Creating a Concept-Based Unit for the 9-12 Mathematics Classroom

Transcription

1 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

2 Agenda Understand the idea of a concept Identify concepts Know the components of a concept-based unit

3 Why Concept-Based Instruction? Increases student understanding Increases student thinking Creates the motivation for learning

4 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

5 Two Dimensional Curriculum Model- (Topic-based) Processes & Skills Factual Content Concepts & Principles KNOW DO Three Dimensional Curriculum Model- (Concept-based) From H. Lynn Erickson

6 A Shift in Thinking Making a case for concept-based curriculum & instruction Attributes of 2-Dimensional Model Coverage centered Intellectually shallow Inability to transfer factual knowledge Students not prepared for 21 st Century Attributes of 3-Dimensional Model Idea centered Intellectual depth Concepts & generalizations transfer Students prepared for a changing world From H. Lynn Erickson

7 Timeless Universal Abstract A concept is an organizing idea Represented by 1 or 2 words Examples share common attributes Examples of Mathematics Concepts: Patterns & Sequences Linear Functions Scatter Plots Graphs Order System From H. Lynn Erickson

8 Your Conceptual Mind Identify 2 4 mathematical concepts from a course or courses that you teach.

9 Mathematics Concepts Grade Three Grade Six Algebra I Rational Numbers 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 Positive Integers Common Factors Common Multiples Proper Factor Factor Pair Square Numbers Prime Composite Expressions 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 9

10 Timeless Universal Abstract A concept is an organizing idea Represented by 1 or 2 words Examples share common attributes Examples of Mathematics Concepts: Patterns & Sequences Linear Functions Scatter Plots Graphs Order System From H. Lynn Erickson

11 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

12 5 Things That Concept-Based Curriculum & Instruction Does Aligns curriculum, instruction and assessment Emphasizes & identifies what students should Know, Understand & Do Identifies concepts in curriculum rather than just facts Organizes the concepts/content into instructional units /lessons that contextualize the standards Unites big ideas for deeper understanding

13 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

14 Graphic Organizer for Graphs In small groups use the graphic organizer to identify characteristics that make graphs - the concept graphs. Graphs

15 Macro and Micro Concepts Macro Concepts provide BREADTH of understanding (interdisciplinary) Micro Concepts provide DEPTH of understanding (discipline specific)

16 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)

17 Identifying Concepts A. Micro B. Macro Order

18 Identifying Concepts A. Micro B. Macro Rational Numbers

19 Identifying Concepts A. Micro B. Macro System

20 Identifying Concepts A. Micro B. Macro Common Factor

21 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?

22 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 23

24 The Structure of Knowledge 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. slope line graph Measurement of distance and speed From H. Lynn Erickson 24

25 Concepts and RBT Knowledge is: Factual Conceptual Procedural Metacognitive

26 Mathematics is concept-based, but we need to ensure that students attain conceptual understanding.

27 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

28 References Erickson, H. L. (2008). Stirring the head, heart, and soul: Redefining curriculum, instruction, and concept-based learning (3 rd 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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31 Contact Information Carmella Fair NC Department of Public Instruction Secondary Mathematics Consultant

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