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. 4

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? 6

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). 7

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. 8

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. 9

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. 11

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. 12

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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 14

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? 15

Teaching strategies 16

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) 17

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. 18

Final student comment What was that question about problem solving on the exam? Worst question ever…. 19