high school session 1: exploring the critical areas module 1: a closer look at the common core state...
TRANSCRIPT
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High School Session 1:Exploring the Critical Areas
Module 1:A Closer Look at the Common
Core State Standards for Mathematics
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Expected Outcomes
• Participants will deepen their understanding of the structure of the CCSS for Mathematics and at least one suggested pathway course.
• Participants will deepen their understanding that the critical areas suggest a possible grouping of the standards into coherent blocks for each high school course.
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• Focus• Coherence• Clarity• Specificity
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Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement.
Richard Elmore, Ph.D., Harvard Graduate School of Education
Principle #2: If you change one element of the instructional core, you have to change the other two.
The Instructional Core
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Adapted from the Public Education Leadership Project at Harvard University
STRUCTURES
POLICIES, PROCESSES & PROCEDURES
RESOURCES
HUMAN, MATERIAL, M
ONEY
STAKEHOLDERS
CULTURE
Organizational Elements
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The high school standards are listed within conceptual categories
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CCSSM High SchoolConceptual Categories
• Number and Quantity (N)• Algebra (A)• Functions (F)• Modeling (*)• Geometry (G)• Statistics and Probability (S)
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CCSSM High SchoolConceptual Categories
• The big ideas that connect mathematics across high school
• A progression of increasing complexity• Description of the mathematical content to
be learned, elaborated through domains, clusters, and standards
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Domains
• Overarching “big ideas” that connect topics across the grades/courses
• Descriptions of the mathematical content to be learned, elaborated through clusters and standards
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Clusters of Standards
• Indicate WHAT students should know and be able to do
• May appear in multiple grade levels/courses with increasing developmental standards as the grade levels progress
• Reflect both mathematical understandings and skills, which are equally important
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Conceptual Category
Cluster Headings
Cluster Headings
Cluster Headings
Cluster Headings
DOMAIN
DOMAIN
DOMAIN
DOMAIN
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Algebra
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Domain
Cluster Headings
Standards
Conceptual Category
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Each course, outlined in the Pathways document is organized around Critical Areas (Units).
Traditional Pathway: High School Algebra I
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Five critical areas in an Algebra I course
1. Relationships Between Quantities and Reasoning with Equations
2. Linear and Exponential Relationships3. Descriptive Statistics 4. Expressions and Equations5. Quadratic Functions and Modeling
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Task: Examining the Critical Areas
• What are the important mathematical ideas for this critical area?
• What types of evidence would convince you that a student understands these ideas?
• What common misconceptions do students have when studying these critical areas? What challenges have you had in teaching these areas?
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Whole group discussion
• What are the similarities in the types of evidence that would convince you that a student understands these ideas?
• Are there common themes in student misconceptions and in challenges to teaching?
• Compare the concepts in the critical areas with those that you are currently teaching. In general, how are they similar? How are they different?
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Reflection
• How do the critical areas help to bring focus to the standards for the course that you examined today?
• How will you use the critical areas to inform your curriculum and guide your instruction?
• What questions do you still have about the conceptual categories and critical areas?
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