Introducing Nonroutine Math Problems to Secondary Learners 60+ Engaging Examples and Strategies to Improve Higher-Order Problem-Solving Skills
Offering secondary math educators an innovative holistic and process-orientated approach for implementing nonroutine problems into their curriculum, this book defines and establishes practical strategies to develop students’ problem-solving skills. The text focuses on the process skills necessary to solve nonroutine problems in mathematics and other subjects, with the goal of making students better problem-solvers both in and outside of the classroom.
Chapters present and define a curriculum of over 60 nonroutine problems in mathematics and other content areas, and explore the pedagogy to implement this type of curriculum consistent with the NCTM Standards and Principles to Action. Four different models of implementation are discussed, alongside a structured approach through seven difficulty levels (with examples), to ensure that every student, independent of their mastery of mathematics content, can improve their ability to solve nonroutine problems. It emphasizes to students how to transfer their problem-solving skills to other real-world areas, including increasing ecological awareness, appreciating diversity and addressing significant and meaningful problems in their life, school and community. The curriculum introduced in this book can be included as a component of a traditional four-year academic high school curriculum aligned with the Common Core Mathematical Practices, or as part of a one-year isolated required or elective mathematics course.
Based on extensive field-testing this approach has been effective in both traditional mathematics courses and math electives such as a course in Problem-Solving. This book provides the necessary guidance to allow each mathematics teacher to effectively integrate the approach in their classrooms. This book is ideal for secondary mathematics teachers of all levels, as well as teachers of mathematics electives.
1. Introduction 2. Conceptual framework and pedagogy 3. Introductory problems 4. Geometry 5. Algebra and precalculus 6. Prediction, estimation, probability and miscellaneous mathematics content 7. Introductory nonroutine problems in a non-mathematical context 8. Ecology problems and problems that attempt to increase the student's appreciation of diversity 9. Practical applications affecting students’ lives 10. Models of implementing a curriculum of nonroutine problems 11. Additional nonroutine problems and resources
'Introducing Nonroutine Math Problems provides a tested, creative, and practical approach to developing mastery in problem solving through mathematics–but what is more revelatory is that it cultivates the deep processes that are equally relevant to the immediate problems of our lives and our world. For both self and for schooling, it is transformative, masterful, and meaningful.'
--Tobin Hart, Ph.D, Professor of Psychology, University of West Georgia
'Bob London’s research-based, holistic approach is discussed with depth and clarity in Introducing Nonroutine Math Problems to Secondary Learners. It is supported by an extensive use of strategies and examples, thereby making it an excellent context and resource for exploring the CCMP.'
-- Dr Marian de Souza, Retired from Australian Catholic University, Australia
'Introducing Nonroutine Math Problems is an amazing contribution to mathematics education and to learning that is relevant, holistic, and engaging. Written in a personal style, Dr. London guides educators through each process and activity. This book will change your classroom and touch your students’ lives.'
-- Sam Crowell, co-author, Emergent Teaching