Week 1

Introductory session: Introduction to learning and teaching mathematics; Unit overview and expectations
Tutorial/workshop: negotiate the unit; unit overview, expectations

More images
see: www.radiolaria.org

The Snowflake Curve

Fibonacci Numbers and Nature

Energiser:

Week 2

TJ591-Learning and teaching mathematics-Summary of responses

A Snowflake Primer
... The basic facts about snowflakes and snow crystals ...
http://www.its.caltech.edu/~atomic/snowcrystals/primer/primer.htm

Guide to Snowflakes
... A look at the different types of falling snow ...
http://www.its.caltech.edu/~atomic/snowcrystals/class/class.htm

Historic Snowflakes
... Early observations and studies of snow crystals ...
http://www.its.caltech.edu/~atomic/snowcrystals/earlyobs/earlyobs.htm

Snow Crystal Photographs
... Capturing the fleeting beauty of snowflakes ...
http://www.its.caltech.edu/~atomic/snowcrystals/photos/photos.htm

They are not all 6 sided!

Unusual Snow Crystals
... Some exotic examples from the snow crystal menagerie ...
http://www.its.caltech.edu/~atomic/snowcrystals/unusual/unusual.htm

Note: I have ordered this book for the TRC. When it comes in I will put a link to it's call number here.

Hexagonal water ice

http://www.lsbu.ac.uk/water/ice1h.html

http://www.nyu.edu/pages/mathmol/modules/water/info_water.html

http://library.tedankara.k12.tr/chemistry/vol2/hydrogen%20bonding/z20.htm

http://snowflakebentley.com/snowflakes.htm

The Rasmussen & Libbrecht Collection

http://www.its.caltech.edu/~atomic/snowcrystals/photos/photos.htm

Mt Helen Loans Desk 700.92 B446w Check availability of CD-ROM

http://vermontsnowflakes.com/tshirts.htm#tp

http://vermontsnowflakes.com/books.htm#stp

Mt Helen TRC 551.57 BEN-S

Mt Helen TRC BEN-F

Links from: http://snowflakebentley.com

No Flakes Like Snowflakes!
Microsoft's, "No flakes like snowflakes!"
Few things are as awe-inspiring as snowflakes, those miniature masterpieces of symmetry. This activity invites students to explore snowflakes from the inside by making their own.
http://www.microsoft.com/education/default.asp?ID=flake

Why do snowflakes crystallize into such intricate structures?
By Mark Chan
Hong Kong

Scientific American's, "Why do snowflakes crystallize...?"
An article on why snowflakes crystallize into such intricate structures.
http://www.sciam.com/askexpert_question.cfm?articleID=0008E59D-D49B-1C71-9EB7809EC588F2D7
Printer friendly version

Cool Math Links

http://www.charlesgilchrist.com/SGEO/Gal1001.html

http://www.ies.co.jp/math/java/geo/pytree/pytree.html

http://www.statkart.no/skme/produkt/delta/internasjonale/lena_sat-stor.jpg

References to readings:

The Reading on Constructivisim was from:

Bobis, Janette et al. 1999, Mathematics for children : challenging children to think mathematically,
    Prentice Hall, Frenchs Forest, N.S.W.

The ALACT diagram was from:

Korthagen, F.A.J. (2001). Linking theory and practice. The pedagogy of realistic teacher education.
   Mahwah NJ: Lawrence Erlbaum Ass.

Korthagen, F.,(2001) Linking practice and theory: The pedagogy of Realistic Teacher Education. New Jersey: Lawrence Erlbaum.

The title of the Journal
Teachers and teaching: theory and practice
The article:
Wolf, N.(2003) learning to teach mathematics for understanding in the company of mentors Vol.9, No.2, May 2003

Geometry in the Real World: Students as Architects

Read the atricle

Designing a School for the Future

Every spring at Mountlake Terrace High School near Seattle, Washington, students in Eeva Reeder's geometry classes work feverishly to complete an architectural challenge: Design a 2,000-student high school to meet learning needs in the year 2050, fitting it on a given site. In a period of six weeks, students must develop a site plan, scale model, floor plans, perspective drawing, cost estimate, and written proposal. Read the whole article

Eeva Reeder on Projects and Assessment
Eeva Reeder, a former math teacher at Mountlake Terrace High School in Washington State, elaborates on a geometry project in which her students created designs for a "state-of-the-art" high school. 12/3/2001
Video | Audio only

Examples of student projects
Video presentations

LINKING PRACTICE AND THEORY:
THE PEDAGOGY OF REALISTIC TEACHER EDUCATION
Fred A.J. Korthagen
IVLOS Institute of Education
Utrecht University
The Netherlands
e-mail: F.Korthagen@ivlos.uu.nl
http://educ.queensu.ca/~ar/aera2001/Korthagen2001.pdf

http://educ.queensu.ca/~ar/aera2001/Korthagen2001.pdf

Measuring What Counts: Memorization Versus Understanding

Ideal as a teacher of mathematics?
• Encouraging and understanding to each individual (19)
• Fun (18)
• Make maths enjoyable (13)
• Meaningful to everyday life (10)
• Interesting (9)
• To help children understand (5)
• Patient (3)
• Engaging (3)
• Strategies (different)(3)
• Inclusive (3)
• Use the best approaches (3)
• Connect with children
• Be persistent
• To be understood
• Never give up on a student
• Passionate
• Use materials
• Flexible
• Interactive
• Positive(2)
• Encourage confidence
• Individualized learners(2)
• Interaction
• Exciting
• Keep the learning aspect alive
• imagination
• Reach maximum potential
• Setting challenging material(2)
• Knowledge of content(2)
• Help children in their learning
• Listens to what the student is asking(2)
• Hands on
• Exploration
• Positive attitude (a class)(2)
• Children will benefit in some way from my influence
• Competent in teaching theories
• Cultivation of student-centred learning
• Individually achieve
• Work together to achieve
• Clear
• Assessable
• Relevant
• New ideas
• Comfortable environment
• Comfortable pace
• Show students the theory of maths
• Help children to be proud of their endeavours
• Disadvantaged
• Make maths easier (2)
• Successful

Week 3

Music and the Fibonacci Series
http://goldennumber.net/music.htm

Phi for Neo-phi-tes
http://goldennumber.net/neophite.htm

Dr. Levin's Golden Mean Gauges
http://goldennumber.net/gauges.htm

Phi: That Golden Number

The Golden section ratio: Phi

Behind the Cafe Union Building Next Monday

Mathematics
Level 4: Space 4.2

Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and cross-sections using conventional spatial terms.

This is evident when the student is able to:

• describe a three-dimensional object in detail (e.g. this triangular prism has 6 vertices and 5 faces, and 2 of the faces are parallel)
  
• classify shapes and objects according to properties (e.g. the triangles in this group all have equal length sides and equal angles)
  
• use knowledge of a shape’s properties to construct a figure using a computer program (e.g. construct a rectangle using LOGO)

Stella: Polyhedron Navigator
http://www.software3d.com/Stella.html

Stella: Polyhedron Navigator

http://www.fi.uu.nl/wisweb/en/ Link updated March 20 2007

http://www.fi.uu.nl/toepassingen/00297/toepassing_wisweb.en.html

http://www.fi.uu.nl/wisweb/en/

http://www.fi.uu.nl/wisweb/en/home/welcome.html

List of Geometry Applets Link added March 20 2007

overview of WisWeb-applets Link added March 20 2007

Renders.
A gallery of images rendered using POV-Ray, from models exported by Great Stella.
Includes animations!
http://www.software3d.com/Renders.html

Reflective comments from week 2
Note: I have not typed in all the comments yet August 5, 2004

A selection of Week 2 Reflections:

1. Briefly outline your most memorable mathematics experience:

Being walloped across the back of the head by Sister Carmel (The old Nun) with a cane because I didn’t know my eight times table. I now know my eight times table, when I hear the number eight I remember that occasion.

Winning Math’s competitions in Primary School. Passing tests in high school. Reasonably good at Math’s in P.S. Just an average student in high school.

I don’t think I have one I’ve always struggled with math’s, it must be a repressed memory now.

Having a really good teacher one year – learnt a lot, enjoyed math's as a subject.

2. Explain how you think you have gained your understanding of mathematical concepts?

Through good math's teachers. Going through concepts & problems over & over. Understanding what we were doing & why we were doing it.

3. What do you think are the most important consideration when learning mathematics?

Be patient with your learning as you will learn in the end it just might need some time to find your own concept of learning.

To not get frustrated when you can’t understand the problem.

Keeping it fun. Also keeping at a level that students can relate to. Having an understanding of the uses of math’s also assists in learning.

• Clear instructions/ teaching
• Persistence
• Understanding of a topic & it’s relevance
  

4. What do you think are the most important considerations when teaching mathematics?

Again patients not all students will learn straight away it may take time to learn even the basics.

Again keeping it fun and not mundane. Actively involving the students and encouraging. Not making students feel worthless if they are struggling.

5. How do you feel about the prospect of teaching mathematics?

At the moment I am probably lacking some confidence but maybe after this unit and field work this lack of confidence may improve. From experience I know how not to teach math’s.

[I] feel fine with this thought, confident that I can cope with this.

Good if it’s with the younger children Grade 5/6 math’s just scares me, math’s is still very intimidating to me.

Nervous, but confident that preparation would hold me in good stead.

• Scarred!!!
• What is I confuse students
• what if I don’t understand [the] topic myself.
  

6. What would you like to learn about during this semester, related to the teaching and learning of mathematics?

I would like to learn how to make teaching math’s fun. My overall experience during school was not good and it was in general boring, I want to gain confidence.

7. How might this outcome (Q. 6 ) be achieved?

8. How might success be measured (Referee to question 6)

When I can get in front of a classroom full of children and be able to answer all their questions confidently.

9. Any other comments?

I think the main thing is that I don’t want to teach math’s like I was taught screaming and abusing a child because the don’t know what 8*8 is isn’t exactly a good way to teach math’s. I believe patents is the key to teaching math’s!

I was nervous prior to starting this but I can not eager to see what I can learn.

I was scared of the complex math's and I want to be able to stop that from happening to others (students)

Week 4

Interactive online geoboard	Interactive online pattern blocks
Run the program (requires a Java-capable browser.) Windows 95/NT version (zip file, approx 100Kb)	Tess is a program for drawing symmetric illustrations. While you draw, Tess will automatically maintain the plane symmetry group you have chosen. http://www.peda.com/tess/download.html
http://www.peda.com/poly/

At this page you find some selected links ordered by topic, where we have laid emphasis on interactive learning material which needs no download or additional software, although some spreadsheets (requiring Microsoft Excel to run on your computer) and other media have been included.
http://www.univie.ac.at/future.media/moe/einzelthemen.html

Great MathsWebsites to Explore
http://www.virtualteacher.com.au/maths.html

Top: Science: Math: Recreations: Games and Puzzles (83)

"Prime Curios!"

The Largest Known Primes

What is a prime number? How can you find prime numbers? What's the 'Sieve of Eratosthenes'? What's the largest known prime?
Excellent resource from Ask Dr. Math®

On-Line Encyclopedia of Integer Sequences

The First 10,000 Primes

Fractals
There's lots of information on the Web about fractals, but most of it is either just pretty pictures or very high-level mathematics. So this fractals site is for kids, to help them understand what the weird pictures are all about - that it's math - and that it's fun! Teachers: Every lesson has a print version for classroom use.

http://www.mersenne.org/prime.htm

Internet PrimeNet Server Serious research. Totally for fun.
Join a search of mathematical discovery and become a part of Internet history.
USD $100,000.00 Research Discovery Contest

Mastermind Game

1) Pick a number and write it down so you will not forget it. e.g. 12,347
For simplicity do not use the same digit twice

2) On the board draw a line for each digit in the number that you picked. e.g. ____ ____ , ____ ____ ____

3) Students guess a possible answer e.g 17,409

4) On each line wrie the number that students guess and above the digit draw symbol or use a tick, cross, or circle depending if the digit that was guessed matches the number you picked.

Key

	or a tick	Correct digit in correct place.
	or use a circle	The digit does not exist in the answer.
	or use a cross	The digit exists in the answer but it is not in the correct place.

Example game

					A lucky guess with the digit 1
1	7	4	0	9
					We now know that the digit eight is not in the answer. Try new positions for the 4 & 7.
1	3	8	7	4
					Forget to include the digit 3 in our guess.
1	5	7	4	6
					Success.
1	2	3	4	7

Week 5

How to Get Students to Talk in Class
http://ctl.stanford.edu/Handouts/web/get_students_talking.html

Designing Effective Discussion Questions
http://ctl.stanford.edu/Handouts/web/asking_questions.html

Tips on Discussion Leading
http://ctl.stanford.edu/Handouts/web/discussion_leading.html

Self-Help for Beginning Teachers
http://teaching.uchicago.edu/selfhelp/other.html

MathsNet.com http://www.mathsnet.net/puzzles.html
maths learning games www.schoolzone.co.uk/students/learninggame/mathslearninggames.htm
Fibonacci Numbers and Nature http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html

Maths Links This site has links to some good looking resources
http://www.angelsoft.co.uk/clmaths.htm

		The famous Six-in-One by Allan W. Johnson: www.magic-squares.de/gallery/complex/example29.html
http://www.grogono.com/magic/makeyourown5.php

http://www.math.hmc.edu/funfacts/submit.shtml

http://www.math.hmc.edu/funfacts/

http://www.math.hmc.edu/funfacts/allfacts.shtml

http://www.mathnstuff.com/math/spoken/here/2class/cspred0.htm

http://www.free-magic.com/tricks/math-trick.html

http://www.physlink.com/Reference/MathConstants.cfm

IHES DISCOVERY 5th Grade

http://www.mcescher.nl/indexuk.html

The Garden of Our School

Week 6

Literacy & Numeracy Week - EYS - Resources - Useful Books
View this list as a word document

Contents:
Literature related to Number
Literature related to Measurement
Literature related to Space (shape)
Literature related to Space (location)
Literature related to Chance and Data

Literature related to Number

Anno, Mitsumasa., Anno’s Counting Book. London: Macmillan 1985
Baker, Jeannie., One Hungry Spider. Sydney: Scholastic 1982
Bang, Molly., Ten, Nine, Eight. Harmondsworth UK: Puffin 1985
Blake, Quentin., Cockatoos. London: Red Fox, 1994
Blaxland, Wendy., One for you and one for me. Sydney: Scholastic (Reading Discovery) 1996
Carle, Eric., The Very Hungry Caterpillar. Harmondsworth UK: Puffin 1974
Clements, Rod., Counting on Frank. Sydney: Williams Collins 1990
Comber, Barbara., Dad’s Diet. Sydney: Ashton Scholastic 1987
Hutchins, Pat., The Doorbell Rang. London: Puffin 1984
Nightingdale, Sandy., One Pink Pig. Harmondsworth UK: Puffin 1983
Schieszka, Jon & Smith, Lane., Maths Curse. Melbourne: Puffin 1998
Trinca, Rod., One Woolly Wombat. Puffin 1983

back to top

Literature related to Measurement

Allen, Pamela., Mr Archimedes Bath. Sydney: Collins 1980
Allen, Pamela., Who sank the boat? Melbourne: Puffin 1988
Carle, Eric., The Bad-Tempered Ladybird. Harmondsworth UK: Puffin 1982
Drew, David., The ball, the stick, the plane and the feather. Melbourne: Longman Aust. (InfoActive) 1998
Gosset, Rachel., Snap likes gingersnaps. Sydney: Scholastic 1996
Hutchins, Pat., Happy Birthday Sam. Harmondsworth UK: Puffin, 1982
Hutchins, Pat., Titch. Harmondsworth UK: Puffin 1972
Hutchins, Pat., You’ll Soon Grow into Them Titch. Harmondsworth UK: Puffin 1985
Pienkowski, Jan., Sizes. Harmondsworth UK: Puffin 1983

back to top

Literature related to Space (shape)

Armstrong, Shane., I Like Shapes. Scholastic (Reading Discovery) 1996
Hutchins, Pat., Changes, Changes. London: Bodley Head 1971
Sutton, Eve & Dodd, Lynley., My Cat Likes to Hide in Boxes. Harmondsworth UK: Puffin 1985
Jonas, Ann., The Quilt Julia. McRae 1985

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Literature related to Space (location)

Allen, Pamela., A lion in the Night. Ringwood Victoria: Puffin 1988
Allen, Pamela., Alexander’s Outing. Viking Penguin, Melbourne 1993
Burningham, John., The Shopping Basket. London: William Collins (Picture Lions) 1983
Carle, Eric., The Secret Birthday Message. London: Hamish Hamilton 1988
Drew, David., Find the way home. Melbourne: Longman Australia (InfoActive) 1997
Drew, David., The World. Melbourne: Longman Australia (InfoActive) 1997
Hirst, Robin., My Place in Space. Melbourne: Roland Harvey Books, 1996

back to top

Literature related to Chance and Data

Ahlberg, Janet & Alan., The baby’s catalogue. Harmondsworth UK: Puffin 1986
Bogart, Jo Ellen., 10 for Dinner. Ontario: Scholastic-TAB 1989
Drew, David., All sorts of things. Melbourne: Longman Australia (InfoActive) 1998
Drew, David., Sharks. Melbourne: Longman Australia (InfoActive) 2000
Drew, David., What Did You Eat Today? Melbourne: Thomas Nelson Australia (Informazing) 1988
Drew, David., What’s your favourite? Melbourne, Longman (InfoActive) 1998
Lester, Alison., Clive Eats Alligators. Melbourne: Oxford University Press 1985

Source:
Literacy & Numeracy Week - EYS - Resources - Useful Books
http://www.sofweb.vic.edu.au/litnumweek/eys/resources/books.htm

Useful Books. This website has been developed to support schools in their implementation of Literacy and Numeracy Week celebrations, both with the school and the local community. The website offers support for planning activities and events, a wide range of student activities and events from an individual level to a whole school level, resources that can be used and a range of ways literacy and numeracy can be promoted within the school community.

back to top

From the Children's Picture Book Database at Miami University Your Search for Numbers produced 143 item(s).

BOOKS THAT COUNT A selection of books to support maths at KS1 This
book list is arranged in themes. This book list is arranged in themes. Titles are suitable for children of nursery (N), reception class (R) and Year 1 (Yr1) age.
http://www.slamnet.org.uk/Numeracy/booklist.PDF

Google search for "using children's literature to teach math"

Counting by powers of ten

"One, ten, hundred, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion, ..."

Names are on threes... on 3, 6, 9 (thousand, million, billion). Each ,000,.

The names "billion" and "trillion" mean different things in different countries. This is the US version.
There are a few more names after "trillion", but they are almost never used.
http://www.vendian.org/envelope/dir0/counting_by_tens.html

See also Names of Large Numbers

Week 7

PowerPoint from Lecture Week 7

Version for printing handouts

A list of some interesting looking maths resources
http://www.rctednet.net/numeracy/english/curriculum/number.htm

This is a facinating site that is well worth a look

Interactive Mathematics Miscellany and Puzzles
http://www.cut-the-knot.org/front.shtml

Other sites of interest
http://www.cut-the-knot.org/collection.shtml

A Broken Calculator
http://www.cut-the-knot.org/Curriculum/Arithmetic/BrokenCalculator.shtml

The Broken Calculator TEC Lesson Plan
http://www.schools.pinellas.k12.fl.us/educators/tec/brk_cal/brkcal.html

'Broken Calculator' Activity Links
http://www.tecknoquest.com/apple/igoilearn/broken_html

Broken calculator

Some of the keys on the calculator do not work. Can you make a target answer using only the working keys?

Can you make all the numbers from 1 to 20 if only the following keys work?

2 3 + - = clear

What numbers can you make if only these keys work?

4 + - x = clear
http://atschool.eduweb.co.uk/ufa10/investig.htm

The Island of Discarded Calculators
http://www.mste.uiuc.edu/dildine/broken

http://www.math.com/students/tools.html Calculators & Tools

s

WisWeb is the website of the Freudenthal Institute for secondary education (students of 12 to 18 years old).
The main focus of the site are applets; small computer programs that run over the internet.

http://www.fi.uu.nl/wisweb/welcome_en.html
http://www.fi.uu.nl/toepassingen/00014/toepassing.xml?style=wisweb&language=en

Free Running Record Calculator220 KB

Week 8

Talk:Arabic numerals

http://www.orthohelp.com/number.htm

It's all about angles !
It's the number of angles. If one writes the numbers down (see below) on a piece of paper in their older forms, one quickly sees why. I have marked the angles with "o"s.
No 1 has one angle.
No 2 has two angles.
No 3 has three angles.
No 4 (which used to be written +) has four angles.
etc.

and "O" has no angles

http://www.orthohelp.com/number.htm

Week 9

Hello Rupert, Michelle Smith here. I have a problem for you, I have asked the same question of Robyn and Greg and as of yet have not received and answer. The one of the focuses of TJ591 is  to make Mathematics meaningful and to give it relevance to our everyday life. Well I am hoping that you will be able to give my a realistic application for linear algebra. Both my children are learning about linear algebra and both of them are struggling with the concept as they are not able to see any relevance for usage of linear algebra in their lives. My son is doing year 11 and my daughter is in year 9 doing year 10  extensions and neither of their teachers are able to give them a real life application for the use of linear algebra, my son believes that the process could possibly be used by pilots, however he is not completely sure of this, .Although if this is the case then I van understand the children's frustrations as neither of them aspire to being a pilot. Thanks for taking the time to read my request Michelle Smith.

Thak a look at:

Why Is Math Important?

Why Should I Study Calculus?

Linear Algebra and Its Applications

David C. Lay,
University of Maryland - College Park

ISBN 0-201-70970-8 • © 2003

Case Studies and Applications

Linear Models in Economics, p. 1
Computer Graphics in Automotive Design, p. 105
Diet Problems, p. 93

 

Mail Message
From: Greg Neal <gregn26@bigpond.com>
To: Rupert Russell, Robyn Brandenburg
Subject: Re: linear algebra

Message: Dear Rupert

Thank you for your involvement. Michelle raised the question after the
monday forum - not sure when i was supposed to provide details and answers.
Like you I did a search and found numerous relevant sites. Unfortunately my
new firewall prevents me from accessing many but I will pass on a list to
michelle for her own search. evidence points to being interested in linear
algebra and matrix theory, in engineering economics, computer science,
operations research and management scienceo

sites worth exploring include:
http://mathforum.org/linear/linear.html - has a link/forum to ask questions
http://joshua.smcvt.edu/linearalgebra/
http://www.math.unl.edu/~tshores/linalgtext.html
http://www.ms.washington.edu/courses/math387-lamp/glossary.html - could not
access site but worth a look maybe
cheers
Greg

Race to a flat PDF File 79 KB

 

Week 10

PowerPoint from Lecture Week 10

Version for printing handouts

Caution this is a 14Mb file which will take about 4 hours to download via a modem.

Links from the above PowerPoint

CALCULATORS ON-LINE CENTER

Calculators in the math's room

See list of links from the presentation

Age Calculator
http://javascript.internet.com/calculators/age-calculator.html

Day of Week

Blood Alcohol Content (BAC) Calculator
http://www.ou.edu/oupd/bac.htm
University of Oklahoma Police Department

An Australian Blood Alcohol Concentration (BAC) Calculator

Body Mass Index (BMI) Calculator

Calculate your ideal weight

Calculate your target heart rate for fitness

Online Abacus

The Abacus vs. the Electric Calculator

Feynman vs. The Abacus

MARTINDALE'S

CALCULATORS ON-LINE CENTER
http://www.martindalecenter.com/Calculators.html

Calculator use
http://mathforum.org/t2t/message.taco?thread=6284&message=5

Why Use Calculators (and Other Technologies) in the High School Math Classroom?

Number Shapes
http://www.blackdouglas.com.au/calchange/cch_act/numshap.htm

Put a number inside a square.
Then put a number at each corner of the square so that the four 'corner' numbers add up to the number in the square.

Wipe Out
http://www.blackdouglas.com.au/calchange/cch_act/wipeout.htm

As with other Calculating Changes activities the value of Wipe Out lies not in doing it once, but rather in threading it through the curriculum for just a few minutes in say two/three sessions per week for 6 - 8 weeks. Each representation offers students the familiarity of known structure within the stimulation of a new challenge. Far from becoming boring, this approach provides security through which children collect and organise their personal conceptual data, as they struggle to make sense of how numbers work.

Materials
One Calculator per child

Procedure
Introduce the activity to the class by writing a 3 digit number on the board, eg: 352
What is this number?
Insist on an answer in place value form (eg: three hundred and fifty-two) rather than just a statement of the digits (three-five-two or three fifty-two).
Ask the children to write the number on their calculator.
Your challenge is to make your screen become 302 by taking away one number.

As you say this write the 302 under the 352, draw an arrow between them and write 'take away ONE number'.

You may also have to explain that by one number you don't necessarily mean one digit.

As the children discover they need to subtract 50 in order to successfully wipe out the 5, they hold their 'successful' calculator in the air to invite you to see them do it. You will easily be able to get around most of the class before needing to write up the next example.

Week 11

Mathematics Summation 2003

Summation criteria 2003

Instructions for the summation 2003

TJ591- Mathematics Summation
Date: Tuesday October 28, 2003
Allocated time- One hour
Total- 30%

It was stated in the National Statement on Mathematics for Australian Schools (AEC, 1991) that there is no definite correct approach or style for the teaching of mathematics. However it is stated that generally teaching should be informed by a thorough understanding of how learning occurs and of the nature of the mathematical activity. The teaching of any particular concept will be influenced by the nature of the concept itself and by the abilities, attitudes and experiences of students.

(The National Statement on mathematics for Australian Schools, 1991- Australian Education Council and Curriculum Corporation)

Discuss this statement with reference to your aspirations as a teacher of mathematics. Consider your proposed teaching context (P-6, P-10) and the who, what, how and why of mathematics teaching and learning. Consider your theoretical underpinnings upon which your beliefs about teaching and learning are based.

Refer to tutorials, round tables, forums, information sessions and other mathematics education experiences.

Summation criteria TJ591, Semester 2, 2003

• Links to theories of learning and teaching mathematics
• Reflective practice and 'small t' theory
• Real maths and school maths; real- life context
• Planning sessions- the environment, lesson planning, 'affective issues'   related to the teaching/learning of mathematics
• Resources for teaching- materials, people, environment
• Assessment procedures
• Learning styles
• Professional experience
• Activities/ tasks from roundtables/forums/info sessions

Overall clarity of expression, cohesion, development of a 'line of
thought' Excellent … Very good… Good … Satisfactory… Poor

Instructions

TJ 591: Summation, Week 13, 2003

A one hour summation of your understandings of the teaching and learning of mathematics, based on the experiences and understandings gained throughout the semester. You will reflect on your role as a teacher and learner of mathematics. (This will be situated within a context- i.e. a response to a question/quote.)

Consider:
Your anticipated 'context' (P-6, P-10)
Particular issues related to that context with reference to mathematics
How do children learn mathematics?
What factors influence this learning?
What will you need to consider when organising for mathematics learning?
What will be your role as teacher?
What underlying assumptions do you have about the teaching and learning of mathematics?
What activities/experiences have affected the way you feel?
Are there any difficulties that you might foresee?
What forms of assessment would be the most beneficial?

Criteria for assessment

• Level of understanding of the concepts and processes linked to the teaching and learning of mathematics.
• Succinct/well written/clearly expressed
• Related to mathematical experiences/reflection
• Related to lectures, tutorials, forums (specific examples)
• Your role as teacher/learner of mathematics-'small t theory' /big T theory

Mathematics Summation 2002

TJ591- Mathematics Summation
Date: Tuesday June 4, 2002
Allocated time- One hour
Total- 30%

It was stated in the National Statement on Mathematics for Australian Schools (AEC, 1991) that there is no definite correct approach or style for the teaching of mathematics. However it is stated that generally teaching should be informed by a thorough understanding of how learning occurs and of the nature of the mathematical activity. The teaching of any particular concept will be influenced by the nature of the concept itself and by the abilities, attitudes and experiences of students.

(The National Statement on mathematics for Australian Schools, 1991- Australian Education Council and Curriculum Corporation)

Discuss this statement with reference to your aspirations as a teacher of mathematics. Consider your proposed teaching context (P-6, P-10) and the who, what, how and why of mathematics teaching and learning.

Refer to tutorials, forums, lectures and other mathematics education experiences.

Mathematics Summation 2001

TJ591- Learning and Teaching Mathematics
Date- Tuesday October 29, 2001.
Time allocation- One hour
Assessment- 30%

"Teachers teach mathematics as they were taught mathematics."

Discuss in light of the issues that have been considered throughout the semester. Refer to a broad range of mathematical issues and refer to lectures, forums, tutorials/workshops, presentations, readings and professional experience.

Week 12

Line Graphs

http://www.literacycenter.net/lessonview_en.htm

http://www.mathsisfun.com/maths_links.html

Mandelbrot Images
http://members.atlantic.net/~caggiano/mandel/mandel.html

Web resources for teaching with technology
http://mathweb.uccs.edu/haefner/resources/archive1resouces.htm

6. Fractal programs
http://fractals.iut.u-bordeaux1.fr/f-art-faq/faq06.html

http://fractals.iut.u-bordeaux1.fr/f-art-faq/index.html

Here are various selected topics related to Geometry and Trigonometry
http://mcraefamily.com/MathHelp/Geometry.htm

Manipula Math Applets

Angles and Parallel Lines Applets
http://www.ies.co.jp/math/products/geo1/menu.html

Introduction to Trigonometric Functions Applets

Slide Rule
http://www.ies.co.jp/math/java/misc/slide_rule/slide_rule.html

Solid of Rotation Applet
http://www.ies.co.jp/math/java/calc/rotate/rotate.html

Calculus Applets
http://www.ies.co.jp/math/java/calc/

Life32 by Johan Bontes
http://psoup.math.wisc.edu/Life32.html

Recreational Mathematics
http://mathworld.wolfram.com/topics/RecreationalMathematics.html

Mathworld Animated GIFs
http://mathworld.wolfram.com/topics/AnimatedGIFs.html

- Solid Of Rotation (SOR) -
http://criticalmass.sourceforge.net/sor.php

There is quite a bit of history on this item. One of the assignments in a computer graphics course at the University of Victoria was to rotate a number of Bezier curves around an axis and display the result in 3D using a single light source. This was on Sun Sparcs using X. Since then the program has mutated to match my platform preference at a given time (DOS, Windows, Linux). The latest mutation has been to SDL/OpenGL and the result runs happily on Linux and Windows. Screenshot junkies might find the following of interest: by Frank Becker

Week 13