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Inquiry is the first step toward achieving resolution. This statement holds true for any aspect of life, but especially mathematics. Whether it’s derivatives, functions, or some other concept, asking questions and probing into each step fosters learning. In this textbook, Falbo is committed to demonstrating the effectiveness of this approach, one that he likens to the non-verbal version of the Socratic Method that has made its way from ancient times into today’s modern-day classrooms, forcing young minds to think deeper and challenge themselves further.
Falbo explains how his inquiry-based learning (IBL) method is essentially a variation of Moore’s method, which emphasizes collaboration, communication, and, more specifically, students becoming teachers. At its core, it comes down to a simple belief: if you can teach it to others, then you must know it well enough to thrive yourself. While asking questions is great, the book is centered around asking the right questions. And undoubtedly, the more questions that are asked, the easier it becomes to identify what the right questions are.
Going through the different units of the textbook, the breakdown and consistent teaching pattern make the work easy to integrate within a classroom environment as well as that of self-study. In other words, the book itself provides a guide map for the question-answer inquiry format, acting as the teacher for students who choose to advance their knowledge of calculus without a formal classroom setting. As Falbo provides his methodology on how best to use this textbook within a classroom environment, one interesting strategy that stands out is that of using the solutions as “hints.” Within an IBL structure, this implements a placebo effect, where one student is asked the question while having looked at part of the solution, while the other is completely new to the problem being presented.
At the beginning of each new unit and section, Falbo presents a refreshing narrative or an example that readers can relate to. For example, when discussing asymptotes, he fittingly compares the idea of “getting close but never reaching” to a bungee jumper that hurls himself off the bridge. Math is as engaging as can be within the scope of this textbook. Complex concepts like related rates and the chain rule are easy to understand with Falbo’s step-by-step process but also within the structure of the text. The different steps are spread out nicely, and it rarely feels like the reader is being forced to process multiple steps at once, which is generally why college students often become overwhelmed when attempting such a feat.
From sections on useful tricks to speaking to the student through his prose between parts of a question, it almost feels as though the author is present right alongside the students. In fact, his arrangement of the work clearly takes into account many of the questions that he believes students might encounter. He then focuses on proactively presenting counters and solutions. Whether one is a self-learner, a student, or an educator determined to help students understand math from the vantage point of inquiry, Falbo’s work and focus on the IBL method is a valuable tool and a worthwhile read.