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Concept Mapping in Mathematics - Research into Practice
von: Karoline Afamasaga-Fuata'i
Springer-Verlag, 2009
ISBN: 9780387891941 , 220 Seiten
Format: PDF, OL
Kopierschutz: Wasserzeichen
Preis: 96,29 EUR
Concept Mapping in Mathematics
2
Foreword
5
Contents
7
Contributors
8
Introduction
10
Part I A Historical Overview of Concept Mapping
14
1 The Development and Evolution of the Concept Mapping Tool Leading to a New Model for Mathematics Education
15
Introduction: The Invention of Concept Mapping
16
The Use of Concept Maps in Mathematics
19
CmapTools and the Internet
19
A New Model for Education
20
Expert Skeleton Concept Maps
22
Adding Concepts and Resources Using CmapTools
22
Collaboration Among Students
23
Exploration with Real World Problems
24
Written, Oral, and Video Reports and Developing Knowledge Models
24
Sharing and Assessing Team Knowledge Models
26
In Conclusion
26
Part II Primary Mathematics Teaching and Learning
29
2 Analysing the 0Measurement0 Strand Using Concept Maps and Vee Diagrams
30
Introduction
30
Literature Review of Concept Mapping and Vee Diagrams
31
Methodology
32
Data Collected and Analysis
33
"Length" Concept Maps
33
Volume "Concept Maps"
38
Vee Diagrams of Mathematics Problems
46
Journal of Reflections
52
Critical Ability to Analyse Topics and Problem
52
Solve Mathematics Problems
53
Communicate Effectively
53
Develop a Deep Conceptual Understanding of a Topic
53
Discussion
53
Implications
55
3 Concept Mapping as a Means to Develop and Assess Conceptual Understanding in Primary Mathematics Teacher Education
58
Introduction
58
Developing the Concept of a Positional System in Teacher Education
59
Maryannes Map
60
Death by Decimal
66
Summary
67
4 Using Concept Maps and Vee Diagrams to Analyse the 0Fractions0 Strand in Primary Mathematics
69
Introduction
69
Definitions of Concept Maps and Vee Diagrams
70
Case Study
71
Context
71
Data Collected and Analysis
72
Task 1 Data and Analysis
72
Early Stage 1 and Stage 1 Concept Maps
72
Stage 2 Concept Map
74
Stage 3 Concept Map
75
Stage 4 Concept Map
77
Task 2 Data and Analysis
78
Overview "Fractions" Concept Map
78
Concept Maps and Vee Diagrams of "Fraction" Problems
85
Discussion and Implications
91
5 Concept Maps as Innovative Learning and Assessment Tools in Primary Schools
97
Introduction
97
Methodology
98
Results
99
Professional Development Workshops and Reflection Sessions
99
Teachers' Professional Development Workshop
99
Reflection Sessions
100
On-Going Professional Support for the Teachers
101
Preparation of Teaching and Learning Resources
101
Initial Site Visits
101
Classroom Observation Visit
102
Portfolio of Teacher Resources
102
More Site Visits and Reflection Sessions
103
Concept Mapping Activities
105
First Mapping Activities
105
Second Mapping Activities
107
Additional Mapping Activities
110
Teachers' Self-Designed Final Mapping Activities
113
Post-Activity Reflective Session
117
Discussion
117
Reflective Sessions
118
School Realities
118
On-going Professional Support
119
Summary of Class Contributions
119
Innovation and Professional Practice
120
Implications
121
Part III Secondary Mathematics Teaching and Learning
124
6 Evidence of Meaningful Learning in the Topic of 0Proportionality0 in Second Grade Secondary Education
125
Theoretical Background
125
The Topic of the Proportionality
127
Research Planning and Design
129
The Setting in Which the Concept Maps were Used
130
Description and Discussion of the Findings
132
The Way in Which the Pupils Differentiate Concepts from Links
133
Utilisation of Concepts
133
Propositions Formed from Links Between Concepts
133
Levels of Hierarchy
135
Crossed Links
136
Conclusion
140
7 Concept Mapping as a Means to Develop and Assess Conceptual Understanding in Secondary Mathematics Teacher Education
144
Case Study
144
Epistemological Value
152
8 Concept Mapping a Teaching Sequence and Lesson Plan for 0Derivatives0
155
Introduction
155
Methodology
156
Data Collected
157
Data Analysis
157
Learning to Concept Map
158
Overview Concept Maps
160
Teaching Sequence Concept Map
162
Lesson Plan Concept Map
165
Discussion
170
Concept Maps of Critical Analysis
171
Workshop Discourse
172
Socio-Mathematical Norms
172
Practical Management of the Learning Ecology
173
Main Insights and Implications
173
9 Curricular Implications of Concept Mapping in Secondary Mathematics Education
176
Introduction
177
Concept Mapping and Historical Research as a Combined Epistemological Tool
177
Conceptual Analysis From a Cultural Historical Perspective
178
Historical Foundation
178
Conceptual Essence of the Logarithm Concept from a Cultural-Historical Perspective
180
More Fully Developed Concept Map of a Logarithm
180
The Problem of Generative Metonymy
183
Conceptual Representation the Teachers View
183
Conceptual Representation The Students View
184
Curriculum Proposal
186
Lesson 1: "Introducing the Logarithm"
187
Lesson 2: "The Logarithmic Graph"
188
Lesson 3: "Logarithms, So What?"
189
Lesson 4: "Logarithmic Scales and Logarithmic Graph Paper"
190
Curriculum Design Questions to Use in Conjunction with Concept Mapping
191
Conclusions and Implications
192
10 Using Concept Maps and Gowin0s Vee to Understand Mathematical Models of Physical Phenomena
194
Introduction
194
Theoretical background: Concept Maps and Gowins Vee
195
What is a Concept Map?
197
Gowins Vee
203
Phases of the Implementation of the Strategy
204
Phase I: Learning About Concept Maps and Gowin's Vee
205
Phase II: Eliciting Basic Conceptual Knowledge of Mathematical Functions
206
Phase III: Acquisition of the Concept "model" in Physics
206
Phase IV: Students Training in the Application of the Concept "Model" to Physical Phenomena
206
The Evaluation of the Strategy
206
The Strategy -- Trial and Results
207
Phase I: Learning About Concept Maps and Gowin's Vee.
207
Phase II: Eliciting Basic Conceptual Knowledge of Mathematical Functions
207
Phase III: Acquisition of the Concept "Model" in Physics
209
Phase IV: Modelling Physical Phenomena
219
Conclusions
219
11 Applying Concept Mapping to Algebra I
222
Introduction
222
Developing an Algebra I Course Through Concept Mapping
224
Course Prerequisites
224
Narrative on the Development of Polynomials
225
Working With Monomials
226
Polynomials are Developed From Monomials
228
Operations on Polynomials
229
Degree of a Polynomial
230
Evaluating Polynomials and Solving Polynomial Equations
231
Quadratic Polynomials
232
Part IV University Mathematics Teaching and Learning
240
12 Enhancing Undergraduate Mathematics Learning Using Concept Maps and Vee Diagrams
241
Introduction
241
Theoretical Framework
243
Methodology
245
Data Analysis
246
Concept Maps
246
Vee Diagrams
247
Data Collected and Analysis
247
Concept Map Data
248
Student 1's Topic ' Laplace's Transform (LT)
248
Student 2--s Topic -- Trigonometric Approximations
249
Student 3--s Topic -- Least Squares Polynomial Approximations (LSPA)
250
Student 4--s Topic -- Multivariable Functions
251
Student 5--s topic -- Numerical methods
252
Student 6--s Topic -- Partial Differential Equations (pdes)
254
Vee Map Data
254
Overall Criteria
254
Specific Criteria
257
Discussion
257
Conclusions and Implications
258
13 Concept Mapping: An Important Guide for the Mathematics Teaching Process
262
Introduction and Antecedents
262
Concept Maps and The Learning Process
265
Basic Processes and The Learning of Mathematics
267
Concept Mapping for Mathematics Teaching Process: Some Examples
268
"Critical Point of a Function" Concept Map
269
"Extreme Point" Concept Map
271
"Real Numbers" Concept Map
272
"Displacement of Functions" Concept Map
273
Mathematics Problem Concept Maps
273
"Solution of Certain Inequalities" Concept Map
274
"Elements of a Function" Concept Map
274
Cognitive Development of the Learner
276
Concept Map and Students: Important Considerations
276
The Intervention and Its Methodology
277
Results
277
Discussion and Implications
278
14 Concept Mapping and Vee Diagramming 0Differential Equations0
281
Introduction
281
Concept Mapping and Vee Diagram Studies
282
Theoretical Perspectives
283
Nats Case Study
285
Nats Data and Analysis
286
Concept Map Data Analysis
286
Concept Map Criteria
286
Concept Map Data
288
Vee Diagram Data Analysis
291
293
Discussion
295
Implications
297
15 Using Concept Maps to Mediate Meaning in Undergraduate Mathematics
300
Introduction
300
Mathematics Education in Samoa
301
Literature Review
302
Theoretical Framework
302
Relevant Studies
304
Concept Mapping and Vee Diagram Studies
304
Methodology of the Study
305
Analysis of Concept Maps
305
Concept Maps Collected
306
Examples of "Good" Concept Maps
309
Student 3: Fia -- Numerical Methods
309
Student 4: Vae -- Limits and Continuity
310
Student 9: Toa -- Normal Distributions (ND)
313
Example of an "Above Average" Final Concept Map
315
Student 5: Heku -- Motion
315
Example of an "Average" Final Concept Map
315
Student 2: Loke -- Differentiation
315
Example of a "Below Average" Final Concept Map
317
Student 8: Pasi -- Integration
317
Example of a "Poor" Final Concept Map
318
Student 1: Pene -- Indeterminate Forms
318
Discussion
319
Implications
325
Part V Future Directions
328
16 Implications and Future Research Directions
329
Index
335
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