Mathematics Education Across Time Place

What is mathematics, and what aspects of it should be taught in schools? How and to whom should it be taught, and how should its understanding be assessed? These questions continue to drive curriculum development, school organization, teaching methods, and research agendas. No one today doubts that mathematics should be taught in our schools, but this was not always so. Mathematics Education Across Time and Place aims to help mathematics teachers, teacher educators, and anyone else interested in mathematics education appreciate the path this discipline has taken through the ages. To understand the historical and social context for schools and the place of mathematics within them, we meet a variety of mathematics educators from different times and places. Though fictional, their lives and social circumstances are based on historical documents and professional sources. They range from ancient Greece to modern Zimbabwe; from Persia to British Columbia; from Islamic Baghdad to revolutionary Paris; from Elizabethan England to twentieth-century New York; and from the rural one-room schools of North America to the modern comprehensive secondary school. By sharing the teachers' lives, we come to understand how they developed their love for teaching mathematics, and how their work fit into the larger social context of their time.

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics—how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings—and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories. A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.) This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children’s mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories’ evolution--from small-scale day-to-day conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.

What is mathematics, and what aspects of it should be taught in schools? How and to whom should it be taught, and how should its understanding be assessed? These questions continue to drive curriculum development, school organization, teaching methods, and research agendas. No one today doubts that mathematics should be taught in our schools, but this was not always so. Mathematics Education Across Time and Place aims to help mathematics teachers, teacher educators, and anyone else interested in mathematics education appreciate the path this discipline has taken through the ages. To understand the historical and social context for schools and the place of mathematics within them, we meet a variety of mathematics educators from different times and places. Though fictional, their lives and social circumstances are based on historical documents and professional sources. They range from ancient Greece to modern Zimbabwe; from Persia to British Columbia; from Islamic Baghdad to revolutionary Paris; from Elizabethan England to twentieth-century New York; and from the rural one-room schools of North America to the modern comprehensive secondary school. By sharing the teachers’ lives, we come to understand how they developed their love for teaching mathematics, and how their work fit into the larger social context of their time.

This book presents a contemporary focus on significant issues in STEM teaching, learning and research that are valuable in preparing students for a digital 21st century. The book chapters cover a wide spectrum of issues and topics using a wealth of research methodologies and methods.

What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.