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This volume and its companion for prekindergarten through grade 6 furnish the coherence and direction that teachers need to use problem solving to teach mathematics.
This book shows how problems can be the vehicle for learning mathematics itself, and presents a comprehensive pedagogy based on classroom discourse, assessment, critical and creative thinking.
Help your students to think critically and creatively through team-based problem solving instead of focusing on testing and outcomes. Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as outcomes rather than as individuals who require guidance on thinking critically and creatively. Awesome Math focuses on team-based problem solving to teach discrete mathematics, a subject essential for success in the STEM careers of the future. Built on the increasingly popular growth mindset, this timely book emphasizes a problem-solving approach for developing the skills necessary to think critically, creatively, and collaboratively. In its current form, math education is a series of exercises: straightforward problems with easily-obtained answers. Problem solving, however, involves multiple creative approaches to solving meaningful and interesting problems. The authors, co-founders of the multi-layered educational organization AwesomeMath, have developed an innovative approach to teaching mathematics that will enable educators to: Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration Encourage and reinforce curiosity, critical thinking, and creativity in their students Get students into the growth mindset, coach math teams, and make math fun again Create lesson plans built on problem based learning and identify and develop educational resources in their schools Awesome Math: Teaching Mathematics with Problem Based Learning is a must-have resource for general education teachers and math specialists in grades 6 to 12, and resource specialists, special education teachers, elementary educators, and other primary education professionals.
"The book emphasizes that effective mathematics teachers plan lessons that include a more complete development of mathematical ideas, use visuals supporting mental imagery, present opportunities for kinesthetic learning activities, provide chances for children to communicate their understanding of mathematics, and allow for continual monitoring of student learning. Lessons include straightforward, easy-to-use learning activities illustrating specific mathematical concepts and skills, visuals to help develop mental imagery, and opportunities for active student learning."--publisher website.
Problem-solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem-solving skills, this book helps teachers engage students in the process. Problem Solving in Mathematics, Grades 3-6 presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can Use the strategies with students at different grade levels Incorporate these strategies into a mathematics program Apply each strategy to real-life situations Make each strategy an integral part of students' thinking processes With helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics! Book jacket.
Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the role of teachers in problem-solving classrooms and their professional development, moving onto—secondly—the role of students when solving problems, with particular consideration of factors like group work, discussion, role of students in discussions and the effect of students’ engagement on their self-perception and their view of mathematics. Finally, the book considers the question of problem solving in mathematics instruction as it overlaps with problem design, problem-solving situations, and actual classroom implementation. The volume brings together diverse contributors from a variety of countries and with wide and varied experiences, combining the voices of leading and developing researchers. The book will be of interest to any reader keeping on the frontiers of research in problem solving, more specifically researchers and graduate students in mathematics education, researchers in problem solving, as well as teachers and practitioners.
This engaging book offers an in-depth introduction to teaching mathematics through problem-solving, providing lessons and techniques that can be used in classrooms for both primary and lower secondary grades. Based on the innovative and successful Japanese approaches of Teaching Through Problem-solving (TTP) and Collaborative Lesson Research (CLR), renowned mathematics education scholar Akihiko Takahashi demonstrates how these teaching methods can be successfully adapted in schools outside of Japan. TTP encourages students to try and solve a problem independently, rather than relying on the format of lectures and walkthroughs provided in classrooms across the world. Teaching Mathematics Through Problem-Solving gives educators the tools to restructure their lesson and curriculum design to make creative and adaptive problem-solving the main way students learn new procedures. Takahashi showcases TTP lessons for elementary and secondary classrooms, showing how teachers can create their own TTP lessons and units using techniques adapted from Japanese educators through CLR. Examples are discussed in relation to the Common Core State Standards, though the methods and lessons offered can be used in any country. Teaching Mathematics Through Problem-Solving offers an innovative new approach to teaching mathematics written by a leading expert in Japanese mathematics education, suitable for pre-service and in-service primary and secondary math educators.
This updated edition presents ten strategies for solving a wide range of mathematics problems, plus new sample problems.
The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.
This book is the first in the series of the yearbooks of the Association of Mathematics Educators in Singapore. It is highly unique as it addresses a focused theme of mathematics education. The chapters of the book, illustrate the immense diversity within the theme and presents research that translates into classroom pedagogies. The thirteen chapters of the book illustrate how mathematical problems may be crafted and infused in classroom teaching. Several novel pedagogies, such as learning mathematics through productive failure, problem posing and generative activities are presented in the book. The chapters are comprehensive and laden with evidence-based examples for both mathematics educators and classroom teachers of mathematics. The book is an invaluable contribution towards the already established field of research of mathematical problem solving. It is also a must read for graduate research students and mathematics educators.
