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Integrating Computers And Problem Posing In Mathematics Teacher Education (Hardcover): Sergei Abramovich Integrating Computers And Problem Posing In Mathematics Teacher Education (Hardcover)
Sergei Abramovich
R1,881 R1,754 Discovery Miles 17 540 Save R127 (7%) Shipped within 7 - 12 working days

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.

Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers (Paperback):... Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers (Paperback)
Sergei Abramovich
R858 Discovery Miles 8 580 Shipped within 7 - 12 working days

The book is written to enhance the preparation of elementary teacher candidates by offering teaching ideas conducive to the development of deep understanding of concepts fundamental to the mathematics curriculum they are to teach. It intends to show how the diversity of teaching methods stems from the knowledge of mathematics content and how the appreciation of this diversity opens a window to the teaching of extended content.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.Also, the book can support graduate level mathematics education programs which have problem-solving seminars/courses in their curriculum. The book is well-informed with (available in English) the mathematical standards and recommendations for teachers from Australia, Canada, Chile, England, Japan, Korea, Singapore, and the United States.

Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers (Hardcover):... Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers (Hardcover)
Sergei Abramovich
R1,802 R1,683 Discovery Miles 16 830 Save R119 (7%) Shipped within 7 - 12 working days

The book is written to enhance the preparation of elementary teacher candidates by offering teaching ideas conducive to the development of deep understanding of concepts fundamental to the mathematics curriculum they are to teach. It intends to show how the diversity of teaching methods stems from the knowledge of mathematics content and how the appreciation of this diversity opens a window to the teaching of extended content.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.Also, the book can support graduate level mathematics education programs which have problem-solving seminars/courses in their curriculum. The book is well-informed with (available in English) the mathematical standards and recommendations for teachers from Australia, Canada, Chile, England, Japan, Korea, Singapore, and the United States.

Exploring Mathematics With Integrated Spreadsheets In Teacher Education (Paperback): Sergei Abramovich Exploring Mathematics With Integrated Spreadsheets In Teacher Education (Paperback)
Sergei Abramovich
R859 Discovery Miles 8 590 Shipped within 7 - 12 working days

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. The content of the book is a combination of mathematical ideas and concepts associated with pre-college problem solving curriculum and their extensions into more advanced mathematical topics.The book provides prospective and practicing teachers with a foundation for developing a deep understanding of many concepts fundamental to the teaching of school mathematics. It also provides the teachers with a technical expertise in designing spreadsheet-based computational environments.Consistent with the current worldwide guidelines for technology-enhanced teacher preparation, the book emphasizes the integration of context, mathematics, and technology as a method for teaching mathematics. Throughout the book, a number of mathematics education documents developed around the world (Australia, Canada, England, Japan, Singapore, United States) are reviewed as appropriate.

Exploring Mathematics With Integrated Spreadsheets In Teacher Education (Hardcover): Sergei Abramovich Exploring Mathematics With Integrated Spreadsheets In Teacher Education (Hardcover)
Sergei Abramovich
R1,804 R1,684 Discovery Miles 16 840 Save R120 (7%) Shipped within 7 - 12 working days

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. The content of the book is a combination of mathematical ideas and concepts associated with pre-college problem solving curriculum and their extensions into more advanced mathematical topics.The book provides prospective and practicing teachers with a foundation for developing a deep understanding of many concepts fundamental to the teaching of school mathematics. It also provides the teachers with a technical expertise in designing spreadsheet-based computational environments.Consistent with the current worldwide guidelines for technology-enhanced teacher preparation, the book emphasizes the integration of context, mathematics, and technology as a method for teaching mathematics. Throughout the book, a number of mathematics education documents developed around the world (Australia, Canada, England, Japan, Singapore, United States) are reviewed as appropriate.

Revisiting Fibonacci Numbers through a Computational Experiment (Paperback): Sergei Abramovich, Gennady A. Leonov Revisiting Fibonacci Numbers through a Computational Experiment (Paperback)
Sergei Abramovich, Gennady A. Leonov
R4,092 R2,725 Discovery Miles 27 250 Save R1,367 (33%) Shipped within 7 - 12 working days

The material of this book stems from the idea of integrating a classic concept of Fibonacci numbers with commonly available digital tools including a computer spreadsheet, Maple, Wolfram Alpha, and the graphing calculator. This integration made it possible to introduce a number of new concepts such as: Generalized golden ratios in the form of cycles represented by the strings of real numbers; Fibonacci-like polynomials the roots that define those cycles dependence on a parameter; the directions of the cycles described in combinatorial terms of permutations with rises, as the parameter changes on the number line; Fibonacci sieves of order k; (r, k)-sections of Fibonacci numbers; and polynomial generalizations of Cassinis, Catalans, and other identities for Fibonacci numbers.The development of these concepts was motivated by considering the difference equation f_(n+1)=af_n+bf_(n-1),f_0=f_1=1, and, by taking advantage of capabilities of the modern-day digital tools, exploring the behavior of the ratios f_(n+1)/f_n as n increases. The initial use of a spreadsheet can demonstrate that, depending on the values of a and b, the ratios can either be attracted by a number (known as the Golden Ratio in the case a = b = 1) or by the strings of numbers (cycles) of different lengths. In general, difference equations, both linear and non-linear ones serve as mathematical models in radio engineering, communication, and computer architecture research. In mathematics education, commonly available digital tools enable the introduction of mathematical complexity of the behavior of these models to different groups of students through the modern-day combination of argument and computation.The book promotes experimental mathematics techniques which, in the digital age, integrate intuition, insight, the development of mathematical models, conjecturing, and various ways of justification of conjectures. The notion of technology-immune/technology-enabled problem solving is introduced as an educational analogue of the notion of experimental mathematics. In the spirit of John Dewey, the book provides many collateral learning opportunities enabled by experimental mathematics techniques. Likewise, in the spirit of George Polya, the book champions carrying out computer experimentation with mathematical concepts before offering their formal demonstration.The book can be used in secondary mathematics teacher education programs, in undergraduate mathematics courses for students majoring in mathematics, computer science, electrical and mechanical engineering, as well as in other mathematical programs that study difference equations in the broad context of discrete mathematics.

Computers in Education - Volume 2 (Hardcover, New): Sergei Abramovich Computers in Education - Volume 2 (Hardcover, New)
Sergei Abramovich
R2,971 R1,992 Discovery Miles 19 920 Save R979 (33%) Shipped within 7 - 12 working days

This two-volume collection of diverse international experiences and perspectives on the current use of computers in education is a joint effort of fifty-seven authors from sixteen countries. Most of the chapters describe current work of the authors on the use of computers in their respective areas of education. The material of this volume should be of interest to teacher educators in the areas of science, technology, engineering and mathematics (STEM) education involved in the use of computers as teaching tools; tertiary education faculty in STEM areas; curriculum developers; policy makers at different levels; and college students in STEM-related programs.

Computer-Enabled Mathematics - Integrating Experiment & Theory in Teacher Education (Hardcover, New): Sergei Abramovich Computer-Enabled Mathematics - Integrating Experiment & Theory in Teacher Education (Hardcover, New)
Sergei Abramovich
R1,900 R1,294 Discovery Miles 12 940 Save R606 (32%) Shipped within 7 - 12 working days

This book addresses core recommendations by the Conference Board of the Mathematical Sciences -- an umbrella organisation consisting of sixteen professional societies in the United States-regarding the mathematical preparation of the teachers. According to the Board, the concept of a capstone course in a mathematics education program includes teachers' learning to use commonly available educational software with the goal to reach a certain depth of the mathematics curriculum through appropriately designed computational experiments. In turn, the notion of experiment in the teaching of mathematics sets up a path toward enhancing the "E" component of the teachers' literacy in the STEM disciplines. This book discusses experiences in teaching a computer-enhanced capstone course for prospective teachers of high school mathematics.

Computers in Education - Volume 1 (Hardcover): Sergei Abramovich Computers in Education - Volume 1 (Hardcover)
Sergei Abramovich
R2,961 R1,982 Discovery Miles 19 820 Save R979 (33%) Shipped within 7 - 12 working days

This two-volume collection of diverse international experiences and perspectives on the current use of computers in education is a joint effort of fifty-seven authors from sixteen countries. Most of the chapters describe current work of the authors on the use of computers in their respective areas of education. The first volume includes chapters describing history and future trends of educational computing, technological infrastructure of Brazilian public education, the use of e-textbooks by college students in the United States, on-line leaning at the middle school level in Australia, theoretical aspects of knowledge sharing in technology-supported environments, the interplay between learning theories and technology, the integration of Web 2.0 tools in education, knowledge authoring in e-learning environments, application of technology to special education, and the use of computers in the teaching of physical education.

Topics in Mathematics for Elementary Teachers - A Technology-Enhanced Experiential Approach (Hardcover, New): Sergei Abramovich Topics in Mathematics for Elementary Teachers - A Technology-Enhanced Experiential Approach (Hardcover, New)
Sergei Abramovich
R2,076 R1,773 Discovery Miles 17 730 Save R303 (15%) Shipped within 7 - 12 working days

This book reflects the author's experience in teaching a mathematics content course for pre-service elementary teachers. The book addresses a number of recommendations of the Conference Board of the Mathematical Sciences for the preparation of teachers demonstrating how abstract mathematical concepts can be motivated by concrete activities. Such an approach, when enhanced by the use of technology, makes it easier for the teachers to grasp the meaning of generalization, formal proof, and the creation of an increasing number of concepts on higher levels of abstraction. A strong experiential component of the book made possible by the use of manipulative materials and digital technology such as spreadsheets, The Geometer's Sketchpad, Graphing Calculator 3.5 (produced by Pacific Tech), and Kid Pix Studio Deluxe makes it possible to balance informal and formal approaches to mathematics, allowing the teachers to learn how the two approaches complement each other. Classroom observations of the teachers' learning mathematics as a combination of theory and experiment confirm that this approach elevates one's mathematical understanding to a higher ground. The book not only shows the importance of mathematics content knowledge for teachers but better still, how this knowledge can be gradually developed in the context of exploring grade-appropriate activities and tasks and using computational and manipulative environments to support these explorations. Most of the chapters are motivated by a problem/activity typically found in the elementary mathematics curricula and/or standards (either National or New York State - the context in which the author prepares teachers). By exploring such problems in depth, the teachers can learn fundamental mathematical concepts and ideas hidden within a seemingly mundane problem/activity. The need to have experience in going beyond traditional expectations for learning is due to the constructivist orientation of contemporary mathematics pedagogy that encourages students to ask questions about mathematics they study. Each chapter includes an activity set that can be used for the development of the variety of assignments for the teachers. The material included in the book is original in terms of the approach used to teach mathematics to the teachers and it is based on a number of journal articles published by the author in the United States and elsewhere. Mathematics educators who are interested in integrating hands-on activities and digital technology into the teaching of mathematics will find this book useful. Mathematicians who teach mathematics to the teachers as part of their teaching load will be interested in the material included in the book as it connects childhood mathematics content and mathematics for the teachers.

Computational Experiment Approach to Advanced Secondary Mathematics Curriculum (Hardcover, 2014 ed.): Sergei Abramovich Computational Experiment Approach to Advanced Secondary Mathematics Curriculum (Hardcover, 2014 ed.)
Sergei Abramovich
R2,562 R2,329 Discovery Miles 23 290 Save R233 (9%) Shipped within 7 - 12 working days

This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, thebook addresses a call for the preparation of teachers capable of utilizing modern technology tools for the modeling-based teaching of mathematics with a focus on methods conducive to the improvement of the whole STEM education at the secondary level. By the same token, using the book's pedagogy and its mathematical content in a pre-college classroom can assist teachers in introducing students to the ideas that develop the foundation of engineering profession."

Topics in Mathematics for Elementary Teachers - A Technology-Enhanced Experiential Approach (Paperback, New): Sergei Abramovich Topics in Mathematics for Elementary Teachers - A Technology-Enhanced Experiential Approach (Paperback, New)
Sergei Abramovich
R1,126 R976 Discovery Miles 9 760 Save R150 (13%) Shipped within 7 - 12 working days

This book reflects the author's experience in teaching a mathematics content course for pre-service elementary teachers. The book addresses a number of recommendations of the Conference Board of the Mathematical Sciences for the preparation of teachers demonstrating how abstract mathematical concepts can be motivated by concrete activities. Such an approach, when enhanced by the use of technology, makes it easier for the teachers to grasp the meaning of generalization, formal proof, and the creation of an increasing number of concepts on higher levels of abstraction. A strong experiential component of the book made possible by the use of manipulative materials and digital technology such as spreadsheets, The Geometer's Sketchpad, Graphing Calculator 3.5 (produced by Pacific Tech), and Kid Pix Studio Deluxe makes it possible to balance informal and formal approaches to mathematics, allowing the teachers to learn how the two approaches complement each other. Classroom observations of the teachers' learning mathematics as a combination of theory and experiment confirm that this approach elevates one's mathematical understanding to a higher ground. The book not only shows the importance of mathematics content knowledge for teachers but better still, how this knowledge can be gradually developed in the context of exploring grade-appropriate activities and tasks and using computational and manipulative environments to support these explorations. Most of the chapters are motivated by a problem/activity typically found in the elementary mathematics curricula and/or standards (either National or New York State - the context in which the author prepares teachers). By exploring such problems in depth, the teachers can learn fundamental mathematical concepts and ideas hidden within a seemingly mundane problem/activity. The need to have experience in going beyond traditional expectations for learning is due to the constructivist orientation of contemporary mathematics pedagogy that encourages students to ask questions about mathematics they study. Each chapter includes an activity set that can be used for the development of the variety of assignments for the teachers. The material included in the book is original in terms of the approach used to teach mathematics to the teachers and it is based on a number of journal articles published by the author in the United States and elsewhere. Mathematics educators who are interested in integrating hands-on activities and digital technology into the teaching of mathematics will find this book useful. Mathematicians who teach mathematics to the teachers as part of their teaching load will be interested in the material included in the book as it connects childhood mathematics content and mathematics for the teachers.

Computational Experiment Approach to Advanced Secondary Mathematics Curriculum (Paperback, Softcover reprint of the original... Computational Experiment Approach to Advanced Secondary Mathematics Curriculum (Paperback, Softcover reprint of the original 1st ed. 2014)
Sergei Abramovich
R3,092 Discovery Miles 30 920 Shipped within 7 - 11 working days

This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, the book addresses a call for the preparation of teachers capable of utilizing modern technology tools for the modeling-based teaching of mathematics with a focus on methods conducive to the improvement of the whole STEM education at the secondary level. By the same token, using the book's pedagogy and its mathematical content in a pre-college classroom can assist teachers in introducing students to the ideas that develop the foundation of engineering profession.

Using and Developing Measurement Instruments in Science Education - A Rasch Modeling Approach (Paperback, New): Sergei... Using and Developing Measurement Instruments in Science Education - A Rasch Modeling Approach (Paperback, New)
Sergei Abramovich
R1,039 Discovery Miles 10 390 Shipped within 7 - 11 working days

A volume in Science & Engineering Education Sources Series Editor Calvin S. Kalman, Concordia University This book meets a demand in the science education community for a comprehensive and introductory measurement book in science education. It describes measurement instruments reported in refereed science education research journals, and introduces the Rasch modeling approach to developing measurement instruments in common science assessment domains, i.e. conceptual understanding, affective variables, science inquiry, learning progression, and learning environments. This book can help readers develop a sound understanding of measurement theories and approaches, particularly Rasch modeling, to using and developing measurement instruments for science education research. This book is for anyone who is interested in knowing what measurement instruments are available and how to develop measurement instruments for science education research. For example, this book can be a textbook for a graduate course in science education research methods; it helps graduate students develop competence in using and developing standardized measurement instruments for science education research. For use as a textbook there are summaries and exercises at the end of each chapter. Science education researchers, both beginning and experienced, may use this book as a reference for locating available and developing new measurement instruments when conducting a research study.

Using and Developing Measurement Instruments in Science Education - A Rasch Modeling Approach (Hardcover, New): Sergei... Using and Developing Measurement Instruments in Science Education - A Rasch Modeling Approach (Hardcover, New)
Sergei Abramovich
R1,908 Discovery Miles 19 080 Shipped within 7 - 11 working days

A volume in Science & Engineering Education Sources Series Editor Calvin S. Kalman, Concordia University This book meets a demand in the science education community for a comprehensive and introductory measurement book in science education. It describes measurement instruments reported in refereed science education research journals, and introduces the Rasch modeling approach to developing measurement instruments in common science assessment domains, i.e. conceptual understanding, affective variables, science inquiry, learning progression, and learning environments. This book can help readers develop a sound understanding of measurement theories and approaches, particularly Rasch modeling, to using and developing measurement instruments for science education research. This book is for anyone who is interested in knowing what measurement instruments are available and how to develop measurement instruments for science education research. For example, this book can be a textbook for a graduate course in science education research methods; it helps graduate students develop competence in using and developing standardized measurement instruments for science education research. For use as a textbook there are summaries and exercises at the end of each chapter. Science education researchers, both beginning and experienced, may use this book as a reference for locating available and developing new measurement instruments when conducting a research study.

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