Mathematics Task Centre Learning A Model For Teaching and Learning WORKING MATHEMATICALLY

If teachers of mathematics had to teach football, 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 Models Design of specific units to teach concepts, practise skills and try applications Tasks 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 Centre Students 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 MATHEMATICALLY Work With Problems Select Strategies Ask - What happens if …? Check/Learn from Results – Publish Work Development of necessary skills Working Like a Mathematician 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 practice has come together

Plan for Success Danger 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 questioning Checklist completed after each session Note-taking or anecdotage for feedback/reporting Mathematics Reports Less frequent – eg 1/term or 2/semester Requires 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

This presentation was prepared by Damian Howison MacKillop College, Swan Hill, Vic dhowison@mackillopsh.vic.edu.au