Common Core State Standards – Introduction Mathematics
TITLE & FOCUSTitle: Common Core State Standards – Introduction Mathematics
Descriptions: Participants will build awareness of mathematic curriculum shifts, mathematical practices, “Accessible Mathematics,” and the increased level of rigor relevant to the Common Core State Standards in Mathematics. They will develop a deeper understanding of cognitive rigor and use Hess’ Cognitive Rigor Matrix to develop classroom learning activities and assessments. The application focus is for participants to build an understanding of the higher rigor in the Common Core for Mathematics and to plan professional development activities using Hess’ Cognitive Rigor Matrix to increasing rigor of learning activities and assessments.
NOTES:
PD hrs: If you are interested in facilitating this workshop for “Professional Development Hours” through ASU, please contact us at for details (including an Attendance Roster Form and a Participant Feedback Form)
FEDBACK: We would appreciate feedback regarding the quality of this PD Facilitator Kit and/or suggestions for improvement (including participant feedback and/or recommended changes to the Facilitator PowerPoint and/or Facilitator Guide). Please email feedback, comments, or suggestions for improvements to (be sure to include the exact name of the workshop).
TARGETED LEARNING FOR THIS WORKSHOP
NOTE: It is recommended that the targeted objectives, guiding questions, and key vocabulary be posted during the workshop.
Key Vocabulary
· Mathematical shifts, Mathematical practices, Accessible mathematics
· Rigor, Cognitive Rigor Matrix, Scaffolding
· Bloom’s Taxonomy of Thinking, Webb’s Depth or Knowledge
Key Words
· ISLLC workshop, administrator professional development, college and career readiness,
· Common Core, Mathematical Shifts, Mathematical Practices, Bloom’s Taxonomy of Thinking, Webb’s Depth of Knowledge
Targeted Objectives:
· Participants will identify key concepts of the mathematical shifts and practices and create a mind map to present whole group and then develop a lesson that incorporates a minimum of one mathematical practice.
Guiding Questions
· What are the implications for classroom teachers in regards to the mathematical shifts?
· What are the implications for classroom teachers in regards to the mathematical practices?
· How can the book Accessible Mathematics be used to guide teachers in developing more rigorous math lessons?
· If we keep doing the same as before what will happen?
· What do teachers need to know and be able to do to enact these shifts in their practice?
· What can we do as leaders of our school to ensure we are supporting teachers in this shift?
· What are the characteristics of an effective mathematics lesson in a mathematics classroom?
· How can we ensure that instruction supports the Math Standards for Math Practices?
· How can “Accessible Mathematics” be used as a resource in your school?
· How can the mathematical practices inform “field testing
· What must teachers consider for effective mathematical instruction?
· What are the implications for classroom teachers in regards to the mathematical shifts?
· What are the implications for classroom teachers in regards to increasing rigor?
· What is the focus of the mathematical shifts?
· What does coherence mean in regards to the Mathematical Shifts?
· How do the Mathematical Shifts increase rigor?
· What is the different in rigor between students in kinder and students in 8th grade?
· What makes math rigorous and how is rigor increases?
· What is the different between mental tasks and depth of knowledge?
· What do teachers need to consider when looking at the CCSS?
· How is cognitive demand determined?
· What needs to be considered when determining the performance expected of the students?
· How is this process similar to strategies or systems that you have used in the past?
· How is application of Hess’ Cognitive Rigor Matrix different from past tools?
· How might you use this with your learning team to plan math intervention?
· What tools do leaders need in order to teach staff how to obtain higher rigor in their teaching?
· What instructional strategies can teachers use to develop students tools?
· What thinking strategies need to be taught and used on a regular basis to increase rigor?
InTASC Standards
· Standard 1: Content Pedagogy;
· Standard 2: Student Development;
· Standard 4: Multiple Instructional strategies;
· Standard 7: Planning
ISLLC Standard
· ISLLC 2 Teaching and Learning, Educational leaders ensure achievement and success of all students by monitoring and continuously improving teaching and learning.
· Elements:
o A: Nurture and sustain a culture of collaboration, trust, learning, and high expectations.
o B: Create a comprehensive, rigorous and coherent curricular program
o C: Create personalized and motivating learning environment for students
Research-Based Critical Behaviors
· Key Process:
o Planning—Articulate shared direction and coherent policies, practices, and procedures for realizing high standards of student performance.
o Implementing—Engage people, ideas, and resources to put into practice the activities necessary to realize high standards for student performance.
· Core Component:
o High Standards for Student Learning—There are individual, team, and school goals for rigorous student academic and social learning.
o Rigorous Curriculum (content)—There is ambitious academic content provided to all students in core academic subjects.
o Quality Instruction (pedagogy)—There are effective instructional practices that maximize student academic and social learning.
Agenda and Segment Titles / Slide Numbers / Time in Minutes / Notes
Introduction and/or Overview of Workshop / 1-4 / 10
Mathematical Shifts / 5-13 / 55
Break / 14 / 10
Mathematical Practices / 15-25 / 85
End of 3 hr session/lunch break for 6 hr session / 26-28 / 10
Total Time 1st session / 180 min (3 hrs)
Lunch Break for 6 hr session / 29 / 60 / Not calculated into total session time
Intro to 2nd 3hr session / 30-31 / 10
Accessible Mathematics: Instructional Shifts / 32-37 / 70
Break / 38 / 10
Accessible Mathematics: Reflection / 39-44 / 85
End of 2nd 3hr session/end of 1st 6 hr session / 45-46 / 5
Total Time 2nd session / 180 min (3 hrs)
Review of previous session/Intro to 3rd 3hr session/2nd 6 hr session / 47-50 / 10
Identifying Rigor / 51-61 / 80
Break / 62 / 10
Increasing Rigor / 63-70 / 70
End of 3hr session/lunch break for 6hr session / 71-72 / 10
Total Time 3rd session / 180 kin (3 hrs)
Lunch Break for 6 hr session / 73 / 60 / Not calculated into total session time
Intro to 3rd 3hr session/2nd half of 6hr session / 74-75 / 10
Exploring the Standards / 76-85 / 55
Break / 86 / 10
Lesson Planning & Assessment / 87-94 / 30
Professional Development – Planning Time / 95-98 / 70
End of 4th 3hr session/end of 2nd 6 hr session / 99-100 / 5
Total time for 4th session / 180 min (3 hrs)
Materials, Handouts, Readings, Videos, and other items needed
Participants are expected to purchase the book Accessible Mathematics
General Materials (items used throughout whole workshop, and office supply items needed)
· Facilitator Guide CCSS Introduction Mathematics
· Facilitator PowerPoint: CCSS Introduction Mathematics
· Agenda (facilitator makes this on chart paper)
· Poster Paper
· Computer and Projection system
1st 3hr Segment/Session
Handout
· Math Challenge
· Math Shifts Overview
· Overview of Math CCSS
· Math Practices Overview
· Math Practices Worksheet
· Math Instruction (3-column)
Readings
· None
Videos
· Bungee Jump http://www.learner.org/vod/vod_window.html?pid=925
Other technologies or resources that are used
· None
2nd 3hr Segment/Session
Handout
· Accessible Mathematics
· Characteristics of Rich Mathematical Tasks
Readings
· Accessible Mathematics chapter 1-10
· Accessible Mathematics pages 89-95
Videos
· None.
Other technologies or resources that are used
· .None
3rd 3 hr Segment/Session
Handout
· Math Shifts
· Bloom’s-Taxonomy Of Thinking
· Webb’s-Depth Of Knowledge
· Cognitive Rigor Matrix
· Cognitive Rigor Matrix – Volume
· Math Practice Worksheet
· How is Rigor Increased?
Readings
· Accessible Mathematics chapter 1-10
· Accessible Mathematics pages 89-95
Videos
· Karen Hess Full Version 23 minutes: http://vimeo.com/21111138
· Karen Hess Short Version 2.5 minutes: http://vimeo.com/20998609
· My Favorite “No”: https://www.teachingchannel.org/videos/class-warm-up-routine
· Solving a Problem? Make a Plan: https://www.teachingchannel.org/videos/math-problem-solving-plan
Other technologies or resources that are used
· None
4th 3hr Segment/Session
Handout
· OPTIONAL – Facilitate may need to download prototype assessments (see slide 93 & Prototype Assessment Folder)
· Grade 3 Examples
· Hess’ Matrix Math/Science
· Hess’ Cognitive Rigor Matrix (blank)
· ORID analysis
· Shaping up a Summary
Readings
· None
Videos
· None.
Other technologies or resources that are used
· None
RESOURCES
Footnotes:
· Arizona Department of Education – Common Core Training of Trainers
· 2010 Mathematics Standards Overview Arizona Department of Education: Standards and Assessments Division
· Stein, Smith, Henningsen, & Silver (2000), Implementing Standards-Based Mathematics Instruction; New York, New York: Teachers College Press
· Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human (1997) Making Sense: Teaching and Learning with Understanding; Portsmouth, New Hampshire: Heinemann
· Webb’s Depth of Knowledge: Karin K. Hess, Ed.D., Senior Associate National Center for Assessment, Dove, NH,
· Rigor is NOT a Four Letter Word, Barbara R. Blackburn, Winthrop University, www.barbarablackburnonline.com www.eyeoneducaton.com
References:
· Leinwand, Steven (2009). Accessible Mathematics, Portsmouth, New Hampshire: Heinemann
Other General Resources: These are items available through ASU for this Workshop (do not repeat items from materials section)
· InTASC Standards (for teacher workshops)
· ISLLC Standards Rubric (for leader workshops)
· Core Components & Key Processes (for leader workshops connected to VAL-Ed principal behaviors)
Content Experts: Julius Koenigsknecht, Toni Reynolds, Michelle Brady, Seu Hee Kim, Sandy Meko
Presentation Notes
Management Considerations, Notes, etc
Management Notes:
· Ask the superintendent in advance to prepare a welcome and remarks regarding WHY this workshop is important for participants.
· Check with the superintendent in advance to see if s/he prefers to use established district team norms.
· Directions / Notes relevant to each individual PowerPoint slide are listed in the PowerPoints notes section
· Typically, each segment of the workshop begins with a slide entitled “Intended Outcome”
· Closure for each segment and/or the end of the workshop should be adjusted/adapted to the facilitators style
Notes to Inform Pacing / Adjusting Lesson (FACILITATORS: After studying this workshop, you may make additions to these items)
· See workshop pacing guidelines in notes section of presentation
· Slide 93 is optional – if you want to emphasize the increasing rigor on future state assessments, use this slide and download prototype assessments from PARCC or Smarter Balance
Follow-up Strategies
Suggestions for Follow-up Activities
· Work with your leadership team to develop a plan to implement the mathematic shifts and practices.
· Be an active member of a grade level planning team and assist them using the Mathematical instructional shifts and practices to plan lessons.
Individual Reflection Questions for Coaching (reflecting on workshop concepts, understandings, options, or application)
· What are some big ideas for the development and intended outcome of the CCSS?
· How do the combined mathematic shifts and practices impact rigor?
· What must you consider for implementation and accountability of the shifts and practices?
· How has your thinking changed about math instruction?
· How can thinking and cognition tools help teachers identify rigor in the standards and design rigorous learning and instruction?
· How did thinking and cognition processes evolve from Bloom’s taxonomy to Webb’s DOK to Hess’s Matrix?
Group Discussion Questions for Online Forum (sharing what he/she is “doing” in his/her school)
· How will you introduce the Mathematical Instructional Shift and Mathematical Practices?
· Discuss how you are actively participating planning or implementing CCSS Math Standards.
· How have you modeled raising rigor and complexity with job embedded tasks and learning at your own site?
· Describe the structures or systems you have established to be a part of the continuous learning cycle in regards to the CCSS Mathematics standards.
· Why is it imperative that teachers plan for various DOK levels in lessons?
· How can Hess’ Cognitive Rigor Matrix help teachers identify rigor, design lessons, and/or develop assessments?
· What tools do leaders need in order to teach staff so that they can teach at the higher level of rigor?
· Discuss how you are actively participating planning or implementing CCSS Mathematic Standards.
· How have you modeled raising rigor and reevaluating objectives using the Hess Matrix at your own site?
· Describe the structures or systems you have established to be a part of the continuous learning cycle in regards to the CCSS Mathematic Standards?
Quiz Questions:
· Identify the mathematical shifts and which ones were combined.
· Identify the mathematical practices.
· Define rigor and discuss how the mathematical shifts and practices have increased instructional expectations of math instruction.
· Describe how Hess’ Cognitive Rigor Matrix combines Bloom’s taxonomy and Webb’s DOK matrix.
· Identify how rigor can be increased.
· Describe how rigor is increased from kinder to 8th grade.
· Identify the impact of increased rigor on assessment development.
· Explain DOK, what is the purpose?
Page 1 of 5