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Teaching Mathematics in an Internet World
by Trevor Brown
As teachers we are continually looking for innovative and exciting
ways to motivate and stimulate our students to think mathematically.
We would like them to see why some people study math and how it is
used to solve a variety of problems.
There are many technical questions which invariably arise in the
mathematics classroom, questions such as: How many faces does a
cylinder have? Is 1 a prime number? What is 0? When these arise, we
are not always sure what the "right" answer is.
Sometimes we simply would like to see different ways of approaching
a topic - different ways of teaching multiplication of integers,
subtraction of fractions, tessellation, etc. When these situations
arise we invariably consult the various math journals or guides to
assist us. Now, we can use the internet to access answers to these
questions quickly and efficiently.
The following sites are very useful in providing many valuable and
worthwhile starting points for teachers in grades kindergarten to
grade 8. These sites provide wonderful mathematical investigations
for our students and answers to the many perplexing questions that
invariably arise in the classroom. Although it would be hard to find
a math task that wouldn't fit into the Ontario curriculum, the
problems found on these sites present particularly rich mathematics
tasks.
NRICH
www.nrich.maths.org.uk
This is a site well worth visiting. Here a teacher and student can
find an amazing collection of rich mathematical tasks and
mathematical games that will stimulate mathematical thinking and
will engage your students for a significant period of quality time.
The very extensive archive contains all of the problems presented to
date. In addition to these features, there is a section where
teachers can pose their own questions, and carefully written
articles on various aspects of mathematics and editorial comments
which will be of interest to the mathematics community.
MATH CENTRAL
mathcentral.uregina.ca
This is a Canadian site originating from the University of Regina.
There are many easy-to-use but by no means trivial lessons for
elementary students posted at this site. There is an excellent unit
on the teaching of probability. In addition to these lessons,
teachers can visit the "Teachers' Place" where many pedagogical
issues are discussed - questions like: What do you think of Kumon
Math? How would you extend the Pythagorean Theorem?
MATH FORUM
www.mathforum.com
This site in addition to posting weekly and monthly problems in the
different areas of mathematics, has a very extensive archive. One of
the many advantages of the archive that will be of interest to all
teachers, is the students' written responses to past problems. There
is a generic comment on the written responses for a given problem.
Teachers can use these features to stimulate students to write and
justify their thinking and compare their responses to the exemplars
posted on the internet.
ST. FRANCES XAVIER
www.stfx.ca/special/mathproblems
Looking for some challenging problems for your students? This site
has some engaging problems that will stretch your students. If you
would like to bring "closure" to a set of tasks in a certain area of
mathematics, then the problems listed here could stimulate some
additional ideas. Many of the problems of this site are content
specific - an added advantage.
PBS
www.pbs.org/teachersource/math
There are many issues which are of paramount interest to teachers -
assessment, evaluation, rich learning tasks, open-ended questions,
etc. This site which is constantly expanding, identifies some of the
significant educational issues and offers some carefully worded
responses.
DR. MATH
www.mathforum.com/dr.math
Puzzled by questions such as: How many sides does a cube have? Why
the order of operations? Find a number that has 13 factors. If you
would like answers to these and many similar questions, then this
site is for you. Here a teacher will find answers to the many
questions that teachers and others have posed. Once you start
reading the questions and the different responses you will find it
very difficult to "sign off." Very contagious!
MEGAMATH
www.c3.lanl.gov/mega-math/
Looking for a site that can stimulate a lot of independent thinking
and encourage students to mathematize? Then this site offers many
possibilities - from investigating the four-colour map problem to
exploring knots. For students who believe that math is
uninteresting, this site will show them some very exciting areas of
mathematics - areas not normally presented in the elementary
classroom.
MUSE
http://www.cricketmag.com/ProductDetail.asp?pid=12
Why are manhole covers round? What is the recycle logo? Answers to
these and other intriguing math questions can be found at this site.
The articles are very short and easy to read and can be used to
stimulate mathematical thinking in the classroom.
CENTRE FOR INNOVATION IN THE TEACHING OF MATHEMATICS
http://www.ex.ac.uk/cimt
Would you like a collection of some exciting math "games" for your
students? This site presents a wonderful rationale for using math
games in your classroom and a significant collection of easy-to-use
and friendly math games. In addition, there are puzzles, challenges
and activities for teachers and students.
ABACUS INTERNATIONAL MATH CHALLENGE
http://www.gcschool.org/abacus.html
This site offers a variety of challenging problems for students in
grades 3-6. This is a very active site with new problems being added
almost on a monthly basis. The previous problems are all stored in
the archives. This is a site worth visiting.
MATHMAGIC
http://www.mathforum.com//mathmagic
This site has been around for some time. The sponsors encourage
students to work together in solving the problems. There are some
wonderful investigations here for students from K-8. Previous
problems can be retrieved from the rather extensive archive.
Samples from the sites
Here are some of the innovative math tasks available through the
described sites:
NRICH: Counting Down
The rules are simple. Start with any number of counters in any
number of piles. Two players take turns to remove any number of
counters (e.g. their choice of 1, 2, 3 or 4) from a single pile. The
loser is the player who takes the last counter.
MATH FORUM: True or False
I have four, two-digit numbers written on my paper. The sum of these
four numbers is less than 100.
True or false: Each number is less than 25.
Bonus: If all the numbers on my paper are different, what is the
largest number I could possibly have written?
ABACUS: Rectangular Puzzle
You have several 5 x 11 rectangles. Using only these rectangles, can
you make:
A) a 39 x 54 rectangle?
B) a 39 x 55 rectangle?
(You have to use the small rectangles so that they cannot overlap
each other, but you may not have space between them either.)
MUSE: Covering Up by Ivars Peterson
Have you ever wondered why the cover of a manhole is nearly always
round? Why couldn't it be oval or square?
ST. FRANCIS XAVIER: Minimum Moves
Batman has been imprisoned by the Riddler. To escape he must find
the quickest way to move the tower of plutonium disks from one post
to another so that the disks have the same arrangement as on the
original post. He may move only one disk at a time. What is the
minimum number of moves he must make in order to move the ten disk
tower and have it appear the same?
Trevor Brown is a Mathematics Consultant with the Toronto District
School Board.
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