Basic Principles of Chinese Philosophy (2 vols.)

This book shares ideas about integrating mathematical problem posing with the use of computing technology in the context of K-12 mathematics teacher preparation. Problem posing has been on the mathematics education agenda for a long time. Over the centuries, it appeared in different didactic forms as a way of enriching one's learning experience through investigating mathematical ideas, exploring conjectures, and solving worthwhile problems. In the digital era, mathematics teacher training may include learning the skill of formulating different mathematical problems that the appropriate use of technology affords. As shown in the book, problem posing skills can be supported by two major theoretical positions that stem from technology integration: didactical coherence of a posed problem (Chapter 2) and technology-immune /technology-enabled (TITE) problem posing (Chapter 3). In order to connect theory and practice of mathematical problem posing in the digital era, the book includes examples of problems posed by teacher candidates enrolled in different technology-rich mathematics education courses taught by the author over the years. These examples are analyzed through the lenses of the proposed theory. In addition, the book shows how technology can be used to reformulate rather advanced problems from the traditional (pre-digital era) problem-solving curriculum. The goal of reformulation of such problems is at least two-fold: to make them compatible with the modern-day emphasis on democratizing mathematics education, and to find the right balance between positive and negative affordances of technology. In particular, an argument can be made that through achieving such a balance one uses technology appropriately.