With sample problems and solutions, this book demonstrates how teachers can incorporate nine problem solving strategies into any mathematics curriculum to help students succeed.
This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.
This updated edition presents ten strategies that are effective tools for teaching students how to solve problems, both in mathematics and in real-life situations. The authors demonstrate how the strategies can be used to solve a wide range of problems and provide about 200 examples that illustrate how teachers can include these techniques in their mathematics curriculum. In many cases, the methods presented make the solution of a problem easier, neater, and more understandable-and thereby more enjoyable. This new edition includes references to current standards, revisions and clarifications throughout the text, and a number of new problems that can be used to teach the different strategies.
Many schools throughout the United States are now employing coaches to support teachers in the teaching of mathematics. Very often, these are professionals selected from the current teaching ranks who did not receive any special training to serve as a coach. This book provides the skills, knowledge, and lessons from experience that lead such a mentor to function effectively. Aside from describing the basic duties of an effective math coach, we also provide a plethora of resources to enrich instruction, improve problem-solving direction, and provide teachers with a wide variety of techniques to enhance their teaching effectiveness.
Foreword by Nobel Laureate Herbert A. Hauptman The authors present ten strategies, illustrated through 200 problems, that you can incorporate into your curriculum to help your students become effective problem solvers.
Every year new secondary mathematics teachers take up positions in middle and high schools. The luckiest novices receive assistance from a coach or mentor: a master mathematics teacher who makes constructive comments, models effective approaches, and illuminates other practical aspects of teaching secondary math. But many new teachers don't have this advantage and must further their development on their own. If you are one of these teachers, this is the book you need. In these pages, veteran mathematics educators Alfred S. Posamentier, Daniel Jaye, and Stephen Krulik present a treasure chest of ideas to guide new secondary math teachers through the challenging first few months and also provide more experienced teachers with interesting alternatives to familiar methods. The topics covered include * The most effective instructional practices * The best uses of the textbook * Designing successful lessons * Creating homework that promotes learning * Incorporating challenge * Teaching reasoning and problem solving * Strategies for assessment and grading * Specific innovative ideas for teaching key concepts * Options for extracurricular activities * Long-term professional enrichment and growth. It's during the first few years of a teacher's experience that he or she develops the habits, methods, procedures, and techniques that tend to define a career. Exemplary Practices for Secondary Math Teachers provides both a foundation for excellence and a touchstone for years to come.
Effective Techniques to Motivate Mathematics Instruction offers pre-and in-service teachers best practices and techniques that can be used to motivate students in the first few minutes of any lesson in mathematics. Veteran teacher educators Posamentier and Krulik show how a bit of creativity and planning up front pays back by enabling a successful lesson on even the most challenging mathematics topic. Organized around nine different motivational techniques, each chapter includes a variety of illustrative examples of how the technique may be applied. Designed to complement any methods textbook, this practical, accessible guide helps future math teachers ease the transition from successful student to successful teacher by developing the tools needed to create motivational introductions in their classes.
Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.
Effective teaching is largely reliant on the teacher’s ability to capture the genuine interest of the students for the material to be taught. This naturally rests on the planning that the teacher exerts in preparation for the lesson. Perhaps the single most important aspect of any lesson is the beginning of the lesson where the teacher must motivate the students for the ensuing lesson. This can be done in many ways and is also largely measure a function of the teacher’s personality and voice. Studies have shown that what a teacher says accounts for 7% of the effectiveness package, the tone of the teacher’s voice and the enthusiasm accounts for 38%, and the “body language” accounts for 55%. Teachers should be entertaining, without ever losing control of the lesson, and yet not be completely scripted to prevent accommodation to the quirks of any class. Yet even the finest style of presentation – an important part of any teaching performance – can only offer a portion of the overall effectiveness. The content of what is said is paramount! This then leads us into the theme of the book, namely, the techniques that can be used to motivate students in the first few minutes of almost any lesson in mathematics. This could be the most difficult part of a lesson to plan. It requires a modicum of creativity and yet it pays back by enabling a successful lesson. It is a very worthwhile investment of time.
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