Outline
ICME: MAPPING DIAGRAMS: FUNCTION VISUALIZATION
The 14th International Congress on Mathematical Education
Shanghai, 11th ‒18th July, 2021
Topic Study Group 23 Visualization in the teaching and learning of mathematics
Session 3 (Jul 14, 2021 20:15-20:26 CST = July 14 , 2021 05:15-05:26 PDT)
MAPPING DIAGRAMS: FUNCTION VISUALIZATION OF REAL AND COMPLEX ANALYSIS AND MATRIX ALGEBRA
Martin Flashman
Humboldt State University
Arcata, CA USA
Questions? Comments?
email: flashman@humboldt.edu
GeoGebra Book: https://flashman.tiny.us/ICME14
Mapping diagrams can provide a coherent framework for developing a sensible visual approach for learning and teaching function concepts starting from basic arithmetic through the key ideas of algebra and culminating with calculus, complex analysis, and linear algebra. The author will present many recently created figures for linear functions in a variety of contexts demonstrating how mapping diagrams enhance their study by providing visualizations for many fundamental concepts. Dynamic figures created with GeoGebra are included.
Table of Contents
ICME: Introduction
ICME: MAPPING DIAGRAMS FOR REAL LINEAR FUNCTIONS
ICME: COMPLEX LINEAR FUNCTIONS
ICME: CONCLUSION: NOT THE END -- ONLY A BEGINNING.
References
ICME Paper
MORE: What is a (real) mapping diagram (MD)?
MORE: Some Historical Uses of Mapping Diagrams
MORE: Visualizing Functions
- Mapping Diagram (Real) from Function Table Activity
- Mapping Diagram Composition Adjust Arrows
- example.TGG.0
- example.DTA.0
- example.DTS.0
- example.DTCOM.0
- Mapping Diagram, Spreadsheet, Graph, Realign, Focus
- Visualizing Numeric Transformations
- Guess My Rule with MD
- Mapping Diagram, Spreadsheet, Graph, Realign, Focus
MORE: MD to visualize solving linear and nonlinear equations.
MORE: Linear Complex Functions
MORE: Matrix Linear Transformations on R^2
- More: Linear Operators, Transformations, and Algebra.1
- More: Linear Operators, Transformations, and Algebra.2
- More: Matrix Transformation on Circle
- Linear MD: R^2 to R
- 2x2 Matrix Transformation Traditional Views
- Introducing 2x2 Matrix Transformation Mapping Diagrams
- Matrix Transformation on Circle
- Matrix Multiplication/Composition
- Eigenvectors and Mapping Diagrams I
- Eigenvectors and Mapping Diagrams II
MORE: Solving Linear (Matrix) Equations