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One of my sisters took the CBEST a month or so ago and failed the math part.
This is the test that all teachers and credential-seekers have to take to
teach in California. My sister has severe math phobia.

She can take it again on June 8th. She has a WONDERFUL job offer for fall -
at 3 times her current pay rate and a job she really really wants to do. But
she can't have the job if she doesn't pass this test on June 8th.

So I've been intensively tutoring her, every chance we get.

She has a REALLY hard time being willing to TAKE time to think about the
"sense" of what she's doing. She wants to just memorize computational
techniques and not "think" about meaning at all. But --- it doesn't work. She
can't retain the methods of doing the computations and she can't figure out
which to use in what problems AND the multiple choice test answers are all
based on common mistakes in applying computational techniques - so when she
makes one of those common mistakes, the answer IS there and she chooses that
and then gets the problem wrong. (We have lots of practice tests.)

So - finally, today, we had MANY hours together in an empty house- no
interruptions. I convinced her to just play along with me - give me a couple
of hours to NOT just show her how to do computations, but to help her get the
underlying meaning of what she was doing.

We played games. Now, these were very pointedly math games - we didn't play
just any old games - I made these up or got them from books and they were
very specifically designed to build an understanding of specific mathematical
ideas. (Remember, she isn't a kid and we don't have time for these concepts
to build up, slowly and naturally, over time. AND she suffers from truly
sever math phobia.)

But - they were games. I mean - they were NOT really obviously and directly
showing her how to solve problems on the test.

We played one game that helped her understand fractions, for example. I made
strips of colored paper -- one 12 inches long, cut one into 2 6-inch pieces,
cut another into 4 3-inch pieces, another into 8 pieces and another into 16
pieces. All different colors. I made a spinner with the numbers 1/2, 1/4,
1/8, 1/8, 1/16 and 1/16 on it. To start, I covered the long strip with the
two halves. Then she spun and had two choices --- she could "trade" one of
the pieces on the long strip for other strips - as long as they were
equivalent to the one she took off the long strip AND contained at least one
strip that was the fraction she'd spun. The other option was to simply remove
the fraction she'd spun from the long strip IF she had such a piece there.
The goal was to uncover the long strip in as few spins as possible. I had her
play it a bunch of times just as a solitaire game while I made strips for
myself and then we played against each other, trying to be the one to get our
long strip uncovered first - alternating turns.

By the time she'd played a while, she had a MUCH better "number sense" about
fractions. Before that, she'd constantly made the mistake of thinking things
like 1/8 was smaller than 1/10 -- because instead of understanding about
fractions, she'd just see the 8 and 10 and think 10 is bigger and so 1/10
must be bigger. After we'd played this game, it was obvious to her that the
bigger denominator, the smaller the fraction since it meant something is
divided into more, and therefore smaller, pieces. She no longer has to try to
MEMORIZE that a bigger denominator means a smaller fraction - it is just
something that is clear to her. She also "gets" the relationship between
fractions.

After she'd played a while with those pieces, I added 1/3, 1/6, and 1/12
pieces and created a new spinner with those added (took off 1/2 from the
spinner).

Later, when we were working on using fractions - I kept these pieces all
sitting out, lined up in strips, so she could look at them while adding or
subtracting. Having spent time PLAYING with them, they were her friends and
it was automatic for her to reach for them to figure out things like 1/3 plus
1/4. (She covered both the 1/3 and the 1/4 strips up with 12ths so she could
see that the 1/3 strip was equivalent to 4 1/12ths and the 1/4 strip was
equivalent to 3 1/12ths and so together they were 7/12ths.)

Now, I have "taught" her how to do this umpteen times, but this time she
"discovered" it for herself, using "toys" she'd been playing with. I could
see the light go on and that was it -- she quickly absorbed all the other
stuff about fractions. We covered everything else in another hour or two and
then went on to play some decimal games and covered decimals and percentages.


SHE was amazed at how quickly she was able to really TRULY learn so much
material after she'd spent some time "just playing." She felt the difference
in her grasp -- the difference between UNDERSTANDING and memorizing a
computational technique.

She's also gone to a psychologist recently, at my suggestion, to get help
with techniques to reduce her panic during math tests. She got LOTS of help -
breating and physical muscle relaxing exercises and self-talk exercises to
practice several times a day, which she's been doing for almost 2 weeks. It
seems to have really really helped - even during our study session her
anxiety seemed far less obstructive today.

Just thought this was something some of you might find interesting.

--pam