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Is this an exceptionally hard set of questions to answer?
Posted:
Sep 28, 2002 9:47 PM
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On 19 September 2002, I asked the participants in the sci.math and
misc.education newsgroups for advice on a subject I figured they
would know more about than I: what materials are best for math
learners of kindergarten to eighth grade level. Perhaps because of
the vagaries of Usenet newsgroup propagation, I never saw any
answers to the questions I asked--but it seems hard to believe
that no one here has anything to see in response to those
questions. Because the original thread has been retitled and is
fading off many Usenet servers, let me ask the questions again.
Hi, this is an open invitation to hear opinions from any and all
of you who read this. I'm wondering what materials (textbook
series, and nontextbook books, manipulatives, software, games, or
whatever) you would recommend for young people learning elementary
(kindergarten through middle school) mathematics. I'll describe
some particular special cases I am interested in, but I am also
interested in the general case of a heterogeneous classroom or a
homeschooling family of unknown characteristics. I am a parent of
four young children (only two have reached school age) and I may
face any of the situations I list below, so I appreciate your
answers.
SPECIAL CASE 1 (MATHEMATICALLY GIFTED CHILD)
What, particularly, would you recommend for a learner who shows
evidence of unusually high ability in math? (Left unconsidered
here is whether "unusually high ability" comes from nature or from
nurture, and whether it is evidenced by standardized test scores,
advancement in grade placement, or some other proxy of ability.)
For the highest-ability young mathematics learner, what materials
are especially suitable for maintaining interest in and correct
understanding of mathematics, and for building a foundation for
later advanced study of math? Are there any materials that are
particularly UNsuitable for learners in this special-case
population?
SPECIAL CASE 2 (MATH-DISABLED CHILD)
What, particularly, would you recommend for a learner who shows
evidence of unusual difficulty in learning math? (Again, I am not
restricting this question to any particular kind of causation or
ascertainment, and you are welcome to consider subcases of either
low "general intelligence" or "specific learning disability" in
answering this question.) For the lowest-ability young mathematics
learner, what materials are especially suitable for building
understanding of mathematics and helping the learner to understand
and apply as much math in the "real world" of adult living as
possible?
SPECIAL CASE 3 (MATH-EAGER CHILD)
What, particularly, would you recommend for a learner who shows
consistent, sustained, avid interest in learning mathematics
(irrespective of the learner's level of math ability)? For the
most-eager mathematics learner, what materials are especially
suitable for appealing to that intrinsic interest and using that
as a foundation for deeper learning of mathematics? Here I'm
especially interested in suggestions for materials beyond the
scope of school textbooks, and indeed in suggestions for
activities (math competitions, perhaps?) outside the scope of
schoolwork.
SPECIAL CASE 4 (MATH-AVERSE CHILD)
What, particularly, would you recommend for a learner who shows NO
interest in learning mathematics, doubts the usefulness of math,
and would rather do almost anything else besides learning math
(again, irrespective of the learner's ability level)? For the
learner turned off by math, what materials are especially useful
for evoking interest in math and showing either an inherent
attractiveness of or a linkage between math and subjects the
learner is already interested in?
GENERAL CASE
What, particularly, would you recommend for a learner or group of
learners who have unknown membership in the special-case
populations above? What would you recommend for a schoolteacher
teaching a school class of mixed ability and interest levels? What
would you recommend to a homeschooling parent who poses a question
on-line and doesn't identify his or personal math background in
much detail? In other words, what math materials might tend to be
optimal for the broadest range of special cases encountered in the
general population? Are any math materials that are well-suited to
special populations BADLY suited to the general population? I
would be interested to know what math materials you would
recommend as having broadest usefulness and likely benefit, and I
wouldn't mind knowing what materials you do NOT recommend to
anyone, no matter what the learner's special characteristics. Are
some math materials actually harmful, worse than using nothing at
all?
Thanks for any and all opinions you express, materials you
recommend, or comments you have on my questions. If you would like
to reach me by email, feel free to write to
kmbunday AT earthlink DOT net
and later I will anonymously ("a private correspondent said, '. .
. '") digest private comments for the group.
By the way, what is the scope of "elementary (K-8) mathematics"?
What subjects (or more narrow topics) are surely included in
mathematics learners should learn by eighth grade? What subjects
(or topics) need not be learned by that age, or even SHOULDN'T be
learned by that age?
Thanks for letting us all know your thoughts on this important
issue.
--
Karl M. Bunday "pray for us" 2 Thessalonians 3:1
Learn in Freedom (TM) Web site http://learninfreedom.org
kmbunday AT earthlink DOT net (preferred E-mail)
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