Mathematics Task Centre Learning

A Model For Teaching and Learning

WORKING MATHEMATICALLY

A focus for the Working Mathematically teacher is to help students develop mathematical skills in the context of problem posing and solving.

Afzal Ahmed, one time professor of mathematics at Chichester, UK, once quipped:

If teachers of mathematics had to teach football, they would start off with a lesson on kicking the ball, follow it with lessons on trapping the ball and end with a lesson on heading the

ball. At no time would they play a game

of football.

Such is not the case when teaching a Working Mathematically curriculum.

[“Working Mathematically - an investigative approach to learning.”Maths300, Curriculum Corporation]

Outcomes

For students

Working Mathematically

Use of Concrete Materials - more real, less abstract

Positive Environment

Group Work and Individual Learning

Working at Own Pace and Ability

Outcomes

For teachers

Learn while you teach!

Get to know students better…

…As students…As students learning mathematics

Create open, active, enjoyable learning environments

Effective Mixed-Ability Teaching

Students are extended normally and naturally

Task-Centre Learning ModelsDesign of specific units to teach concepts, practise skills and try

applicationsTasks brought into the classroom within a Curriculum Unit

Tasks aimed at a concept or solving problems around a strand

Possibly a model for us in the future?

An actual Task CentreStudents brought into the task centre

‘Separate’ but still integral part of curriculum

A ‘working mathematically’ time each week/fortnight for each class

Tasks housed centrally; secure, accessible, manageable

Room set up for group work, appropriate displays

A Focus and Identity

Tangible presence of the mathematics faculty in the school

A place for KLA meetings, parent meetings, maths clubs

What is a Task?

A problem for students to solve

Concrete materials supplied

The tip of an ‘iceberg’

Each task has three lives:

A problem for a pair of students

A whole-class problem to solve

A deeper investigation (guided)

From Fermat’s Last Theorem (author Simon Singh)

"It was so indescribably beautiful; it was so simple and so elegant. I couldn't understand how I'd missed it and I just stared at it in disbelief for twenty minutes. Then during the day I walked around the department, and I'd keep coming back to my desk looking to see if it was still there. It was still there. I couldn't contain myself, I was so excited. It was the most important moment of my working life. Nothing I ever do again will mean as much."

(This is how mathematician Andrew Wiles describes his experience upon finally solving a mathematical problem that had not been solved by all the great mathematicians. He first became interested in the problem when aged 10.)

Is it possible that we can create happy, healthy, cheerful, productive, inspiring classrooms where all students can experience that same joy of discovery?

[Text of an address to the Annual Conference, Mathematical Association of Victoria, December 5th, 2002.]

WORKING MATHEMATICALLYWork With Problems Select Strategies

Ask - What happens if …?

Check/Learn from Results –

Publish Work

Working Like a Mathematician

Development of necessary skills

BALANCED CURRICULUM

Why TASKS?

Directly linked to the ‘sister’ project Maths300

Teaching and Learning Variety

Teaching and Assessing ‘Working Mathematically’ – VELS

Supported with a ‘living’ website and PD programs

Decades of good teaching and learning practicehas come together

Plan for SuccessDanger of adopting a ‘Butterfly’ approach.

Students casually drifting from one task to the next

Students may be resistant to exploring the iceberg. ‘I’ve done what the card says.’

Assessment and Record-keeping are critical to the successful use of tasks Two-tier Approach

Regular Short ‘Journalling’Completion – signature and questioningChecklist completed after each sessionNote-taking or anecdotage for feedback/reporting

Mathematics ReportsLess frequent – eg 1/term or 2/semesterRequires teaching ‘how to write a report’Provide a format to students

Effective, Safe and Careful Use, Storage and Maintenance of Tasks

What This Means for Us as Teachers Next Year.

Learning to explore the ‘iceberg’ of a task and helping students do the same.

become familiar with, learn to use,

and learn to teach the ‘working mathematically’ process.

Become familiar with 20-25 tasks per Year Level

Adopt a structured, common assessment model

Formation of a TASK FOCUS GROUP

And so, what happened?......

We got our room set up

And so, what happened?........

Some displays that could be referred to.

Every student Yr 7 – 10 timetabled through the centre at least once per fortnight.

Working in pairs.

Publishing, recording (given framework)

We sorted our tasks. Manageable.

Organised. Accessible……..

...though, not always secure!

Learning new teaching practice.

For teachers, ongoing learning and growing, professionally and supportively.

What did staff have to say?

• Students who cannot relate to abstract ideas see Mathematics in a tangible light.

• Increased engagement – particularly of the boys who find articulating ideas when writing difficult.

• Allows students to demonstrate problem solving skills that cannot be easily displayed in textbook activities

• Great idea of a task centre maths room• The tasks certainly enable students/teachers to

identify Working Mathematically• I have seen students totally focussed on achieving a

solution• I have been challenged to try different ways of

teaching

What did students have to say?

• It’s interesting because we use what we have learned in maths to solve the problems.

• Some people find it easier to use objects to complete a question instead of just numbers on paper.

• We need practice with problem solving and we don’t do it as much in the classroom

• It allows us to try our maths skills and think for ourselves a lot, rather than just the standard method and procedure which can limit us a bit

• I love how it challenges me and I enjoy trying to find formulas for different problems.

• I enjoyed going further into the problem.

• I liked how we got to choose from a wide range of problems and how we got to work with partners.

• It gives us a wider range of academic skills.

• Good environment to work in. Good set up.

• I learned a lot from it and I’m heaps better at problem solving now.

• I think I often learned things without realising

• Teachers get to see who can solve problems, not just do sums.

• They are good for building friends and it is good when you can complete a task because it makes you feel good

• If you answer the question quickly you can come up with ways to extend the problem

• It will open up different strategies for us. It will even help our tests.

• I like using my mind. I have never really been asked to go to a problem and extend on it as much as I have here.

• I personally think that my problem solving has improved out of sight. My maths textbook and my mathsmate has improved a lot.

• I know how to use the problem solving strategies and when and where to use the different ones.

• More sessions? No..because if you have more sessions you would have already done all of the tasks halfway through the year….(Would you be able to get more tasks?)

What’s going to be different next year?

• Use some tasks within some units of work.

• Increased tasks used as a whole class.

• Encourage journal writing rather than two-page reporting

• Use of software

• Build up task cameos on a more regular basis

Acknowledgement

Material used in this presentation has come from

Mathematics Task Centre Project

Maths300

Black Douglas Professional Education Services

Please visit http://www.blackdouglas.com.au/taskcentre

and http://www.curriculum.edu.au/maths300

• Damian Howison

• MacKillop College, Swan Hill, Vic

• dhowison@mackillopsh.vic.edu.au

This presentation was prepared by