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? Claw.jpg.

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

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

WELCOME

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

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

PROBLEM #2

Corner-to-Corner• need 9 volunteers at every site!

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

WELLNESS BREAK

REVIEW

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

PROBLEM #3

I LIKE WINE ...

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PROBLEM #3

I LIKE WINE ...• 45?• 55?• 100?

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• repeatFive cards?Six cards?...

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!

TEACHING MATHEMATICS

Peter Liljedahl, SFU

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

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)?

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 ...

MATHEMATICAL PROCESSES - PSAI: page 6 -

Students are expected to:1. use communication in order to learn and express their understanding

[C]2. make connections among mathematical ideas, other concepts in

mathematics, everyday experiences and other disciplines [CN]3. demonstrate fluency with mental mathematics and estimation [ME]4. develop and apply new mathematical knowledge through problem

solving [PS]5. develop mathematical reasoning [R]6. select and use technology as a tool for learning and for solving

problems [T]7. develop visualization skills to assist in processing information, making

connections and solving problems [V]

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.

WHERE IS THIS COMING FROM?

WNCP, NCTM, UKS, WACF, ...

Predicated on the theory that humans learn with and from: • experiences• discourse• thinking

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

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]

BUT YOU ALREADY KNEW THAT

• • • • • • • •

SO WHAT DOES THIS LOOK LIKE?

• • • • • • • •

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

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

START HELPING STUDENTSLEARN HOW TO THINK

7 processes are thinking skills• teach them• model them• scaffold them• value them (evaluate them)

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

WELLNESS BREAK

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?

QUESTION/ANSWER

THANK [email protected]