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Patterns, Functions, and Algebra

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[Channel-talkalgebra] multiplication facts

From: <askey@math.wisc.edu>
Date: Wed May 02 2007 - 11:04:51 EDT

This was a message I got from a teacher about ten years ago.
Dick Askey

I want to tell you an experience I had about ten years ago when I taught
remedial math to special education students who were learning disabled and
educably mentally retarded. Most of the students came to me at the 9th or
10th grade level with the goal of passing the Tennessee State Proficiency
Test. At that time, and I hope it is the same today, but doubt it, the
students were *not* allowed to use calculators on the test.

My students knew no multiplication facts, and since the test included 3
digit by 3 digit multiplication, long division with 2 digit divisors,
fraction/decimal equivalents, and +, -, * and division of fractions,
knowing multiplication facts was a prerequisite to mastering the other

Since these students were already at the high school level, you could
consider them chronic non-learners or failures, yet each year, every
student in my special education classes passed that proficiency test... and
with flying colors. Their scores on the proficiency test were much higher
than the "passing level" mandated. The overall average of all my students
for all the years I taught in that position (10 years) was 92%, whereas 70%
correct was the passing level. This average was higher overall than the
average of the entire school which was a highly academic,
college-preparitory school.

One of the things I did with the students that was highly effective was the
method I used to get them to learn their multiplication facts. I gave them
sheets each day at the beginning of class which were as below. I'm sure
you've seen this:

0 1 2 3 4 5 6..... were across the top and down the side

1 *1* *2* *3* *4*.....

2 *2* *4* *6* *8*.....

3 *3* *6* *9* *12*.....

4 *4* *8* *12* *16*...

5 ....


from zero to 10. Once the students had filled out their sheets (as where
the *'s are)(not knowing the mult facts, they would sometimes just have to
count by 3's and 4's, etc, to fill in the sheets with the products) at the
beginning of class each day, they were free to use them to look up the
facts they didn't know as they did their math assignments. I wouldn't
allow them, however to carry a sheet over to the next day. They had to
continuously make new sheets.

Every student I ever taught, no matter how deficient in mathematics,
learned the multiplication facts very quickly. Soon I would pretend to be
out of the sheets, and the students began to make their own to use. After
that, as they grew in proficiency, making the sheet was too tiresome, and
they began to do their work without them.

The sheets were not destructive in the way that calculators are because in
making the sheets, the students gained a good understanding of numeration
and sequences of numbers. Having to make them anew each day, assured me
they would get the practice they needed.

A calculator is entirely different than this. With a calculator, the
student pushes in 2 arbitrary numbers, and a third number magically comes
up as the product. The students does not get to see time after time, as
with the sheet, the numbers' relationships to other numbers. And this
makes all the difference. Also, my students weaned themselves from their
crutch very quickly when making the sheet became more of a bother than
thinking the answer.

My point, I guess, is that there are effective ways to teach even children
who do not learn math easily.

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Received on Wed May 2 13:23:14 2007


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