Suggestions
for helping your children enjoy mathematics
(and
be better thinkers)
by
Dale R.
Reed
Daily mathematical
exercises and explorations will improve everyone’s
ability to understand and enjoy Mother Nature's
fascinating world.
Letter to
Parents from Dale
Enjoying mathematics and becoming a better
thinker
This is a
collection of math suggestions from
homeschoolers and others. Only a few of the
"I's" and "me's" in this
document are actually me (Dale). The document
is growing as a result of my posting to various
discussion lists requesting homeschoolers to
reply with what they do to enjoy learning math
in their families. There are also some ideas
from the SeattleTimes/Real_Life/ Parenting
column. Please use this document as a menu to
choose from to better provide material and
methods for your children’s mathematical learnings.
These
suggestions were accumulated to help you help
your children develop their mathematical skills
and gain an appreciation for the fact that
Mother Nature and all her wonders can be better
understood and enjoyed with mathematical
analysis. Mathematics is a universal language
that different generations and cultures use to
communicate with each other.
One of
things that separates us from animals and
robots is the creative use of our brains. But
we must consciously develop our ability to
think by using our brains in work and play.
Mathematics is a universal language
that thinking people from different
generations and cultures use to communicate
with each other. To become a better thinker
you must think difficult thoughts. Solving
math problems are pushups for the brain.
~~Dale R. Reed~~
|
Exercises
Five days a week,
about one hour a day, the student should work through a
mathematics text book. The student should maintain a
notebook of carefully/neatly worked problems done with a
quality mechanical pencil, pink-pearl eraser and a
straight edge. Each homeschooled youngster should keep
this notebook with his grammar, history, and other
notebooks that make up his portfolio of studies and
accomplishments.
Prior to purchasing
a book be sure to evaluate your child’s capabilities.
For example Saxon provides placement tests that you can
download at http://www1.saxonpub.com/. They have several
different levels from K-2 up to Algebra 2. Even if you
don't want to use Saxon, the middle grades test do a
great job of showing up weak areas such as fractions or
decimals.
Before buying a math
book borrow (from another homeschooler or the library) a
copy and use it at home for a couple weeks. Also be aware
that all (including Saxon) materials, change over the
years. You may prefer an older version over a newer one
or visa versa. Be aware that many (especially Saxon)
textbooks are expensive but built tough so you can often
buy used books at local bookstores and/or online. Many
homeschooling Moms, sometimes with their children’s
help, have collections of used books for sale.
I started homeschooling my daughter in 1st grade and
continued on with Modern Curriculum Press workbooks for
math because that is what she was used to and Saxon for
the lower grades was far beyond my budget! They were
ultra simple and easy to use for both of us. She is in
3rd grade now and enjoys math. She seems to be able to
move more quickly that the MCP books so we gave an ACSI
workbook a try. So far so good.......
OK, now on to Key To
Algebra http://www.keypress.com/index.html.
I think this
series is wonderful. It is from the same publishers as
Miquon Math, which is what we used (and loved) for the
lower levels. So far dd has done Decimals, Fractions,
Geometry and Algebra. The way the series is set up is
that there are these booklets (3-4 for Fractions,
Decimals and Percents, 8 for Geometry and 10 for Algebra)
the student works through. The publisher says the grade
range is 4-12 for each series except Algebra, which is
5-12. There is very little text, using mostly examples to
give instruction, which works especially well with
right-brained, visual learners. The first Algebra book
deals exclusively with integers - adding, subtracting,
multiplying and dividing positive and negative numbers.
It became a little tedious for dd, but I think a bright
(or mathematically inclined) 8yo can certainly handle it.
One of the best things about this series is that the
booklets are quite inexpensive -- $2.95 each. So it you
get one and it doesn't work out, you won't have lost your
shirt.
My kids and I have
been using Open Court for 3 years now, and I am impressed
with it. We used Saxon prior to that (early grades), and
I did value the attention given to repetition with math
facts and use of manipulatives. My oldest wanted more
"real world" problems, so we decided to use
Open Court, which, according to the owner of Math
"N" Stuff in Seattle is not out of print, just
being printed in limited amounts, since SRA/McGraw Hill
bought it. The SRA/McGraw Hill program is almost the same
as Open Court, just a bit more glossy and high grade
paper, hence more expensive. We really like the
"Thinking Stories" that are part of the
program. I was fortunate enough to get 4th and 8th grade
when I needed them... and we loved them! My youngest is
doing the 8th grade level now (at age 11) and enjoying
it. I liked using the 8th grade one with my son... made
it so he didn't have to do Saxon Algebra 1/2... went
straight to Algebra I. And THAT is one of the main
reasons he can do most of the problems in his head. Open
Court is KING when it comes to encouraging mental math...
they even teach shortcuts for things like 43x47... by the
time you are done, you KNOW how to complete a square in
factoring polynomials, and it makes sense.
First of all, Open
Court math books are not workbooks/worksheets. They are
textbooks that you don't write in. You just write the
answers down on a piece of paper, and some daily lessons
are ALL discussion or experimentation. These books
involve the kids in discussion like you'd expect from a
literature course or something... they're something else!
The fourth grade book, for example, starts out by having
kids (and parents!) estimate how many apples are in a
bin. You get to make successive guesses as they give you
more and more information, and you learn a lot in the
process. There are pages where part of the problem is
blotted out by "accidental" ink spills, and the
kids figure out what they can still determine, given the
information left. There are problems for which
"Cannot determine from available information"
is a valid answer. It really IS "real math"...
from real life... with just enough silliness thrown in to
make you smile while you're doing it.
McGraw Hill has
several different math series. So far our favorite is the
Explorations and Applications.
Nancy's been working
in Harold R. Jacobs, "Mathematics: A Human
Endeavor" for a year and loves it. It doesn't dumb
her down and she's loving Math. It's challenging, but she
keeps at it. Jacobs also published Algebra and Geometry
books that are worth considering.
A math book I have used with both kids and loved is
Family Math by Jean Stenmark, Virginia Thompson, and Ruth
Cossey. Lots of easy to make and play games for all
levels (mostly elementary, but some middle school). My
kids at 7 had a hard time translating math to the written
page, so we just didn't do it. If you think about it, it
is a hard concept, taking a concrete concept such as 7
apples minus 2 pears and reducing it to symbols on a
written page.
So, for younger kids, the more concrete and hands on, the
easier math is to grasp. We played dominoes and added
totals (good for adding into the 100s), counted and
graphed stuffed animals and toys, used large size number
lines and hopped from number to number by 2s, 3s, 5s,
etc.
For fractions, I bought a set of "fraction bar
games", which are plastic bars divided into halves,
thirds, etc. There are suggestions for games to play to
familiarize players with the concepts of equivalencies,
adding fractions, naming fractions, etc.
We also did a lot of oral word problems early on, even
with multiplication and division (although they didn't
know they were doing that). To pass time in car rides, or
other boring situations they often beg me to give them
word problems. Only they called them "Betsey
problems" because they often featured a character
named Betsey.
Other fun books are Math for Smarty Pants and other books
by Marilyn Burns, though those are more for 9 and up (in
my experience).
I started coming up
with a mental list of situations where Saxon works, and
where Saxon doesn't work. First, Saxon uses a
repetitive review approach. You keep doing a few of the
same kinds of problems nearly all the way through the
book. As such, it is designed to help kids prevent
mathematical facts from falling out of their heads. Some
kids need this (and those kids know they do); some kids
don't. Some kids, in fact, have minds that NEVER forget a
math fact. I was one of those kids, and Saxon would have
driven me batty if I had to use it to learn from. (Now
that I already know algebra, I do the problems alongside
my son for recreational purposes, but I'd have hated to
learn from it.) Face it, some kids like to tackle a new
concept, nail it down, and move on... using it as
necessary, but never having to LEARN it again. Saxon
isn't good for those kids.
Also, there are other math books that use the repetitive
learning approach. Rod and Staff (which, unfortunately,
only goes through 8th grade, but is a good pre-algebra
book at that level) not only reviews continuously, but
notes, with each review problem, what lesson the concept
was originally taught. In addition, it has WONDERFULLY
comprehensible explanations. When my son was in 4th grade
and struggling with adding fractions with different
denominators, I turned to the 8th grade Rod and Staff
book. There were 2 pages of explanation, which my son
instantly understood. We'd spent hours and hours and
pages and pages trying to get this through his head (and
I'm a good explainer). So I was impressed.
University of Chicago's math program puts out another
continuous review higher math series. Their book is
preferred over Saxon by many public schools. It is more
colorful, more engaging, and it doesn't neglect showing
kids a REASON for learning all this stuff.
Which brings me to another drawback/asset (depending on
the kid) of Saxon's books. Saxon is intensely effective
on training kids to follow steps to a solution. They
memorize the steps. They do not always get the concept
behind the steps, unless they are naturally geared that
way. My son very conceptual. He does Saxon math problems
in his head and skips the steps. (We race to a solution,
and he sometimes wins.) But he HATES writing down the
steps, passionately. We still use Saxon, but we adapt it.
If you have a kid who whines, "But why do I have to
LEARN this? What use is it?" and you are attempting
to use Saxon, be forewarned that you will have to
supplement the text to answer those questions. University
of Chicago's stuff answers them while it teaches.
Saxon also neglects practical math. Its problems touch
richly on scientific applications, but not on day-to-day
mathematical uses. Your child will not learn to balance a
checkbook, read a meter, complete an income tax form,
calculate interest on a loan, or maintain a revolving
credit account wisely. These things are easy to teach in
a homeschool setting, but remember you will have to do
it; the text won't fit it in neatly between percentage
calculations and factoring polynomials.
Saxon teaches geometry, but barely touches on proofs. I
ran across a description somewhere of classical
education's main reason for teaching Euclidean geometry:
It was a LOGIC course. So... if you want THAT kind of
geometry for your kids, you'll need to use another
geometry text. And if you are like me, wanting your kids
to have exposure to constructing proofs, but not be
buried in them, you may find that the Bob Jones geometry
book is a happy compromise, with clear explanations and
just the right dose of fun. Be warned, however, that BJU
does NOT do repetitive review. They expect you to get it
the first time around and then be able to use it.
All this said, there are definite instances where I'd
recommend Saxon. For kids who don't mind tedium, are
geared learning steps before concepts, and appreciate
John Saxon's dry humor and don't miss the "why I
have to learn this" explanations, Saxon sets
mathematical technique FIRMLY in the student's head. For
kids who can learn from anything, anywhere, Saxon works
well, too, and it's admittedly readily available and easy
to resell.
We use A Beka for
almost all of our work. We are now starting our 5th year
of use and I have found that for my eldest it is just
what she has needed. The first 3 years were very colorful
and had a wonderful way of explaining the concepts. It
has the concept of building math one step upon each
previous step with just a touch of review in each lesson.
We have now reached a point that she is able to teach
herself. I just set the lesson schedule and she knows
what she needs to do. My youngest is flying through her
math and seems to have a grasp of what it is all about.
One of the things I have liked is how they work their way
through basic math and gently work a child to beginning
algebra with a introduction to the first skills needed in
3rd grade. I have looked at Saxon and it appears to be
similar and we should be able to easily switch if we
decided to at any point now. I would highly recommend the
A Beka for the first 3 years at least. From there it
appears that the two are fairly equal.
We use a fair amount
of A Beka, but have always avoided their math. I can't
say we tried it and didn't like it. We never tried it
because the pages looked too busy and they seemed to jump
from one concept to another without enough practice in
between for the younger grades. However, I have not
looked at the upper grades and look forward to hearing
the other responses.
The Gnarly Gnews http://www.gnarlymath.com
math newsletter has
been invaluable because of the great information on the
history of mathematical discoveries.
“Algebra Unplugged”,
by Kenn Amdahl & Jim Loats, is also absolutely
fabulous for a humerous overview of material covered in
an Algebra One course (it was a great refresher for me,
too). The authors talk about the danger of memorizing the
quadratic equation without an understanding of the
underlying theory--they say it is the biggest reason kids
crash and burn in higher math
after Algebra One.
http://www.bluestockingpress.com/pages/frameset.html
Mathematics Most preschool children enjoy letters, words,
and numbers. They like to mimic their parents and older
siblings. They enjoy "reading" and "counting." So, why
does this interest and enthusiasm in numbers and words
often disappear after "structured" learning begins?
http://www.academicsuperstore.com/index.html
“They took my notice of intent for my older son (12 yo)
and will keep it on file for a year before we have to
send another one.”
The three most
important math skills are:
Estimation, measuring and logic/problem solving. Before
children can begin to really learn these, or any other
"math skills" they first need a strong concrete
understanding of math. By this I mean real world
experience, not abstractions. Before you can estimate the
distance from here to that tree you must have a confident
sense of how long a foot actually is. This requires ample
time to play and fiddle and figure out how things work.
Families can play
mathematical games together.
One way parents can
be creative is to make good use of games. Games are not
only educational, they also each children many social
skills. children learn how to listen, to follow
directions, to agree on rules, to take turns, to plan
ahead and to act cooperatively. They also help to bring
families together for fun, laugher and communication.
Games: "Tic Tac
Twice" (a strategy game) and "True Math"
from Aristoplay (800 634-7738) (Their games "Quickword"
and "True Science" are great, too) Also,
Muggins Math games (they even have algebra games)
available from most major home school suppliers.
Other games and
activities are Tripoly (a card game involving poker and
Michigan Rummy), Cribbage, Pool (great for geometry and
physics), Darts (adding and multiplying on your feet,
literally). While playing Concentration with my
4-year-old I told him to say the number on the card to
himself before turning it over, and that would help him
to remember it better the next time around. He followed
my advice and greatly improved his game. He also began to
carry over this technique to other situations he
encountered and his memory greatly improved. Also try
Hearts, Cootie, Go Fish, Crazy Eights, Spit and of course
Jigsaw puzzles(either done by one person or with everyone
working on it) are especially nice for long rainy
weekends. There are competitive games like Monopoly and
GO and cooperative games like Community, Our Town and
Harvest Time for younger children. There are also games
families can play that can start a lively family
discussion. Such games are Scruples for Kids and the Self
Esteem Game. War game is a good mental math game. Both of
our boys enjoyed just doing simple problems like; what's
half of X, what's 4 times X, etc. When they got stumped,
usually they found the answer if we could relate it to
money. I have picked up some easy logic material from
Critical Thinking Books and Software. But most of their
stuff is for much older kids, at least it stumps me quite
often!
Krypto is produced
by The Making People Happy Games Co., PO Box 1125,
Fairfield, CT 06432. To play, each player is dealt five
cards with numbers on them. A target card is turned over
and then you try to add, subtract, multiply or divide the
five cards in such a way that you equal the target card.
Julie says, "I got a deck for Christmas from a
friend who homeschools. It says for all ages but I think
that is a bit optimistic. My seven year old and I tried
to play it today. I played his hands, too, but it seemed
like it would be a very fun game once we get going with
it."
Idea: We have a
"Do It In Your Head" policy in our house (most
of the time). This morning, my youngest son (12) and I
played "Where In the World" (also by Aristoplay).
Everyone adds up his own score at the end of the game.
Each card is worth 1 to 60 or so points. We each add our
cards up in our heads then switch cards to double check
one another. He added his 20 cards faster than I added my
16 cards. He also beat me fair and square in the game by
identifying 20 European countries on a blank map,
including two I had never even heard of.
My kids and I play a
lot of "21" or "Blackjack" ... which
is great for quick, mental counting. We play with
pennies, nickels and dimes and quarters.
Simple Games are:
Cards(War, FanTan, Hearts), Dominos, Cards(Rummy) and
Triminoes. Make up new rules for dominoes. There are many
different ways of playing dominoes that you and your
children can invent. It is very important that parents
play the games with their children and multiple children
can keep score to correct each other. Harder problems can
be worked on a calculator but easier ones can be worked
in the parents and children's head with older children
using advanced scoring levels while younger children can
help them and/or confirm some intermediate calculations.
Don't forget the old
standbys of Popular Board Games for simple math concepts
are: Monopoly(Parker Brothers) and LIFE(Milton Bradley),
checkers(regular and Chinese), chess, and backgammon.
Other favorites of
one family are: Bowling (ignore the computer and use a
score sheet). Tangoes (Chinese tangrams), and Coupons
(not really a game, but a neat activity and a way to
comparison shop)
"Adult"
Games for intermediate math concepts are: Rail Baron and
The Stock Market Game from Avalon Hill, Executive
Decision, Stocks and Bonds, Stock Market Specialist and
Win, Place or Show-Horse Racing Game all from 3M
Bookshelf Games.
Gambling Games such
as one that uses a Roulette Wheel. Once they understand
the big advantage the house has your children will be
amazed that anyone gambles in Reno or Las Vegas.
Keno (Our state
lottery has Keno everywhere and the State House advantage
is obscene. Danny likes to pick four numbers and follow
their progress while we eat lunch. We always
"lose," so I figure this is a pretty good
lesson to learn now, while the money is pretend).
Play calculating
games with very young children but use: poker chips,
playing cards, dominoes, cuisenaire rods, wood blocks,
measuring cups, clocks, calendars, calculators, tape
measures, puzzles and tangrams. We keep all of our toys
in bins on shelving. Just cleaning the playroom requires
sorting and classification. We have a marvelous dollhouse
that is made from modular rooms that can be stacked in a
variety of configurations. Sometimes we use the poker
chips to count, but mostly we stack them in interesting
patterns. Since they lock together they will stand in a
tower. This makes them infinitely preferable to counting
chips. For little kids, games like Candy Land and Cooties
work to develop the skills they need--counting and
sorting.
Parents must
indicate their enthusiasm for applying math in their
everyday living.
When taking trips together, over the dinner table…
whenever there set an example of a person who is
continually calculating/approximating numbers in your
head and on paper. Determine how much cheaper(in
percentages) it is to buy food in larger quantities and
how much more an automobile costs if it is purchased on
time instead of cash. It is a good exercise to measure
and draw plan views of each floor of your house
calculating the square footage, etc. The height of trees
can be estimated using a angle measuring device, a tape
measure, and the tangent function. Various electrical
calculations for appliances in the home are easy once you
learn how to use Ohms law.
Parents and their
children would enjoy learning how to program the computer
in Logo.
I
have a Logo1.doc WORD document
that I (Dale) will send you via e-mail if you whistle.
With Logo your children can create 2d and 3d knots,
beautiful Fractals (trees and ferns for example), even
chaos. I am beginning to learn how to program with the L3
code from Magic
Square. It is very similar
to Logo but is easier to program and runs much faster.
But L3 has the disadvantage that there is no user
community to exchange ideas and programs with. There is
an almost entirely graphical programming language
described at ToonTalk
that is interesting
to some children. Of course there are Visual Basic, HTML,
and C++ for older youngsters that are interested in
learning “real” programming languages.
For computer
programs, there are Sammy's Science House and Thinkin'
Things I, both by Edmark, and Tesselmania by Mecc. Math
Blaster offers Basic Drill and Practice in an Arcade
Game, School Mom is a Tutorial, and Windows Arithmetic
offers Examples, Problems and Solutions.
We began getting
ready for our homeschool SAT test
by
drawing a small poster, Math Champion, for Sam &
Clair's work areas. They took markers and made these
posters as the beginning of our full-on math studies. We
all throw in the phrase, Math Champions during our
studies to know what we are working towards. I give them
silly math breaks: go find something blue, they bring it
back and I ask them to add the corners in the object or
some such math question. Or, pretend your sister doesn't
know how to multiply, teach her! Or, quick run out to the
garden pick a bouquet with 2 flowers of each color &
tell me how many you have, what's the equation? Just some
of the silly things I have to do to keep math fun. The
more I do this, the longer the stretches of actual study
time.
The parents must
keep up to date on which tests
the children will be expected to do well in the future
and make sure the parents and the children can do the
problems. There are not only the Certificate of Mastery
tests mentioned below but I predict more and more testing
for all of us in the future not only to obtain government
licenses to do certain jobs but also testing at work. Or
to put it another way I expect the end of compulsory
education as we shift toward mandatory(at least if you
want the job) knowledge and skills.
The State of
Washington(and most other states) via a Commission for
Student Learning has published samples of the mandatory
high stakes Fourth, Seventh, and Tenth Grade Tests that
lead to the Certificate of Mastery resulting in a
diploma. Supposedly there will be no more social
promotions in the government schools. Watch for articles
in the paper and find web sites with sample problems. Of
course you can always visit your local government school
and find out what math books they are using. Probably you
should talk to the math teachers for they may be
supplementing the state supplied material.
Another
fascinating and potentially useful mathematical brain
teaser for young and old is the study and tying of knots.
There is lots of info in cyberspace, for instance Knot
Plot, but you can also get
started by simply buying some rope, finding a Boy Scout
Manual and start tying. My (Dale) two sons and I enjoyed
tying knots when the boys were smaller. Especially the
knots that tie a fish hook on the end of a fishing line.
And tying and untying knots is fine exercise for
arthritic hands hence it is something grandchildren and
grandparents can enjoy doing together.
Miscellaneous
mathematical references and incentives to learn
mathematical skills.
Many people find it
interesting and useful learning the relationships between
their location on earth, the time of day, the positions
of the sun and other celestial bodies, compass directions…
One book on these issues is “Emergency Navigation,
Pathfinding Techniques for the Inquisitive and Prudent
Mariner” by David Burch of http://www.starpath.com.
There are
mathematical reference and history books such as
Encyclopedias (World Book), The World Book of Math Power
and the Schaum's Outline series
http://www.pbg.mcgraw-hill.com/schaums/schaums-home.html.
And of course the
are all the inexpensive books from The Dover Book Company
such as the two books for older students and their
parents by Morris Kline, "Mathematics and the
Physical World," and "Mathematics for the
Nonmathematician."
John Stillwell wrote
an book for older students “Mathematics and Its History”
in 1989.
"A History of
the Circle, Mathematical Reasoning and the Physical
Universe, Ernest Zebrowski, Jr. First Paperback printing
2000.
Some older children
will appreciate Douglas R. Hofstader’s ideas as
published in his many books including “Matamagical
Themas: Questing for the Essence of Mind and Pattern,”
1985.
I like to study and
think about the drawings done by M.C. Escher http://www.worldofescher.com.
Intricate repeating patterns, mathematically complex
structures, spatial perspectives all require a
"second look." In Escher's work what you see
the first time is most certainly not all there is to see.
I recently enjoyed
reading “Longitude The True story of a Lone Genius Who
Solved the Greatest Scientific Problem of His Time” by
Dava Sobel, 1995.
“Calculus Made
Easy” by Silvanus P. Thompson and Martin Gardner, was
re-published in 1998. This first complete revision in
over 75 years of the million-copy bestseller-includes
more than 20 new problems. Those of you (and all of you
should) that subscribe to Scientific American know of
Martin Gardner’s popular scientific and mathematical
publications during the last 50 years. I bet most 12+
year olds will enjoy learning from this interesting book.
“The Universal
History of Numbers” by Georges Ifrah published in 2000
is a informative large paperback book about the
prehistory to the invention of the computer.
http://www.cuisenaire-dsp.com
will send you catalogs of useful mathematical materials.
Josh Rappaport of http://algebrawizard.com/sample.html
has written an Algebra book, “Algebra Survival Guide”
and publishes an free monthly E-Mail Newsletter called
the “Algebra Times.”
http://www1.moe.edu.sg/syllabuses/default.asp
The subject syllabi designed by the Curriculum
Planning & Development Division, Ministry of
Education have been revised to incorporate the 3 MOE
initiatives on Thinking Skills, Information Technology
and National Education. The revised primary and secondary
syllabuses which will be implemented progressively in
schools, can be found at this site.
http://www.marquis-soft.com
Graph Paper Printer A program of interest for a very wide
range of users. It prints numerous kinds of graph papers,
music manuscripts and a great variety of pattern papers.
http://www.math.hmc.edu/faculty/gu/curves_and_surfaces/
A digital library of mathematically interesting and
important curves and surfaces.
http://www.magicofmath.org
The Magic of Math site is an initiative of the Akamai
Foundation. The Magic of Math site aims to provide a
forum to communicate and share the delight of mathematics
with children (K-12). We hope to foster an enjoyment and
pursuit of mathematics knowledge by providing interesting
and fun mathematics content, offering kids a chance to
speak with math "whizzes", and encouraging math
creativity.
And there are
hundreds of interesting mathematical sites in cyberspace:
http://br.crashed.net/~akrowne/crc/math/c/c858.htm
The simplest curves can be represented parametrically
http://www.figurethis.org/index.html
Family members, as children's first teachers, are crucial
to student success. And the more adults become engaged in
their children's education, the greater the chances that
children will succeed.
http://mathforum.com
Ask Dr. Math, discussion groups…lots of links.
http://www.cut-the-knot.com/content.html
Interactive Mathematics Miscellany and Puzzles.
http://www.nctm.org/corners/family/index.htm
Welcome! Caregivers will find information for helping
children learn mathematics. If you are a student, test
out our online resources for activities and mathematics
help. Please check back often, we'll be expanding this
area in the coming months.
http://www.math.com/
The world of math online.
http://www.ams.org
http://www.ams.org/mathweb/mi-mathbytopic.html
The
American Mathematical Society was founded in 1888 to
further mathematical research and scholarship. The
Society currently has approximately 30,000 members
throughout the United States and around the world. It
fulfills its mission through programs that promote
mathematical research, increase the awareness of the
value of mathematics to society, and foster excellence in
mathematics education.
http://math.exeter.edu/rparris
Peanut software -- free mathematics software.
http://www.mathcats.com/contents.html
Welcome to the Magic Chalkboard! Wave your wand over
today's answer, then click!
http://www.homeworkhigh.com/maths/frame.html
Send your Math homework questions to our experts.
http://members.aol.com/keithenev/index.htm
There is a lot of fun stuff here for school kids.
http://mathworld.wolfram.com/
9555 entries, 167956 cross-references, 3814 figures, 84
animated graphics, 934 live Java
http://www.ccl.tufts.edu/cm
http://www.pen.k12.va.us/Anthology/Div/Winchester/jhhs/math/mathhome.html
Department of Mathematics John Handley High School
http://www.math.niu.edu/links/math.html
Math-related Web Links
http://www.mcs.surrey.ac.uk/personal/R.Knott/Fibonacci/
Fibonacci numbers, the Golden section and the Golden
string.
http://www.hotsource.com.au/
One of the main lessons learned in math class is a
sense of having rigid limitations.
http://www.coh.arizona.edu/inst/edp512s97/math.html
Math Resources from around the word
http://www.mathgym.com.au/htdocs/home_sch.htm
http://www.cpsc.ucalgary.ca/Redirect/bmv/index.html
http://math.rice.edu/~lanius
Cynthia Lanius Executive Director CEEE http://ceee.rice.edu
http://math.rice.edu/~lanius/frac/
Fractals Unit for Elementary and Middle School Students.
Fractal Links
http://math.rice.edu/~lanius/Lessons/
http://www.ex.ac.uk/cimt
The Centre for Innovation in Mathematics Teaching,
established in 1986, is a focus for research and
curriculum. Includes a Conversion Calculator for Units of
LENGTH, ENERGY… And many other math resources including
puzzles and recreations.
http://www.homeschool.com/
Math information
http://www.sciam.com/explorations/1999/102599math/index.html
http://www.coolmath.com/index.html
http://www.stats.org/index.html
http://adagio.physics.usfca.edu/phys110/applets/pendulum/index.html
Welcome
to the Pendulum Lab! This is a virtual laboratory where you can do hands-on experiments at rigid pendula.
Together with the material presented in the lecture
room, you can learn basic issues
like harmonic oscillator and resonance but also advanced
topics like parametric resonance, nonlinear dynamics, and
chaos. Playing with the pendula in the lab, you only need
curiosity and a browser which can run Java applets.
However, to understand the mini-lecture, it is helpful to
have some basic knowledge of calculus.
http://www.erving.com/turtle/index.htm
Using MicroWorlds andAppleWorks Spreadsheets to Explore
Geometry Concepts
http://www.rpi.edu/~eglash/eglash.htm
http://physicsweb.org/TIPTOP/VLAB/
What follows is a list of physics related Java Applets
(also some VRML)
http://www.blarg.net/~math/
Highline School District #401, Seattle, WA Advanced Math
Program
http://www.maa.org/Welcome.html
http://random.org/
http://www.fourmilab.ch/hotbits/ http://lavarand.sgi.com/
Random numbers
http://www-maths.mcs.st-andrews.ac.uk/
http://www.mathgoodies.com/
Math Goodies is a free educational web site featuring
interactive math lessons, homework help, worksheets,
puzzles, message boards, and more! We have over 400 pages
of free math activities and resources for teachers,
students, parents, and homeschoolers.
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html
http://www.knowledgeadventure.com/features/parents/
http://exploringdata.cqu.edu.au
Exploring Data curriculum support materials for teachers
of introductory statistics.
http://www.funbrain.com
http://www.mathkits.com
http://www.nctm.org/
For more than 75 years, NCTM members have taken the lead
in changing mathematics education for the better.
http://www.webmath.com/
Everyday math, Personal financing, unit conversion,
math@home, Fractions, number line, story problems,
Ratios, calculations, Metric, sequences, decimals,
Algebra, Geometry, graphs, plots, Trig, Calculus, Create
a quiz, practice, etc....k-8 section and everyone
section. QuickTime movies.
http://www.sciam.com/askexpert
http://www.newton.dep.anl.gov/
Click here to ask a question
http://www.homeschoolmath.com/
http://hypertextbook.com/
http://hypertextbook.com/chaos/
A Textbook in the Making
http://www.journey.sunysb.edu/ProjectJava/home.html
Currently, undergraduate students from the Department of
Computer Science, Department of Chemistry, and staff from
the Center for High Pressure Research at the University
are developing interactive Java applets designed for use
as instructional tools in Earth Science, Computer
Science, Mathematics, Physics, Chemistry, and related
disciplines.
http://www.sunysb.edu/philosophy/research.htm
Philosophical research is a major emphasis at Stony
Brook, with a number of very different areas of
cutting-edge work. http://www.blarg.net/~math
http://mtl.math.uiuc.edu/index.htm
Professional Development Consortium for Mathematics
Teachers Bulletin board, downloads.
http://www.uio.no/~kjetikj/compass/
My main motivation for writing these pages is to let
people have the same nice experiences I have had when I
have been, well, nowhere... Places you see just by
coincidence. The compass is an indispensable tool to find
your way home, or to go nowhere.
http://aleph0.clarku.edu/~djoyce/home.html
Beautiful Fractals and interactive exercises.
http://www.hawaii.edu/suremath/home.html
Students will enjoy solving word problems easily and
dependably. They will become happy campers in the forest
of problem solving.
http://www-history.mcs.st-andrews.ac.uk/history/#
The MacTutor: History of Mathematics archive, School of
Mathematics and Statistics, University of St. Andrews,
Scotland Biographies Index History Topics Index Famous
curves index, Mathematicians of the day.
The links below are concerned
with subjects similar to what I studied in Antarctica
more than 40 years ago. Some of these URLs may inspire a
future Engineer or Scientist to study their math so they
can have adventures someday also.
http://image.gsfc.nasa.gov/poetry/
to see what “poetry” means.
http://www.polar.org
Under contract to the National Science Foundation (NSF),
Raytheon provides a wide range of science support to the
United States Antarctic Program. RPS is hiring for the
2000/2001 season of the US Antarctic Program.
This list was
updated 05/23/00. A number of job descriptions have been
added. Click on a Job Category below for a list of
opportunities and job descriptions.
http://sec.noaa.gov/
http://www.vlf.it/
The first on the Long Wave topic.
http://web.tiscalinet.it/vlfradio/
Those weird signals: Nature Radio Signals and strange
emissions at very low frequency.
http://www.altair.org/
http://seattlep-i.nwsource.com/antarctica/
Journey to Antarctica. Two PI reporters aboard the Coast.
http://www.ibmpcug.co.uk/~irdial/vlf.htm
http://www.lwca.org/
The World of Radio Below 500 kHz
http://www.geo.mtu.edu/weather/aurora/
http://www.triax.com/vlfradio/natradio.htm
http://vcourseware3.calstatela.edu/GeoLabs/
Geology Labs On-Line is a comprehensive project to
develop Web-based lab activities that enhance the
learning and teaching of Geology and other Earth and
Environmental Science topics for introductory College and
High School courses. These "Virtual" labs are
interactive where students learn by "doing" and
not just clicking and viewing.
http://www.pfrr.alaska.edu/~pfrr/AURORA/INDEX.HTM
http://www-pw.physics.uiowa.edu/mcgreevy/
http://www.education.noaa.gov
http://www.invent.org/
The National Inventors Hall of Fame celebrates the
creative and entrepreneurial spirit of great inventors.
The creative genius of invention is showcased through
exhibits and presentations which allow visitors to
experience the excitement of discovery, creativity, and
imagination. By nurturing the inventive spirit, the
National Inventors Hall of Fame is addressing the
specific problems of declining technological leadership
and creativity in America.
An inspiring
children’s book is "Man, the Inventor" by M.
H. Chandler (1965, Odhams Books Limited, London). Each
section begins with how the invention (or discovery)
might have come about and how it developed through
history to be used in different ways. I found an
inexpensive copy in a cyberspace used book store.
http://www.midnightscience.com/
Dedicated to once again building and experimenting with
radio electronics.
http://www.its.caltech.edu/~atomic/snowcrystals/
This site is all about snow crystals and snowflakes.
http://www.teelfamily.com/activities/snow/
Homeschooling family with interesting information on
snow.
http://www.space.com
http://amanda.berkeley.edu/
http://lahr.org/john-jan/earth_science/TableTop/earthshaking/earthshaking_lab.html
Earthquakes can provide a useful context for teaching or
reviewing many basic physics concepts, such as sliding
and static friction, forms of energy and conversion from
one form to another.
http://elf.gi.alaska.edu/sprites.html
http://www.amasci.com/
SCIENCE HOBBYIST
http://www.execpc.com/~rhoadley/magindex.htm
magnetism and the cool experiments
http://ritz.otago.ac.nz:808/~omnipal/NTsprites.html
http://micro.magnet.fsu.edu/index.html
Welcome to the Molecular Expressions Website featuring
our acclaimed photo galleries that explore the
fascinating world of optical microscopy.
http://www.fnal.gov/
Fermilab. What is the universe made of? How does it work?
Where did it come from?
http://image.gsfc.nasa.gov/poetry/inspire/
The latest research concerning whistlers, dawn chorus,
hiss, etc. encouraging youngsters to build their own
equipment and do their own measurements. The resulting
data is published in “The Inspire Journal” that I
receive via snailmail every few months.
http://www.spaceweather.com/
Sometimes some beautiful aurora photographs
http://www.spaceweather.com/glossary/inspire.html
A pure note whistler has traveled along a signal magnetic
field line. It is heard as a clear whistling sound…
And of course there is
my favorite subject, lightning. I (Dale) am a retired
Electromagnetics Engineer and designed the Induced
Lightning protection for the fly-by-wire Boeing 777.
There is lots of
information about lightning in cyberspace, for instance: http://www.lightningstorm.com/lightningstorm/learning/index.jsp
and http://www.lightning.org/ and http://www.nationalgeographic.com/lightning/
To follow the
adventures of explorers who use mathematics to find the
way back home surf to http://www.goals.com/ and http://www.yourexpedition.com
http://www.howstuffworks.com/
clear explanations complete with excellent graphics about
the world we live in.
Teaching Students to
Think
by Dr. Art Robinson
If you are looking
for curriculums, including math, consider the offerings
at http://www.robinsoncurriculum.com/ Be
sure to check out the Robinson Forum and listen to New:
Robinson Radio - Informal Discussions with Dr. Art
Robinson. There is a mostly negative review of Robinson's
curriculum at http://eho.org/features/robrev.htm
Here is an example
of how Art homeschools his children:
On the basis of our experience with home schooling (we now
have, through our curriculum, about 40,000 students) I
have concluded that the teaching of math and science, if
done in an appropriate manner, can add greatly to the
student's inclination and ability to think. This should
begin at an early age.
Our curriculum requires that during the first year of
school, the student learn to read well and also learn the
addition, subtraction, multiplication, and division
tables through 12s by instant, rote memory.
These tables are learned primarily by flash card
exercises after an initial period in which the student
learns their conceptual means. Most students are ready
for this first year at some time between ages 5 and 7,
girls being ready a little earlier than boys.
After this initial year, the student starts with the
Saxon 5/4 arithmetic book and progresses at his own pace
through the nine Saxon books, including calculus. A fixed
number of problems are worked each day, with the number
metered so that the student finishes in two or three
hours and has an average error rate on the initial
attempt of less than 5%. The student grades his own paper
and then must find the correct solutions to any missed
problems. Most children are capable of finishing calculus
between ages 14 and 17.
A key requirement is that the student never be helped
with his math. He is learning problem solving--not the
solutions to problems. If the student says he cannot work
a problem, the response is that he will just have to
remain at his desk until he figures out the solution. If
started early in life, rarely if ever will a problem
remain unsolved. In any case, even if there is such a
problem, it should remain unsolved. Never should it be
worked for the student.
Today, my 13-year-old Matthew is sitting at a desk near
the one at which I am writing. He is halfway through
Advanced Math, the book before Calculus.
He knows that he can assemble a set of facts and deduce a
right answer by thinking for himself. He does so every
morning except Sunday.
If you want a man to think, put him in a position where
he must think, every day, for the months and years that
he is growing up. If you want him to trust and parrot,
give him lots of practice in memorizing things told to
him by authorities. The choice is clear and the results
are as expected.
|
You can write to Dale R. Reed
in
Seattle,
Washington USA.
Updated
6/13/2001