Loose-leaf Version for Reconceptualizing Mathematics


Book Description

Learn by doing with active resources, discussions, and support in Reconceptualizing Mathematics and Achieve! Student-centered lessons model the teaching that will eventually be expected of you as you gain valuable hands-on experience with technology, problem solving, and quantitative reasoning.




Mathematics for Equity


Book Description

In this book, nationally renowned scholars join classroom teachers to share equity-oriented approaches that have been successful with urban high school mathematics students. Compiling for the first time major research findings and practitioner experiences from Railside High School, the volume describes the evolution of a fundamentally different conception of learners and teaching. The chapters bring together research and reflection on teacher collaboration and professional community, student outcomes and mathematics classroom culture, reform curricula and pedagogy, and ongoing teacher development. Mathematics for Equity will be invaluable reading for teachers, schools, and districts interested in maintaining a focus on equity and improving student learning while making sense of the new demands of the Common Core State Standards. Book Features: Core principles of an equity-centered mathematics program. Examples of how to focus and organize the collaborative work of a math department to develop a shared pedagogy. Student experiences with an equity pedagogy that focuses on building perseverance, flexibility in thinking, and deep conceptual understanding. Connections between reconceptualizing learners and teaching, and achieving deep mathematics learning and equitable outcomes. Contributors include: Jo Boaler, Ilana Seidel Horn, Judith Warren Little, and Rachel Lotan. “Mathematics for Equity provides a kaleidoscopic view, in the voices of teachers, researchers, and students themselves, of one of the nation’s most ambitious and successful attempts at teaching mathematics for equity. It shows what it takes to create a climate that supports students and teachers in engaging in meaningful mathematical activity—and, alas, how vulnerable such environments are to the wrong kinds of ‘accountability.’ Read it and learn.” —Alan H. Schoenfeld, University of California at Berkeley “Want to fix what's wrong with mathematics instruction in your school? Read this book with your colleagues and do what it inspires you to do. Written by the brave teachers and former students who did it, as well as researchers.” —Phil Daro, writing team, Common Core Standards, Strategic Education Research Partnership




Reconceptualizing Mathematics


Book Description

More and more, prospective elementary teachers are being asked to develop what the Conference Board of Mathematical Sciences (CBMS) calls “the habits of a mathematical thinker.” This breakthrough text became the new standard for training future elementary math teachers by doing just that, helping them absorb the ideas underlying essential math concepts, rather than just working problems and memorizing facts. Created from extensive math education research and class-testing, the book’s innovative pedagogy, convenient format (three-hole punched, perforated pages, wide margins), and supporting technology make it the ideal text for helping today’s students become tomorrow’s teachers










Reconceptualizing Early Mathematics Learning


Book Description

This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and early school settings indicate that young learners do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe characteristics of structural development in young students’ mathematics. Collectively, the chapters highlight the importance of providing more exciting, relevant, and challenging 21st century mathematics learning for our young students. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualising the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed.




Reconceptualizing STEM Education


Book Description

Reconceptualizing STEM Education explores and maps out research and development ideas and issues around five central practice themes: Systems Thinking; Model-Based Reasoning; Quantitative Reasoning; Equity, Epistemic, and Ethical Outcomes; and STEM Communication and Outreach. These themes are aligned with the comprehensive agenda for the reform of science and engineering education set out by the 2015 PISA Framework, the US Next Generation Science Standards and the US National Research Council’s A Framework for K-12 Science Education. The new practice-focused agenda has implications for the redesign of preK-12 education for alignment of curriculum-instruction-assessment; STEM teacher education and professional development; postsecondary, further, and graduate studies; and out-of-school informal education. In each section, experts set out powerful ideas followed by two eminent discussant responses that both respond to and provoke additional ideas from the lead papers. In the associated website highly distinguished, nationally recognized STEM education scholars and policymakers engage in deep conversations and considerations addressing core practices that guide STEM education.




Powerful Problem Solving


Book Description

How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter.







Social Constructivism as a Philosophy of Mathematics


Book Description

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.