Transcript TASK CENTRE LEARNING

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 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
Ask - What
happens if …?
Select Strategies
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 twopage 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
• [email protected]