Mathematics Instruction In the Age of Common Core State Standards

What Should Instruction Look Like? 1.Mathematical Practices in Meaningful Ways 2.A Blend of Explicit – Interactive – Implicit Instructional Strategies

CA Mathematics Framework (2013) Adopted by the State Board of Education in November 2013 Pre-publication edition available at hapters.asp hapters.asp Publication edition should be available by this Summer

What Should Instruction Look Like? 1.Mathematical Practices in Meaningful Ways 2.California Mathematics Framework (2013)  Adopted by the State Board of Education in November 2013  Pre-publication edition available at ters.asp ters.asp  Publication edition should be available by this Summer

What Should Instruction Look Like? 1.Mathematical Practices in Meaningful Ways 2.California Mathematics Framework (2013)  Adopted by the State Board of Education in November 2013  Pre-publication edition available at ters.asp ters.asp  Publication edition should be available by this Summer

After School Job(4 th /5 th Grade) Leonard needed to earn some money so he offered to do some extra chores for his mother after school for two weeks. His mother was trying to decide how much to pay him when Leonard suggested the idea: “Either you pay me $1.00 every day for the two weeks, or you can pay me 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, and so on, doubling my pay every day.”

After School Job(4 th /5 th Grade) Which option does Leonard want his mother to choose? Write a letter to Leonard’s mother suggesting the option that she should take. Be sure to include drawings that explain that will explain your mathematical thinking.

DayStart with $1 Start with 1¢ 1$11¢ 2$12¢ 3$14¢ 4$18¢ 5$116¢ 6$132¢ 7$164¢ 8$1$1.28 9$1$ $1$ $1$ $1$ $1$ $1$81.92 After School Job(4 th /5 th Grade)

Instructional Strategies Chapter The purpose of this chapter is not to prescribe the usage of any particular instructional strategy, but to enhance teachers’ repertoire.

ExplicitInteractiveImplicit Teacher serves as the provider of knowledge Instruction includes both explicit and implicit methods Teacher facilitates students learning by creating situations where students discover new knowledge and construct own meaning Much direct teacher assistance Balance between direct and non-direct teacher assistance Non-direct teacher assistance Teacher regulation of learning Shared regulation of learning Student regulation of learning Directed discoveryGuided discoverySelf-discovery Direct instructionStrategic instructionSelf-regulated instruction Task AnalysisBalance between part-to- whole and whole-to-part Unit approach BehavioralCognitive/metacognitiveHolistic Instructional Models

General Instructional Models 1.5 E Model (interactive) ▫Engage-Explore-Explain-Elaborate-Evaluate 2.3 Phase Model (explicit) ▫I do – we d0 – you do 3.Singapore Model (interactive) 4.Concept Attainment Model (interactive) 5.Cooperative Learning Model (implicit) ▫Students work together to solve a problem and provide input 6.Cognitively Guided Instruction (implicit) 7.Problem-Based Learning (interactive)

Additional Instructional Strategies Discourse in the Mathematics Classroom Student Engagement Strategies Tools for Mathematics Instruction Examples of Tasks Incorporating Math Practices Real World Problems

Evidence Centered Assessment ASSUMPTION: Assessment is the process of making an argument, based on evidence, that reasons about what students say, do or make in a particular task situation to a more general claim or inference about what they can know, do, or have accomplished ELA Claims: 1.Reading 2.Writing 3.Speaking/Listening 4.Research Math Claims: 1.Concepts and Procedures 2.Problem Solving 3.Communicating Reasoning 4.Modeling and Data Analysis

WHEN WE GET SCORE REPORTS SBAC’s Achievement Levels Each level encompasses a range of student achievement. ▫Thorough Understanding ▫Adequate Understanding ▫Partial Understanding ▫Minimal Understanding Advanced? Proficient? Basic? Below Basic & FBB?

Content Domains Grades K - 12

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

NOT YOUR MOTHER’S ALGEBRA 1 (based on sample “Traditional” pathway in CA Framework draft) These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step.” - CCSS (2010, p.5) Common Core Grade 8  Pre-Algebra  Some “1997 High School Geometry  “1997 Algebra 1A” Common Core Algebra 1  “1997 Algebra 1B”  “1997 Algebra 2A “  Some AP Statistics Topics Common Core Geometry  More “1997 High School Geometry  Transformational Geometry  Some AP Statistics Topics Common Core Algebra 2  “1997 Algebra 2B”  1997 Trigonometry  Some Math Analysis  Some AP Statistics Topics

Grade Level Chapter Outlines Introduction to the Grade Cluster Level Emphases Connecting Math Practices and Content Standards Based Learning at the Grade ▫Laid out by domain and interfaces with the shifts, emphases, and rigor

Setting Performance Standards Setting standards for four Performance Levels at each grade September 2014, using Field Test data Grade-level panels of 30 per content area recommend cut scores ▫At least two representatives from each Governing State on each grade level panel Concurrent “crowd sourced” recommendations from the field Recommendations presented to chiefs for approval in late September

6 th Grade Mathematics

3 rd Grade Mathematics

4 th Grade Mathematics

5 th Grade Mathematics

7 th Grade Mathematics

8 th Grade Mathematics

11 th Grade Mathematics