This work deals with chess and mathematical thinking. In the last years the interest in chess activity by educational agencies notably increased. Chess is an historical strategy game, played over the world with the same rules. The International Chess Federation (FIDE) has 181 member countries. In this book, chess is seen from different points of view: cognitive, epistemological and historical. Chess and mathematics have several common features, in particular about logic and geometrical concepts. Is chess a useful tool for Education, in particular for Mathematics Education? This book tries to give a response to this question, but, as a consequence of reflections about the nature of the teaching/learning processes and about this experimental work, it could be more correct to reformulate the question in a different way: What conditions, methods and approaches are advisable to make chess a useful practice for Education, in particular for Mathematics Education?
In the book, the authors provided broad information about the mathematical proof, its types, teaching mathematical proof, as well as about the essential role of the mathematical proof in development of the logical thinking. Besides, the proof by the method of analysis and synthesis, proof by contradiction, and proof by analogy had been widely analysed and presented to the reader. The authors came to the conclusion that the mathematical proof is an important mean in development of the logical thinking.
Drawing on instructive stories, this book reveals the strategic ways of thinking that always give a player - in life as in chess - the edge. It also reveals how and why the game of chess is a fitting and powerful teacher of how to be prepared for, and how to win in, even the most competitive situations.
Thinking is the most precious cognitive ability with which man is elevated among all animal.Thinking has several kinds and each kind has several components.This book has given a clear analysis of the different kinds of thinking and focuses on the Impact of Critical Thinking Skills on achievement in Mathematics at secondary school.Critical Thinking Skills in mathematics is the ability and disposition to incorporate prior knowledge,mathematical reasoning and cognitive strategies to generalise,prove or evaluate unfamiliar mathematical situations in a classroom for reflective manner.Students must be stimulated to think critically on their own to resolve dilemmas,take stands on issues,judge propositions about knowledge or ideas at school level.Successful mathematics teaching and learning process involves practice of critical thinking skills through Mathematics.The mathematics teacher should make sincere and consistent effort in acquiring and developing abilities and skills by learners in the classrooms.
This book is about mathematical thinking, learning and understanding. It is about ways in which good representations capture mathematical ideas, and about building broad and deep knowledge by understanding the links between those ideas. It draws on research in mathematics education and psychology to explain why some misunderstandings and confusions arise for almost everyone, and it describes ways to think about mathematical ideas correctly and with confidence.
"Chess and Maths" is an investigation that discovers links between mathematics and a game of chess. Algorithms, Theories and its examples considered in the book prove that when making a move you're actually solving a maths problem that you aren't aware of. Also it was shown how a computer functioned by a machine programming plays chess via mathematic data. Investigations with computer programming led to imagine the way computer sees the chess board and how it thinks via numbers. Part II analyses the most productive and efficient openings currently in a game of chess by usage of maths. Mathematical methods of set theory were used to find a probability of success of the openings, while heuristic evaluation function was used to examine productiveness of the openings.
Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas.* Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction* Explains identification of techniques and how they are applied in the specific problem* Illustrates how to read written proofs with many step by step examples* Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter* The Instructors Guide and Solutions Manual points out which exercises simply must be either assigned or at least discussed because they undergird later results
The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Mathematical identity is defined as the students’ knowledge, abilities, skills, beliefs, dispositions, attitudes and emotions, that relates to mathematics and mathematics learning. A key part of this relationship that students have with mathematics is the students’ evolving sense of self to understand how mathematics fits with this self. Research shows that students’ identity has many facets or multiple identities that are formed throughout their life history; engagement with their peers, family, and teachers; as well as engagement with mathematical tasks. Doing mathematics can be viewed as mathematical activity that involves integrating mathematical thinking by using mathematical facts and knowledge, and requires active student learning. Mathematical tasks used in the classroom form the basis for student’s learning and different tasks are used to develop different types of skills and thinking. These tasks often appear in curricular or instructional materials in textbooks.
Analyzing mathematical thinking while solving problems has been an interest for many researchers although it is rather challenging even in paper-and-pencil environments. Researchers, could not find a direct method to monitor and analyze mathematical thinking, have developed indirect methods such as thinking/talking aloud, keeping log files, and eye-tracking to analyze mathematical thinking. The Frame Analysis method was developed by Dr. Karadag to add a new approach to the field. The method is basically based on recording student activities in computer screen by employing a screen capture software and analyzing the captured data frame by frame. It is a qualitative analysis approach to the thick data collected from the field. The work done was completed under the supervision of Professor Douglas McDougall. I deeply acknowledge his contribution as the supervisor. It would not be made possible without his support.
Your quick and easy guide to chess Kings, queens, knights—does chess seem like a royal pain to grasp? Taking the intimidation out of this age-old pastime, Chess For Dummies, 4th Edition is here to help beginners wrap their minds around the rules of the game, make sense of those puzzling pieces, and start playing chess like a champ. From using the correct chess terminology to engaging in the art of the attack, you'll get easy-to-follow, step-by-step explanations that demystify the game—and give you an extra edge. Chess isn't a game you can master—it's an activity that requires patience, strategy, and constant learning. But that's all part of the fun and challenge! Whether you're playing chess online, in a tournament, or with a family member or friend, this hands-on guide gets you familiar with the game and its components, giving you the know-how to put the principles of play into action from the opening to the endgame. Grasp the principles of play and the nuances of each phase of the game Familiarize yourself with the pieces and the board Pick the perfect chess board and set Know each of the pieces and their powers If you find yourself in a stalemate before you even begin a game, this friendly book helps you put your chess foot forward!