
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 noncommutativity and nonassociativity 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

