Connected Mathematics 3: Pedagogy Training
-
Upload
kerry-duran -
Category
Documents
-
view
39 -
download
2
description
Transcript of 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 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
CMP3 Program Philosophy
• Guiding Principles– Problem-centered– Big ideas in depth– Coherence– Conceptual + procedural– Concepts + skills– Inquiry-based– Effective technology– High expectations
CMP3 Program Philosophy
• 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?
CMP3: Instructional Phases
CMP3: Instructional Phases
• 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
CMP3: Instructional Phases
• 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?
CMP3: Instructional Phases
• 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?
CMP3: Instructional Phases
• 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
CMP3: Instructional Phases
• 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?
CMP3: Instructional Phases
• 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 + 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 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
CMP3 Alternate Pathways
• THE “CMP3 RECOMMENDED PROGRAM ” : – Students put on track after Grade 7
Grade 6 Grade 7
Grade 8 Algebra 1
Grade 8 On-Level
CMP3 Alternate Pathways
• 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
• 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