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Home > TJ591 Learning and Teaching Mathematics I

TJ591 Learning and Teaching Mathematics I

Please note that this page is no longer in curent use. I will update it from time-to-time but I am no longer teaching at the University of Ballarat where I taught TJ591 and other units.

8 February 2018


I wanted to check in to make sure you got the email I sent you before with supportive parenting resources. I thought they’d be a good fit for this page on your site:http://www.rupert.id.au/TJ591/index.php. If you think they are, do feel free to share them there (or anywhere else you think makes sense). I included practical, everyday parenting tips, plus a few that will help both children and their parents with their emotional health. Also, if you’d like me to write a research-based article on parenting just for your site, please let me know. Thanks!

Choosing a Preschool: Simple Tips for Parents

16 Easy Ways to Raise a Bilingual Child

One Man’s Trash: Safety Tips for Secondhand Furniture and Toys

Helping Your Firstborn Adjust to New Siblings

The Caregiver’s Guide to Helping Homesick Children Cope

10 Ways Parents Can Help Children Adjust to High School

Preventing Parent Burn Out

Single Parenting After Losing a Partner to Suicide


Tilda Moore, tildam@openeducators.org



Teachers report that one of the biggest professional challenges they encounter is inadequate guidance for lesson planning. In fact, more than 40 percent said their schools or districts gave them few to no resources to plan curriculum, and what was provided usually wasn’t helpful.

I’m a home educator and completely understand the struggle. I do a lot of my own supplemental lesson plan research, which is how I came across your website. I thought I had a few pieces that would look great on this page: http://www.rupert.id.au/TJ591/index.php -- can you share them there?

Banking Lesson Plan for ESL and EFL Students

The Educator’s Guide to Real Estate Lesson Plans

Fraction Lesson Plans

What’s Cooking?: A Culinary Curriculum for Cultivating Foodie Kids

Earth and Space Science Units and Lessons for Grades 7-9

The Teacher’s Guide to Substance Abuse Prevention: Using Local News and Experts to Make a Difference in Your Community

Theater Class: Emergency Lesson Plan Activities

The Story Of Building & Rebuilding The White House

I hope these resources meet your standards, but if you’d prefer I don’t reach out in the future, please send me an email with the word REMOVE in the body.

Thanks for your time!


Jenny Wise, specialhomeeducator.com



Dear Kim, from Ms. Ward's classroom in Delaware.

Thank you for recommending the following website:"Math Made Fun: A Resource for Parents and Students" http://www.netcredit.com/blog/extra-credit-math-made-fun-a-resource-for-parents/

I am sitting in my office in Ballarat, Victoria Australia at the moment. I don't exactly know where Delaware is or how far away it is from Ballarat. Could you find out for me and make a map showing where you are and how far away it is.

PS can you please list the distance in Miles and Kilometers as we use Metric in Australia and we changed from using Miles to kilometers when I was 5 years old.

It's strange I still know how long an inch is in my head but I use metric for everything else.


Kind regards,




Thanks Kelly for passing on another recommendation from the kids in your class:

A list of online calculators


Thanks Kelly for your encouragement and for passing on the recommendation from the kids in your class for the the following site:

Web Support: Math and Science Resources




Thanks Frannie, I am glad you have found this page useful.

I have induced your recommend link the www.mortgagecalculator.net/math-calculators page. You may also like the http://www.calculator.net/ page

PS I like the binary calculator see below for what you get when you Goggle binary : - )

Google Bibary






Recommended by Sarah Smithlink added September 25, 2010

Thanks Sarah, I had forgotten about the Lemonade Stand game, There
are some other nice resources in the Teaching Kids Money site that you recommended.

LEmonade Stand




Maths Dictionary for Kids
An animated, interactive dictionary for students which explains over 500 common mathematical terms
link added June 9, 2007


Locations of visitors to this page


Cluster Map 502 visits

502 visits shown above - 11 Jul 2009 to 2 Sep 2009
Total since 8 Jul 2006: 10,774. Previous 24hrs: 17.


TJ591- Mathematics Summations see week 11 below:

Mathematics Summation 2003

Summation criteria 2003

Instructions for the summation 2003

Mathematics Summation 2002

Mathematics Summation 2001


Week 8 Lecture Notes Week 8 Lecture Notes 4,707 KB

Websites used in Presentation:

Site URL
The Mathematical Association of Victoria http://www.mav.vic.edu.au
A Maths Dictionary for Kids http://www.teachers.ash.org.au/jeather/maths/dictionary.html
MicroWorlds http://www.microworlds.com
What a Crowd http://www.rupert.id.au/microworlds
Math Cats http://www.mathcats.com
Pattern Blocks http://matti.usu.edu/nlvm/nav/vm1_asid_171.html
Geoboards http://matti.usu.edu/nlvm/nav/frames_asid_277_g_1_t_3.html?open=activities
A Broken Calculator http://www.cut-the-knot.org/Curriculum/Arithmetic/BrokenCalculator.shtml
A Broken Calculator http://www.fi.uu.nl/toepassingen/00014/toepassing.xml?language=en
National Library for Virtual Manipulatives http://matti.usu.edu/nlvm/nav
K-12 Teaching Materials http://archives.math.utk.edu/k12.html
The Geometer’s Sketchpad http://www.keypress.com/sketchpad
Calculators http://www.avlandesign.com/calc.htm
Polyhedrons http://www.chainwave.com/Poly/Default.htm
3D Simulation of folding Nets http://www.fi.uu.nl/toepassingen/00297/toepassing.xml?&language=en
Small Stella 3D Polyhedron simulator http://home.aanet.com.au/robertw/Downloads.html
Galaxy http://www.galaxy.com/galaxy/Science/Mathematics/Software/
The Expanding Circle http://www15.addr.com/~dscher/expcircle.html
To Excel in the Classroom http://www.forsyth.k12.ga.us/kadkins/spreadsheet.htm
Pictographs for young children http://www.forsyth.k12.ga.us/kadkins/picgraph.htm
Using the If formula will allow you to create self checking activities in Excel http://www.forsyth.k12.ga.us/kadkins/ifthen03.htm

Resources | Links | Discuss | Submit | About

Home > Elementary Resources > Math > Statistics and Probability

A List of Daily Math Graph & Yes/No Questions.

The following data sets can be downloaded as Excel spreadsheets by simply clicking on the desired title. The downloaded lists can then be sorted, manipulated, and graphed on your computer in the same way that any spreadsheet is manipulated. http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html
The house of Mathematics software provides the free-software for education.
You will experience a new mathematical world !
The Plane Graphic Calculator is a software tool that interactively displays a graphical view of mathematical functions.

This calculator is intended primarily as an educational aid to understanding the geometric interpretation of mathematical functions.

Classrooms that Excel Resources http://www.sabine.k12.la.us/class/excel_resources.htm
LT Technologies | Teacher Resources - Internet Links | Spreadsheets http://www.lttechno.com/links/spreadsheets.html

Contains a really great list of links to resources for math students, all the way from basic arithmetic to calculus and discrete math. 

Thank to Suzy Maguire for this link

Math’s Fonts http://www.rupert.id.au/fonts
Fractals http://matti.usu.edu/nlvm/nav/frames_asid_136_g_4_t_3.html
Teacher Roles In Computer-Enriched Classrooms http://www.kidsource.com/kidsource/content2/integrate.computers.html
Ask Dr. Math
Students can ask questions about math problems.
It is fun to read the student questions and see the
answers. Try it. You might learn something new.
ENIAC http://www.library.upenn.edu/special/gallery/mauchly/jwm8b.html
The term “bug” has been used for problems in machinery since electricity was invented. But the first computer bug was actually a moth! In 1945, a computer being tested at Harvard University stalled when a moth got caught inside. The engineers taped the moth into their computer log with the note, “First actual case of bug being found.” http://perso.wanadoo.fr/pc-informatik/histoire1.htm



Unit Description

Example Portfolio from 2004

Clarification on requirements for the Research Project

Research Project - 30% Individual (Due: Week 9, Friday September 17, 2004)
• Plan, implement and reflect on an activity/lesson conducted during your placement in schools.
• You may plan with your buddy, but each preservice teacher (PST) is to hand in a separate report
• This may be an individual, group or whole class activity
• Think about the learning, the content, the reflection on the learning
• Gather data about the students’ reflections
• Write your response using the ALACT model

I have confirmed with Robyn that you must plan & implement an activity. It does not have to be a whole class activity if you organise a small group activity that will be fine.

If you are having problems arranging an activity within your class please let me know ASAP Rupert.


Statement on plagiarism for inclusion in Semester 2 2004 Unit Descriptions

Plagiarism is the presentation of the expressed thought or work of another person as though it is one’s own without properly acknowledging that person. The University’s Statute 6.1 Student Discipline and Regulation 6.1 Student Discipline make it clear that plagiarising is a breach of student discipline and may incur a range of penalties.

Trevor Hastings
Chair, Academic Board
18 June 2004

CSF II Mathematics


Animated Mandelbrot

What are Fractals?


Teaching Primary Mathematics
Image location

Booker, G., Bond, D., Sparrow, L., & Swan, P., (2003). Teaching Primary Mathematics, NSW: Pearson.

Check availability 3rd Edition Mt. Helen Campus Library Call Number 510.7 TEA3
Check availability 2nd Edition Mt. Helen Campus Library Call Number 510.7 TEA2

More information

Illustrated maths dictionary
Image location

de Klerk, J. (1990) Illustrated Maths Dictionary for Australian Schools. ( 2nd edition)
Longman Cheshire.
Check availability


Grimson, L. & Pegg, J. (eds.) (1995).Teaching secondary school mathematics: Theory into practice, Harcourt Brace, Aust.,
Check availability Mt. Helen Campus Library Call Number 510.712 T22ss


Australian Association of Mathematics Teachers (AAMT)

Mathematical Association of Victoria (MAV)

61 Blyth Street
telephone: (03) 9380 2399
facsimile: (03) 9380 8323
e-mail: office@mav.vic.edu.au

What is the MAV?

The Mathematical Association of Victoria is a membership-driven Association that provides a voice, leadership and professional support for mathematical education. Through our programs and services we aim to promote mathematics, mathematics education, and its importance to society. Our Association has over 1,700 members from all sectors of education and has been an active non-profit professional Association for nearly 100 years.


www.edulists.com.au Mailing Lists

Yr7-10maths Year 7-10 Mathematics Teachers' Mailing List


see also:

yr11it Year 11 Information Technology Teachers' Mailing List
Yr7-10it Year 7 - 10 Information Technology Teachers' Mailing List



Statement on the Use of Calculators and Computers for
Mathematics in Australian Schools 1996


CSF II Online


Board of Studies. (2000). Curriculum and standards framework II: Mathematics. Carlton: Victorian Author.
     Retrieved November 12, 2001, from: Victorian Curriculum and Assessment Authority Web site:

Deakin University Maths Education Resources page




http://thesaurus.maths.org Maths Thesaurus



Primary Resources




The Mathematical Association of Victoria (MAV) has an outstanding web-site

Maths Dictionary for Kids








Worms Web » Mathematics

Week 1

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




Radiolaria have exsted snce Cabran times, 570 million years ago, and are still one of the main constituents of marine plankton today. Alive or as skeletons, they are among the most amazingly beautiful animal forms. They have an intricate skeletal structure, with a central perforated capsule and radiating rods. In the living aminal, the central capsual seperates a body on inner cytoplasm from the outer layer. White, M. (1993). The nature of hidden worlds- animals and plants in prehistoric Australia and New Zealand. Auckland: Reed Books.

Radiolaria are marine protists that are most abundant in tropic waters. The remains of their beautiful houses can be found on the bottom of the ocean as well as in fossilised rock.


More images
see: www.radiolaria.org

The Snowflake Curve

Google search for primary maths resources

Google search for "primary maths resources"

Fibonacci Numbers and Nature



Number Bingo
contributed by Sash Hamidi

Sash writes: 'Get the children to draw up a 7 x 7 grid (good skills!) and number 1-49. They put numbers in any box, no set order - they must make sure their layout is different to other children. Tell them to put 1 somewhere, then 2, then 3 ...etc so they don't lose track of the numbers! The teacher they uses various operations to ask questions - children work out answer and shade in the box. Winner is the first to get a line. Less able can team up to build confidence - it goes quite quickly! When they have mastered this, change the numbers - I have used negative numbers, 50-98, multiples of 10, etc...it is quite easy to extend. It takes about 15 mins to do. I first saw this done in a Stanmore school by a shy teacher named Ian Tyler - cheers Ian!'


Week 2

TJ591-Learning and teaching mathematics-Summary of responses

A Snowflake Primer
... The basic facts about snowflakes and snow crystals ...

Guide to Snowflakes
... A look at the different types of falling snow ...

Historic Snowflakes
... Early observations and studies of snow crystals ...

Snow Crystal Photographs
... Capturing the fleeting beauty of snowflakes ...

They are not all 6 sided!

12 sided Snow Crystal 3 sided Snow Crystal

Unusual Snow Crystals
... Some exotic examples from the snow crystal menagerie ...


The Snowflake: Winter’s Secret Beauty 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

Hexagonal water ice

Hexagonal water ice


Hexagonal water ice




The Rasmussen & Libbrecht Collection


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



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.

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.
Printer friendly version

Cool Math Links


Snow Flakes and Sacred Geometry





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


Fred A.J. Korthagen
IVLOS Institute of Education
Utrecht University
The Netherlands
e-mail: F.Korthagen@ivlos.uu.nl

The ALACT model


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

Phi for Neo-phi-tes

Dr. Levin's Golden Mean Gauges

Phi: That Golden Number

The Golden section ratio: Phi

Behind the Cafe Union Building Next Monday


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
Stella: Polyhedron Navigator

Stella: Polyhedron Navigator

Stella: Polyhedron Navigator

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




List of Geometry Applets Link added March 20 2007

overview of WisWeb-applets Link added March 20 2007

A gallery of images rendered using POV-Ray, from models exported by Great Stella.
Includes animations!

The 5 Platonic Solids


The 13 Archimedean Solids

From: http://www.scienceu.com/geometry/facts/solids/


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 Mathematics


Interactive online geoboard

Pattern Blocks

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.



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.

Great MathsWebsites to Explore

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

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.



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.


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
We now know that the digit eight is not in the answer. Try new positions for the 4 & 7.
Forget to include the digit 3 in our guess.

Week 5

Google search for "how to get students to talk"

How to Get Students to Talk in Class

Designing Effective Discussion Questions

Tips on Discussion Leading

Self-Help for Beginning Teachers

Google search for mastermind maths



maths learning games


Fibonacci Numbers and Nature
Animated fibonacci spiral

Maths Links This site has links to some good looking resources

Google search for "magic squares"

Magic Square Magic Square

The famous Six-in-One by Allan W. Johnson:





Maths Resources
Games? Simulations? Some web sites below include them as a tool for learning. You might be saying, "I don't have time for such things in my class!" But, before you pass them by, read What about simulation as an educational tool? and Thinking and Learning Skills Potentially Developed by Playing Some Simulation/Adventure/Role-playing Video Games by R. Morgan.

Computing Technology for Math Excellence: http://www.ct4me.net is devoted to resources for teaching and learning
mathematics (K-12 and calculus) and the standards movement in education.

Math resources include sites for basic skills mastery, problem solving and critical thinking, using data, homework assistance, games, simulations, virtual math manipulatives, project-based learning, field trips for math, standardized testing, and more. Over 70 software products that have potential to raise achievement levels of students are included. Read about education and technology news, including No Child Left Behind, and research on topics in math education, implementing standards, and standardized testing. Educators will appreciate the resources on technology integration,
multimedia in projects, web design, national math initiatives, math methodology, and professional development.









The Garden of Our School
The Garden of Our School

Week 6

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

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

back to top

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

Literacy & Numeracy Week - EYS - Resources - Useful Books

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.

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

Google search for "who sank the boat" maths


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.

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, ..."

One 100 1. "ten to the zero"
ten 101 10. "ten to the one"
hundred 102 100. "ten to the two"
thousand 103 1,000. "ten to the three"
ten thousand 104 10,000. "ten to the four"
hundred thousand 105 100,000. "ten to the five"
million 106 1,000,000. "ten to the six"
ten million 107 10,000,000. "ten to the seven"
hundred million 108 100,000,000. "ten to the eight"
billion 109 1,000,000,000. "ten to the nine"
ten billion 1010 10,000,000,000. "ten to the ten"
hundred billion 1011 100,000,000,000. "ten to the eleven"
trillion 1012 1,000,000,000,000. "ten to the twelve"
ten trillion 1013 10,000,000,000,000. "ten to the thirteen"
hundred trillion 1014 100,000,000,000,000. "ten to the fourteen"


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.


See also Names of Large Numbers


Week 7


PowerPoint from Lecture Week 7

Version for printing handouts

 Week 7 Lecture Notes


A list of some interesting looking maths resources

This is a facinating site that is well worth a look

Interactive Mathematics Miscellany and Puzzles

Other sites of interest


Google Search for "broken calculator" maths

A Broken Calculator

The Broken Calculator TEC Lesson Plan

'Broken Calculator' Activity Links


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

The Island of Discarded Calculators

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

Excellent Broken Calculator Applets

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.



Free Running Record Calculator

Free Running Record Calculator220 KB


Week 8

Talk:Arabic numerals


Early numbers originally used by the early Phoenician traders


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.

and "O" has no angles




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://www.ms.washington.edu/courses/math387-lamp/glossary.html - could not
access site but worth a look maybe

Race to a flat PDF File 79 KB



~ Break ~      Monday 22 September – Friday 3 October


Week 10

PowerPoint from Lecture Week 10

Version for printing handouts

Week 10 PowerPoint

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

Links from the above PowerPoint


Comment / URL

Small Stella Demo Used to create 3D models and 2D Nets
Cut-outs , Nets (PB) Play with 3D models online
The role of calculators in primary mathematics  
Google search  Search for calculator games classroom
Google Search  Search for calculator activities classroom
Games & Activities  
Games & Activities

Counting forwards and backwards in patterns, using calculators. If you press the button four more times what will the answer be?


Games & Activities  http://mathforum.org/t2t/message.taco?thread=372&message=2
Number Shapes  http://mathforum.org/t2t/message.taco?thread=372&message=2
Broken Calculator Problems



Target Games All of these games should be played several times for players to see the strategies involved. In each case there are significant numbers that determine the result.
Wipe Out  http://www.blackdouglas.com.au/calchange/cch_act/wipeout.htm
CSF II Outcome Statements  http://www.vcaa.vic.edu.au/csfcd/ma/lima--01.htm
The Abacus  http://www.dotpoint.com/xnumber/mechanical1.htm
Napier’s Bones  http://www.dotpoint.com/xnumber/mechanical1.htm
Slide Rules

The HP Museum is well worth a visit


Leonardo da Vinci’s Design  http://www.dotpoint.com/xnumber/mechanical1.htm
Schickard’s Machine




The Pascaline http://www.dotpoint.com/xnumber/mechanical1.htm
The Difference Engine http://www.dotpoint.com/xnumber/mechanical1.htm
The Difference Engine http://ed-thelen.org/bab/bab-t-337.jpg
Troncets or Slide Adders www.dotpoint.com/xnumber/mechanical1.htm
Old ads http://www.webcom.com/calc/
Electromechanical Calculators http://www.oldcalculatormuseum.com/index.html
Nixie tube display http://www.taswegian.com/MOSCOW/display.html
Graphical Calculators http://education.ti.com/us/product/tech/73/features/features.html
Calculator Skins Briomsoft http://www.biromsoft.com/
Beautiful Calculator http://www.rayslab.com/
PG Calculator http://www.pgcalc.x4.pl/eng/index.html
Design a Calculator http://www.ace-centre.org.uk/html/software/softdemo.html
saMagicSquares http://www.softars.com/
GraphSight Junior http://www.cradlefields.com
Derive 5 http://www.derive-europe.com/
Websites http://www.casio.edu.shriro.com.au/new.html
Texas Instruments http://education.ti.com/us/product/main.html
Books http://wwwstaff.murdoch.edu.au/~kissane/calcbooks.htm
Library Catalogue http://innopac.ballarat.edu.au/
BookCrossing.com Well, the books our members leave in the wild are free... but it's the act of freeing books that points to the heart of BookCrossing



Calculators in the math's room

See list of links from the presentation

Age Calculator

Enter your date of birth
Month Date Year Hours

You have been living for:
In months:
In weeks:
In days:
In hours:
In minutes:
In seconds:
In Milliseconds:
Your next birthday will be in:

Free JavaScripts provided
by The JavaScript Source

Sun Sign:
Chinese Sign:

Free JavaScripts provided
by The JavaScript Source


Day of Week

Day Month Year

Day of the week Time

Free JavaScripts provided
by The JavaScript Source

Blood Alcohol Content (BAC) Calculator
University of Oklahoma Police Department

Google Search for "BAC Calculator "

Google search for Australian pages containing "BAC Calculator"

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


Google search for "early calculators"



Google search for "why use calculators"

Calculator use

Google search for "don't use calculators"

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

Number Shapes

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

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.

One Calculator per child

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


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.)

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





Mandelbrot Images

Web resources for teaching with technology

6. Fractal programs


Here are various selected topics related to Geometry and Trigonometry

Manipula Math Applets

Angles and Parallel Lines Applets

Introduction to Trigonometric Functions Applets


Slide Rule

Solid of Rotation Applet

Calculus Applets

Life32 by Johan Bontes

Recreational Mathematics

Interlocked turning gears along the length of a Möbius strip (M. Trott 2001, pers. comm.).

Mathworld Animated GIFs


Solid of Rotation

- Solid Of Rotation (SOR) -

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



Mathematics learning forum: Role of ICT in the construction of pre-service teachers' content knowledge schema

Australian Journal of Educational Technology
2003, 19(2), 176-191.

Integrating Computers in the Constructivist Classroom:
Enrich Your Students Learning Environment With Computers

Other Resources

The followiing list was compiled by Kylie Astbury
This website is about the basic rule PEMDAS (Please Excuse My Dear Aunty Sally). There are 10 questions in the pre-test and once you answer the 10 questions you get a score telling you how many you got right. Once you have completed the pre-test you can move onto the tutorial where it gets a little bit more tricky.
This website has many topic that you can research on the index column.
The topics have many related topics within them that allow you to explore the different aspects in each topic.

This website is about making maths fun hence the name.
The topics include:
- number and algebra
- shapes, space and measures
- handling data and
- Miscellaneous (everything else)
It also has fun little quizzes that test your timetables, logical quizzes, fraction and many more
fun little activities that allow children to appreciate maths.

This web page is designed to make maths more interactive and get children more involved, with the topics including introduction to statistics, topics in pre-algebra, integers and number theory. This site also provides links to homework help forums, puzzles that you can print off and do them from home and links to discounted math books.
This web site has a variety of links aimed at helping many people improve with their maths skills. There are many teaching tips for all age groups and has online math resources. This site has advise on home schooling and many fun little activities for the children to play on to familiarise them with useful math terms.

APA citation:
Russell, R. (2019, November 07, 10:27 am). TJ591 learning and teaching mathematics I.
     Retrieved April 06, 2020, from http://www.rupert.id.au/TJ591/index.php

Last refreshed: April 06 2020. 03:44.18 pm

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