Math Instructional Leadership Cadre Session 1 September 21 st and 23 rd

Math Instructional Leadership Cadre

Session 1September 21st and 23rd

Year 2 – The Big Picture

Problem Solving with the Standards for Mathematical

Practice

~ MPS 1 & 6 ~ Session 1: MPS 2 & 3 Session 2: MPS 4 & 5 Session 3: MPS 7 & 8

Deeper Understanding

1. Collegial Discussions2. PARCC Tasks3. Balanced Assessment

* Lesson Study *

What does a classroom look like and sound like when all students are

engaged in learning mathematics?

1) Odd or Even?2) Flag your part.3) Read the intro.4) Read your parts.5) Take notes.6) Read conclusion.7) Share with your partner.

3-bullet notes:

Summary Statement

Supporting Detail

Example

Never Say Anything a Kid Can Say

Never Say Anything a Kid Can Say

Big Ideas

Partner Reflections

Classroom Application

Collegial Discussions

Mutually respectful conversations between student colleagues in a group or classroom environment

provide a structure for those conversations

Discussion Sentence Stems

Agreement

I agree with ______ because _____.

I like what _____ said because _____.

I agree with ____ because _____; then on the other hand _____.


Disagreement

I disagree with ____ because ____.

I’m not sure I agree with that because _____.

I can see that _____; however, I disagree with (or can’t see) ______.


Clarifications

Could you please repeat that for me?Could you explain that a bit more, please? I’m not sure I understood you when you said _____. Could

you say more about that? Is there evidence for the position?


Confirmation

I hear _____.

I believe ______.

I discovered ______.

I learned that ______.


Confusion

I don’t understand _____.

I am confused about ______.

Can you explain that another way?

I have a questions about _____.


Extension

I was thinking about what _____ said, and I was wondering what if _____.

This makes me think _____. I want to know more about ______. Now I am wondering _____. Can you tell me more about _____?


Review

I want to go back to what _____ said.

I like _____.

I noticed that _____.

Mathematical ProficiencyAdding It Up

What makes a student mathematically proficient?

“Students must learn mathematics with understanding, actively building new knowledge from experience and

prior knowledge.”

Mathematically proficient students:Conceptual UnderstandingProcedural FluencyStrategic CompetenceAdaptive ReasoningProductive Disposition

Conceptual understanding

comprehension of mathematical

concepts, operations, and

relations

Procedural Fluency

skill in carrying out procedures flexibly,

accurately, efficiently, and appropriately

Strategic Competence

ability to formulae, represent, and

solve mathematical

problems

Adaptive Reasoning

capacity for logical thought,

reflection, explanation, and

justification

Productive Disposition

habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own

efficacy

Standards for Mathematical Practice


1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Common Core Standards for Mathematical Practice

Overarching Habits of Mind

MP1 Make sense of problems and persevere in solving them.

MP6 Attend to precision.

Reasoning & Explaining

MP2 Reason abstractly and quantitatively.

MP3 Construct viable arguments and critique the

reasoning of others.

Modeling & Using Tools

MP4 Model with mathematics.

MP5 Use appropriate

tools strategically.

Seeing Structure & Generalizing

MP7 Look for and make use of

structure.

MP8 Look for and express regularity in

repeated reasoning.

Frayer Model

DefinitionCharacteristi

cs

Example Non-Example

MP1 Make sense of problems and persevere in solving them.

Work to make sense of your problem.

Make a plan.Try different approaches.

productive strugglestrategy, planning, effort,

not giving up

How many different plans do you have in your group?

Explain them.I can do it. Sí, se puede.

I think I can. I think I can.I think I can…

I quit.

MP1


cs

Example Non-Example

MP1 Make sense of problems and persevere in solving them.Productive Struggle: “Students are more likely to retain what they learn when they expend effort solving problems that are within reach and grappling with key mathematical ideas that are comprehensible but not yet well formed.” Carnegie Foundation for the Advancement of Teaching 2013

MP6 Attend to precision.

Communicate your mathematical thinking clearly and precisely.Be accurate when you

count, measure, & calculate.

accuracy, vocabulary, attention to detail

vocabulary word wall, peer editing

“What’s another word for that?”

“How might you label the answer?”

“that thing”numbers w/o labels

“The number on the top of the fraction…”

MP6


cs

Example Non-Example

MP2 Reason abstractly and quantitatively.

Explain the meaning of numbers, words, pictures, symbols, tables, graphs,

and concrete objects.

contextualize & decontextualize,

in & out of context

Singapore bar model,“What do the numbers

used in the problem represent?”

“This shows…”

“Ours is not to reason why, just invert and multiply.”

MP2


cs

Example Non-Example

MP3 Construct viable arguments and critique the reasoning of others.

Explain both what to do and why it works.

Work to make sense of others' mathematical

thinking.

communicate, back it up, prove it

I agree with Paco, because…

I see it a different way…What evidence do you see

to support…?What I hear you saying is…

a silent classroom

MP3


cs

Example Non-Example

Resources to Deepen Understanding

Frayer Model


(Commentary & Elaboration for K-5)

Problem Solving Tasks

Classroom Implementation Guides

Deepening Our Understanding

Questions to Consider

How does the task elicit that Practice Standard?

How can the practices be used to influence instruction?

Supporting Mathematical Proficiency

Through Student Talk in the Classroom

Provide time for and facilitate discussion Encourage and facilitate students in justifying their conclusions,

communicating, and responding to others Ask questions to clarify and improve students’ arguments Expect precision in communication (written and oral) Provide a variety of tools and technology Provide opportunities to look for patterns

Supporting Mathematical Proficiency

Through Problem Solving Provide time to think and problem solve Encourage students to check answers using different methods Provide problems that require flexible use of objects and properties

of operations Provide situations that apply to everyday life Focus on conceptual understanding Provide a variety of tools and technology Provide opportunities to look for patterns

Lesson Study

If you want to improve instruction, what could be more obvious than collaborating with fellow teachers to plan, observe, and reflect on lessons? Catherine Lewis, 2002

If you want to build pedagogical knowledge, what could be more obvious than collaborating with fellow teachers to design and study lessons?

Cerbin & Kopp, 2006

What is Lesson Study? PLC structure, originated in Japan A means to learn about subject matter, teaching, and

students By collectively crafting coherent, effective standards-

based lessons & assessments

Student Outcomes: increase learning on a specific topicTeacher Outcomes: deepen knowledge of content,

pedagogy, & student thinking

Lesson Studyplanning

teaching

observing

reflecting

Teaching improvement cycle

Examine practice to become more

effective

Cycle develops habits of self-reflection and

critical thinking

Benefits of Lesson Study

Think Think carefully about the goals of a particular lesson, unit, and discipline.

Study Study the best available curriculum materials.

Deepen Deepen knowledge of subject matter and of instruction.

ConnectThink carefully about long-term goals for students and connect those with daily practice.

Strengthen Strengthen collaboration with colleagues.

Develop Develop the eyes to see students.

Easy Steps to Engage in a Complex Process

Form a lesson study group

Conduct the research lesson and colloquium

Consolidate learning. Plan next steps.

Form a lesson study group

4 to 6 teachers is optimal

Develop ground rules for working together

Team members need trust, commitment, and a willingness to participate

Focus the lesson study Identify a specific content goal

Identify the content area Select a specific topic within that content area

Fundamental to subsequent learning Persistently difficult for students Difficult to teach New to the curriculum

Identify a broad, long-term goal for student development Where do you want students to be five to ten years down the road? What is the gap between these qualities and who they are now? Examples: become active learners, enjoy subject-area, become aware of

their own learning

Plan the research lessonCreating a plan to guide learning

1. Lesson Goal2. Unit Goals3. Broad, subject-area goals4. Long-term goals for student development

Study existing possibilities and build on the best available Consider the whole unit – lessons don’t occur in isolation Anticipate student thinking – ideas, road bumps, and potential responses

Plan the research lesson

Construct a Data Collection Plan

How does each element of the lesson support or interfere with learning?

What did the student say, do, and hear?Pinpoint methods to collect students’ nonverbal behavior

and activities

The research lesson

Goal: improve the teachingEngage in instruction

Take note of students’ learning, responses, and outcomesPay attention to “points of

notice”

Colloquium

Consolidate learning. Plan next steps.

Structured protocolFree discussion & reflective

questionsShare data on students’

responsesWhat motivated students’

learning?

Reflective Questions for Colloquium What aspects of our lesson study work are valuable? What aspects

are challenging?

How is lesson study helping us develop our knowledge of subject matter and of student learning and development?

How is lesson study leading us to think in new ways about our everyday practice?

References for Lesson Study (2015). Powerful Designs for Professional Learning.

Oxford, OH: Learning Forward. Schmoker, M. (2006). Results Now. Alexandria, VA:

ASCD.

Documents

Math Instructional Leadership Cadre Session 1 September 21 st and 23 rd