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Working Mathematically

Our attitude is that in best practice classrooms all students can learn to work like a mathematician. On this page we detail the meaning of Working Mathematically and include illustrations from classrooms and learners of all ages.

Red Square  Working Mathematically Process

Red Square  Notes from an Inspector's Notebook

Red Square  From Teachers & Schools

Red Square  Working Mathematically Anthem


Eric The Sheep, Year 3 Kingsley Park Primary School, Victoria

Red Square  Working Mathematically Curriculum Scaffold

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Notes from an Inspector's Notebook

John Hibbs is a retired HMI (Her Majesty's Inspector) and lifelong learner and teacher through hands-on problem solving. He is a great supporter of our site and occasionally shares items from his extensive diaries of mathematical adventures journeyed throughout his career. They provide an insight into the way mathematician's think.
  • April 2005
    Are there other shapes which replicate themselves like the Sphinx does?
  • July 2005
    Glaeser's Dominoes
  • March 2006
    Variations on the Task 46, Duelling Dice.
  • August 2006
    Investigating Worms - or rather the trails that 'mathematical worms' might leave behind.
Sophie Germain
The image is of Sophie Germain, whose work on Fermat's Last Theorem in 1738 was to remain the most important contribution to the problem for over 100 years until 1840. Click on the image to visit a web site with a complete biography. It is also where we sourced this picture. 		 

     From Teachers & Schools

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Working Mathematically

The process of Working Mathematically - learning to work like a mathematician - is the scaffold for all our services and resources. In its early days the Task Centre Project asked professional mathematicians to detail what they did. We compiled their responses to create our statement of the:

Working Mathematically Process

First give me an interesting problem.

When mathematicians become interested in a problem they:

Questions which help mathematicians learn more are: When mathematicians have a problem they: A mathematician's strategy toolbox includes:

If one way doesn't work I just start again another way.

This process is also available as a PDF document.

From Teachers & Schools

Mathematician's Tool Shed
Harry Kanasa, John Paul College, Queensland, has taken the strategy toolbox section above and turned it into a Strategy Tool Shed. The visual nature of the presentation will add meaning for many students, and the addition of the multiple intelligences checklist will appeal to many teachers.
Mathematician's Tool Shed
Harry is very happy for others to make use of this creation, so if you would like to save it:
  1. Click the drawing to call up a higher resolution version, then
  2. Right click (Windows) or click and hold (Mac) and choose Save Picture As...
Benalla College Charter
Benalla College, Victoria, Australia is one school that has used our professional services to help the staff shift towards a Working Mathematically curriculum. This is the charter they developed:

Maths Charter
WORKING MATHEMATICALLY

STATEMENT
WE WANT TO SHIFT OUR MATHS CURRICULUM TO ONE THAT REFLECTS:

  • Active engagement of students through 'hands on' activities and demonstrations using the model of 'working mathematically'.
     
  • Mathematics as a 'visual', motivating, challenging learning experience!
     
  • Building on the knowledge students bring to the classroom and is relevant to the students.
     
  • Stimulates students' curiosity through the use of diverse materials and tasks.
     
  • Responds and caters to the individual needs of each student from concrete to abstract thinkers.
     
  • Student ownership in the Maths classes achieved by providing a structured, relaxed, supportive and open atmosphere where students are encouraged to be active problem solvers and are able to justify and explain, without fear, where they are at.
     
  • Students experiencing 'success' and 'feeling good' about doing Maths by 'modeling' their work to their peers.
     
  • Evidence of achievement in response to a task as measured against previously published outcome expectations.
     

Working Mathematically Anthem
On December 5th, 2002, Doug Williams gave a keynote address to the Annual Conference of the Mathematical Association of Victoria entitled Learning to Work Like a Mathematician. He closed the address with a song. At the request of many present this song has been made available below.
Right Click on the tune and choose Save Link As... to download a Midi file. The text of the address is available at the Web Papers link on the Black Douglas site.

(Tune: Advance Australia Fair)

Maths teachers all let us rejoice
Our subject is not trite!
It's far more than the daily toil
Of "Is this wrong or right?"
The theme we weave each time we teach
Must challenge students to
Engage with problems in the way
That math'maticians do!
In joyful classrooms let us work
Like math'maticians do!

Alternative arrangements of the tune:

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