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Welcome! Please arrange yourselves in groups of 6 so that group members represent: A mix of grade levels A mix of schools 1

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2 Core Matters Mathematics Session 1 October 2009 Session 1 October 2009

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Considering Who We Are: That’s Me! Please stand if the statement applies to you. 3

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Considering Our Work: Hopes and Fears As you consider your role in Core Matters Mathematics: ● What concerns or fears do you have for this work? ● What hopes do you have for this work? 4

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Community Agreements ● Stay focused on goals and purposes ● Challenge ideas, not others; share airtime ● Be willing to take risks ● Phrase questions and responses for the benefit of everyone ● Take care of your own needs, physically and intellectually ● Be respectful of our time together by keeping electronic devices either off or on vibrate ● Start and end on time 5

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6 Core Matters Mathematics Goals ● Develop a comprehensive view of robust mathematics learning ● Deepen our knowledge of how students develop both conceptual and procedural understanding of number and operations ● Explore the learning trajectory for arithmetic to algebraic thinking ● Enhance our classroom practices to support ALL learners in accessing rich, important mathematics ● Incorporate enhanced instructional and assessment strategies into classroom practice

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Focus for Today ● How does work with arithmetic develop algebraic thinking? ● What is mathematical proficiency? ● What do we know about how students learn mathematics? ● How do our mathematics program materials support students’ development of mathematical understanding? 7

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Consecutive Sums ● 1, 2, 3 ● 24, 25 ● 100, 101, 102 ● 1 + 2 + 3 = 6 ● 24 + 25 = 49 ● 100 + 101 + 102 = 303 ● 2, 4, 6 ● 1, 3, 5 ● 4, 7 8

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Consecutive Sums Your task: Explore consecutive sums involving whole numbers. Look for patterns and make conjectures. ● Spend a couple of minutes working individually on the problem. ● On cue, continue working with group. ● When prompted, prepare a poster of your findings. 9

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Consecutive Sums Some Suggestions ● Look at specific cases: You might try to find all the ways to write each number from 1-35 as a consecutive sum. ● Questions to consider: What numbers are impossible? What numbers can be written as a consecutive sum in more than one way? What patterns do you see? 10

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Consecutive Sums: Learnings ● Take a few minutes to look at the posters. Note similarities and differences. ● By describing patterns and generalizations in their own words, students are building the foundation for algebraic thinking. 11

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Adding It Up: Helping Children Learn Mathematics ● Product of 18-month project that synthesized the rich and diverse research on mathematics learning ● Research from teaching and learning, cognitive psychology and mathematics education ● Turn and talk: What does it mean for a student to be mathematically proficient? 12

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Overview ● Read Overview (pp. 1-3 in packet) ● Turn and Talk: How does this align with your original thinking about mathematical proficiency? 13

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Mathematical Proficiency: What It Means for Anyone to Learn Mathematics Successfully

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Strands of Mathematical Proficiency Strands of Mathematical Proficiency: Use a jigsaw to read and discuss the strands of mathematical proficiency 1: Conceptual Understanding 2: Procedural Fluency 3: Strategic Competence 4: Adaptive Reasoning 5: Productive Disposition 6: Properties of Mathematical Proficiency 15

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Why Should We Care? ● Fewer than 40% of DPS students are proficient in mathematics. ● There is a 35 point achievement gap between our African-American and Latino students and their Anglo and Asian- American peers. ● Students who have historically been less successful in school have the most potential to benefit from instruction focused on mathematical proficiency. 16

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Why Should We Care? ● The currency of value in the job market today is more than computational competence. ● Rather, it is the ability to Apply knowledge to solve problems Adapt acquired knowledge Learn new concepts and skills Apply mathematical reasoning View mathematics as a useful tool that must constantly be sharpened. Adding It Up 17

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Connections to Consecutive Sums Where do you see the strands of mathematical proficiency in the Consecutive Sums problem? ● Consider individually ● On cue, discuss in your small group 18

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Lunch Please return at: 19

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20 How Students Learn: Mathematics in the Classroom A 4 Protocol ● What Assumptions does the author of the text hold? ● What do you Agree with in the text? ● What do you want to Argue with in the text? ● What parts of the text do you want to Aspire?

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Applying the Principles Create a visual representation of your assigned Principle: ● What would the Principle “look like” in action in a classroom? ● What would the Principle “sound like” in action in a classroom? 21

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Personal Reflection Journal: What are the implications for your practice? 22

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Connections to Consecutive Sums How were the Principles embodied in the Consecutive Sums task? ● Consider individually ● On cue, stand up-pair up 23

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Needs Assessment In preparation for future Core Matters Mathematics sessions, please individually complete the Needs Assessment 24

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Following Break Return to grade-level groups 25

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Connections to Our Mathematics Program Materials ● Individually, study your Everyday Math’s Teacher’s Guide: ECE—Lessons C.14 and N.4 Kindergarten—Lessons 3.5 and 1.14 Grade 1—Lesson 3.1 ● With a partner, look for how the activity supports students’ development of mathematical proficiency what we know about how students learn mathematics 26

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Connections to Our Mathematics Program Materials ● Individually, study your Everyday Math’s Teacher’s Guide: Grade 2—Lesson 4.1 Grade 3—Lesson 4.1 ● With a partner, look for how the activity supports students’ development of mathematical proficiency what we know about how students learn mathematics 27

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Connections to Our Mathematics Program Materials ● Individually, study your Everyday Math’s Teacher’s Guide: Grade 4—Lesson 4.1 Grade 5—Lesson 4.1 ● With a partner, look for how the activity supports students’ development of mathematical proficiency what we know about how students learn mathematics 28

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Next Steps ● Analyze an Everyday Mathematics Open Response task For Strands of Mathematical Proficiencies For Principles from How Students Learn Mathematics ● Collaborate with other teachers Predict challenges for your students and discuss how to provide access Consider what prerequisite skills are needed 29

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Next Steps Bring to November’s session: 5 student papers (unscored/ungraded) that represent different levels of student work in your classroom 30

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