Mathematics Curriculum Evaluation Toolkit Transitioning to the Common Core May 16, 2014 Pam Tyson & Hilary Dito

Workshop Goals Review Background Documents and Information on the Common Core State Standards in Mathematics (CCSSM) with California Additions* Learn to Use Curriculum Evaluation Toolkit to Support Textbook and Other Materials Alignment with the Common Core State Standards in Mathematics with California Additions

SBAC SCORE REPORTS Achievement Levels Each level encompasses a range of student achievement. – Thorough Understanding (4) – Adequate Understanding (3) – Partial Understanding (2) – Minimal Understanding (1)

Assessment Claims for Mathematics “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” 1. Concepts and Procedures “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” 2. Problem Solving “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” 3. Communicating Reasoning “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.” 4. Modeling and Data Analysis

Mathematical Practices are cross- cutting. They relate to the content standards at ALL grade-levels Standards of Mathematical Practice

Describe the “habits of mind” of a mathematically expert student or practitioner – Standards for mathematical proficiency reasoning, problem solving, modeling, decision making, and engagement Focus on mathematical knowing (as opposed to knowledge) as a practice (activity) The California Framework Provides Grade-Level Descriptions (Grade 6, pp. 5-6) 8

Another Way to Think About Mathematical Practices 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 7.Look for an make use of structure 8.Look for and express regularity in repeated reasoning 1. Make sense of problems and persevere in solving them 6. Attend to Precision Key Reasoning & Explaining Modeling & Using Tools Seeing structure & generalizing Overarching habits of mind of a productive mathematics thinker

Grade-Level Chapter Outline Summary of the Current and Previous Grade Level Topics Review of Focus, Coherence and Rigor Cluster Level Emphases Standards for Mathematical Practice Content Standards-Based Learning Complete List of Grade Level Cluster Names and Standards

Three Shifts

Focus CDE Mathematics Framework, Overview Chapter, page 2 “Instruction should focus deeply on only those concepts that are emphasized in the standards so that students can gain strong foundational conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.”

K-8 Areas To Understand Deeply GradeKey Areas of Focus in Mathematics K-2 Place value, addition and subtraction – concepts, skills, and problem solving 3-5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional reasoning: early expressions and equations 7 Ratios and proportional reasoning: arithmetic of rational numbers 8 Linear algebra

Focus Read pages 1-3 of the Grade Six chapter of the Framework What are the implications for classroom instruction? Share one insight with a partner

Focus WHAT STUDENTS LEARN IN GRADE SIX

Standards Page(s) Domain Standard Cluster Refer to pages of the Grade Six chapter of the Framework

Focus

6 th Grade Mathematics

Activity: Cluster Emphases by Grade Turn to the Content Standards Pages in the framework chapter (Grade 6: pages 58-62) Highlight the Major Clusters green Highlight the Supporting Clusters blue Highlight the Additional Clusters yellow How do the supporting clusters and the additional clusters reinforce the major clusters?

SBAC’s 11 th Grade Mathematics CCSSM Cluster = SBAC Targets

The CCSSO Publisher Criteria has a footnote that says between 65% and 85% in K-2. “Is there sufficient focus on the major clusters for students to understand mathematical concepts, reach fluency expectations in the standards, and apply their knowledge and procedural skills and fluency to new situations?”

Standards-Based Learning At Grade 6 Turn to page 6 of 62 in the CA Frameworks Chapter. Note the different ways that content based learning is outlined in this chapter. Compare what you noticed with a partner.

Coherence CDE Mathematics Framework, Overview Chapter, page 3 “Some of the connections in the standards knit topics together at a single grade level. Most connections are vertical, as the standards support a progression of increasing knowledge, skill, and sophistication across the grades.”

25 Learning Trajectories typical, predictable sequences of thinking that emerge as students develop understanding of an idea modal descriptions of the development of student thinking over shorter ranges of specific math topics

26 Learning Trajectories learning progressions which characterize paths children seem to follow as they learn mathematics. Are too complex and too conditional to serve as standards. Still learning trajectories point to the way to optimal learning sequences and warn against the hazards that could lead to sequence errors.

Shape Composing Trajectory Based on Doug Clements’ & Julie Sarama’s in Engaging Young Children In Mathematics (2004).

Content Domains Grades K - 12

William McCallum

Mathematical Rigor Mathematical Knowing consists of a combination of a)Conceptual Understanding b)Procedural Skills c)Applications/Problem Solving

a) Conceptual Understanding Is about more than “how to get the answer.” It also includes understanding what the answer means from a number of perspectives. Students are able to see math as more than a set of mnemonics or discrete procedures. Mathematics is about sense making.

b) Procedural Skill and Fluency The standards require speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts.

c) Application in the Everyday World Provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level- appropriate math to make of and across science content.

Documents to Review Before Using the Evaluation Toolkit 1.California Mathematics Frameworks (2013) – Three Mathematics Shifts Brought on by CCSSM – Cluster-Level Emphases – Mathematical Practice Standards – Other Grade Level Content Information 2.University of Arizona’s Progressions Documents for the Common Core Math Standards 3.Smarter Balanced Assessment Consortium’s (SBAC’s) – Four Rating Levels – Four Assessment Claims for Mathematics

Three Shifts CA Mathematics Frameworks, 2013 Progressions Document

CCCOE Mathematics Curriculum Evaluation Toolkit Outline Section One: One/Two Major Topics In-Depth Section Two: The Mathematics Content Section Three: Assessments Section Four: Universal Access Section Five: Teacher Supports

SBAC SCORE REPORTS Achievement Levels Each level encompasses a range of student achievement. – Thorough Understanding (4) – Adequate Understanding (3) – Partial Understanding (2) – Minimal Understanding (1)

Reflecting on our work with the Mathematics Framework, How will the framework guide your instructional planning? What are your next steps to gain understanding in regards to implementing CCSS?