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Juli K. Dixon, Ph.D. University of Central Florida Empowering Learners through the Common Core State Standards in Grades K-2

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A student was asked to solve and the student did this… = 60

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A student was asked to solve and the student did this… = = 10

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A student was asked to solve and the student did this… = = = 70

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A student was asked to solve and the student did this… = = = = 73

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Perspective… We know we want students to explain and justify mathematics in these ways, but how do we get them here?

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Perspective… How is this related to the Common Core State Standards (CCSS)?

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Background of the CCSSM Published by the National Governors Association and the Council of Chief State School Officers in June 2010 Result of collaboration among 48 states Provides a focused curriculum with an emphasis on teaching for depth Consists of Content Standards and Standards for Mathematical Practice

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Background of the CCSSM Minnesota adopted the CCSS in ELA/literacy only 45 States + DC have adopted the Common Core State Standards

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Background of the CCSSM … standards must address the problem of a curriculum that is a mile wide and an inch deep. These Standards are a substantial answer to that challenge (CCSS, 2010, p. 3).

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Background of the CCSSM … standards must address the problem of a curriculum that is a mile wide and an inch deep. These Standards are a substantial answer to that challenge (CCSS, 2010, p. 3). So what do these standards look like anyway?

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Content Standards Wordle for Grades K-2

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Content Standards Define expectations for students at each grade level Use concepts from earlier grades Emphasize need to justify mathematical moves Indicate understanding and skill are equally important Include expectations that students demonstrate understanding of procedures

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Content Standards Critical Areas – describe areas of focus Domains – group related clusters Clusters – group related standards Standards – define what students should know and be able to do

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Content Standards Measurement and Data K.MD Describe and compare measurable attributes. 1.Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 2.Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Classify objects and count the number of objects in each category. 3.Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

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Content Standards Measurement and Data K.MD Describe and compare measurable attributes. 1.Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 2.Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Classify objects and count the number of objects in each category. 3.Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Domain Cluster Standard Cluster

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Perspective… One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the students mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from (CCSS, 2010, p. 4).

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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students (CCSS, 2010, p. 6) Perspective…

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The Standards for Mathematical Practice are based on: Making Sense of the Mathematical Practices The National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (NCTM, 2000), and The National Research Councils (NRC) Adding It Up (NRC, 2001).

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NCTM Process Standards: Making Sense of the Mathematical Practices Problem Solving Reasoning and Proof Communication Representation Connections

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NRC Strands of Mathematical Proficiency: Making Sense of the Mathematical Practices Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition

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NRC Strands of Mathematical Proficiency: Making Sense of the Mathematical Practices Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition

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Standards of Mathematical Practice Wordle

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

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Perspective… The following represents a recommendation from the Center for the Study of Mathematics Curriculum (CSMC, 2010)

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Perspective… Lead with Mathematical Practices 1Implement CCSS beginning with mathematical practices, 2Revise current materials and assessments to connect to practices, and 3Develop an observational scheme for principals that supports developing mathematical practices. (CSMC, 2010)

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Content Standards Counting and CardinalityK.CC Compare Numbers. 6.Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, eg., by using matching and counting strategies. Domain Cluster Standard

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Solve this…

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Perspective… What do you think Kindergarten children will do?

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Perspective… Consider how the student is allowed to struggle through a problem in this kindergarten video.

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Perspective… Are you observing this sort of productive struggle in classrooms? Is it important?

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Perspective… What does this have to do with the Common Core State Standards for Mathematics (CCSSM)?

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The 8 Standards for Mathematical Practice: With which practices were the grade K students engaged? 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning

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The 8 Standards for Mathematical Practice: 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning With which practices were the grade K students engaged?

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Perspective… In an effort to simplify students learning pathways and minimize barriers (stigler, et. al., 1999), teachers often provide students with efficient procedures too early. When we do this – we minimize students opportunities to engage in these practices.

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Reason abstractly and quantitatively 2

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Reasoning abstractly and quantitatively often involves making sense of mathematics in real-world contexts. Word problems can provide examples of mathematics in real-world contexts. This is especially useful when the contexts are meaningful to the students. 2

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Reason abstractly and quantitatively Consider the following problems: Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have all together? Jessica has 8 key chains. Alex has 15 key chains. How many more key chains does Alex have than Jessica? 2

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Reason abstractly and quantitatively Consider the following problems: Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have all together? Jessica has 8 key chains. Alex has 15 key chains. How many more key chains does Alex have than Jessica? Key words seem helpful 2

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Reason abstractly and quantitatively Consider the following problems: Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have all together? Jessica has 8 key chains. Alex has 15 key chains. How many more key chains does Alex have than Jessica? Key words seem helpful, or are they…. 2

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Reason abstractly and quantitatively Now consider this problem: Jessica has 8 key chains. How many more key chains does she need to have 13 key chains all together? 2

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Reason abstractly and quantitatively Now consider this problem: Jessica has 8 key chains. How many more key chains does she need to have 13 key chains all together? How would a child who has been conditioned to use key words solve it? 2

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Reason abstractly and quantitatively Now consider this problem: Jessica has 8 key chains. How many more key chains does she need to have 13 key chains all together? How would a child who has been conditioned to use key words solve it? How might a child reason abstractly and quantitatively to solve these problems? 2

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Reason abstractly and quantitatively Consider this problem: Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have all together? I know that = 16, so… 2

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Reason abstractly and quantitatively Consider this problem: Jessica has 8 key chains. Alex has 15 key chains. How many more key chains does Alex have than Jessica? I know that = 16, so… 2

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Reason abstractly and quantitatively Now consider this problem: Jessica has 8 key chains. How many more key chains does she need to have 13 key chains all together? 8 + __ = 13 (How might making a ten help?) 2

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Reason abstractly and quantitatively What happens when this child gets to 2 nd grade? 2

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Consider this Kindergarten class. With which Standard(s) for Mathematical Practice are they engaged? Empowering Young Learners

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Consider this Kindergarten class. What did you notice? Empowering Young Learners

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The 8 Standards for Mathematical Practice: With which practices were the grade K students engaged? 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning

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The 8 Standards for Mathematical Practice: With which practices were the grade K students engaged? 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning

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Use appropriate tools strategically This practice supports hands-on learning This practice supports hands-on learning Tools must include technology Tools must include technology Tools also include non-technological tools such as manipulatives, number lines, and paper and pencil Tools also include non-technological tools such as manipulatives, number lines, and paper and pencil Mathematically proficient students know which tool to use for a given task. Mathematically proficient students know which tool to use for a given task. 5

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The 8 Standards for Mathematical Practice: With which practices were the grade K students engaged? 1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look for and make use of structure 8Look for and express regularity in repeated reasoning

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Construct viable arguments and critique the reasoning of others 3 What does this look like in a grade K- 2 class? How can we be intentional about providing opportunities for students to engage in this practice?

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Consider this: Empowering Young Learners

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Consider this: Was the language you used in talking through the solution precise? Empowering Young Learners

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

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Consider this: I heard a student say this… Empowering Young Learners

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Attend to precision Consider this: 6 Does our math talk sound more like this?

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

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How do we support the transition to the Common Core? Teachers need content knowledge for teaching mathematics to know the tasks to provide, the questions to ask, and how to assess for understanding. Teachers need content knowledge for teaching mathematics to know the tasks to provide, the questions to ask, and how to assess for understanding. Math Talk needs to be supported in the classroom. Math Talk needs to be supported in the classroom. Social norms need to be established in classroom and professional development settings to address misconceptions in respectful ways. Social norms need to be established in classroom and professional development settings to address misconceptions in respectful ways.

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Juli K. Dixon, Ph.D. University of Central Florida Empowering Learners through the Common Core State Standards in Grades K-2

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