Being a mathematician
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Being a mathematician

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Being a Mathematician

Being a Mathematician

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  • 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

Transcript

  • 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:
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  • 3. READ AND UNDERSTAND THE PROBLEM
    Describe the problem using words/symbols/diagrams.
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  • 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.
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  • 5. SEEK PATTERNS AND MAKE HYPOTHESES
    Record:
    any data collected
    patterns found
    possible hypotheses and theories.
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  • 6. USE MATHS SKILLAND PROBLEM SOLVING STRATEGIES
    List the problem solving strategies and math’s skills used.
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  • 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.
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  • 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
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  • 9. START AGAIN.
    Solve another problem using the skills and knowledge you have learnt as a mathematician.
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