, in an effort to drive their point home.

Of course when the teacher calmly asks the student to do the calculation again, and then the calculator displays 16, the student is just ready to explode.

Part of the problem is that the high schools assume that the students are on, or very close to grade level.

The assumption is that the child already learned how to do arithmetic manually, and has learned how to estimate answers, and has learned to check answers for reasonability. For the overwhelming majority of high school students, this assumption is a very bad one.

A large percentage of American high school students are on somewhere between a 3rd and 5th grade level in math, regardless of what you may have read or heard.

Many high school students will swear on their lives that 3 minus 5 equals positive 2, or, that the problem simply cannot be done, and has no answer, since we're "not allowed" to subtract a bigger number from a smaller one. If you allow such a student to use a calculator for every single exam, and for every single computation, they will never learn anything, and they will never learn any computational skills for the real world.


The average IQ of 4 people is 110. If three people each have an IQ of 105, what is the IQ of the fourth person ?


If f(x) = (12 - x)3/2, and n = f(3), what is the value of 2n?

For the solutions please visit my website kenthetutor.org or email at kenrochelle@gmail. com

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