Peter Liljedahl

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The NEW curriculum – lessons learned from January BREAK Linking ACTIVITY to the CURRICULUM LUNCH Linking the CURRICULUM to ACTIVITY BREAK Implementation and beyond: HOW DO WE KNOW IT IS WORKING and WHAT NEXT? 3

How tall is Connor? 4

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1.Solve problems that involve linear measurement, using: SI and imperial units of measure estimation strategies measurement strategies. 2.Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure. 1.Solve problems that involve linear measurement, using: SI and imperial units of measure estimation strategies measurement strategies. 2.Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure. 7

1.Interpret and explain the relationships among data, graphs and situations. 3.Demonstrate an understanding of slope with respect to: rise and run rate of change 1.Interpret and explain the relationships among data, graphs and situations. 3.Demonstrate an understanding of slope with respect to: rise and run rate of change 8

4.Describe and represent linear relations, using: words ordered pairs tables of values graphs equations. 5.Determine the characteristics of the graphs of linear relations, including the: slope 4.Describe and represent linear relations, using: words ordered pairs tables of values graphs equations. 5.Determine the characteristics of the graphs of linear relations, including the: slope 9

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. 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. 10

Mathematics is one way of understanding, interpreting and describing our world. There are a number of characteristics that define the nature of mathematics, including change, constancy, number sense, patterns, relationships, spatial sense and uncertainty. 11

Mathematics education must prepare students to use mathematics confidently to solve problems. Mathematics education must prepare students to use mathematics confidently to solve problems. 12

Still about:  specific outcomes  achievement indicators Also about:  goals for students  mathematical processes  nature of mathematics CONTENT CONTEXT 13

 What is the value AND feasibility in considering both the specific outcomes and the front matter (goals for students, mathematical processes, nature of mathematics) within our teaching?  What are the consequences of not doing so? 15 minutes 14

finish at 10:30 15

start again at 10:45 16

A boy has $80 to buy 100 budgies. Blue budgies cost $3 each, green budgies cost $2 each, and yellow budgies cost $0.50 each. If he want to ensure that he has at least one budgie of each colour, how many of each colour does he need to buy? Is there more than one answer? How do you know you have ALL the solution? 17

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2-3 people identify in what ways this activity meets: goals for learning mathematical processes nature of mathematics 2-3 people identify in what ways this activity meets: specific outcomes achievement indicators SHARE and COMPARE 19

How many budgies? MATHEMATICAL THINKING 20

START  giving thinking questions  using group work  randomizing groups  using vertical work surfaces  talking about thinking strategies (different from solution strategies)  assessing thinking  evaluating what you value STOP / REDUCE  answering stop thinking questions  levelling  thinking that a lesson is about generating notes  assuming that students can't  stop emphasizing the use (and creation) of pre- requisite knowledge  using assessment as a stick 21

 WATCH THE BUILDING A CULTURE OF THINKING WEBINAR!  start on day 1  6 consecutive tasks  non-curricular  no pre-requisite knowledge needed  interesting  random groups  working on feet  take pictures 22

 How do we live with the possibility that some of these activities bring together curriculum from many different topics within 10C? 15 minutes 23

finish at 12:15 24

start again at 1:00 25

26... if the base = n? base = 4 How many UPRIGHT triangles are there...

base size 1 = 10: base size 2 = 6: base size 3 = 3:1+2 base size 4 = 1:1 triangular numbers # of triangles = the sum of the first n triangular #'s 27

t n = n (triangular # n) t n + t n-1 = s n (square # n) 28

base size 1 = 10: base size 2 = 6: base size 3 = 3:1+2 base size 4 = 1:1 triangular numbers # of triangles = the sum of the first n triangular #'s 29

T n = t 1 + t 2 + t t n (tetrahedral # n) T n = T n-1 + t n T n + T n-1 = P n (pyramidal # n) 30

P n = n(n+1)(2n+1)/6 n+1 n n 1 31

T n = T n-1 + t n → T n-1 = T n - t n T n + T n-1 = P n → T n + T n - t n = P n → 2 T n - t n = P n P n = n(n+1)(2n+1)/6 2 T n – n(n+1)/2 = n(n+1)(2n+1)/6 T n = n(n+1)(n+2)/6 SHAZAM! 32

Tetrahedral Numbers 33

 Where did this question come from?  the exercises intended for the end of a lesson  Where do I use it?  at the beginning of the lesson  Do the students figure out the problem on their own?  most figure it out to some level – few to the final formula  Do they struggle with it?  definitely  So, why do it?  they learn from their struggles  my lesson on it has more meaning to them  my lesson is more about formalizing the learning that has already happened  it is normal within my classroom UPSIDE DOWN LESSON 34

review: sin is the y-coordinate cos is the x-coordinate ask: If sin t = 0.5, 0 o < t ≤ 360 o, find t. 35

use: 36

try: 2. If sin t = -0.8, 0 o < t ≤ 360 o, find t. 3. If sin t = 1.1, 0 o < t ≤ 360 o, find t. 4. If cos t = 0.5, 0 o < t ≤ 360 o, find t. 5. If cos t = -0.65, 0 o < t ≤ 360 o, find t. 6. If cos t = 1.0, 0 o < t ≤ 360 o, find t. 7. If sin t = 0.7, 0 o < t ≤ 720 o, find t. 8. If tan t = 1, 0 o < t ≤ 360 o, find t. 9. If tan t = -0.5, 0 o < t ≤ 360 o, find t. 37

 What are YOUR challenges in making a rich task out of something as simple as: If sin t = 0.5, 0 o < t ≤ 360 o, find t. 15 minutes 38

finish at 2:30 39

start again at 2:45 40

Your behaviour on the tasks – positive engaged found solutions shared helped persevered intrinsic motivation self selected audience my obvious charm my careful selection of the task my introduction of the task your trust in me 41

Your behaviour on the tasks – negative never engaged bored tried but gave up checked socialized waited left lack of intrinsic motivation inherent anxiety fatigue distracted inappropriate task wrong set-up too much/little time impression I will give answer 42

Your behaviour on the tasks – a priori didn't come came late sat in the back sat alone end of year coaching report cards easily accessible chairs not Dan Brownesque enough wrong title wrong topic 43

Different interpretations of behaviours:  intrinsic characteristics (you)  immediate influence (me)  contextual influence (the day)  outside influence (life) 44

Different interpretations of behaviours:  intrinsic characteristics (you)  me as speaker  contextual influence (the day)  outside influence (life) I would have a source of constant feedback! 45

Use the mirror that is your classroom:  students are sensible  student behaviour is sensible (at some scale)  student behaviour is a sensible reflection of our teaching  look for thinking  look for discussion  look for engagement  look for enjoyment always remember the soccer pitch 46

 What will you do to prepare for teaching 10C in September? 15 minutes 47

finish at 3:25 48

 Everything I have told you is guaranteed to fail unless YOU think it is important enough to make it work!  This is not a PANACEA! There are other dragons to slay (assessment, didactics, notes, practice, review)!  You will enjoy teaching in a THINKING classroom!  Your students will enjoy THINKING!  Your students will LEARN! 49

finish at 3:30 50