Less Arithmetic and More Real Math
From Rosalind Hoe Swee Yoke
Richard Larson's caution in the last STEM Pals newsletter against schools training students to be "test-taking machines" is very timely, especially with the current emphasis on Tiger Moms and Dragon Dads. The issue of focused, deep study and accomplishments in a student's area of interest needs to be addressed. As a Math teacher in Malaysia, I see so much mindless repetition of drilling in math questions in order to ensure that students are ready for public exams, all factory-produced to score the all important "A".  There is so much emphasis on the "how", that math teachers have sacrificed the "why" of Mathematics.

Let me illustrate:
From grades 1-2, students are required to memorize the Times Tables.  Woe to the unfortunate kid who has poor memory power!  He is publically humiliated by having the Times Tables pinned on his uniform and forced to parade in the canteen during recess time.  As a result, they commit everything to memory and do not have the foggiest idea what really is 8 x 8. So some compassionate math teachers shared a novel method on how to remember the 9 Times Table (at least a part of it).  This is how it is done.  I wonder if American primary kids know about this.

Question:  What is 6 x 9?

The student is taught to raise both palms.
Now, count from the left pinky finger....1,2,3,4,5,6.
When you reach 6, you bend that finger.......(which will be your right thumb)
Teacher asks:  How many fingers are upright to the left of the bent finger? ( the student yells 5!)
Teacher asks:  How many fingers are to the right of the bent finger?  (the student yells 4!)

Teacher replies happily..."Ok, everyone..the answer is 54!

(Applause for the teacher.
She is happy....and her students are even happier)

But why does it work? I asked my grade eleven students and no one could give me any answers except: "but that's what we were taught!"

So, I proceeded to prove to them why the finger method worked.

Proof:

9n = 10n............... - n

Now on the dotted line , I wrote "-10 +10", so this is what I will get.

9n = 10n  -10 +10   -n

Now we factorize the right side of the equation and we get,

9n = (n-1)10  + (10-n)

So going back to the original math question.....:what is  6 x 9 ?

"(n-1)10" represents six fingers minus one, gives us 5.  5 has a place value of ten...hence (6-1) times 10.
"n-10"  represents the remaining fingers to the right of the bent finger..........Ta-ra!

All this could have been taught in grade 4, thus giving mathematically inclined students exposure to factorization and some introduction to proof.....both of which are so essential in the development of budding mathematicians.  But instead, factorization is only taught in grade 9 while Rigorous Proof is only taught in grade 11.

Yes, I do agree with Prof Larson. Less is more.  Cut out the mindless rote learning and brain numbing repetition of similar exercises.  With the time now available, we can do with less arithmetic and more real Math during a student's formative years.

Rosalind Hoe Swee Yoke is Head of the Mathematics Department at the Chung Hwa Confucian National Type High School in Penang, West Malaysia. She has taught at the school for 18 years.

Back to newsletter