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.
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Sample Chapter(s)
Preface
Sample of chapter 6, section 6.8
Sample of activity set 1–3
Chapter 2: Teaching Operations in Grades 1-4
Chapter 3: Conceptual Shortcuts
Chapter 5: Activities with Addition and Multiplication Tables
Contents:
- Preface
- Teaching PreK — K Mathematics
- Teaching Operations in Grades 1–4
- Conceptual Shortcuts
- Decomposition of Integers Into Like Addends
- Activities with Addition and Multiplication Tables
- Using Technology in Posing and Solving Problems
- Fractions
- From Fractions to Decimals to Percent
- Ratio as a Tool of Comparison of Two Quantities
- Geometry
- Elements of Combinatorics: Counting Through a System
- Elements of Probability Theory and Data Management
- Developing Technology Used in the Book
- Appendix — Activity Sets: 300 Problems and Questions
- Bibliography
- Index
Readership: Prospective teachers of elementary mathematics, teacher educators, graduate students in mathematics education doctoral programs.
"This book fully covers the curriculum of elementary schools in the countries of Central Europe – even if the author adapted it, as he himself states, to the curricula of the USA, England, Australia, Singapore, and other non-European countries. (The fact that the curricula of elementary schools in most countries are similar is of course a positive message; I mention it in this context just because this book is a very useful companion not only in the countries Abramovich mentions, but certainly also in the above mentioned countries of Central Europe (I can confirm it, because my more than 40 years experiences in teaching mathematics for prospective mathematics teachers at elementary schools in the Czech Republic, Slovakia, Poland, Hungary, Austria, Germany) and certainly also in other countries.)
I appreciate that Abramovich shares a lot of both evidently personal experiences and other researchers' results to help readers understand the issue of teaching elementary mathematics. I am convinced that elementary math teachers will use the book effectively in their teaching now, and for the next several decades as well - that's how relevant this book is!"
Tomáš Zdráhal
Palacký University Olomouc, Czech Republic
"Dr Abramovich is a leader on the use of technology for teaching and learning mathematics. His knowledge of technology, pedagogy, and mathematics become apparent in this book, where he also weaves in the history of mathematics. These connections include reference to Egyptians' use of unit fractions and their early version of a base-10 number system.
His focus on mathematical images is supported by numerous illustrative figures. He also includes a chapter explaining how teachers and students might use various technologies (including spreadsheets and geometry software) to reproduce the dynamic images and investigations referred to in the other chapters. In sum, the book brings together mathematics, history, imagery, and technology to engage future teachers and other readers in some of the most interesting aspects of elementary school mathematics."
Anderson Norton
Professor, Department of Mathematics, Virginia Tech
Sergei Abramovich is Professor of mathematics education at the State University of New York (SUNY Potsdam) School of Education in the United States. He did all his studies at St. Petersburg (then Leningrad) State University, Russia, earning PhD in mathematics (1981). He is author/co-author/editor of ten books and 230 articles on mathematics education, differential equations, and control theory. His service to educational community includes two founding editor-in-chief appointments (Open Mathematical Education Notes, Bosnia & Herzegovina/United States and Advances in Educational Research and Evaluation, Singapore) and membership on editorial boards of another six professional journals published in Australia, England, Russia, and the United States.
