Conceptual Understanding in Mathematics: A Handbook on the Reasoning Behind Selected Mathematical Topics

By Brian R. Evans

This brief handbook is intended for educators, parents/guardians, students, or anyone simply interested in understanding the reasoning behind selected basic, and not so basic, mathematical topics. Another intention of the handbook is to present the reader with a selected group of counterintuitive results found in mathematics, which would prove interesting for the reader and for students in mathematics. Despite the emphasis on understanding in the educational research literature and teacher education programs, many students continue to learn mathematics procedurally with a lack of real conceptual understanding. Research shows that many new teachers revert to teaching the way they were taught when they were in school, and not the way they were taught to teach in their teacher education programs. Moreover, teachers often claim that they believe in teaching for understanding and through problem solving, but continue to teach their students procedural knowledge only. Perhaps for some teachers it can be a lack of understanding in their own mathematical background that prevents them from teaching from an understanding perspective. When a person learns mathematics procedurally without real understanding, he or she is more likely to later forget what was learned rather than if the mathematics if fully understood initially. This handbook is intended for those interested in knowing the "why" behind selected mathematical concepts. Further, this book presents mathematics in a motivating way to make the subject more interesting. There is a reciprocal relationship between understanding and enjoying mathematics because people generally find mathematics more interesting when they truly understand what they are learning.The contents of this book begin with the basics structure of the number system and then progresses through basic operations, exponents, logarithms, compound interest, fractions, decimals, percentages, area of selected shapes, counting techniques, and calculus. As the book progresses, the mathematics becomes more sophisticated. The author recommends the reader attempt to understand the content of the entire book, but acknowledges that some readers may wish to stop at a certain point or ask someone for more assistance. In some cases, skipping to other sections of the book may prove useful. For example, it might make sense to skip the sections on exponents, logarithms, and compound interest in order to get to the section on fractions after the reader read about basic operations. The book is meant to be an overview of important topics, but some readers may focus on one or more sections only. Mathematics is a fascinating subject and hopefully this brief handbook will be a start for further mathematical explorations. If approached from the right perspective, mathematics can be enjoyable and engaging, and understanding the deep mathematical ideas behind the basic concepts will motivate a person to want to learn more. This is a major shift in the way in which mathematics can be viewed.

• Format: Paperback
• Language: English
• ISBN: 1515378020
• ISBN13: 9781515378020
• Release Date: August 2015
• Publisher: CreateSpace Independent Publishing Platform
• Length: 188 Pages
• Weight: 0.45 lbs.
• Dimensions: 8.0" x 0.4" x 5.0"