SASE
Contextualised group work –
teaching a broader mathematics
curriculum to first year science
students:
Case study – Problem solving
Jo-ann Larkins
School of Applied Sciences and
Engineering
Federation University Australia
Today’s presentation
• Participate in an example of contextualised
group work activity – theme of problem solving
• Brainstorm around how you can incorporate
contextualised group work techniques in your
classroom
• Examples of the types of teaching strategies /
activities you can use to engage groups of
students
Polya: “The Father of Problem
Solving”
• George Pólya was a
Hungarian mathematician.
• He made fundamental contributions
to combinatorics, number theory,
numerical analysis and probability
theory. He is also noted for his work
in heuristics and mathematics
education.
Heuristics
• Heuristic (Greek: "find" or "discover") refers
to experience-based techniques for problem
solving, learning, and discovery that gives a
solution which is not guaranteed to be optimal.
• Where an exhaustive search is impractical,
heuristic methods are used to speed up the
process of finding a satisfactory solution via
mental shortcuts.
• Examples of this method include using a rule of
thumb, an educated guess, an intuitive
judgment, stereotyping, or common sense.
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Polya's Problem Solving
Techniques
• In 1945 George Polya published the
book How To Solve It which quickly
became his most prized publication.
• It sold over one million copies and
has been translated into 17
languages.
• In this book he identifies four basic
principles of problem solving.
1. Understand the problem
• Do you understand all the words used in
stating the problem?
• What are you asked to find or show?
• Can you restate the problem in your own
words?
• Can you think of a picture or diagram that
might help you understand the problem?
• Is there enough information to enable you
to find a solution?
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2. Devise a plan
• There are many reasonable ways to
solve problems.
• The skill lies in choosing an
appropriate strategy.
• This best learned by solving many
problems. You will find choosing a
strategy increasingly easy.
• (You are going to create a list of
strategies in this session).
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3. Carry out the plan
• This step is usually easier than devising
the plan. In general, all you need is care
and patience, given that you have the
necessary skills.
• Persist with the plan that you have
chosen.
• If it continues not to work discard it and
choose another. Don't be misled, this is
how mathematics is done, even by
professionals.
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4. Look back
• Much can be gained by taking the
time to reflect and look back at what
you have done, what worked, and
what didn't.
• Doing this will enable you to predict
what strategy to use to solve future
problems.
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http://www.3vadmin.com/problem-solving-skills/
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What strategies do you use?
• In groups come up with a list of the
strategies you use to solve
problems.
• You should be able to come up with
at least 10 different ones.
• Think of the sort of problems you’ve
had to solve in class as well as real
world problems.
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What strategies do you use?
• I want to collect your group’s output
at the end of this session so write it
on the blank paper provided.
• You can be creative and create a
mind-map or flowchart type output
rather than a list.
• You have 10 minutes.
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Problem Solving Strategies
• Guess and check
• Look for a pattern
• Make an orderly
list
• Draw a picture
• Eliminate
possibilities
• Solve a simpler
problem
• Use symmetry
• Use a model
• Consider special
cases
• Work backwards
• Use direct
reasoning
• Use a formula
• Solve an equation
• Be ingenious
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Using contextualised group work in
Teaching
We’ve just participated in an activity inviting
students to consider abstract thinking skills
necessary for mathematics using a group based
approach.
Two questions:
• Where does your unit have content that lends
itself to a group approach?
• Other than discussion, how can you use groups
to improve understanding / engage students?
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Teaching strategies
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What I’ve tried
• Relay maths tasks – fastest correct answers
• Teach the teacher – teach your peers – develop
an example and demonstrate in groups –
student’s choice of area within current topic
• Using props for context – containers for volume,
Molecular models for 3D geometry
• Creating checklists / templates / how to do
strategies through student centred discussion
(e.g. what’s essential in graphs and tables for
lab reports from examining real life student
work)
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What I’ve tried
• Role play: You are a …. Explain this concept /
graph / diagram – very effective in literacy
around data and graphing.
• Case studies – problem solving and applying
the skills in a discipline based context.
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Final student comment
What was that question about problem
solving on the exam? Worst question
ever….
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