Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Norm Krumpe Posts: 53 Registered: 12/6/04
What are the "basic" facts?
Posted: Jun 21, 1995 6:17 PM

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

Date Subject Author
6/21/95 Norm Krumpe
6/22/95 Norm Krumpe
6/23/95 A. Karassowitsch
6/23/95 Norm Krumpe
6/29/95 Janet V Smith
7/1/95 Arthur Howard
6/23/95 Norm Krumpe
6/23/95 Norm Krumpe
6/23/95 Norm Krumpe
6/30/95 Norm Krumpe
7/6/95 Chi-Tien Hsu
7/1/95 MCotton@aol.com
7/1/95 Kevin J.Maguire
7/1/95 Norm Krumpe
7/1/95 Norm Krumpe
7/2/95 MCotton@aol.com
7/2/95 Norm Krumpe
7/2/95 Steve Means
7/4/95 MCotton@aol.com
7/4/95 Norm Krumpe
7/6/95 Eileen Abrahamson