Understanding Analysis and its Connections to Secondary Mathematics Teaching

Nicholas H. Wasserman is Associate Professor of Mathematics Education at Teachers College, Columbia University. Previously, he taught mathematics for six years at the secondary level, in both a large public school in Austin and a private school in Manhattan. His scholarly interests focus on secondary teachers' mathematical knowledge and development, particularly how advanced mathematics can be relevant for teachers and influence their secondary classroom teaching and practice.Tim Fukawa-Connelly is Associate Professor of Teaching and Learning in the College of Education and Human Development at Temple University. His scholarly interests include teacher development, the relationship between what happens in mathematics classrooms and student learning, and hiking to as many waterfalls as possible.Keith Weber is Professor of Mathematics Education at Rutgers University. His scholarly interests include how students and mathematicians reason in advanced mathematics and the relationship between mathematical activity and mathematical learning.Juan Pablo Mejía Ramos is Associate Professor of Mathematics and Mathematics Education at Rutgers University, jointly appointed in the Department of Mathematics (within the School of Arts and Sciences) and the Department of Learning and Teaching (within the Graduate School of Education). He is mainly interested in mathematical argumentation and proof, particularly the ways in which university students and research-active mathematicians construct, read and present arguments and proofs in mathematics.Stephen Abbott is Professor of Mathematics at Middlebury College. His research interests include classical and functional analysis as well as an ongoing fascination with the intersection of mathematics and the arts. He has held visiting positions at Saint Olaf College and the University of Virginia, was editor of Math Horizons (published by the MAA) from 2008-14, and is the author ofUnderstanding Analysis (Springer, 2015).

• Chapter 1: Teaching Principles.-  Chapter 2: Equivalent Real Numbers and Infinite Decimals.- Chapter 3: Sequence Convergence and Irrational Decimal Approximations.- Chapter 4: Algebraic Limit Theorem and Error Accumulation.- Chapter 5: Divergence Description and Criteria and Logic in Communication.- Chapter 6: Continuity and Definitions.- Chapter 7: Intermediate Value Theorem and Implicit Assumptions.- Chapter 8: Continuity, Monotonicity, Inverse Functions and Solving Equations.- Chapter 9: Differentiability and the Secant Slope Function.- Chapter 10: Differentiation Rules and Attending to Scope.- Chapter 11: Taylor’s Theorem and Modeling Complex with Simple.- Chapter 12: The Riemann Integral and Area-Preserving Transformations.- Chapter 13: The Fundamental Theorem of Calculus and Conceptual Explanation.