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The Effective Learning and Teaching in Higher Education series is packed with up-to-date advice, guidance and expert opinion on teaching in the key subjects in higher education today, and is backed up by the authority of the Institute for Learning and Teaching. This book covers all of the key issues surrounding the effective teaching of maths- a key subject in its own right, and one that forms an important part of many other disciplines. The book includes contributions from a wide range of experts in the field, and has a broad and international perspective.
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.
Develop a deep understanding of mathematics. This user-friendly resource presents grades 6–8 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Make connections between elementary fraction-based content to fraction operations taught in the middle grades. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to grow as both learners and teachers of mathematics. Gain clarity about the most productive progression of mathematical teaching and learning for grades 6–8. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Fraction Operations and Integer Concepts and Operations 2 Ratios and Proportional Relationships 3 Equations, Expressions, and Inequalities 4 Functions 5 Measurement and Geometry 6 Statistics and Probability Epilogue: Next Steps References and Resources Index
This Handbook presents an overview and analysis of the international `state-of-the-field' of mathematics education at the end of the 20th century. The more than 150 authors, editors and chapter reviewers involved in its production come from a range of countries and cultures. They have created a book of 36 original chapters in four sections, surveying the variety of practices, and the range of disciplinary interconnections, which characterise the field today, and providing perspectives on the study of mathematics education for the 21st century. It is first and foremost a reference work, and will appeal to anyone seeking up-to-date knowledge about the main developments in mathematics education. These will include teachers, student teachers and student researchers starting out on a serious study of the subject, as well as experienced researchers, teacher educators, educational policy-makers and curriculum developers who need to be aware of the latest areas of knowledge development.
This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning.
In today′s higher education climate academic staff are encouraged to focus not only on the up-to-date content of their teaching, but also to identify the most effective ways to engage students in learning, often alongside other key transferrable skills. This had led to a growing requirement for staff to adopt a scholarly approach to learning and teaching practice, and to undertake scholarship of learning and teaching as part of ongoing professional development. This text explores broad best practice approaches to undertaking enquiry into learning and teaching in higher education. It provides an introduction for staff who have been educated within a range of academic disciplines, often with high-level but very focused knowledge about, and understandings of, research processes to the potentially new world of educational enquiry. This is complemented by chapters exploring what educational enquiry means in the context of different academic disciplines, including physical sciences, mathematics, engineering, the life sciences, the arts, the humanities, the health professions, and law. It also includes: An overview of research methodology including data collection, literature reviews, good ethical practice, and research dissemination Case studies of actual research projects to support understanding of how to carry out educational enquiry in practice. Lecturers, why waste time waiting for the post arrive? Request and receive your e-inspection copy today!
Select the right task, at the right time, for the right phase of learning It could happen in the morning during homework review. Or perhaps it happens when listening to students as they struggle through a challenging problem. Or maybe even after class, when planning a lesson. At some point, the question arises: How do I influence students′ learning—what’s going to generate that light bulb "aha" moment of understanding? In this sequel to the megawatt best seller Visible Learning for Mathematics, John Almarode, Douglas Fisher, Nancy Frey, John Hattie, and Kateri Thunder help you answer that question by showing how Visible Learning strategies look in action in the mathematics classroom. Walk in the shoes of middle school teachers as they engage in the 200 micro-decisions-per-minute needed to balance the strategies, tasks, and assessments seminal to high-impact mathematics instruction. Using grade-leveled examples and a decision-making matrix, you’ll learn to Articulate clear learning intentions and success criteria at surface, deep, and transfer levels Employ evidence to guide students along the path of becoming metacognitive and self-directed mathematics achievers Use formative assessments to track what students understand, what they don’t, and why Select the right task for the conceptual, procedural, or application emphasis you want, ensuring the task is for the right phase of learning Adjust the difficulty and complexity of any task to meet the needs of all learners It’s not only what works, but when. Exemplary lessons, video clips, and online resources help you leverage the most effective teaching practices at the most effective time to meet the surface, deep, and transfer learning needs of every student.
Core concepts in education are changing. For example, professional performance or expertise is not uniquely the fruit of specialist knowledge acquired at professional schools, but the sum of influences exerted by a complex web of continuous learning opportunities for which an individual is well (or ill) prepared by their schools and their workplace. The key contributory factors to professional expertise are how professional schools connect to professional practice, how schools prepare graduates for continuous learning, and how the workplace endorses continuous development. Thus, the question this volume addresses—how to design learning and working environments that facilitate the integration of these three elements—is at the heart of contemporary pedagogical theory. The authors also ask a second vital question: how do we educate learners that go on to maximize their life’s learning opportunities by regulating their own ongoing learning? Learning at the Crossroads of Theory and Practice argues that with the theory of learning at a crossroads, this is an unprecedented opportunity for learning about learning. The book sheds light on different elements of this challenge: integrating theory and practice in business education, generating and fully exploiting workplace learning opportunities, and enriching our classrooms by coupling theoretical knowledge with the richness of real-life experience.
This volume offers insights from modeling relations between teacher quality, instructional quality and student outcomes in mathematics across countries. The relations explored take the educational context, such as school climate, into account. The International Association for the Evaluation of Educational Achievement’s Trends in Mathematics and Science Study (TIMSS) is the only international large-scale study possessing a design framework that enables investigation of relations between teachers, their teaching, and student outcomes in mathematics. TIMSS provides both student achievement data and contextual background data from schools, teachers, students and parents, for over 60 countries. This book makes a major contribution to the field of educational effectiveness, especially teaching effectiveness, where cross-cultural comparisons are scarce. For readers interested in teacher quality, instructional quality, and student achievement and motivation in mathematics, the comparisons across cultures, grades, and time are insightful and thought-provoking. For readers interested in methodology, the advanced analytical methods, combined with application of methods new to educational research, illustrate interesting novel directions in methodology and the secondary analysis of international large-scale assessment (ILSA).
Winner of the Mathematics Association of America's 2021 Euler Book Prize, this is an inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish“This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math Project"A good book is an entertaining read. A great book holds up a mirror that allows us to more clearly see ourselves and the world we live in. Francis Su’s Mathematics for Human Flourishing is both a good book and a great book."—MAA Reviews For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity’s most beautiful ideas.In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award‑winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires—such as for play, beauty, freedom, justice, and love—and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother’s, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher’s letters to the author appear throughout the book and show how this intellectual pursuit can—and must—be open to all.