Mathematics Professor Emeritus Clement E. Falbo explores the Inquiry-Based Learning (IBL) of calculus through questions and answers in this comprehensive textbook. As he explains in the preface, “This process is akin to the Socratic method initiated 2,400 years ago. It worked then, and it works really well today.” This method of teaching math through student-led presentations of problems in class has been aptly demonstrated to teach mathematics more effectively than passive-listening instructor lectures. This method is now known internationally as the Moore method or Texas method, as it was embraced by the author’s mentor, Dr. R.L. Moore, and his colleagues at the University of Texas, Austin, in the 1930s through the 1970s. Falbo studied with Moore in the 1950s, and the text is based on his notes taken as a student.

Many mathematicians who experienced this student-led teaching method to maximize student participation also use IBL today with their own refinements, referred to as “Modified Moore Methods.” Though users of the IBL method sometimes eliminate textbooks from the classroom, this text is promoted as containing Dr. Moore’s system of calculus problems designed to stimulate student-based discovery of solutions. Calculus is considered a difficult mathematic subject in that it requires more abstract and creative thinking than the algebra, geometry, and pre-calculus studies that the discipline is based on. Calculus has its own vocabulary, with some new symbols and processes defined in the discipline.

Calculus is considered to be one of the most frustrating mathematical subjects to master, and the term for the discipline itself is derived from Latin, meaning “small stone.” Perhaps in keeping with this meaning, Dr. Falbo leaves no stone unturned in the twenty-five chapters of this textbook, which walk the student through the various types of first-year calculus problems, supported by an appendix of answers to chapter exercises and chapter homework exercises in the back matter. Dr. Falbo occasionally discusses various concepts in prose narrative, but much of the text relies on mathematical fluidity and familiarity with all mathematic subjects leading up to the study of calculus. Math novices or students who have math fluency difficulties, for example, won’t find much narrative in this book that supports the overall understanding of calculus.

However, students with math fluency should have no problem grasping the carefully presented mathematical concepts written as formulas to be solved. At times, the axioms helpfully relate to real-world problems, such as estimating the weight of a marble tabletop based on its density. Students with mathematical knowledge gaps or who are uncomfortable with math often have an easier time learning mathematical concepts through the application of real-world situations in problems. While most people studying calculus are degree-seeking math majors, sometimes calculus can be a required course for non-math major students, who often value math texts that embrace environmental science or other subjects that help to better illustrate mathematical concepts. On the flip side, studies have shown that overexplaining or giving too much detail in math textbooks sometimes impairs learning.

Thankfully, this textbook applies the principle of using real-world data in some chapters but also strikes a healthy balance by supposing reader familiarity and fluency with mathematical axioms in others, a somewhat expected situation in this advanced subject. Dr. Falbo’s many years of studying and teaching mathematics qualify him as an authority on teaching calculus and creating a calculus textbook with an approach that supports IBL. The author’s textbook could prove to be an excellent resource for students who are studying the subject.

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