Mathematics Framework: Instructional Strategies and Modeling June 26, :30-3:30

Outcomes/Agenda Explore multiple instructional models that will be required for successful CCSS implementation. Discuss a variety of strategies needed to support students in understanding the mathematics being addressed. Understand how different instructional strategies support the eight mathematical practices and 21 st Century skills.

Opening Task As a table group or grade span: – Select an opening task. Migdalia’s Savings (grade 2) After School Job (grades 4/5) Ms. Olsen’s Sidewalk (grade 7) Three-Second Rule (high school) – Complete the task on your own. – Share how you completed the task.

Instructional Strategies Kid Snippets “Math Class” At91D7k At91D7k

21 st Century Skills (4 C’s) Critical Thinking Collaboration Communication Creativity

Focus Shift 1: Focus Coherence Shift 2: Coherence Rigor Shift 3: Fluency Shift 4: Deep Understanding Shift 5: Application Shift 6: Dual Intensity Instructional Shifts Combined

Standards for Mathematical Practice

8 Critical Areas- Fifth Grade

Novel Ideas Activity List four instructional models/strategies that come to mind for teaching mathematics

Novel Ideas Draw a line under your list At your table group, have each person share their list If a shared idea is not on your list, add it to your list under the line you drew

Overarching Principals of Instructional Design Instruction is organized around the solution of meaningful problems Instruction provides scaffolds for achieving meaningful learning Cooper 2006

Overarching Principals of Instructional Design (continued) Instruction provides opportunities for ongoing assessment, practice with feedback, revision, and reflection The social arrangements of instruction promote collaboration, distributed expertise, and independent learning. Cooper 2006

Instructional Models Continuum Mercer and Mercer (2005) suggest that instructional models can be placed along a continuum of choices that range from explicit to implicit instruction. California Mathematics Framework - p. 9 (2013) Explicit Instruction Interactive Instruction Implicit Instruction

Explicit Instructional Models Support – Practice to mastery – Teaching of discrete skills – Development of skill and procedural knowledge

Implement Instructional Models Link information to students’ background knowledge Develop conceptual understanding Develop problem solving abilities

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 learningStudent 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 Continuum of Choices

Journal Prompt After reading the chart, reflect about where the majority of your instruction falls on the continuum.

Think – Pair - Share Based on your understanding of the Common Core, where on this continuum do you feel math instruction should be?

CA Mathematics Framework Instructional Strategies – wchapters.asp wchapters.asp

What Does the Framework Say? Read Instructional Strategies, Page 1, lines 4-9

Common Core Instruction… “The purpose of this chapter [training] is not to prescribe the usage of any particular instructional strategy, but to enhance teachers’ repertoire.” California Mathematics Framework, Instructional Strategies Chapter, p.1

General Instructional Models 5 E Model (interactive)-page 10 3 Phase Model (explicit) – page 10 Singapore Model (interactive)- page 11 Concept Attainment Model (interactive)- page 11 Cooperative Learning Model (implicit)- page 12 Cognitively Guided Instruction (implicit)- pages Problem-Based Learning (interactive)- pages 13-14

Group Presentation Choose an instructional model to explore What is it? What does it look like? When is it useful? What does the teacher do? What does the student do? Include citations for any information you discovered.

Instructional Strategies Specific to the Mathematics Classroom Discourse in the Mathematics Classroom Number Talks Five Practices for Orchestrating Productive Mathematics Discussions Anticipating Monitoring Selecting Sequencing Connecting

Instructional Strategies Specific to the Mathematics Classroom Student Engagement Strategies Appointment Clock Carousel-Museum Walk Charades Clues Coming to Consensus Explorers and Settlers Find My Rule Find Your Partner Four Corners

Instructional Strategies Specific to the Mathematics Classroom Student engagement strategies – Give One – Get One – Inside Outside Circle – Jigsaw – KWL

Instructional Strategies Specific to the Mathematics Classroom Student engagement strategies – Line up – Making a List – Numbered Heads Together – Partner Up – Quiz, Quiz Trade – Socratic Seminar – Talking Sticks

Instructional Strategies Specific to the Mathematics Classroom (continued) Student engagement strategies – Team Share Out – Think Pair Share – Think Write Pair Share – Whip Around – Wrap Around – Y-Chart

Instructional Strategies Specific to the Mathematics Classroom Review the instructional strategies Select one that is new to you and that you are willing to implement in your classroom or share with a colleague. Share with small group – State specific strategy and why you selected it.

Instructional Strategies Specific to the Mathematics Classroom Use of Tools for Mathematics Instruction ▫Visual Representations ▫Interactive Technology ▫Concrete Models ▫Concept Maps Use of Tasks Incorporating Math Practices Use of Real World Problems

Reflection How would you structure a lesson around the opening task? Refer to your Novel Ideas List, models, and instructional strategies. Think about Standards for Mathematical Practice 21 st Century Skills Share with other grade span team

Reflection How are you incorporating the Standards for Mathematical Practice into your lesson How are you incorporating 21 st Century Skills in your lesson?

Putting It All Together What is the interaction between: The Continuum The Models The Strategies

Outcomes/Agenda Explore multiple instructional models that will be required for successful CCSS implementation. Discuss a variety of strategies needed to support students in understanding the mathematics being addressed. Understand how different instructional strategies support the eight mathematical practices and 21 st Century skills.