cfair.creating a concept-based unit -...
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Creating a Concept-Based Unit for the 9-12 Mathematics Classroom
October 29, 2009 NCCTM Mathematics Conference
Presented By
Carmella Fair NC Department of Public Instruction Secondary Mathematics Consultant
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Agenda
• Understand the idea of a concept • Identify concepts • Know the components of a concept-based
unit
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Why Concept-Based Instruction?
• Increases student understanding
• Increases student thinking
• Creates the motivation for learning
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Why is the use of concepts important?
• Changes in society impact education – Increased use of technology – Change in job demands – Increase in global interdependence – Change in social norms and structures
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Two Dimensional Curriculum Model-
Processes & Skills
Factual Content
(Topic-based)
(Concept-based) Three Dimensional Curriculum Model-
Concepts & Principles
KNOW DO
From H. Lynn Erickson
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Attributes of
2-Dimensional Model
Attributes of
3-Dimensional Model
Coverage centered Idea centered
Intellectually shallow Intellectual depth
Inability to transfer factual knowledge
Concepts & generalizations transfer
Students not prepared for 21st Century
Students prepared for a changing world
A Shift in Thinking Making a case for concept-based curriculum & instruction
From H. Lynn Erickson
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• Timeless • Universal • Abstract • Represented by 1 or 2 words • Examples share common attributes
A concept is an organizing idea
Examples of Mathematics Concepts:
Patterns & Sequences – Linear Functions – Scatter Plots – Graphs –Order – System
From H. Lynn Erickson
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Your Conceptual Mind
Identify 2 – 4 mathematical concepts from a course or courses that you teach.
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Mathematics Concepts Rational Numbers Positive Integers Common Factors Common Multiples Proper Factor Factor Pair Square Numbers Prime Composite Expressions
Grade Three Grade Six Algebra I
Whole Numbers Place Value Number Representations Patterns Number Grids Money Symbols Decimal Point Related Addition/ Subtraction Facts Fact Families Mathematical Models Standard Units Non-Standard Units Estimation Converting Units Units of Measure
Independent/Dependent Quantities Functional Relationships Domain/Range Patterns and Sequences Linear Functions Variables and Symbols Algebraic Expressions Order of Operations Distributive Property Coordinate Plane Graphs Linear Parent Functions Scatter Plots
From H. Lynn Erickson
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• Timeless • Universal • Abstract • Represented by 1 or 2 words • Examples share common attributes
A concept is an organizing idea
Examples of Mathematics Concepts:
Patterns & Sequences – Linear Functions – Scatter Plots – Graphs –Order – System
From H. Lynn Erickson
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Science Social Studies Mathematics Music Order Conflict Order Rhythm Organism Patterns Ratio Melody Population Populations Proportion Harmony System System System Tone Change Change/Continuity Pattern Pattern Evolution Culture Probability Form Cycle Evolution Function Tempo Interaction Civilization Slope Timbre Energy/Matter Interdependence Graph Pitch
From H. Lynn Erickson
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5 Things That Concept-Based Curriculum & Instruction Does
Unites “big ideas” for deeper understanding
Aligns curriculum, instruction and assessment
Emphasizes & identifies what students should Know, Understand & Do
Organizes the concepts/content into instructional units/lessons that contextualize the standards
Identifies concepts in curriculum rather than just facts
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Concept-based Instruction Teaching using concepts as a tool to help students see patterns and connections between facts and related ideas in order to reach a deeper understanding of the content.
What is written
What is taught
What is tested
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Graphic Organizer for Graphs
Graphs
In small groups use the graphic organizer to identify characteristics that make graphs - the concept “graphs.”
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Macro and Micro Concepts
Macro Concepts provide BREADTH of understanding
(interdisciplinary)
Micro Concepts provide DEPTH of understanding
(discipline specific)
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Macro and Micro Concepts Macro Concepts provide BREADTH of understanding
(interdisciplinary)
Micro Concepts provide DEPTH of understanding
(discipline specific)
Example:
System
System of Equations (mathematics)
Governmental Systems (social studies)
Ecosystem (science)
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Identifying Concepts
A. Micro B. Macro
Order
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Identifying Concepts
A. Micro B. Macro
Rational Numbers
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Identifying Concepts
A. Micro B. Macro
System
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Identifying Concepts
A. Micro B. Macro
Common Factor
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Identifying Concepts
Step 1: Identify the focus of a Concept-based unit of Instruction.
Step 2: What standards will be taught/assessed?
Step 3: What concepts (both explicit and implied) will be addressed in this unit?
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Identifying Concepts
Unit Title/Focus:
NCSCOS Standard(s): Math A
Algebra I/IM I Math BC
Geometry/Algebra II IM II/IM III
Concepts: Math A
Algebra I/IM I Math BC
Geometry/Algebra II IM II/IM III
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The Structure of Knowledge
From H. Lynn Erickson
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The Structure of Knowledge
slope line
Measurement of distance and speed
Velocity can be represented mathematically by the slope of a line.
The slope of a graph at a particular point indicates the instantaneous rate of change.
graph
From H. Lynn Erickson
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Concepts and RBT Knowledge is: – Factual – Conceptual – Procedural – Metacognitive
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Mathematics is concept-based, but we need to ensure that students attain conceptual understanding.
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A Conceptual Mind: • Creates connections to prior experience • Works with factual knowledge to develop the
intellect • Creates deeper understanding at factual and
conceptual levels • Recognizes the transferability of knowledge • Creates the motivation for learning
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References
Erickson, H. L. (2008). Stirring the head, heart, and soul: Redefining curriculum, instruction, and concept-based learning (3rd ed.). Thousand Oaks, CA: Corwin Press.
Erickson, H. L. (2007). Concept-based curriculum and instruction for the thinking classroom. Thousand Oaks, CA: Corwin Press.
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Contact Information
Carmella Fair NC Department of Public Instruction Secondary Mathematics Consultant 919-807-3840 [email protected]
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