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Teaching to the New 10C Curriculum Peter Liljedahl
Teaching to the New 10C Curriculum
Peter Liljedahl
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Introduction – a difficult task
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Overview – a plan for the day
The NEW curriculum – lessons learned from JanuaryBREAKLinking ACTIVITY to the CURRICULUMLUNCHLinking the CURRICULUM to ACTIVITYBREAKImplementation and beyond: HOW DO WE KNOW IT IS WORKING and WHAT NEXT?
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Activity #1
How tall is Connor?
How tall is Connor?
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Linking ACTIVITY to CURRICULUM
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Learning Outcomes – pg. 19
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.
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Learning Outcomes – pg. 24
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
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Learning Outcomes – pg. 25
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
Mathematical Processes – pg. 6
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
Nature of Mathematics – pg. 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
Goals for Students – pg. 4
Mathematics education must prepare students to usemathematics confidently to solve problems.
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The New Curriculum
Still about: specific outcomes achievement indicators
Also about: goals for students mathematical processes nature of mathematicsCONTENTCONTEXT
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Local Discussion
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
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Question & Answer
finish at 10:30
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BREAK
start again at 10:45
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Activity #2
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?
How many budgies?
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Linking ACTIVITY to CURRICULUM
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
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What is attainable?
How many budgies?
MATHEMATICAL THINKING
Building a culture of THINKING
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
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Building a culture of THINKING 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
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Local Discussion
How do we live with the possibility that some of these activities bring together curriculum from many different topics within 10C?
15 minutes
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Question & Answer
finish at 12:15
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LUNCH
start again at 1:00
Activity #3
26... if the base = n?
base = 4
How many UPRIGHT triangles are there ...
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How many UPRIGHT triangles?base size 1 = 10:
1+2+3+4base size 2 = 6:
1+2+3base size 3 = 3:
1+2base size 4 = 1: 1
triangular
numbers
# of triangles = the sum of the first n triangular #'s
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How many UPRIGHT triangles?tn = 1 + 2 + 3 + ... + n (triangular #
n)
tn + tn-1 = sn (square # n)
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How many UPRIGHT triangles?base size 1 = 10:
1+2+3+4base size 2 = 6:
1+2+3base size 3 = 3:
1+2base size 4 = 1: 1
triangular
numbers
# of triangles = the sum of the first n triangular #'s
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How many UPRIGHT triangles?Tn = t1 + t2 + t3 + ... + tn
(tetrahedral # n)
Tn = Tn-1 + tn
Tn + Tn-1 = Pn
(pyramidal # n)
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How many UPRIGHT triangles?
Pn = n(n+1)(2n+1)/6
n+1
n
n
1
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How many UPRIGHT triangles?Tn = Tn-1 + tn → Tn-1 = Tn - tn
Tn + Tn-1 = Pn → Tn + Tn - tn = Pn → 2Tn - tn = Pn
Pn = n(n+1)(2n+1)/62Tn – n(n+1)/2 = n(n+1)(2n+1)/6
Tn = n(n+1)(n+2)/6
SHAZAM!
How many UPRIGHT triangles?
Tetrahedral Numbers
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Linking CURRICULUM to ACTIVITY 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 classroomUPSIDE DOWN
LESSON
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Upside Down Lesson – 10Creview:
sin is the y-coordinate
cos is the x-coordinate
ask: If sin t = 0.5, 0o < t ≤ 360o, find t.
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Upside Down Lesson – 10Cuse:
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Upside Down Lesson – 10Ctry:2. If sin t = -0.8, 0o < t ≤ 360o, find t.3. If sin t = 1.1, 0o < t ≤ 360o, find t.4. If cos t = 0.5, 0o < t ≤ 360o, find t.5. If cos t = -0.65, 0o < t ≤ 360o, find t.6. If cos t = 1.0, 0o < t ≤ 360o, find t.7. If sin t = 0.7, 0o < t ≤ 720o, find t.8. If tan t = 1, 0o < t ≤ 360o, find t.9. If tan t = -0.5, 0o < t ≤ 360o, find t.
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Local Discussion
What are YOUR challenges in making a rich task out of something as simple as:
If sin t = 0.5, 0o < t ≤ 360o, find t.
15 minutes
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Question & Answer
finish at 2:30
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BREAK
start again at 2:45
How will we know its working?
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
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How will we know its working?
Your behaviour on the tasks – negative
• never engaged• bored• tried but gave up• checked email• 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
How will we know its working?
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
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How will we know its working?Different interpretations of
behaviours:
intrinsic characteristics (you) immediate influence (me) contextual influence (the day) outside influence (life)
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How will we know its working?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!
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How will we know its working?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
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Local Discussion
What will you do to prepare for teaching 10C in September?
15 minutes
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Question & Answer
finish at 3:25
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Final Word 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!
