Mathematics via Problems: Part 2: Geometry

Zaslavsky and Skopenkov’s Mathematics via Problems Part 2: Geometry is not your average textbook. Though it touches upon most high school geometry topics, it does go beyond the level required by the standards. In fact, it is not an instructive book for students’ first time engaging with relevant geometry content; rather, it is a collection of relevant problems meant to be pondered and discussed. The book serves as a problem-solving agenda for mathematics clubs and communities of practice called “math circles.” Math circles are vertical clubs of mathematicians, from elementary-aged students to professionals and researchers, that support engagement with mathematics via problems.

 

Mathematics via Problems Part 2: Geometry is arranged into eight chapters with many sections and sub-sections. The textbook is arranged by concept with similar ideas placed together, though the rigor and needed scaffolding may be different. For instance, the authors indicate it may be necessary to complete problems placed near the end of the book to fully understand some problems near the beginning. 

 

In addition to its intended use in math circles, this book was also designed with the Mathematics Olympiad and similar competitions in mind where students need to use geometric and algebraic considerations. The problems in this book are not straightforward, as they are intended to require investigation and inventiveness. Some problems include solutions, proofs, proof sketches, or hints, but some do not come with a solution. In fact, some of them have not yet been solved. 

 

The intended audience for this book is wide due to the problems’ open-ended nature and focus on collaboration and discussion. It is ideal for students participating in mathematics competitions at the high school level, extension material for high school students in talented and gifted mathematics programs, supplemental material for undergraduate geometry courses, mathematics clubs, and high school mathematics instructors seeking opportunities for mathematical investigation. 

 

Since the problems included in the book are rather difficult compared to exercises more commonly found in high school geometry textbooks, it is recommended that these problems be used as to supplement other geometry course materials.  

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About the reviewer: Jasmine Sourwine is a Ph.D. student in Mathematics Education at Iowa State University. As a former secondary mathematics instructor, her research focuses on effective strategies to increase equity in mathematics classrooms.