Teaching to the New 10C Curriculum

transcript

Peter Liljedahl

Introduction – a difficult task

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?

Activity #1

How tall is Connor?

Linking ACTIVITY to CURRICULUM

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.

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

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.

The New Curriculum

Still about: specific outcomes achievement indicators

Also about: goals for students mathematical processes nature of mathematicsCONTENTCONTEXT

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

Question & Answer

finish at 10:30

start again at 10:45

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?

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

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

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

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

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

Question & Answer

finish at 12:15

start again at 1:00

Activity #3

26... if the base = n?

base = 4

How many UPRIGHT triangles are there ...

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

How many UPRIGHT triangles?tn = 1 + 2 + 3 + ... + n (triangular #

tn + tn-1 = sn (square # n)

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

How many UPRIGHT triangles?Tn = t1 + t2 + t3 + ... + tn

(tetrahedral # n)

Tn = Tn-1 + tn

Tn + Tn-1 = Pn

(pyramidal # n)

How many UPRIGHT triangles?

Pn = n(n+1)(2n+1)/6

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

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

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.

Upside Down Lesson – 10Cuse:

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.

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

Question & Answer

finish at 2:30

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

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

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

How will we know its working?Different interpretations of

behaviours:

intrinsic characteristics (you) immediate influence (me) contextual influence (the day) outside influence (life)

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!

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

Local Discussion

What will you do to prepare for teaching 10C in September?

15 minutes

Question & Answer

finish at 3:25

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!

Thank You

liljedahl@sfu.ca

finish at 3:30

Teaching to the New 10C Curriculum

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