Todd Swanson of the Hope College mathematics faculty has co-authored the textbook “A Spiral Approach to Financial Mathematics,” offering a new way of learning the concepts.
The book is being published in July by Academic Press, an imprint of Elsevier. An associate professor of mathematics, Swanson wrote the book with Dr. Nathan Tintle of the Dordt College mathematics and statistics faculty, and Nathan Schelhaas, an actuary with Principal Financial Group of Des Moines, Iowa.
The term “spiral” refers to the way that the material has been organized. “A Spiral Approach to Financial Mathematics” begins by introducing key concepts, which are then referenced and built upon throughout as the book goes into greater depth. Chapter topics include savings, loans, annuities, stocks and bonds, and portfolios.
“The traditional approach to teaching FM starts with simple, unrealistic financial situations, with an emphasis on formulas and computation,” the authors note in their preface.
“Alternatively, we start with practical, conceptual problems for which students have a good intuition,” they continue. “For example, while an amortized loan has a challenging formula, the key concepts (e.g., payback must include interest plus principal; the larger the payment the quicker the loan is paid off) are relatively straightforward and intuitive.”
Reviewer Dr. Donna Fengya of William Paterson University praised “A Spiral Approach to Financial Mathematics,” stating, “This book provides a practical, conceptually focused, and dare might I say, revolutionary approach to the coverage of Financial Mathematics. What makes the authors’ approach unique is that standard topics are first presented in a manner appropriate for students without a calculus background, and are later revisited to provide a complete and thorough coverage for more mathematically advanced students. Excel examples are masterfully included in every chapter to encourage students to explore a variety of topics which enhances intuitive feel and understanding of underlying concepts.”
The book is divided into two units. The first unit is geared toward students who wish to gain a solid mathematical foundation with which to inform their future personal and professional financial decision making. The second unit provides more technical and detailed concepts for students who hope to pass the financial mathematics examination required for actuarial certification.
The authors modeled their approach on the Guidelines for Assessment and Instruction in Statistics Education published by the American Statistical Association in 2007. The ASA calls for instructors to emphasize statistical literacy and develop statistical thinking, use real data, stress conceptual understanding rather than mere knowledge of procedures, foster active learning in the classroom, use technology for developing conceptual understanding and analyzing data, and use assessments to improve and evaluate student learning. Swanson and Tintle had applied the guidelines in the 2015 book “Introduction to Statistical Investigations,” which they co-authored with Jill VanderStoep an adjunct assistant professor of mathematics at Hope; Dr. Beth Chance of California Polytechnic State University; Dr. George Cobb, an emeritus member of the Mount Holyoke College faculty; Dr. Allan Rossman of California Polytechnic State University; and Dr. Soma Roy of California Polytechnic University.