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.

What is it that enables students to learn from some classroom activities, yet leaves them totally confused by others? Although we can't see directly into students' minds, we do have Cognitive Load Theory, and this is the next best thing. Built on the foundation of all learning, the human memory system, Cognitive Load Theory details the exact actions that teachers can take to maximise student outcomes.Written under the guidance, and thoroughly reviewed by the originator of CLT, John Sweller, this practical guide summarises over 30 years of research in this field into clear and easily understandable terms. This book features both a thorough discussion of the core principles of CLT and a wide array of classroom-ready strategies to apply it to art, music, history, chemistry, PE, mathematics, computer science, economics, biology, and more.

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

This book provides a comprehensive, up-to-date look at problem solving research and practice over the last fifteen years. The first chapter describes differences in types of problems, individual differences among problem-solvers, as well as the domain and context within which a problem is being solved. Part one describes six kinds of problems and the methods required to solve them. Part two goes beyond traditional discussions of case design and introduces six different purposes or functions of cases, the building blocks of problem-solving learning environments. It also describes methods for constructing cases to support problem solving. Part three introduces a number of cognitive skills required for studying cases and solving problems. Finally, Part four describes several methods for assessing problem solving. Key features includes: Teaching Focus – The book is not merely a review of research. It also provides specific research-based advice on how to design problem-solving learning environments. Illustrative Cases – A rich array of cases illustrates how to build problem-solving learning environments. Part two introduces six different functions of cases and also describes the parameters of a case. Chapter Integration – Key theories and concepts are addressed across chapters and links to other chapters are made explicit. The idea is to show how different kinds of problems, cases, skills, and assessments are integrated. Author expertise – A prolific researcher and writer, the author has been researching and publishing books and articles on learning to solve problems for the past fifteen years. This book is appropriate for advanced courses in instructional design and technology, science education, applied cognitive psychology, thinking and reasoning, and educational psychology. Instructional designers, especially those involved in designing problem-based learning, as well as curriculum designers who seek new ways of structuring curriculum will find it an invaluable reference tool.

With the rapid changes in the social, political, economic and technological landscape around the world, today’s learners face a more globally competitive job market after leaving school. The 21st century, which is characterized by the emergence of knowledge-based societies, expects learners to be comfortable in dealing with ambiguities and complexities in the real world and to be able to use knowledge as a tool at their workplace. This book will help readers develop an in-depth understanding of authentic problem solving and learning, and how it can be used to make a difference in their school or learning communities for the development of 21st century competencies. Comprising 20 chapters written by Singapore-based and international authors, the book is organized into three themes: authentic problems, authentic practices, and authentic participation. It details innovative school practices (e.g. productive failure) concerning the design of problems, learning activities, learning environments, and ICT tools for authentic problem solving and learning. Along with theoretical explanations of authentic learning processes and outcomes, the book also elucidates how students learn by generating and exploring solutions to complex problems and which cognitive functions are needed at different stages of problem-based learning. Presenting coherent descriptions of instructional design principles, successful cases and challenges encountered in K-12 schools and learning communities, the book provides useful information, new insights, and practical guidance for school directors, parents, teachers and researchers seeking to develop authentic learning environments for 21st century learners.

Learn to Code by Solving Problems is a practical introduction to programming using Python. It uses coding-competition challenges to teach you the mechanics of coding and how to think like a savvy programmer. Computers are capable of solving almost any problem when given the right instructions. That’s where programming comes in. This beginner’s book will have you writing Python programs right away. You’ll solve interesting problems drawn from real coding competitions and build your programming skills as you go. Every chapter presents problems from coding challenge websites, where online judges test your solutions and provide targeted feedback. As you practice using core Python features, functions, and techniques, you’ll develop a clear understanding of data structures, algorithms, and other programming basics. Bonus exercises invite you to explore new concepts on your own, and multiple-choice questions encourage you to think about how each piece of code works. You’ll learn how to: Run Python code, work with strings, and use variables Write programs that make decisions Make code more efficient with while and for loops Use Python sets, lists, and dictionaries to organize, sort, and search data Design programs using functions and top-down design Create complete-search algorithms and use Big O notation to design more efficient code By the end of the book, you’ll not only be proficient in Python, but you’ll also understand how to think through problems and tackle them with code. Programming languages come and go, but this book gives you the lasting foundation you need to start thinking like a programmer.

Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.