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Being a mathematician
- 1. Being a Mathematician We are all mathematicians
- 2. What Mathematicians Do Read and understand the problem Explore the problem Seek patterns and make hypotheses Use problem solving strategies and math’s skills Look for all possible solutions and ‘what ifs’. Tell – Explain how you got your answers and what you have learnt. Start again. Mathematicians get: R E S U T L S
- 3. READ AND UNDERSTAND THE PROBLEM Describe the problem using words/symbols/diagrams. E S U T L S R
- 4. EXPLORE THE PROBLEM What might the answer look like? What is the important information? How could this problem be solved? Jot down some initial thoughts. E S U T L S R
- 5. SEEK PATTERNS AND MAKE HYPOTHESES Record: any data collected patterns found possible hypotheses and theories. E S U T L S R
- 6. USE MATHS SKILLAND PROBLEM SOLVING STRATEGIES List the problem solving strategies and math’s skills used. E S U T L S R
- 7. LOOK FOR ALL POSSIBLE SOLUTIONS AND ‘WHAT IFS’ Record all possible solutions. Have you found them all? Are they correct? Explore and solve a ‘what if’ question. Record your ‘what if’ and your findings. E S U T L S R
- 8. TELL – EXPLAIN HOW YOU GOT YOUR ANSWERS AND WHAT YOU HAVE LEARNT Explain using words/symbols/diagrams Your solution(s) to the problem How you got your solution – process of discovery How you know your solution is correct What you have learnt E S U T L S R
- 9. START AGAIN. Solve another problem using the skills and knowledge you have learnt as a mathematician. E S U T L S R
Editor's Notes
- Find an interesting, meaningful or worthwhile problem to solve.In the past, mathematics has been solution-focused: children set out to find the correct answer that invariably sat in the back of their textbook. But 'real' mathematicians don't know all the answers - they start with a problem they find interesting, and work through a number of strategies to find a solution.In Working Mathematically, we teach children to think like mathematicians, but first, we have to get them interested! Each maths300 lesson begins with a story shell, which is designed to pique students' interest and engage them in the process.READ AND UNDERSTAND THE PROBLEM
- Informally explore, experiment, collect dataWhen mathematicians have a problem they:Read and understand the problem.Plan a strategy to start the problem.When mathematicians become interested in a problem they:Explore the problem to collect and organise data about it.Discuss and record notes and diagrams.EXPLORE THE PROBLEM
- Form patterns in data, create conjectures, hypotheses, theoriesSeek and find patterns or connections in the organised data.Make and test hypotheses based on the patterns or connections. SEEK PATTERNS AND MAKE HYPOTHESES
- Use a toolbox of problem solving strategies to prove or disprove theoriesUse known toolbox of basic skills.Look in their skills toolbox for mathematical skills which could help.USE PROBLEM SOVLING STRATEGIES AND MATH’S SKILLS
- Extend or generalise – what else can we learn?Check their answer and think about what else they can learn from it.Can I check this another way?What happens if..?How many solutions are there?How will I know when I have found them all?LOOK FOR ALL POSSIBLE SOLUTIONS AND ‘WHAT IFS
- Publish/Communicate Publish their results.TELL – EXPLAIN HOW YOU GOT YOUR ANSWERS AND WHAT YOU HAVE LEARNT