Ideal for preservice mathematics teachers who are taking methods courses or are student teaching, this research-based, activity-oriented guide offers a highly effective framework for teacher reflection and self-assessment. Highlighting inquiry-based, learner-centered teaching and grounded in a cognitive perspective, Becoming a Reflective Teacher of Mathematics, Third Edition features: Detailed observation instruments for observing other teachers Reflective activities that provide a structure for beginning teachers to think about their teaching Guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers The Third Edition of Becoming a Reflective Teacher of Mathematics is aligned with the latest standards for teaching mathematics including the Common Core State Standards-Mathematics, and the latest assessments for mathematics teacher certification which place a high priority on reflective practice. Thoroughly revised and updated throughout, the Third Edition continues to provide preservice and in-service mathematics teachers with practical ideas for developing and honing reflective and self-analytical skills needed to advance and improve instruction.

"Becoming a Reflective Mathematics Teacher: A Guide for Observations and Self-Assessment" offers what every mathematics teacher educator or supervisor has been looking for. Ideally suited for use with students who are taking a methods course or who are student teaching, this activity-oriented, research-based text:
*supplies detailed observation instruments that preservice teachers can use when they observe other teachers. Each instrument focuses on a critical aspect of instructional practice in mathematics (e.g., tasks, learning environment, discourse). In addition, it requires the observer to make conjectures regarding the teachers' underlying cognitions (e.g., knowledge, beliefs, goals) that might account for the instructional practice they observe.
*offers reflective activities that provide a structure through which beginning teachers can think about their teaching in an insightful, thorough, and productive manner. Students can work through the activities over the period of a year. The structured observations and reflective activities are modular, and the framework applies to all observations of teaching, no matter what the instructional content.
*includes guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers. The unique aspect of these guidelines and instruments is the link they make between teachers' cognitions and their instructional practice.
All instruments and suggested activities are couched within a highly effective framework for teacher reflection and self-assessment that was developed in the spirit of the NCTM professional teaching standards. This framework is grounded in a cognitive perspective on learner-centered teaching. In Part I, the framework is explained and its validity is documented. Part II shows how teachers can use the framework to observe other teachers' classroom work, and to reflect on their own teaching. Part III offers case studies to help readers see how the method works.

Personal story telling is a powerful and interesting medium through which one can share experiences, insights, successes, and difficulties in meaningful contexts. Teaching in general, and mathematics teaching in particular, is much more than what meets the eye. Most people have only experienced teaching from the vantage point of a student and have impressions of teachers and teaching that are simplistic and usually totally incorrect. The lives of mathematics teachers are varied and contrary to what one might think they are. The journeys of exemplary in-service teachers are not linear; there are many bends, potholes, and detours through which they have navigated. The ""road conditions"" of teaching are fodder for the 12 untold stories collected in this volume, whose authors graduated from a special four-year undergraduate mathematics teacher preparation program, containing innovative components, many of which are revealed through the experiences described in their stories. The range of narratives vary in every possible way, from the reasons they became mathematics teachers, to the number of years teaching, to the experiences encountered while teaching, to the different roles they have assumed throughout their careers. Nevertheless, one strand permeates all of the stories: their passion for what they do and their ability to reflect on early college experiences that contribute to their performance. These inspiring narratives will shed light on the developmental processes of mathematics teachers, what it means to teach mathematics, and the components of a secondary mathematics teacher preparation program that can contribute to their expertise.

Ideal for preservice mathematics teachers who are taking methods courses or are student teaching, this research-based, activity-oriented guide offers a highly effective framework for teacher reflection and self-assessment. Highlighting inquiry-based, learner-centered teaching and grounded in a cognitive perspective, Becoming a Reflective Teacher of Mathematics, Third Edition features: Detailed observation instruments for observing other teachers Reflective activities that provide a structure for beginning teachers to think about their teaching Guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers The Third Edition of Becoming a Reflective Teacher of Mathematics is aligned with the latest standards for teaching mathematics including the Common Core State Standards-Mathematics, and the latest assessments for mathematics teacher certification which place a high priority on reflective practice. Thoroughly revised and updated throughout, the Third Edition continues to provide preservice and in-service mathematics teachers with practical ideas for developing and honing reflective and self-analytical skills needed to advance and improve instruction.

Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed-Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features: Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts. Practice Problems provide opportunities to apply what has been learned and complete proofs. Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students. Changes in the Second Edition New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination New problems, simpler proofs, and more illustrative examples Answers and hints for selected problems provided

Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed-Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features: Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts. Practice Problems provide opportunities to apply what has been learned and complete proofs. Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students. Changes in the Second Edition New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination New problems, simpler proofs, and more illustrative examples Answers and hints for selected problems provided

Personal story telling is a powerful and interesting medium through which one can share experiences, insights, successes, and difficulties in meaningful contexts. Teaching in general, and mathematics teaching in particular, is much more than what meets the eye. Most people have only experienced teaching from the vantage point of a student and have impressions of teachers and teaching that are simplistic and usually totally incorrect. The lives of mathematics teachers are varied and contrary to what one might think they are. The journeys of exemplary in-service teachers are not linear; there are many bends, potholes, and detours through which they have navigated. The ""road conditions"" of teaching are fodder for the 12 untold stories collected in this volume, whose authors graduated from a special four-year undergraduate mathematics teacher preparation program, containing innovative components, many of which are revealed through the experiences described in their stories. The range of narratives vary in every possible way, from the reasons they became mathematics teachers, to the number of years teaching, to the experiences encountered while teaching, to the different roles they have assumed throughout their careers. Nevertheless, one strand permeates all of the stories: their passion for what they do and their ability to reflect on early college experiences that contribute to their performance. These inspiring narratives will shed light on the developmental processes of mathematics teachers, what it means to teach mathematics, and the components of a secondary mathematics teacher preparation program that can contribute to their expertise.