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

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 Discussions 2. PARCC Tasks 3. 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

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 _____.

Discussion Sentence Stems 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) ______.

Discussion Sentence Stems 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?

Discussion Sentence Stems Confirmation  I hear _____.  I believe ______.  I discovered ______.  I learned that ______.

Discussion Sentence Stems Confusion  I don’t understand _____.  I am confused about ______.  Can you explain that another way?  I have a questions about _____.

Discussion Sentence Stems 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 _____?

Discussion Sentence Stems Review  I want to go back to what _____ said.  I like _____.  I noticed that _____.

Mathematical Proficiency Adding 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 Understanding  Procedural Fluency  Strategic Competence  Adaptive Reasoning  Productive 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

Frayer Model DefinitionCharacteristics ExampleNon-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 struggle strategy, 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 quit. MP1 DefinitionCharacteristics ExampleNon-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 DefinitionCharacteristics ExampleNon-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 DefinitionCharacteristics ExampleNon-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 DefinitionCharacteristics ExampleNon-Example

Resources to Deepen Understanding Frayer Model Standards for Mathematical Practice (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 topic Teacher Outcomes: deepen knowledge of content, pedagogy, & student thinking

Lesson Study planningteachingobservingreflecting 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. Connect Think 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 groupFocus the lesson studyPlan the research lessonConduct the research lesson and colloquiumConsolidate 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 lesson Creating a plan to guide learning 1. Lesson Goal 2. Unit Goals 3. Broad, subject-area goals 4. 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 teaching Engage in instruction Take note of students’ learning, responses, and outcomes Pay attention to “points of notice” Colloquium Consolidate learning. Plan next steps. Structured protocol Free discussion & reflective questions Share data on students’ responses What 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.