Skip to main content
Algebra for Secondary Teachers:
Engaging Students to Develop Symbolic Meaning
Douglas A. Lapp, PhD
Contents
Search Book
close
Search Results:
No results.
Dark Mode
Prev
Up
Next
\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Colophon
Dedication
Acknowledgements
1
Introduction to Mathematical Standards
1.1
A Brief History of Standards for Mathematics Education: Algebraic Perspectives
1.1.1
A Brief History of Mathematics Standards
1.1.2
Pirie and Kieren Model for Mathematical Understanding
1.1.3
Kaput, Blanton, and Moreno Model for Symbolic Meaning
1.2
Common Core State Standards for Mathematics
1.2.1
CCSS: Content Standards
1.2.2
CCSS: Standards for Mathematical Practice
1.2.3
Applying the Common Core State Standards
2
Concepts of Number and Quantity
2.1
Elementary Concepts of Number
2.1.1
Elementary Whole Number Systems
2.1.2
Extension of the Number System to Integers
2.1.3
Rational and Irrational Numbers
2.1.4
Exercises
2.2
Extending the Number System: Complex Numbers
2.2.1
Complex Numbers and the Common Core State Standards
2.2.2
Preliminary Connections to Complex Numbers
2.2.3
Complex Connections: Applications to the Classroom
2.2.4
A Complex Situation
2.2.5
Pulling Things Together: Basic Geometry
2.2.6
Seeing Connections: Taylor Series
2.2.7
Orbits of Complex Numbers
2.2.8
Exercises
2.3
Introduction to Sequences
2.3.1
Arithmetic Sequences
2.3.2
Geometric Sequences
2.3.3
Recursive Sequences
2.3.4
Figurative Sequences
2.3.5
Understanding Sequences and the Role of Representations
2.3.6
Exercises
2.4
Introduction to Vectors and Matrices
2.4.1
Modeling Data and Moving Between Worlds
2.4.1.1
Linear Combinations and Dealing with Data
2.4.1.2
Transforming Data and Matrix Multiplication
2.4.1.3
Transformations of Vectors
2.4.2
Solving Systems of Equations
2.4.2.1
Finding Scalars: Gaussian Elimination
2.4.2.2
Augmented Matrices and Stripping Away Variable Names
3
Ratio and Proportional Reasoning
3.1
Scaling Up, Scaling Down
3.2
Rates and Proportional Reasoning
4
Algebraic Structure
4.1
What Is Algebra?
4.1
Exercises
4.2
Developing the Concept of Variable
4.2.1
Three Views of Letter Use (Trigueros & Ursini, 2003)
4.3
Inverses, Undoing, and the Role of Structure
4.3.1
The Concept of Inverse: Setting the Stage
4.3.2
Inverse and Algebraic Structure
4.3.3
Algebraic Structure: Digging Deeper
4.3.4
Exercises
4.4
Dopplegangers and the Multiverse
4.5
Algebra and Dynamic Processes
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.
