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Topic: What are the "basic" facts?
Replies: 20   Last Post: Jul 6, 1995 8:34 PM

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Norm Krumpe

Posts: 53
Registered: 12/6/04
What are the "basic" facts?
Posted: Jun 21, 1995 6:17 PM
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I often get frustrated when I hear mathematics educators say something such
as, "Yes, I agree with all the new standards, the use of technology,
cooperative learning, etc. But I still think my students need to learn the
'basic facts.'"

I realize what is typically *meant* by the phrase "basic facts" --
typically, the addition and multiplication tables -- but I question whether
these are truly "basic". If "basic" refers to the building blocks necessary
to proceed further, then I have to argue that 7 x 8 = 56 is hardly "basic".

Is a successful mathematical experience impossible or unlikely if a student
doesn't know the multiplication tables? To me, the commutativity and
associativity of addition and multiplication (and the non-commutativity and
non-associativity of subtraction and division) are far more "basic" than 7 x
8 = 56. Yet, many students believe that 3 - 7 = 7 - 3, even as they enter
junior high. This indicates to me that they are missing some *very* "basic"
facts about subtraction -- facts that I feel are far more important than
memorizing that 16 - 7 = 9.

Think about it from another standpoint. Is it necessary, before reading and
enjoying and understanding a book to first look up and have memorized all
the words that will be encountered in that book? Certainly not. Rather, if
we read a book and encounter a new word, we either try to determine its
meaning from the context, or look it up. Couldn't we do the same with those
"basic" multiplication tables? If a student encounters 7 x 8, he or she can
find out its value at that time, even if it is by calculator. Then, as
certain multiplications are bound to reoccur over the 12 or so years that a
student learns mathematics, the tables will be memorized.

I recognize one of the arguments against this: we can't possibly teach the
multiplication algorithm if students don't know their multiplication tables.
But I'm not quite sure how much I would agree with this argument. Besides,
I have worked with many college students (including those planning on
becoming mathematics educators) who know the algorithm, but still don't
remember how much 7 x 8 is.

Norm Krumpe

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