MATH STUDY and WORKING GROUPS Provoking and Co-Constructing Collective Knowledge and Mobilization through Inquiry and Study

A Practice-Embedded Professional Learning Framework for Studying Mathematics for Teaching

presented by Debby Culotta, Kathy Kubota-Zarivnij and Nancy Palarchio

Toronto Catholic DSB July 4, 2013 (9:00-10:15; 10:45-12:00pm)

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Introductions From Toronto Catholic District School Board •  Nancy Palarchio – special education teacher at

Epiphany of Our Lord •  Debby Culotta – principal at St. Andrew’s Catholic

School) •  Kathy Kubota-Zarivnij – former principal of Epiphany of

Our Lord Catholic Academy; currently principal of program coordinator, K to 12 Mathematics

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Agree or Disagree? AIM of Mathematics Professional Learning

•  To improve student engagement, learning and achievement in mathematics

•  To improve instruction in mathematics •  To develop and support practice-embedded professional

learning networks among teachers, principals/vice-principals, mathematics consultants/coordinators and superintendents, associate director, and director of education

Math Study and Working Groups … an inquiry-study-action framework of learning, collective knowledge production, and system-wide knowledge mobilization

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GOAL - What should teachers and principals know and be able to do mathematically as a result of effective mathematics professional learning?

-Adaptive knowledge of mathematics; principals – facilitator’s process of being able to ask questions and collectively probe mathematics; at least some understanding of mathematical trajectories and more indepth for teachers; varying degrees of understanding knowledge of mathematics (Mathematics for Teaching – mathematics content, students, learning, mathematics teaching) -Critical for administrators to understand the culture of mathematics and think in a mathematical way (reasoning, proving, communication with precision and clarity) – level of comfort and a positive disposition towards mathematics -Learning mathematics and using mathematics to learn (where it starts to fall) -Prepare yourself mathematically (read curriculum, math resource like M Small Big Ideas -Big ideas no matter of the context of mathematics (mathematical processes) -principals - create a culture of a learning stance; all co-create learning orientation – stick with the learning

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ACTION - What should effective mathematics professional learning for teachers and principals be like?

-  Stem from the student desk to be meaningful, appropriate and timely for the adults in the room (for the kids)

-  Differentiated on many levels, based on experience; different pieces for different people

-  Start with observation first (lived experienced), to alleviate anxieties, then come back out to debrief, to wonder and be curious and go back it – first part of the inquiry process that they can question and talk about

-  (e.g., Teachers identified need in numeracy – became focus of the PLC group)

-  Action being iterative – difference between the models depending on what the needs are – whatever it is we are doing, we are refining it, rather than changing topics for deeper questions

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What are Some Challenges In Implementing Mathematics Professional Learning? •  Sufficient time and scheduling of professional learning for

teachers and for principals over a period of time •  Consistent participation of principals and superintendents in the

professional learning sessions •  Sufficient funds for occasional teacher support •  Sufficient occasional teacher support •  Multiple initiatives •  sufficient human resources with specialized knowledge of

mathematics for teaching (especially smaller boards) •  Coherence in understanding system needs for mathematics

professional learning – •  What does differentiated professional learning look like

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What’s the Difference Between a Math Workshop and a Math Study Group? From our math study groups … Collective Knowledge Production

•  Outcome – is greater in a study group because we are capitalizing on everyone’s experience and knowledge and skills

•  Not mutually exclusive – both overlap, but it is how you present

•  More hands on – back to classrooms and try out strategies and come back and discuss to refine Collaborative, participant lead – shared ownership;

•  Apply in actual class setting

•  Scientific approach – come up with something to do, apply it, record it analyze it and see if it works

•  Focus on research – read literature and think about it how it would work with our students

•  Workshop is an event; inquiry or study is a process – regular meetings .. Once every month …

•  Inquiry – thinking and analyzing – feedback GUIDES next study session

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During this session, we will: •  compare metaphors used for designing and implementing

mathematics educational practices to provoke re-conceptualizating of mathematics education in classrooms, schools and district school boards

•  become familiar with a system-wide organization of an inquiry-study-action framework for mathematics professional learning

•  explore a few practice-embedded mathematics professional learning strategies

TCDSB context - based on 3 years of family of schools math study groups and one year of system wide implementation of math study groups and math working groups (K/1, 2/3, 5/6, 7/8 and 9/10)

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Compare the Metaphors for Learning, Curriculum, Teaching, Collective Knowledge Production and Knowledge Mobilization

Linear Metaphor Dynamic Network Metaphors

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Linear Metaphors for Learning, Curriculum, Teaching, Collective Knowledge Production and Knowledge Mobilization

•  Linear metaphors depict learning mathematics as being cumulative over time from month to month and grade to grade

•  Expects students to learn within this linear trajectory (which in reality is not actualized in regular class curriculum or in IEPs) … How helpful is it for a student in grade 8 to have an IEP math focus of grade 5, going into grade 9?

•  Mathematics curriculum is conceived as a checklist of math concepts and skills to learn over time towards end of the year goals

•  Evokes ideas like gap closing and gap narrowing to address situations where some of the mathematics is not accumulated over time – a catch-up cycle never realized Linear Metaphor

Comparing Network Metaphors - Learning, Curriculum, Teaching, Collective Knowledge Production and Knowledge Mobilization

Centralized network has efficient information flow, no interconnections among information

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Distributed network has inefficient information flow, with several interconnections among information

Decentralized network provides multiple interconnections among information (clusters) and efficient information flow through nodes

Decentralized Network Metaphor - Learning, Curriculum, Teaching, Collective Knowledge Production and Knowledge Mobilization

•  Multiple and simultaneous interactions

•  Multiple sources of data simultaneously generated which facilitates inter-related data analysis and feedback

•  Differentiated learning/working/communication sites and pathways

•  Nodes in decentralized networks are sites of collective knowledge production and knowledge mobilization

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Using Decentralized Network Metaphor Re-Conceptualizing Learning, Teaching, Curriculum, Special Education and Other Educational Constructs

Decentralized network metaphor provides a generative and dynamic model for: •  Mathematics learning/teaching – focus on making connections

between concepts and strategies in relation to significant mathematical concepts (nodes) to deepen understanding (strengthening the net through interconnections)

•  Mathematics curriculum – rather than a checklist of expectations, learning trajectories are landscapes with possibilities for multiple pathways for making connections (derived from the creativity and innovation of students’ and teacher’s mathematical thinking and understanding); consider IEP writing, not at one grade level, but across grade level to significant mathematical concepts at age appropriate grade

•  Collective knowledge production and knowledge mobilization across different levels of the system, simultaneously for ongoing feedback loop for continuous improvement

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Differentiating Practice-Embedded Mathematics Professional Learning for System-Wide Knowledge Mobilization - TCDSB 2013-2014

•  (1) Math Study Groups – teachers, principals, superintendent, LNS – self selected school improvement focus of math for grades K/1, 2/3, 5/6, 7/8, or 9/10

•  (2) Math Study Groups (Sites of Collaboration) teachers, principals, superintendent, LNS – self selected school improvement focus of math for grades K/1, 2/3, 5/6, and 7/8; 7-10 or 9/10; K to 12 study group (NEW!);

•  (3) Principal Math Study Groups – principals, LNS, CPCO •  (4) Math Working Groups – classroom teachers, SPED

teachers, Assessment and Programming teachers, principals, Math Dept, superintendent for Differentiated Mathematics Intervention (DMI)

•  (5) Focus Math Learning Sessions – for schools that select literacy as a school improvement focus KKZ, 2013

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Math Study and Working Groups - Underlying Beliefs •  Action is a great restorer and builder of confidence. Inaction is

not only the result, but the cause, of fear. Perhaps the action you take will be successful; perhaps different action or adjustments will have to follow. But any action is better than no action at all. - Norman Vincent Peale

•  If you’re speaking and not getting a reaction, well, you are just making a speech. - Author Unknown

•  Do not wait for extraordinary circumstances to do good action; try to use ordinary situations. - Jean Paul Richter

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Underlying Premise – KAIZEN (改善) •  Japanese term for continuous improvement of processes; ("kai") which means

"change" or "to correct" and 善 ("zen") which means "good”. •  Western philosophy, "if it ain't broke, don't fix it” in contrast to Kaizen philosophy to

"do it better, make it better, improve it even if it isn't broken •  a system of continuous improvement in quality, technology, processes, company

culture, productivity, safety and leadership. •  large-scale pre-planning and extensive project scheduling are replaced by smaller

local experiments, which can be rapidly adapted as new improvements are suggested; process of making changes, monitoring results, making adjustments

•  Japanese companies (e.g., Toyota and Canon – 60 to 70 suggestions per employee per year are recorded, shared and implemented for continuous improvement

Kaizen develops a culture of action for continuous, aligned, small local improvements through improving standardization of processes and continuous feedback loop to eliminate “muda” (waste) (only value-added activity) … yielding significant quality and productivity improvement … “go to the gemba” (site of work – classroom/school)

Math Study Group Roles and Responsibilities

•  Classroom and SPED teachers

•  Principals and Vice-Principals

•  Host Teacher(s), Host

Principal /Vice-Principal, Math Consultant/ Coordinator, Superintendent

•  Implement classroom strategies, gather and analyse evidence of student learning, co-teach, provide feedback for study group planning, record reflections

•  Implement classroom and school strategies, monitor and analyse evidence of student learning, co-teach, provide feedback for study group planning, record reflections

•  Co-plan, prepare, and/or co-facilitate study sessions, co-teach with teachers and principals/vice-principals KKZ, 2013

Math Study Group - Outcomes (Nancy(SET/MLT)) What have we learned to do?

Mathematically -  Not a math person (now is a math person,

over 3 year period now), knowledge of math and developed capacity to teach mathematics -> new found love of mathematics transfers to classroom); awareness and research of learning trajectory

-  Study, learn more mathematics -  Neurons firing – could feel the difference

viscerally, imagine what happens in child’s brain

-  Collaboration – banter ideas to find something greater, strategies throughout day

Inquiry/Study/Action -  Perseverance to solve a

problem, to figure it out in different ways

-  Motivated and stamina for perseverance – in classroom (SPED using 3 part problem solving, bansho (board-writing) to think and reason critically without reliance on facts we can bridge it (co-teach)

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Math Study Group - Outcomes (Debby (P)) What have we learned to do?

Mathematically • Not a math person (am a

math person now), • Mathematical learning that

didn’t have as a student, developed in 3 years and still learning

• Co-teaching to learn mathematics through teaching and interacting with students

• Uses math resources like Big Ideas (Small) always to prepared

Inquiry/Study/Action •  work in groups – risk free, all contribute, learn

from one another’s ideas •  Developed a professional learning culture with

other schools •  Extended learning with the staff – working

together constantly – doing the math, anticipate ways that students approach the math, better able to identify mathematical learning and needs and see how they connect and use them in the lesson;

•  engaged, motivated participants to try and task risks to learn and analyse results to make further improvements

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Math Study Group - Outcomes (KKZ (PMC)) What have we learned to do? (Mathematically, Inquiry/Study)

Mathematically •  Prepare mathematical annotations

for board writing and recording details in assessment for learning seating plan tool using curriculum expectations, Big Ideas from Dr. Small and math education research articles

•  Focus, precise lesson planning (the selection of 3 problems: Before, During and Practice) and discerning the learning trajectory within a lesson and across a series of lessons in relation to student need

Inquiry/Study/Action •  Ask questions to clarify and

deepen understanding to achieve precision

•  Seek out multiple perspectives to get breadth and depth of mathematical and pedagogical understanding and application

•  Listen actively to conceive mathematical details and make mathematical connections to discern relationships

•  Knowledge mobilization of inquiry/study findings in different ways KKZ, 2013

Math Study Group - Outcomes Artifacts and Teaching/Learning Actions

•  Researched lesson plans, assessment for learning tools, student work samples to lesson problems

•  Bansho (board writing) layout planned, implemented and recorded

•  Hypothetical teaching/learning trajectory for a mathematics concept, derived through analysis of a range of student solutions to a problem and knowing of mathematics for teaching

•  Ongoing and focused practice in implementing teaching strategies (e.g., three-part problem solving lesson, bansho (board writing), questioning, coordinating class discussion)

•  Precision in co-teaching moves •  Processes for collective knowledge

production and knowledge mobilization during a public research lesson

•  Strategies for lesson design and classroom implementation, school-wide teacher inquiry/study across system

•  Teacher and principal leadership in mathematics in Sites of Collaboration (e.g., math study group and work group facilitation, public research lessons, workshop and conference presentations)

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What Professional Learning Strategies Did We Use to Achieve These Outcomes? •  Do math as a teacher •  Goal setting and monitoring •  Prepare oneself mathematically •  Selecting Lesson Problems in relation

to Lesson Learning Goals •  Preparing the Mathematical

Organizational Criteria, Mathematical Annotations

•  Anticipating Highlights/Summary (Success Criteria)

•  Co-constructing success criteria derived from the mathematics in students’ solutions in relation to lesson learning goal

•  Noticing and Analysing Mathematics in Students’ Solutions

•  Anticipating and Researching Learning Trajectories (NEW!)

•  Examining Bansho (Board-Writing) for math details in relation to students’ emergent thinking

•  Communicating Mathematics with Precision

•  Public Research Lesson with co-teaching

•  Co-Teaching Moves in relation to Co-Teaching Trajectory (KKZ, 2011)

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Goal Setting and Monitoring - SAMPLE What Questions Do You Have?

Teaching Math Through problem Solving to a Diverse Set of Students? -  How do we develop students’

mathematical talk or discourse in the classroom?

-  How do we get students to be on the task and persevere?

-  How do students learn to listen critically and pay attention to class discussion?

Bansho (Board Writing) - How do I organize the students’ solutions for learning? - What do I annotate mathematically and how to do it concisely? - What resources can I use to help me to know what to annotate? - How do students (and teacher) learn to read the board and not be overwhelmed … is less more?

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What do WE Want to Study? - SAMPLE Our Inquiry Learning Goals – Look for Relationships TCDSB Board Improvement Plan – Learning Goal, Success Criteria, Descriptive Feedback •  Understand and use teaching through problem solving using

the three part problem solving lesson design (Before, During, After (Consolidation), After (Highlights/Summary), After (Practice)

•  Develop ways to prepare for bansho (board-writing) •  Use bansho (board-writing) to record co-construction of

success criteria in relation to lesson learning goal •  Co-Construct descriptive feedback throughout the lesson to

improve student reasoning and understanding of mathematics

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Strategic Organization of Strategies Math Study Group Framework (CIL-MfT)

nested, iterative system of learning (Before, During, After)

Before

During

After

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Math Study Group Monthly Framework

BEFORE (Activation of Knowledge and Experience) •  Goal setting and monitoring •  Observations and queries from classroom implementation •  Student work sample analysis from teacher’s classroom in pairs, small groups and as whole

group to practise noticing and articulating the mathematics in the solutions

DURING (Working On It) •  Do math to study (solving problem in different ways, analyzing and describing mathematically the

range of solutions, review resources/research articless, constructing bansho (board-writing)) •  Preparation for Co-Teaching Public Research Lesson (solve math for each lesson problem,

solve and analyze lesson problems, anticipate the range of solutions and mathematical relationships between the solutions, develop bansho plan

•  Co-Teaching Public Research Lesson (lead voice, board-writer, bansho whisper, inside/outside researchers)

AFTER (Consolidation, Highlights/Summary, Practice) •  Student work samples analysis from public research lesson •  Discussion of public research lesson, in terms of teaching through problem solving using

bansho, co-teaching moves •  Highlights/Summary for classroom and school implementation strategies

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Math Study Group (or CIL-MfT) Based on KKZ’s PhD Research

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Strategic Organization of Strategies Math Working Group Framework (CIL-MfT)

nested, iterative system of learning (Before, During, After)

Before After

During Preparation for Math Working Session

Before – Goals, Research focus findings to date, Classroom Work

During – study math content and pedagogy connected to research foci, public research lesson, specialized research group discussion/writing

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After – Research work update, highlight/summary implementation focus

Mathematics Working Session

Classroom and School Implementation and Practice - practise instructional practices (3 part problem solving lesson design, bansho (board-writing)

- Coteach with colleagues to study students’ mathematical thinking and instruction in relation to research focus

- continue research search

Collaborative Inquiry for Learning “Mathematics for Teaching”

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Math Working Group Monthly Framework

BEFORE (Activation of Knowledge and Experience) •  Goal setting and monitoring; revisiting of research and writing framework •  Observations and queries from classroom implementation and the results of research focus

group work •  Student work sample analysis from teacher’s classroom in pairs, small groups and as whole

group to practise noticing and articulating the mathematics in the solutions

DURING (Working On It) •  Do math to study (solving problem in different ways, analyzing and describing

mathematically the range of solutions, review resources/research articles, constructing bansho (board-writing))

•  Identifying connections to research/writing focus; posing questions to further research) •  Specialized research focus group – discussion and analysis of articles, resources in relation

to classroom implementation and inquiry questions posted

AFTER (Consolidation, Highlights/Summary, Practice) •  Discussion of research work in progress by research focus groups •  Highlights/Summary for classroom and school implementation strategies •  Continue research literature searches and readings

Highlights/Summary Math Study Group - School Strategies •  Do math as a teacher •  Goal setting and monitoring •  Prepare oneself mathematically •  Lesson Co-Planning - Selecting

Lesson Problems in relation to Lesson Learning Goals; Preparing the Mathematical Organizational Criteria Mathematical Annotations and Highlights/Summary (Success Criteria)

•  Co-constructing success criteria

•  Noticing and Analysing Mathematics in Students’ Solutions

•  Anticipating and Researching Learning Trajectories (NEW!)

•  Examining Bansho (Board-Writing)

•  Communicating Mathematics with Precision

•  Co-Teaching Moves in relation to Co-Teaching Trajectory

•  Public Research Lesson KKZ, 2013

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Math Study and Working Groups is based on Gemba Kaizen - Action Oriented for Continuous Improvement of Learning and Teaching Mathematics

•  I am only one, but still I am one. I cannot do everything, but still I can do something; and because I cannot do everything, I will not refuse to do the something that I can .

- Edward Everett Hale

•  Nobody made a greater mistake than he/she who did nothing because he/she could do only a little. - Edmund Burke

Kaizen develops a culture of action for continuous, aligned, small local improvements through improving standardization of processes and continuous feedback loop to eliminate “muda” (waste) (only value-added activity) … yielding significant quality and productivity improvement … “go to the gemba” (site of work – classroom/school)

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Keep In Touch! Lets collaborate and learn together … •  nancy.palarchio@tcdsb.org •  debby.culotta@tcdsb.org •  kathryn.kubota-zarivnij@tcdsb.org

You are welcome to come to: Epiphany of our Lord Catholic Academy (3150 Pharmacy Ave., Scarborough) or St Andrew Catholic Elementary (2533 Kipling Ave., Rexdale), to be part of a 3-part problem solving lesson, bansho (board writing), public research lesson, math study groups, or math working group

CONTACT KKZ