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In
this issue:
_ Letter from Founder Larry Shiller:
Montessori Words of Wisdom
_ Go Figure: This Month's Brainboosters
_ Parent Zone: Your questions answered
_
Funny Bone: Can Canines Count? Study shows dogs are smarter than we think
_ Out in Front: Math in the
News
_ Quotables: Memorable parting words…
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Dear Parent,
In response to the crisis in American education, more than five thousand
public and private schools across the nation have adapted the timeless
Montessori Method of teaching.
At its heart,
Dr. Maria Montessori�s unique educational approach considers children
to be intelligent and highly capable of learning when placed in an environment
and with materials that provides them with respect and privacy. ShillerMath
incorporates proven Montessori methods to help children learn math and
become productive members of society throughout their lives.
Following
is an inspiring excerpt from Maria Montessori�s classic book, The Absorbent
Mind about the scientific principle she calls, �the control of error�
that may just help lighten the burden you may feel in trying to be a perfect
parent!
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"Whatever
is done in school, by teachers, children or others, there are bound
to be mistakes. So we need this rule as a part of school life: namely
that what matters is not so much correction in itself as that each
individual should become aware of his own errors. Each should have
a means of checking, so that he can tell if he is right or not.
I need to know whether I am doing well or badly, and if � at first
� I treated my own mistakes as unimportant, I have now become interested
in them� This is the possibility of 'recognizing one�s mistakes'.
We must provide this as well as instruction and materials on which
to work. The power to make progress comes in large measure from
having freedom and an assured path along which to go; but to this
must also be added some way of knowing if, and when, we have left
the path. If this principle be realized, both in school and daily
life, then it does not matter whether teachers or mothers are perfect
or not. Errors made by adults have a certain interest, and children
sympathize with them�the fact that we can all make mistakes stirs
a deep affection in their hearts."
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ShillerMath
is based on Montessori methods and curriculum, which children appreciate
for the rest of their lives.
Sincerely,
Larry Shiller
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Brain
Boosters:
Guess
the number that when you add 1 and then add 5 is 12.
(Answer: 6 )
Guess the number that when you add 2 and then subtract 4 is 1.
(Answer: 3)
Guess the number that when you subtract 2 and then add 1 is 6
(Answer: 7)
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If
you’ve got ideas to share, need an answer to a question, or simply
want to connect to a larger community of parents this is the place for
you. After all, we all know that finding an elegant solution is the true
beauty of mathematics!
Q:
Pardon me, but I think there is a mistake in your recent newsletter�s
"Go Figure" answer. Your figures result in an answer of 2 not 9. Shouldn't
it read something more like this? 8 + 8 - 8 / 8 + 8 = 9 ? Just making
an observation. Thanks!
Lisa T.
Larry Shiller: Hi Lisa, thanks for
your email and your excellent question. The standard when evaluating mathematical
equations is to evaluate the multiplied by and divided by signs first,
then the plus and minus signs. This is called "precedence." If precedence
other than the standard is desired, parentheses are used. Note that this
is not how a calculator would evaluate an expression! A calculator evaluates
an expression in the order the terms are received. Your example works
with a calculator.
So for our example, 8+ 8 - 8 + 8 / 8 is the same as 8 + 8 - 8 + (8 / 8)
= 8 + 1 = 9. As you correctly point out, the answer is 2 if one uses a
calculator.
Q:
My daughter is in 3rd grade. Up until this year, math was her favorite
subject. Even though she struggled with it, she enjoyed it, and we were
happy with her consistent C grades. This year is awful- she can't seem
to grasp the basics of subtraction, and is in a panic because she's getting
F's in everything, even on things she could do last year. As someone who
loves math, what can you suggest for someone who used to love it, but
is fast developing a phobia? Any kind of fun exercises she could do, books
I could get, or even computer programs would be great. I'll try anything.
Thanks for any help.
Helen R.
Larry Shiller: First, try going back
over the things she felt confident about last year. Then she can attack
the subtraction problems with more confidence. Next, have her take the
diagnostic tests, which are free here.
More than anything, I feel it is of utmost importance to encourage your
daughter and let her know you know she can do it. Many people have a math
phobia because they were discouraged early on and told that they could
not do math. Math appears in so many different places, sometimes elementary
schoolers don't realize that there is more to math than addition, subtraction,
multiplication, and division. I know many people (including math majors)
who struggled early on with concepts like subtraction but eventually came
to love math. So, encourage her lots, and feel free to get back in touch
with any problems she might have.
Click
here to get a personal response to your question
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Can
Canines Count?
According to a new study reported in New Scientist magazine, Fido or Fifi
may be smarter than we think. Scientists at the University of California,
Davis are convinced dogs know when they are being shortchanged on treats
because they have a basic math ability, which enables them to tell, which
pile is bigger than another.
In testing,
dogs were shown treats and then a screen was lowered and the goodies either
left as they were or some were added or taken away. If a treat was added
or taken away the dogs looked at the treats much longer than they did
when the goodies were not disturbed, presumably because they had done
their sums and the numbers did not meet their expectations. Scientists
believe that this math ability could be the result of dogs having descended
from wolves, and that their �counting� skills could have been used to
work out how many allies or enemies they had in a pack.
For the full story see:http://www.engineering.usu.edu/cee/faculty/gurro/Funnies/dogs&math.pdf
FunnyBone quip: Math is 50 percent formulae,
50 percent proof, and 50 percent imagination.
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Neurons
do Math, in the brains of monkeys and frogs, at least. This is the
message of "Single brain cells count," a Nature Science Update
for September 6, 2002 by John Whitfield. Two recent sets of experiments
"showed groups of dots to macaques and recorded the output from individual
neurons in the monkeys' prefrontal cortex. ... The neurons ignore the
dots' size, shape and arrangement and hone in on their number. Each cell's
response peaks at its preferred number and tails off on either side."
Neurons in the brains of female frogs (Hyla regilla) were sampled to understand
how they distinguished between the aggressive calls and the advertisement
calls of males of their species. The only difference between the two calls
is their speed. "Female frogs' male-detector neurons fire only after
they hear five or more rapid pulses. If the pulses are too close or too
far apart, the counter resets to zero - as if the nerve cells measure
the spaces between pulses, rather than the sounds themselves."
Source: American Mathematical Society www.ams.org
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"The most important
motive for study at school, at the university, and in life is the pleasure
of working and thereby obtaining results which will serve the community."
- Albert Einstein
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What
is ShillerMath?
ShillerMath helps kids learn, and parents teach, math. ShillerMath is
based on the proven Montessori approach to home-based math education;
it does not t rely on repetitive drills or pure memorization but instead
provides easy to follow, step-by step activities and tips to help kids
and parents avoid the pitfalls of frustration, anxiety, and boredom. Children
using this approach consistently outperform their peers. Larry Shiller,
ShillerMath founder and President, has a math degree from MIT.
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