“I am new to my school this year. I had little understanding before this project as to what the instructional knowledge and/or experience was of the J/I staff at THIS school. This opportunity provided me with better insight into staff knowledge, understanding and comfort levels with math instruction. This opportunity also gave staff a chance to see me (the principal) as a learner. Working together to learn about math instruction brought us closer together. We know each other as educators at a deeper level, barriers were broken down. This opportunity will have a direct impact on my instructional leadership for years to come.” -Principal

Our Journey

Before we start…

• Describe a mathematician.

• Describe an effective mathematics class.

A question…

• What 1 thing do you want your students to get better at?

Why?

• to create a theory of action– Identify the thing we’re going to do differently– Identify the thing we want to improve in students

• to know who we’re working with• to unearth staff values to each other• to begin to create a community of learners

and a vision for our journey

What is the Best Buy? (Fosnot)

Bob’s Best Buy

This Week Only!

12 cans for $15.00

Maria’s Pet Emporium

Super Sale

20 cans for $23.00

Bob’s 12 cans $15.00

Maria’s 20 cans $23.00

Bob’s 15 ÷ 12 = 1.25

Maria’s 23 ÷ 20 = 1.15

I would shop at Maria’s

A

Bob’s 12 cans $15.00

Maria’s 20 cans $23.00

Bob’s 12 x 5 = 60 15 x 5 = $75.00

Maria’s 20 x 3 = 60 23 x 3 = $69.00

I would shop at Maria’s

B

Bob’s Maria’s

Cans $

1 1.25

2 2.50

3 3.75

6 7.50

12 1524 30

48 60

60 75

Cans $

1 1.15

2 2.30

5 5.75

10 11.50

20 2340 46

60 69

80 92

C

Bob’s 12 cans $15.00

Maria’s 20 cans $23.00

Bob’s 12 ÷ 15 = 0.8

Maria’s 20 ÷ 23 = 0.87

I would shop at Maria’s

D

Maria’s Bob’s

20 cans12 cans

$23 $15

E

Bob’s 12 cans $15.00

Maria’s 20 cans $23.00

At Bob’s once I have paid a dollar per can I have $3 left.

At Maria’s once I have paid a dollar per can I have $3 left.

I would shop at Maria’s because the three dollars over 20 cans is a better deal than three dollars spread over 12 cans. The extra cost above $1 is less per can at Maria’s than at Bob’s.

3/20 < 3/12

F

Bob’s Maria’s

12 cans 20 cans 20-12 = 8

$15.00 $23.00 23-15 = 8

At Maria’s you get 8 more cans for $8.

That would be $1 per can for the extra cans if the first 12 cans cost the same as they cost at Bob’s.

But, since I know that the 12 cans for $15 cost more than $1 per can, then I know Maria’s is a better deal.

G

A Graph?H

A Different Graph?I

Why?

• Deepen our understanding of mathematics• CIL-M model allows for both development of

mathematics and mathematics for teaching knowledge

• Co-teaching lessons creates discussions– I didn’t understand what he was trying to say– I wouldn’t have asked that question– I wouldn’t have waited that long

Professional Development

In Class PD• SUM (many cycles of 1 teacher for 2 year

period – 6 years)• School Based SUM (30 schools – 5 half days)• CIL-M (60 schools – 6 days)• CIL-M (69 schools – 5 days)

What are the conditions that we need to pay attention to?

• Classroom embedded • Research supported• Teacher driven• Over time• Collaborative (A climate that encourages risk-

taking)• ‘Knowledgeable’ other

Bruce. C. (2010). Research Summary for Mathematics Working Group and Research Panel. Trent University

Professional Development

Workshop PD• Coaches’ Sessions• Fosnot Institutes (math team, coaches,

teachers, administrators, superintendents)• From Patterns to Algebra In-service• Content Sessions• DreamBox

Balance• Not every lesson will be problem-based

• But all questions need to promote student thinking not impose teacher thinking

• Effective questioning and appropriate wait time can significantly impact student learning

• Individual practice of concepts developed through problems is a critical component of a balanced program

Why?

• to model our belief in using research findings and research-based resources

• to set the stage for the learning journey and honour the time/collaborative nature/ commitment/etc. that is needed

• to differentiate this learning model from previous forms of professional development

• to build and model a mathematics community• because the math matters!

Where we’re headed

Questioning/Conferring

• What a teacher is thinking:– What mathematical knowledge did you see/hear?– What is the evidence?– What do you think they know?– What are they about to discover?– Should I keep watching, say/ask something or walk

away?– If I’m going to say/ask something, what should it be?

Is it about conceptual understanding or calculations?

Why?

• Questioning/conferring is a skill that is improved by content knowledge and practice

• Questioning seems to be the thing that many of our experienced teachers are struggling with (their inquiries are leading our journey)

Our Journey

1. Focus on mathematics2. Coordinate and strengthen mathematics leadership.3. Build understanding of effective mathematics instruction.4. Support collaborative professional learning in mathematics.5. Design a responsive mathematics learning environment.6. Provide assessment and evaluation in mathematics that

supports student learning.7. Facilitate access to mathematics learning resources.

Monitoring…

• What evidence did we see today which supported our theory of action?– When did we see students being mathematicians?– When did we see students reasoning?

• What did you learn today?– Wait time is really important– ALL students can learn– Students will discover what you wanted to tell them– Do fewer problems more deeply

Monitoring - Survey

Student build on one another’s ideas without continuous teacher intervention. (+)

I use research based big ideas in mathematics to inform my instruction. (+)

I don’t assign many open-ended tasks because I feel unprepared for unpredictable results and new concepts that may arise. (-)

I rely fairly heavily on a textbook. (-)

Teacher Reflections

• I was able to help students see next steps by asking questions instead of telling them how to do things.

• I use more wait time.• Practicing giving feedback through questioning, not fixing but

exploring.• I am more willing to seek advice from colleagues.• The students were better able to clarify their understanding

of problems presented and ask better questions of their peers, challenging rather than sitting back and letting answers be whatever was said.

• The students are more willing to take risks.

Administrator Reflections

• It was wonderful to see how the math talk was so significant to assessing student understanding and planning next steps.

• Gave me background knowledge/info to help planning PLCs and gave me a gauge of where we are in terms of accomplishing goals in SIP

• Having deeper conversations about problem-based instruction. PLC discussions are much richer and more specific.

• The time staff spent together built relationships, built comfort level of having other staff in the classroom and provided a model staff can continue with.

In some languages, learning and teaching are the same word. If learning doesn’t happen, there has been no teaching. The actions of

learning and teaching are inseparable.

Catherine Twomey Fosnot, 2002

In case we missed it…

• Always focus on the mathematics!!!• Continue to develop everyone’s mathematical

and mathematics for teaching knowledge • Mostly job-embedded professional learning• Build community through the work we do• Strong math team• The experiences are important, not just

sharing them

Discuss/Question/Reflect

Consider your own journey with regards to these principles.