Connected Mathematics 3: Pedagogy Training

Connected Mathematics 3: Pedagogy Training

Daniel Anderson, Senior EditorMarta Miko, Marketing Manager

December 9, 2013

Introduction to CMP3

• History:– CMP curriculum development 1991-1997– CMP2 revision 2000-2006– CMP3 published in 2010-2013

CMP3 Authors

CMP3 Program Philosophy

• Core Beliefs:– A focus on the big ideas and the connections among

them– Teaching through student-centered exploration of

mathematically rich problems– Using continuous assessment to inform instruction


• Guiding Principles– Problem-centered– Big ideas in depth– Coherence– Conceptual + procedural– Concepts + skills– Inquiry-based– Effective technology– High expectations


• Criteria for Mathematical Tasks: – Embeds important, useful mathematics– Promotes conceptual and procedural knowledge– Builds on and connects to other important

mathematical ideas– Requires higher-level thinking, reasoning, and problem

solving– Engages students and promotes classroom discourse– Allows for various solution strategies– Creates an opportunity for teacher to assess student

learning

CMP3: How Does It Work?

• Pedagogical Strategies:– Effective Questioning– Cooperative Groups– Active Participation– Situational Context– Written Expression

CMP3: How Does It Work?

• Instructional Phases: Three-Part Lesson– Launch: Present the Problem!

– Explore: Solve the Problem! – Summarize: Discuss solutions to the Problem!

CMP3: Instructional Phases

• Launch: Connecting to Prior Knowledge:– Clarify prior definitions– Review old concepts– Connect the Problem to students’ past experiences

• PREPARATION QUESTIONS:– What prior knowledge do my students need to build on?– How can I use that information to support this Problem?

• Launch: Presenting the Challenge:Help students understand:– the Problem setting– the mathematical context– the challenge

• PREPARATION QUESTIONS:– What are students expected to do?– What do the students need to know to understand the context of

the story and the challenge of the Problem?– What difficulties for students can I foresee?– How can I help without giving away too much of the Problem

solution?


• Launch: Video



• Explore: Providing for Individual Needs:Move about the classroom to– Observe individual performance– Encourage on-task behavior– Ask appropriate questions– Provide confirmation and redirection where needed– Differentiated Learning: students who are struggling and

Going Further


• Explore: PREPARATION QUESTIONS:– How will I organize the students to explore this Problem? Individuals, pairs,

groups, whole class?– What materials will students need?– How should students record and report their work?– What different strategies can I anticipate they might use?– What questions can I ask to encourage student conversation, thinking, and

learning?– What questions can I ask to focus their thinking if they become frustrated or off-

task?– What questions can I ask to challenge students if the initial question is

“answered?”– What difficulties are students having?– How can I help without giving away the solution?– What strategies are students using? Are they correct?– How will I use these strategies during the Summarize?


• Explore: Planning for the Summarize:– What evidence do I have from the Explore that can be

used to support student understanding of the Focus Question during the Summarize?

– How will I organize the discussion?– What will I do if I have insufficient evidence to support

the Summarize?


• Summarize: Orchestrating the Discussion:– Guide students to reach the mathematical goals of the

Problem– Connect new understanding to prior mathematical goals– Begin when most students have made sufficient progress– Students present and discuss their solutions and strategies– Help students enhance their conceptual understanding of

the mathematics– Students refine strategies into efficient, effective,

generalizable problem-solving techniques or algorithms


• Summarize: PREPARATION QUESTIONS :– How can I help students make sense of and appreciate the variety

of methods that may be used?– How can I orchestrate the discussion so that students summarize

their thinking about the Problem?– What questions can guide the discussion?– What concepts or strategies need to be emphasize?– What ideas do not need closure at this time?– What definitions or strategies do we need to generalize?– What connections and extensions can be made?– What new questions might arise and how do I handle them?– What can I do to follow up, practice, or apply the ideas after the

Summarize?


• Summarize: Reflecting on Student Learning :What evidence do I have that students understand the

Focus Question?– Where did my students get stuck?– What strategies did they use?– What breakthroughs did my students have today?How will I use this to plan for tomorrow? For the next time

I teach this lesson?Where will I have the opportunity to reinforce these ideas

as I continue through this Unit? The next Unit?

CMP3: ACE

• The ACE Concept:– Applications – Connections– Extensions

• Homework assignments

• Bell-ringer question• Opener activity

CMP3 + Practice Standards



CMP3 + CCSSfMC

• Considerations for Revisions:– Research and data

feedback from CMP2

– New content and moved content for CCSSM alignment

– Data feedback, field trials, and revisions of new CMP3 materials

CMP3 + CCSSfMC

CMP3 + CCSSfMC

CMP3 Grade 8 Algebra I

• CMP3 offers two paths through Grade 8: Grade 8 and Grade 8 and Algebra I

Grade 8 Content Standards• 8.F.A.1 Understand that a function is a

rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

• 8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Algebra 1 Content Standards• A-REI.D.10 Understand that the graph of

an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve.

• F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

CMP3 Grade 7 Accelerated

• How About the Accelerated Grade 7 Path?– This is not a "recommended" use of CMP3 but rather

information for customers who want to know which CMP3 content corresponds to the Appendix A 7th Grade Accelerated Pathway

– The 7th Grade Accelerated Pathway content is covered in the following Units and Investigations:

• All Grade 7 Units• Grade 8 Looking for Pythagoras: Investigations 2, 3, and 4• Grade 8 Growing, Growing, Growing: Investigations 1 and 5• Grade 8 Say It With Symbols: Investigations 1, 2, and 3• Grade 8 Butterflies, Pinwheels, and Wallpaper: all Investigations

CMP3 Alternate Pathways

• WITH A REGULAR PROGRAM: – Students stuck on a track after Grade 6

Grade 6

Grade 7 On-Level

Grade 7 Accelerated Grade 8 Algebra 1

Grade 8 On-Level


• THE “CMP3 RECOMMENDED PROGRAM ” : – Students put on track after Grade 7

Grade 6 Grade 7

Grade 8 Algebra 1

Grade 8 On-Level


• THE “CMP3 ACCELERATED TRACK” : – Students grouped by ability after Grade 6 – Then, students are re-assessed at the end of Grade 7

Grade 6

Grade 7 On-Level

Grade 7 Accelerated Grade 8 Algebra 1

Grade 8 On-Level

CMP3 vs CMP2

What did our customers LIKE about CMP2?

• Built on feedback from teachers• Common Core-aligned TOC

– No extraneous content– Grade-level alignment with CCSS– Reduced language load

• Carefully curated suite of digital tools

CMP3 vs CMP2

CMP3 vs CMP2

• Technology Toolbox:– Teacher Place– Teachability Teacher Community– Student Place– Skills Practice with MathXL for School

CMP3 vs CMP2Instructional Features CMP2 CMP3

Renowned authorship team Problem-centered curriculum that fosters reflective learners through discussion of solution methods

Three-part lesson structure: Launch, Explore, Summarize

Inquiry-based learning ACE (Applications, Connections, Extensions) homework questions

Mathematical Practices serve as the pedagogical fabric of the program

TOC aligned by grade level to Common Core domains, clusters, and standards

Interactive Class and Student Management features in Dash

Optional: Personalized Skills Practice powered by MathXL

CMP3 vs CMP2

Components CMP2 CMP3

Investigations: print Student Editions (units, single bind, English, Spanish)

Investigations: print Teacher’s Guides

Interactive digital Student Edition (ACTIVe-book – English ONLY)

Interactive Teacher’s Guide with additional point-of-use teaching resources (Dash)

Program Implementation and Overview Guide Program Resources in print Online Teacher Community Assessments CD with ExamView® Teacher Resource DVD Manipulatives Kits

CMP3 Pedagogy Training

Your questions?

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Connected Mathematics 3: Pedagogy Training