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Topic: upper middle schoolers that haven't yet mastered multiplication facts

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Subject:   RE: upper middle schoolers that haven't yet mastered multiplication facts
Author: GED Guy
Date: Dec 17 2004
On Dec  6 2004, Bethy wrote:
> I'm about at wits end. I teach in a very small rural school (one
> school district) and we have a number of students who, at 7th and
> 8th grade, still don't know 75% or more of the multiplication facts.
> I'm not a proponent of rote memorization, but these students need
> some means of quickly retrieving/calculating this information. What
> does the research indicate? Does anyone know of an effective method
> for equipping these students with a procedure so that they can move
> ahead?


This is long.  Sorry.

I work as an administrator in Adult Education - GED Prep, Alternative Education
for Youth and ESL.  I always hate to say I have the solution but I do think that
have the keys to the soloution for most students.  In adult education few of our
students know their math facts.  Most do have the capacity although not the
desire to learn them.

I observed the solution years ago when my wife was asked to tutor a child one
summer.  I saw a 5th grader who knew few facts at the beginning of the summer go
on to blaze through all flash cards in lightning speed by the end of the summer.
When struggling with 16-19 year old students working on their GED I remembered
what my wife did and recreated major parts of it.

One issue to memorization is intellegence.  That is out of your control.
Another issue is "time on task".  That is in your control.  Increase time on
task through motivation.  But motivation is hard.  My wife used candy.  We use a
variety of motivators in Adult Education.

The real genius to my wife's method was coming up with a way for students to see
incrmental improvement.  That was done by measuring time.  It is objective and
very small increments show very small progress.  She worked with one student but
I am working with a class so I "systemitized" her method.  

The basic technique is this.  Have students measure how long it takes them to
complete an operation.  This is the baseline.  Have them work to memorize the
facts.  Remeasure.  The new, improved time shows their progress.  They see this
and they are motivated.  Of course it is the "art" of teaching that leads to
success.  The mechanics and the motivators we use are individualized to our

My wife used a specific approach with flashcards which worked very well and
which we use in our class.  

Work on 1 operation (e.g. +) at a time.  We actually divide each operation into
4 parts.  Thus a student masters 1/4 of addition at a time.  

In pairs (one student flashes cards, one responds) go through 1/4 of the deck
and measure the time.  We have digital egg timers.  Don't spend more than 5
seconds on unknown facts - give them the answer and go on.  

Go through the same cards again, this time sorting cards into 2 piles - known
and unknown.  Work on the unknown pile for 3-5 minutes WITHOUT a timer
(reduces stress).  

Recombine piles, go through whole pile once or twice then again using a timer.
"Wow!  I know them better.  Took me 70 seconds before.  This time I did them in
45 seconds!"  I think that my wife gave out candy for each day an operation was
improved.  We give Hershey Kisses.

Specifically this is what I did:

Divide each operation deck into 4 parts identifing each 1/4 with a different
colored dot.  This allows students to repeat the exact same set of facts and
thus always have comparable times.  We used black, blue, green and red permenant
marker.  Every time someone does the "black addition" they get the exact same
facts.  Bill did black addition in 45 seconds, Jane did black addition in 42
seconds.  Jane knows her facts better.

Create tracking charts for studnets to record their times and see their
progress.  Standard paper.  Rows for each operation and color, columns for date
of time.  We have minimum standars which are:

30 seconds for 1/4 deck on + and -
40 seconds for 1/4 deck on X and /

We had a student that learned that when they hold the deck it is much faster so
for final timings, observed by a teacher, students hold the deck and flip it
themselves.  One student got 1/4 X blue dot (it happens to be easiest for some
reason) in 21 seconds. You try it.  Wow.

Obviously you can create charts on the wall or for students to keep.  Give
rewards and awards for getting an initial timing on an operation, for various
incriments (say 100 seconds, 75 seconds, 50 seconds and 30 seconds). Heck, if it
is a big problem, let a student be exempt from one quiz for each operation they
reach the minimum.  They could get out of 4 quizzes.  Perhaps they get to
replace that grade with an A. Or 2 A's for the second operation.  3 A's for the
3rd.  4 A's for the 4th.  Whatever works.

Key components:
Visible progress to the student
Make the learning part risk free
small steps, genuine praise for small success
carefull with student psyche

Personally I had difficulty with my math tables.  People memorize but then
forget.  I have told my students that doing math without knowing the facts is
like driving a car with 5 lbs of pressure in the tires.  You will get there but
it will take you a lot longer and will do damage (for people the damage is to
the psychie) along the way.

Good luck.  Perhaps they won't then enter my class in a few years!

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