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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.

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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.

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.

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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.

10http://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….