Mathematics Task Centre Learning

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Mathematics Task Centre Learning

• A Model For Teaching and Learning
• WORKING MATHEMATICALLY

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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
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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

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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
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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
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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)

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From Fermats 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.
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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
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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
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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. Ive done what the card
says. Assessment and Record-keeping are critical
to the successful use of tasks Two-tier
Approach Regular Short Journalling Completi
on 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
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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
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And so, what happened?......

• We got our room set up

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And so, what happened?........
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• Some displays that could be referred to.

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

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• Working in pairs.

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• Publishing, recording (given framework)

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• We sorted our tasks. Manageable.
• Organised. Accessible..

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• ...though, not always secure!

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• Learning new teaching practice.

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

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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

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What did students have to say?
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• Its 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
  dont 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

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• 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.

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• Good environment to work in. Good set up.
• I learned a lot from it and Im 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

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• 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.

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• 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?)

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Whats 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

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Acknowledgement
Material used in this presentation has come
from Mathematics Task Centre Project Maths300 Bla
ck Douglas Professional Education
Services Please visit http//www.blackdouglas.com
.au/taskcentre and http//www.curriculum.edu.au/ma
ths300
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This presentation was prepared by

• Damian Howison
• MacKillop College, Swan Hill, Vic
• dhowison_at_mackillopsh.vic.edu.au