Bøker av Sergei (State Univ Of New York At Potsdam Abramovich

The book is intended to serve as a brief companion for mathematical educators of elementary teacher candidates who learn mathematics within a college of education both at the undergraduate and graduate levels. Being informed by mathematics teaching and learning standards of the United States, Australia, Canada, Chile, England, Japan, Korea, Singapore, and South Africa, the book can be used internationally.The teaching methods emphasize the power of visualization, the use of physical materials, and support of computer technology including spreadsheet, Wolfram Alpha, and the Geometer''s Sketchpad.The basic ideas include the development of the concepts of number, base-ten system, problem solving and posing, the emergence of fractions in the context of simple real-life activities requiring the extension of whole number arithmetic, decimals, percent, ratio, geoboard geometry, elements of combinatorics, probability and data analysis.The book includes historical aspects of elementary school mathematics. For example, readers would be interested to know that two-sided counters stem from the binary system with its genesis in the 1st millennium BC China of which Leibnitz (17th century) was one of the first notable proponents. The genesis of the base-ten arithmetic is in the Egyptian mathematics of the 4th millennium BC, enriched with the positional notation with the advent of Hindu-Arabic numerals in the 12th century Europe.

The book is written to share ideas stemming from technology-rich K-12 mathematics education courses taught by the author to American and Canadian teacher candidates over the past two decades. It includes examples of problems posed by the teacher candidates using computers. These examples are analyzed through the lenses of the theory proposed in the book.Also, the book includes examples of computer-enabled formulation as well as reformulation of rather advanced problems associated with the pre-digital era problem-solving curriculum. The goal of the problem reformulation is at least two-fold: to make curriculum materials compatible with the modern-day emphasis on democratizing mathematics education and to find the right balance between positive and negative affordances of technology.The book focuses on the use of spreadsheets, Wolfram Alpha, Maple, and The Graphing Calculator (also known as NuCalc) in problem posing. It can be used by pre-service and in-service teachers interested in K-12 mathematics curriculum development in the digital era as well as by those studying mathematics education from a theoretical perspective.

The book includes material that the author would have shared with teacher candidates should there have been more instructional time than a 3 credit hour master's level course, "Elementary Mathematics: Content and Methods," provides. Thus the book can supplement a basic textbook for such a course by extending content and diversifying methods.

The goal of the book is to technologically enhance the preparation of mathematics schoolteachers using an electronic spreadsheet integrated with Maple and Wolfram Alpha - digital tools capable of sophisticated symbolic computations.