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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
Agenda
• Understand the idea of a concept • Identify concepts • Know the components of a concept-based
unit
Why Concept-Based Instruction?
• Increases student understanding
• Increases student thinking
• Creates the motivation for learning
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
Two Dimensional Curriculum Model-
Processes & Skills
Factual Content
(Topic-based)
(Concept-based) Three Dimensional Curriculum Model-
Concepts & Principles
KNOW DO
From H. Lynn Erickson
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
• 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
Your Conceptual Mind
Identify 2 – 4 mathematical concepts from a course or courses that you teach.
9
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
• 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
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
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
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
Graphic Organizer for Graphs
Graphs
In small groups use the graphic organizer to identify characteristics that make graphs - the concept “graphs.”
Macro and Micro Concepts
Macro Concepts provide BREADTH of understanding
(interdisciplinary)
Micro Concepts provide DEPTH of understanding
(discipline specific)
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)
Identifying Concepts
A. Micro B. Macro
Order
Identifying Concepts
A. Micro B. Macro
Rational Numbers
Identifying Concepts
A. Micro B. Macro
System
Identifying Concepts
A. Micro B. Macro
Common Factor
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?
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
23
The Structure of Knowledge
From H. Lynn Erickson
24
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
Concepts and RBT Knowledge is: – Factual – Conceptual – Procedural – Metacognitive
Mathematics is concept-based, but we need to ensure that students attain conceptual understanding.
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
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.
Contact Information
Carmella Fair NC Department of Public Instruction Secondary Mathematics Consultant 919-807-3840 [email protected]
