Virtual Teacher Newsletter No. 132 September 9th 2006 MATHS WARS
1. Welcome
2. Mind Candy
4. New Printables - PLUTO
5. Technical Stuff – DUO2CORE
6. Web Site Focus – GEORGE POLYA
8. Great Sites PLUTO
9. Readers' Requests/Comments
10 Next Issue
11. Code of 'Netizens'
12. Tips
1. WELCOME EVERYONE. George Polya was a great
mathematician, his simple technique for investigating mathematical
problems is worth a second look today. The forum proved to
big a challenge – What should we include in the new curriculum
is too vast for a quick email. So this forum I have narrowed to
mathematics. Read some of the articles on encouraging
mathematical thinking and let me know your thoughts and
great ideas you are developing. We now only have 8 planets
in our solar system, Pluto is planet non grata, some brilliant sites
on this topic. Have a great fortnight.
Being a professional educator takes time -- time to plan, time
to practice, time to grade, time to communicate -- and I never
have enough time. However, I now realize that adding reflection
and research to my agenda have made my life as a
teacher easier, not more difficult.
-- Judith Koenig, Project teacher
The rewards of effective discourse are many. Not long ago,
I was observing students work out a problem together. When
they finally "got" it, one of the students exclaimed, "We are
so smart." Isn't that what we are striving for? Not "the teacher
is so smart," not "they are so smart," but "we are." In that
statement, I heard both confidence and community. Healthy
discourse promotes these things.
-- Cynthia Lanius, Project teacher
An idea which can be used once is a trick. If it can be used
more than once it becomes a method.
George Polya and Gabor Szego
Hilbert once had a student in mathematics who stopped
coming to his lectures, and he was finally told that the young
man had gone off to become a poet. Hilbert is reported to have
remarked, "I never thought he had enough imagination to be a mathematician."
George Polya
Beauty in mathematics is seeing the truth without effort."
George Polya
The first rule of discovery is to have brains and good luck. The
second rule of discovery is to sit tight and wait till you get a
bright idea." - George Polya
Reviews and product information on Hardware and Software
Nasa’s Pluto Kuiper Belt Printables
And now Apple have the Core 2 Duo
New Imac Duo 2 Core Educational Prices
Apple Student Gallery
Collections of movies, animations, pictures, music and presentations
by students, includes reviews by viewers
6. WEBSITE FOCUS -Prof. George Polya
was a great mathematician. His simple methodology for
working on mathematical ideas is a great basis for
the development of mathematical thinking.

Understand the problem: (what's unknown? What's given?)
Devise a plan (Have you seen this problem, or a similar one,
before? Think of a similar problem with the same unknown,
and see if you can apply it.)
Carry out the plan.
Check the result (And see if you can find another way
of finding it).
The Goals of Mathematical Education
We simply cannot go back to basics, we can’t go backwards
at all. Parrot maths is dead, it does not train mathematical

Procedural, Parrot maths, does not teach students to
think, it teaches them to follow instructions, and Parrot back
the answers. These types of lessons follow the format:
Teacher – Listen to my instruction, follow my instructions,
complete 10 examples using my instructions.

Conceptual mathematics teaches students to think, carefully
planned lessons put the students in the drivers seat,
are designed to connect with previous learning, encourage
students to develop multiple strategies and to explain their
thinking, compare their methods and justify their results.
Basically follow George’s procedure above.

Basic Skills testing, SC and HSC examinations are heavily if
not entirely reliant on Parrot Maths answers, and are touted
by politicians and non-educators as the ultimate solution to
evaluating the educational standards of the Australian
students. Every Educator worth their salt, knows they are
not. A good memory does not an educated student make.

What are our aims in Mathematical Education? What do
our students need to know to function in our society
mathematically? How should we teach mathematics? Is wrote
learning king? Are our examinations undermining fledgling
attempts at conceptual learning and real mathematical thinking?
How do we reform the curriculum to reflect requirements of
the 21st century? What great mathematical stories do you have
to tell? What great mathematics experiences have your
students had?

Mathematically Sane – Promoting the Rational Reform of
Mathematics in Education
Goals of Mathematical Education
Encouraging Mathematical Thinking
Classroom Assessment Techniques Mathematical Thinking
Does it Matter? It sure does. Send you responses in.
7b. What should be in the New Curriculum, what needs to go to
make room for the new stuff?
None of you had any answers to the last forum. It is a biggy.
So I have narrowed the focus this time to just the maths curriculum,
hope you have loads to say about this.
On August 24, 2006, astronomers declared that Pluto is no
longer a planet, thereby downsizing the solar system from nine
planets to eight. After a week of debate, the International
Astronomical Union stripped Pluto of planetary status
because its orbit crosses Neptune's and therefore fails
one of three planetary requirements. Instead, Pluto
(along with Ceres and Xena) is now classified as a dwarf planet.

MSNBC: Pluto: Our New View of the Solar System

In conjunction with Newsweek, MSNBC reports on the new
view of the solar system. Features include an audio interview
with Michael Brown, the Caltech professor who discovered
Xena (a nickname for the dwarf planet 2003 UB313),
a multimedia solar system map, and related articles
(scroll down and look in the right-right column near the
bottom of the page.) When you get to the New World
Order graphic, be sure to click on Detail to enlarge the map.

NASA: New Horizons
Although NASA hasn't updated this website to reflect
Pluto's demotion, I didn't think any discussion of Pluto
would be complete without including the New Horizons
spacecraft (launched January 19, 2006) on its way to a
2015 date with Pluto. Mouse around in the Education
section to discover printable classroom activities, printable
fact sheets, and introductory lessons about Pluto, Charon
(Pluto's satellite) and the Kuiper Belt (a "swarm of bodies"
beyond Neptune.)

NASA: Solar System Exploration: Pluto
Discovered by American astronomer Clyde Tombaugh
in 1930, Pluto takes 248 years to orbit the Sun. Pluto's most
recent close approach to the Sun was in 1989." This NASA site
is a must visit for anyone writing a school report. It includes
fact and figures, an image gallery, and a Kid's Eye View
section with a scale that calculates how much you would
weight on Pluto.
Wonders of Photoshop
Take a look at these photoshop images and composites, roll
your mouse over the images to see the before and after
How To Eat Fried Worms is a great book--but it is about 4 friends who wage a
bet, not a bully. I wish movies would not rewrite the basic story so
drastically. Laura
Hi, Cathy,
I was talking to a friend about one of your many wonderful
articles. Although I have searched your archives, unfortunately
I cannot find it. The article in question is the 8th grade test
people used to have to pass in order to exit school. Can you
please bail me out by letting me know which newsletter it was in?

As always, I thank you for your efforts all the work you do for
us teachers. It's greatly appreciated!
10. NEXT ISSUE - Next newsletter I will be looking at the Art
of teaching. ciao Cathy
11. Code of the 'Netizens'
This Newsletter is not free, despite the misleading advertising
above. The Fee is now due. Each week you must help one
colleague on the Internet who has less knowledge than you.
Help that person even if you have to visit their classroom or
do a little research and get back to them. Trust me, this will
help a lot of people get their computer classrooms running better.
OK I'm trusting you!!!
12. TIPS
1. Double click on highlighted URLS to open in browser.
2. Send in your Questions, Questions will be published with
Answers, send in your Answers, if you have expertise to share.
3. Nominate a brilliant site for review and inclusion in this
4. Nominate a fantastic school site for review and inclusion in
this newsletter.
5. Make contact with other schools using fantastic programs.
6. Prepare and innovative article for this newsletter.
7. Tell 2 colleagues about this newsletter.
The opinions expressed here are purely those of the editor,
Cathy Brown. All other small print clauses apply. Such as:
Use at your own risk. Nothing in life is guaranteed. If it doesn't
work for you send me an email.
Editor: cathy brown
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