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DOING MATHEMATICS

DOING MATHEMATICS. Peter Liljedahl, SFU. PROBLEM #1. If 6 cats can kill 6 rats in 6 minutes, how many cats are needed to kill 100 rats in 50 minutes?. http://commons.wikimedia.org/wiki/File:Claw.jpg. PROBLEM #1.

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DOING MATHEMATICS

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  1. DOING MATHEMATICS Peter Liljedahl, SFU

  2. PROBLEM #1 If 6 cats can kill 6 rats in 6 minutes, how many cats are needed to kill 100 rats in 50 minutes? http://commons.wikimedia.org/wiki/File:Claw.jpg

  3. PROBLEM #1 If 6 cats can kill 6 rats in 6 minutes, how many cats are needed to kill 100 rats in 50 minutes? • 200? • 13? • 12? • 50? • ...? http://commons.wikimedia.org/wiki/File:Husky_rat.jpg

  4. WELCOME • this is going to be different • challenge • opportunity • thank you facilitators • this is going to be different • challenge • opportunity

  5. ROUGH AGENDA Morning • do some problems • discuss them • small group discussion led by facilitator Afternoon • do an active read • discuss it • presentation • small group discussion led by facilitator • question/answer

  6. PROBLEM #2 Corner-to-Corner • need 9 volunteers at every site!

  7. PROBLEM #2 Corner-to-Corner • 5, 13, 21, 29, 37, ... • 4+(3x3), 6+(5x3), 8+(7x3), ... • (2+2)+3(1+2), (3+3)+3(2+3), (4+4)+3(3+4), ... • 2(n-1)+3[(n-2)+(n-3)] • t-tables, graphs, simplification → 8n-11

  8. WELLNESS BREAK

  9. REVIEW What did you notice about this morning ... • in the problems? • in yourself? • in the experience?

  10. PROBLEM #3 I LIKE WINE ... http://commons.wikimedia.org/wiki/File:Wine_barrel.jpg

  11. PROBLEM #3 I LIKE WINE ... • 45? • 55? • 100?

  12. PROBLEM #4 Four cards (A, 3, 2, 4) • put top card face up on the table • move next card to the back of the stack • repeat Five cards? Six cards? ...

  13. GROUP DISCUSSION What skills would students need in order to successfully complete these tasks or tasks like them? • Do not constrain yourself to mathematical pre-requisite knowledge – although that is important. • Attend also to meta-skills such as willingness to take risks, etc. ENJOY YOUR LUNCH!

  14. TEACHING MATHEMATICS Peter Liljedahl, SFU

  15. LOCKHART'S LAMENT* Do an active read of Lockhart's Lament: • read it • discuss it • line by line • paragraph by paragraph • section by section • whole piece • underline and highlight things of interest and importance

  16. LOCKHART'S LAMENT* • Wouldn't it be nice if these were the main goals of mathematics education (3rd to last paragraph)? • Wouldn't it be nice if these were the types of students we were able to produce (2nd to last paragraph)? • Wouldn't it be nice if curriculum was, indeed, constructed to encourage this sort of classroom atmosphere (last paragraph)?

  17. GOALS FOR STUDENTS - PSAI: page 4 - • The main goals of mathematics education are to prepare students to ... • Students who have met these goals ... • In order to assist students in attaining these goals, teachers are encouraged to develop a classroom atmosphere that fosters conceptual understanding through ...

  18. MATHEMATICAL PROCESSES - PSAI: page 6 - Students are expected to: • use communication in order to learn and express their understanding [C] • make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines [CN] • demonstrate fluency with mental mathematics and estimation [ME] • develop and apply new mathematical knowledge through problem solving [PS] • develop mathematical reasoning [R] • select and use technology as a tool for learning and for solving problems [T] • develop visualization skills to assist in processing information, making connections and solving problems [V]

  19. MATHEMATICAL PROCESSES - PSAI: page 6 - • The seven mathematical processes are critical aspects of learning, doing and understanding mathematics. Students must encounter these processes regularly in a mathematics program in order to achieve the goals of mathematics education. • All seven processes should be used in the teaching and learning of mathematics. Each specific outcome includes a list of relevant mathematical processes. The identified processes are to be used as a primary focus of instruction and assessment.

  20. WHERE IS THIS COMING FROM? WNCP, NCTM, UKS, WACF, ... Predicated on the theory that humans learn with and from: • experiences • discourse • thinking

  21. SHIFT IN CURRICULUM • the GOALS FOR STUDENTS and the MATHEMATICAL PROCESSES is now the content of the curriculum • the SPECIFIC OUTCOMES is now the context in which the content is covered content vs. context

  22. FOR EXAMPLE- corner to corner - 10C – Relations and Functions (PSAI – page 25) 4. Describe and represent linear relations, using: • words • ordered pairs • tables of values • graphs • equations • [C, CN, R, V] +[PS]

  23. BUT YOU ALREADY KNEW THAT

  24. SO WHAT DOES THIS LOOK LIKE?

  25. WHAT NEEDS TO CHANGE? • how we look at curriculum • content vs. context • students • need to think and be active participants in their learning ... (NEW TO THEM TOO!) • classroom • environment, culture, norms • teaching • stop letting student opt out of thinking • start helping students learn how to think

  26. STOP LETTING STUDENT OPT OUT OF THINKING • way in which we answer questions • types of questions we ask • how often we level • pre-requisite knowledge • the way we give and use notes • deficit model of students • assessment

  27. START HELPING STUDENTSLEARN HOW TO THINK 7 processes are thinking skills • teach them • model them • scaffold them • value them (evaluate them)

  28. BUILD YOUR OWN LIGHTSABER- examples from the edge - • boardwork • random groups • upside down lesson • student generated notes • partner quizzes • group tests http://commons.wikimedia.org/wiki/File:Lightsabers.png

  29. WELLNESS BREAK

  30. GROUP DISCUSSIONS • What are the things about the new curriculum you find the most exciting? • What are the things you find most troubling? • What are the things you find most challenging? • If you could ask Peter one question what would it be?

  31. QUESTION/ANSWER

  32. THANK YOU liljedahl@sfu.ca

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