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**Silicon Valley Math Initiative Professional Development Series**

NUMBER Santa Cruz County, September 2012

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**Agenda Lunch Math Talk MARS Performance Assessment tasks**

Welcome and Introductions Goals and Norms Problem of the Month (POM) Common Core - Math Practices Performance Assessment introduction Formative Assessment Lesson (FAL) Math Talk MARS Performance Assessment tasks Evaluation 8:30-8:35 Welcome/Introductions 8:35-8:45 Goals and Norms 8:45-10:00 POM – do the math, posters (justification & status) 10:00-10:15 break 10:15-10:40 CCSS MP – read/discuss, connect POM posters to MP 10:40-11:00 MP questioning sort; article – questioning 11:00-11:15 gallery walk with post-its (think about questioning) 11:15-11:30 debrief POM 11:30-11:45 Performance assess intro; do FAL pre-assess 11:45-12:30 lunch 12:30-1:45 FAL 1:45-2:00 Math talk 21x19 (difference of two squares) 2:00-2:15 debrief math talk and read/discuss articles 2:15-2:45 MARS 2:45-3:00 wrap-up and evaluation Lunch

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**Goals To advance teachers’ own understanding of mathematics**

To enhance teachers’ pedagogical knowledge in teaching mathematics

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Norms Reflection: Think of a time when you worked well with others (in collaboration). How would you describe that experience and what made it successful for you? Think of a time when you had a negative experience working in a group. How would you describe that experience and what made it negative for you?

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Norms Identify norms: From your reflection, identify norms you feel need to be in place to foster a community of learners. Share ideas at your table. Be prepared to share whole-group.

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**Problem of the Month (POM)**

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**Doing Mathematics Making Sense by Hiebert et al**

Ideas, expressed by any participant, have the potential to contribute to everyone’s learning and consequently warrant respect and response…. Examining an idea thoughtfully is the surest sign of respect, both for the idea and the author.” Making Sense by Hiebert et al

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**Why a Problem of the Month (POM)?**

George Polya, said, “A problem is not a problem if you can solve it in 24 hours.” Doing math is solving non-routine problems. Perseverance and learning from mistakes are important attributes of good mathematicians.

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How are the POMs used? The POMs are used school-wide to promote problem solving Each problem is divided into five levels, A-E, to meet the learning development needs of all students. A great tool for Differentiated Instruction. Students, teachers and parents learn to ask questions and persevere in solving non-routine problems. The whole school celebrates doing mathematics at school.

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**POM: “Measuring Up” Individually, read through all the levels.**

Then, go back to Level A and start working on the tasks in order. When everyone has had an opportunity to think through the mathematics, then you can begin to collaborate.

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**Creating Posters You will create 2 group posters…**

Your concluding thoughts on an explanation poster for a level you feel you have completed. AND Your current thoughts on a status poster for a level you are still exploring.

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Explanation Poster: The focus of your poster should be on how your findings can be justified mathematically and how your findings make sense. Include words and visuals (such as drawings) as a part of your justification. Status Poster: The focus of your poster should be on your processes so far and where you think you want to go next and/or questions/wonderings you have about this level. Include words and visuals as a part of your justification. *Remember to justify or explain your processes you have used so far and why they make mathematical sense as clearly as you can.

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NORMS for Gallery Walk Discussion is focused on what each of us can learn from each other Be respectful of ALL work The FOCUS of a gallery walk is on the MATHEMATICS of the problem.

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Gallery Walk Protocol Start by looking at EXPLANATION posters for the level you worked on. Are the explanations clear? Have the groups made a viable argument? If they aren’t, what question might your group ask that will push for more precise explanation? (Write your question on a post-it. Notice others’ questions.) Next look at STATUS posters of the level you worked on. Compare and contrast people’s way of thinking on those posters to your own way of thinking. Finally, visit posters of a different level than yours. Compare and contrast.

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**Quick Write What would you like to remember about this POM….**

As a learner, what are you interested in further exploring for your own learning? As a teacher what should you consider when using this POM with students?

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Break

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Math Talks A daily routine

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Math Talks A daily ritual with the entire class for the purpose of developing conceptual understanding of and efficiency with numbers, operations and mathematics. (approximately 10 minutes per day) Math Talks are used to: Review and practice procedures and concepts Introduce concepts and properties about numbers Reinforce procedures and number concepts. Explore mathematical connections and relationships.

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**Math Talk Norms We share ideas and listen to others**

We ask “why does this work” until we understand. We respect one another's opinions We know that we learn from mistakes as well as from correct answers Our goal is for the students, the teacher and the mathematics to agree in the end!

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**Performance Assessments and Formative Assessment Lesson (FAL)**

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**Overview of Performance Assessments**

Purposes: To make sense of student thinking To flush out misconceptions To design instruction Desired responses: students’ explanations of their solution strategies Promotes multiple solutions strategies

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**Formative Assessment Lesson**

“Proportion and Non-proportion Situations” Outline: Give pre-assessment. Use pre-assessment results to inform instruction – do not “correct” student work. Implement lesson. Students return to their original assessment task and try to improve their own responses.

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Lunch

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**Formative Assessment Lesson (FAL)**

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**MARS Performance Assessments**

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**Performance Assessments To Inform Instruction And Measure Higher Level Thinking**

The Mathematics Assessment Resource Service (MARS) is an NSF funded collaboration between U.C. Berkeley and the Shell Centre in Nottingham England. The Assessments target grades 2- Geometry and are aligned with the State and NCTM National Math Standards.

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**Performance Assessments To Inform Instruction And Measure Higher Level Thinking**

Ramp Top Entry level - (access into task) Core Mathematics - (meeting standards) Top of the Ramp - (conceptually deeper, beyond) Core Access

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**A Look at a Progression of MARS Tasks**

Familiarize yourself with the tasks Quiet Think Time What is the mathematics in each of the tasks? What are the mathematical connections between and among these tasks? What misconceptions might students have when completing the task? Each table group will have an opportunity to talk about these questions. Share out to the whole group.

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**Common Core State Standards**

Standards of Mathematical Practice

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**Mathematical Practice**

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

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6. Attend to precision

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**Connecting POM to Math Practices**

Record on your posters which Math Practices you most used. Label any specific examples of these Math Practices on the posters.

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**Research Article “Questioning Our Patterns of Questioning”**

Read the article silently. Be prepared to discuss.

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Evaluation What did you find valuable? OR What will you use right away? What would you like more support with? OR What suggestions do you have?

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