The Number Line through Guided Inquiry is designed to give future secondary teachers a deep understanding of the real numbers and functions on the reals. By presenting just that part of the subject that underlies the high school curriculum, this book offers an alternative to a standard real analysis sequence for advanced undergraduate or beginning graduate students. It will give any student a much deeper understanding of the mathematics that they were taught in high school. Written in a guided-inquiry format, this book consists of a carefully scaffolded sequence of definitions, problems, and theorems that guides students through each topic. Readers solve the problems and prove the theorems on their own and present their results to their peers with the instructor as a mentor and a guide. Students will learn not only the mathematics, but also how to help others learn mathematics. They will learn to think creatively and to make compelling arguments to justify their conclusions. They will learn to listen critically to others and give constructive feedback. Ultimately, they will learn to work as a team to answer the bigger questions and build a common understanding of the broader subject.

Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation. Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry. The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority. This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

This textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content of high school geometry. It begins with a set of points, a measure of distance between pairs of points and ten simple axioms. From there the notions of length, area and angle measure, along with congruence and similarity, are carefully defined and their properties proven as theorems. It concludes with a proof of the consistency of the axioms used and a full description of their models. It is provided in guided inquiry (inquiry-based) format with the intention that students will be active learners, proving the theorems and presenting their proofs to their class with the instructor as a mentor and a guide. The book is written for graduate and advanced undergraduate students interested in teaching secondary school mathematics, for pure math majors interested in learning about the foundations of geometry, for faculty preparing future secondary school teachers and as a reference for any professional mathematician. It is written with the hope of anchoring K-12 geometry in solid modern mathematics, thereby fortifying the teaching of secondary and tertiary geometry with a deep understanding of the subject.

This dynamic approach to an exciting form of teaching and learning will inspire students to gain insights and complex thinking skills from the school library, their community, and the wider world. Guided inquiry is a way of thinking, learning, and teaching that changes the culture of a school into a collaborative inquiry community. Global interconnectedness calls for new skills, new knowledge, and new ways of learning to prepare students with the abilities and competencies they need to meet the challenges of a changing world. The challenge for the information-age school is to educate students for living and working in this information-rich technological environment. At the core of being educated today is knowing how to learn and innovate from a variety of sources. Through guided inquiry, students see school learning and real life meshed in meaningful ways. They develop higher order thinking and strategies for seeking meaning, creating, and innovating. Today's schools are challenged to develop student talent, coupling the rich resources of the school library with those of the community and wider world. How well are you preparing your students to draw on the knowledge and wisdom of the past while using today's technology to advance new discoveries in the future? This book is the introduction to guided inquiry. It is the place to begin to consider and plan how to develop an inquiry learning program for your students.

Today's students need to be fully prepared for successful learning and living in the information age. This book provides a practical, flexible framework for designing Guided Inquiry that helps achieve that goal. Guided Inquiry prepares today's learners for an uncertain future by providing the education that enables them to make meaning of myriad sources of information in a rapidly evolving world. The companion book, Guided Inquiry: Learning in the 21st Century, explains what Guided Inquiry is and why it is now essential now. This book, Guided Inquiry Design: A Framework for Inquiry in Your School, explains how to do it. The first three chapters provide an overview of the Guided Inquiry design framework, identify the eight phases of the Guided Inquiry process, summarize the research that grounds Guided Inquiry, and describe the five tools of inquiry that are essential to implementation. The following chapters detail the eight phases in the Guided Inquiry design process, providing examples at all levels from pre-K through 12th grade and concluding with recommendations for building Guided Inquiry in your school. The book is for pre-K–12 teachers, school librarians, and principals who are interested in and actively designing an inquiry approach to curricular learning that incorporates a wide range of resources from the library, the Internet, and the community. Staff of community resources, museum educators, and public librarians will also find the book useful for achieving student learning goals.

Learning progressions – descriptions of increasingly sophisticated ways of thinking about or understanding a topic (National Research Council, 2007) – represent a promising framework for developing organized curricula and meaningful assessments in science. In addition, well-grounded learning progressions may allow for coherence between cognitive models of how understanding develops in a given domain, classroom instruction, professional development, and classroom and large-scale assessments. Because of the promise that learning progressions hold for bringing organization and structure to often disconnected views of how to teach and assess science, they are rapidly gaining popularity in the science education community. However, there are signi?cant challenges faced by all engaged in this work. In June 2009, science education researchers and practitioners, as well as scientists, psychometricians, and assessment specialists convened to discuss these challenges as part of the Learning Progressions in Science (LeaPS) conference. The LeaPS conference provided a structured forum for considering design decisions entailed in four aspects of work on learning progressions: de?ning learning progressions; developing assessments to elicit student responses relative to learning progressions; modeling and interpreting student performance with respect to a learning progressions; and using learning progressions to in?uence standards, curricula, and teacher education. This book presents speci?c examples of learning progression work and syntheses of ideas from these examples and discussions at the LeaPS conference.

Every child has a right to make sense of math, and to use math to make sense of their worlds. Despite their gifts, students with disabilities are often viewed from a deficit standpoint in mathematics classrooms. These students are often conceptualized as needing to be fixed or remediated. Rethinking Disability and Mathematics argues that mathematics should be a transformative space for these students, a place where they can discover their power and potential and be appreciated for their many strengths. Author Rachel Lambert introduces Universal Design for Learning for Math (UDL Math), a way to design math classrooms that empowers disabled and neurodiverse students to engage in mathematics in ways that lead to meaningful and joyful math learning. The book showcases how UDL Math can open up mathematics classrooms so that they provide access to meaningful understanding and an identity as a math learner to a wider range of students. Weaved throughout the book are the voices of neurodiverse learners telling their own stories of math learning. Through stories of real teachers recognizing the barriers in their own math classrooms and redesigning to increase access, the book: Reframes students with disabilities from a deficit to an asset perspective, paving the way for trusting their mathematical thinking Offers equitable math instruction for all learners, including those with disabilities, neurodiverse students, and/or multilingual learners Applies UDL to the math classroom, providing practical tips and techniques to support students′ cognitive, affective, and strategic development Immerses readers in math classrooms where all students are engaged in meaningful mathematics, from special education day classes to inclusive general education classrooms, from grades K-8. Integrates research on mathematical learning including critical math content such as developing number sense and place value, fluency with math facts and operations, and understanding fractions and algebraic thinking. Explores critical issues such as writing IEP goals in math This book is designed for all math educators, both those trained as general education teachers and those trained as special education teachers. The UDL Math approach is adapted to work for all learners because everyone varies in how they perceive the world and in how they approach mathematical problem solving. When we rethink mathematics to include multiple ways of being a math learner, we make math accessible and engaging for a wider group of learners.