Common Core State Standards for Mathematics, Foundational Overview of the Common Core State Standards for Mathematics, Facilitator Handbook
Common Core State Standards for Mathematics © 2011
Foundational Overview of the Common Core State Standards for Mathematics
Professional Development
Facilitator Handbook
— SAMPLER —
Pearson School Achievement Services
Common Core State Standards for Mathematics © 2011
Foundational Overview of the Common Core State Standards for Mathematics
Facilitator Handbook
Published by Pearson School Achievement Services, a division of Pearson, Inc.
1900 E. Lake Ave., Glenview, IL 60025
© 2011 Pearson, Inc.
All rights reserved.
Printed in the United States of America.
ISBN 115469
Contents
Materials Checklist 3
Facilitator Agenda 5
Preparation and Background 8
Introduction 11
Section 1: Along the Way to Common Standards 13
Section 2: Teach Less, Learn More 24
Section 3: From Standards to Classroom Practice and Assessment 41
Reflection and Closing 51
References 53
Materials Checklist
Computer / N/A / Note 1 / X / X / 1 each / No
Projector / N/A / X / X / 1 total / No
Speakers / N/A / X / 1 total / No
PowerPoint / N/A / X / 1 total / No
Videos / N/A / Note 2 / X / 3 total / No
Participant Workbook / N/A / X / X / 1 each / Yes
Posters/charts / N/A / Note 3 / X / 1 set to reuse / No
Common Core State Standards for Mathematics / N/A / Note4 / 1 per participant / X / 1 per participant / Yes
Chart paper / N/A / 1 pad / Yes
Markers / N/A / 1 set per table / 1 set per table / No
Highlighters / N/A / 1 per participant / 1 per participant / No
Index cards / N/A / Set out 4 per table for Slide 19 (Optional Activity).
Provide extras if you use them for name tents. / 3 per participant / X / 2 packs / Yes
Sticky notes / N/A / Distribute 1 pad per table. / X / 1 pad per table / Yes
Tape / N/A / Use this item to hang charts. / X / 1 roll / Yes
Scissors / N/A / X / 1 pair per table / No
Timer / N/A / Use a timer to ensure pacing during activities and break. / X / No
Spinners
(optional) / N/A / Make (will need large paper clips) or buy 6 section spinners. (See Slide 59.) / X / 1 for every 2 participants / Yes or No
(It depends if spinners are made or purchased.)
Sticker dots in two different colors / N/A / X / 2 dots per participant / Yes
Timeline Cards / N/A / Note5 / X / X / 1 set per table / No
CCSSM Domain Sorting Cards and Answer Key / N/A / Note6 / X / X / 1 set per table / No
PARCC and SBAC documents / N/A / Note7 / X / X / 2–3 per table / No
*Product materials must be ordered by consultant and used for on-site workshop purposes. Participants must be notified prior to workshop that they must bring suggested materials.
Note1 The school district needs to provide a workshop room with a computer for the facilitator. Prior to the workshop, the facilitator should obtain information about how to log in to the system. The facilitator should also confirm that PowerPoint is installed on the computer, and that the computer has Internet access. If the facilitator wishes to use his or her personal computer during the workshop, he or she needs to obtain permission from the district’s Technology Department. Participants can use their personal laptops to explore the Common Core State Standards for Mathematics (CCSSM) if needed.
Note2 Make sure that the videos used in this workshop are in the same folder as the PowerPoint. Be sure to watch the videos and think about possible responses prior to the workshop and check the links in the PowerPoint the morning of the workshop.
· Videos
o Section 1—Phil Daro: How Do You Create Better Standards in Math?
o Section 2—Felisha Video
o Section 3—John Van de Walle: Approach to Teaching
Note3 There is an electronic copy of each of the posters used in this workshop in the Additional Resources folder. As an alternative to creating each chart by hand, you can print them off and have them enlarged to poster size. Charts included in the Additional Resources folder are listed below:
· Section 1
o K-W-L Chart
o 1983 Trainer Chart
· Section 2
o CCSSM Chart
· Section 3
o Reflecting on Implications for Implementation Chart
Note4 The Common Core State Standards are in the warehouse and will be shipped to the workshop site prior to the workshop. Please check with to ensure materials have been shipped. Please contact the school to ensure that materials have arrived.
Note5 The Timeline Cards can be found in the Additional Resources folder. Copy one set of the timeline cards for each table. Printing them on card stock will allow them to be reused.
Note6 The Domain Sorting Cards and Answer Key can be found in the Additional Resources folder. Copy one set of the Cards and one Answer Key for each table. The facilitator can print them on card stock for reuse.
Note7 Copy two to three sets of each document per table. If you copy them on colored paper and ask participants to return them, you can reuse them in each workshop. This will reduce the number of copies needed in the future and help the environment. If participants want their own copies, they can access them online. You can find these documents in the Additional Resources folder.
District- and Teacher-Provided Materials
Ask the district to provide the following materials:
· Workshop room with a computer for the facilitator (if necessary)
· One copy of the CCSSM for each participant
Facilitator Agenda
Foundational Overview of the Common Core State Standards for Mathematics
Section / Time / Agenda ItemsIntroduction / 15 minutes / Slides 1–3
· Introduction and Welcome
· Outcomes
· Agenda
1: Along the Way to Common Standards / 90 minutes / Slides 4–20
· Section 1 Big Questions
· Introduction
o Activity: K-W-L Chart
o Activity: 1983 Chart
o Activity: Critical Documents Timeline
· Common Ground for the Common Core
o Activity: Partner Talk
· Making Sense of Mathematics
o Activity: Math Tasks (K–5 example and 6–12 example)
· Long-Standing Importance
· Mathematical Proficiency Reflection
o Activity: Jigsaw
· International Benchmarking
· College and Career Readiness
· Phil Daro on Common Core Standards
o Video: Phil Daro—Creating Better Standards in Math
· Review Section 1 Big Questions
Break / 15 minutes
2: Teach Less, Learn More / 75 minutes / Slides 21–38
· Section 2 Big Questions
· Overview of the Common Core Standards for Mathematics
o Activity: CCSSM Chart
o Activity: The CCSSM Are/Are Not
· Toward Greater Focus and Coherence
· Grade-Level Standards
o Activity: Standards Card Sort Activity
· Bloom’s Taxonomy and Depth of Knowledge (DOK)
o Optional Activity: Identify the DOK Level
Lunch / 30 minutes
2: Teach Less, Learn More (continued) / 60 minutes / Slides 39–48
· Toward Greater Fluency and Understanding
o Activity: Fair Share
o Video: Felisha
· The Standards for Mathematical Practice
o Revisit the Felisha Video
· Model with Mathematics
· NCTM Process Standards and the Standards for Mathematical Practice
o Revisit the K-W-L chart
· Review Section 2 Big Questions
3: From Standards to Classroom Practice and Assessment / 45 minutes / Slides 49–53
· Section 3 Big Questions
· From Standards to Classroom Practice and Assessment
o Video: John Van de Walle: Approach to Teaching
· A Culture of Thinking and Learning
· The Three-Phase Lesson Structure
o Activity: Modeling the Three-Phase Lesson Structure
· Mathematics Worth Doing
Break / 15 minutes
3: From Standards to Classroom Practice and Assessment (continued) / 60 minutes / Slides 54–63
· Assessment
o Activity: Comparing PARCC and SBAC
· Next-Generation Assessments
o Activity: Assessment Samples
· Mathematical Practices within a Rich Content
o Activity: Integrating the Mathematical Practices into Classroom Instruction
· Modeling Tasks within the Content
· Reflecting on Implications for Implementation
o Activity: Implications for Implementation
· Revisit the K-W-L Chart
· Review Section 3 Big Questions
Reflection and Closing / 15 minutes / Slides 64–68
· Reflection Questions
· Review Workshop Outcomes
· Closing
· References
Total / 6 hours
Preparation and Background
Content Information
Note to Facilitator:
Please check if the state or district in which you will be leading the workshop has created its own state documents. States such as Arizona and New York already have already released state-specific versions of the CCSSM. You should become familiar with the state-specific documents and adapt the workshop materials to use the state-specific CCSSM. Tell participants that their work does not end here.Emphasize this especially for Hawaii. They should continue to look at each unit to determine which lessons and resources will help them meet the CCSSM and where they may need to supplement instruction to achieve a standard. By doing this for all units, they will learn when each standard is met in a program and determine if more support is needed for a specific standard. A suggestion could be to divide the units up between grade level teams and use the correlations documents as a guide.
The Common Core State Standards Initiative is a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO).
These standards were developed for three reasons. First is to provide consistency across states. A set of common standards allows for consistent and quality education across all 50 states. Second, they align with international standards. To compete in global markets, students in the United States cannot lag behind their peers in other countries. The Common Core State Standards for Mathematics (CCSSM) are benchmarked against international standards so that students can compete in a global economy. Last, the standards help prepare students for college and work. Colleges and universities expect students to read complex texts independently, and employers look for workers who have the skill set to solve problems and the ability to integrate new knowledge. Elementary and secondary education need to prepare students for these challenges.
The standards were developed in collaboration with teachers, school administrators, and experts, to provide a clear and consistent framework to prepare our students for college and the workforce. The NGA Center and CCSSO received initial feedback on the draft standards from national organizations representing, but not limited to, teachers, postsecondary educators (including community colleges), civil rights groups, English language learners, and students with disabilities. Following the initial round of feedback, the draft standards were opened for public comment, receiving nearly 10,000 responses.
The Common Core State Standards Initiative (2010a) states the following:
The standards are informed by the highest, most effective models from states across the country and countries around the world, and provide teachers and parents with a common understanding of what students are expected to learn. Consistent standards will provide appropriate benchmarks for all students, regardless of where they live.
These standards define the knowledge and skills students should have within their K–12 education careers so that they will graduate from high school able to succeed in entry-level, credit-bearing academic college courses and in workforce training programs. The standards
· are aligned with college and work expectations;
· are clear, understandable, and consistent;
· include rigorous content and application of knowledge through high-order skills;
· build upon strengths and lessons of current state standards;
· are informed by other top-performing countries, so that all students are prepared to succeed in our global economy and society; and
· are evidence-based.
Workshop Information
Big Ideas
· Teaching less, learning more: Toward greater focus and coherence has two main ideas:
o There are only three or four mathematics “critical areas” for most grades.
o There are progressions of mathematics concepts across multiple grade levels (instead of grades in isolation).
· Mathematical proficiency is more than “getting the answer;” it includes the process of using mathematical concepts effectively as identified in the Common Core State Standards for Mathematics’ (CCSSM) Standards for Mathematical Practice.
· The Standards for Mathematical Practice are consistent for all the grade levels even though they manifest themselves differently as students grow in mathematical maturity.
· Students need to engage in learning tasks that support the deep learning identified in the CCSSM.
· Key features of these learning tasks include
o encouraging productive struggle by using challenging problems;
o connecting the current problems to students’ prior learning;
o highlighting important mathematics in the teacher’s verbal introductions to the lesson and summarization at the end;
o asking questions that emphasize the useful mathematical concepts; and
o providing coherence between current learning and future learning.
Essential Questions
· What are the CCSSM and how are they different from previous standards?
· What are the CCSSM Standards for Mathematical Practice and why are they important for mathematical proficiency?
· What kinds of learning tasks allow students the opportunity to demonstrate their mathematical proficiency?
Activities within the Workshop
· Write about current knowledge about the CCSSM using the K-W-L chart.
· Listen to background information about how CCSSM differs from other standards.
· Discuss the introduction material of the CCSSM (pages 3–5) with a focus on surprises and how to identify differences between CCSSM and prior standards.
· Perform a card sort to examine progressions and specific grade level changes/implications for instruction.
· Write initial thoughts about the mathematical practices.