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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.

Mathematics --- Meaning (Philosophy) --- Study and teaching. --- Philosophy --- Semantics (Philosophy) --- 51:37 --- 51 --- 51 Mathematics --- 51:37 Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Study and teaching --- Mathematics. --- Curriculum planning. --- Mathematics Education. --- Curriculum Studies. --- Learning & Instruction. --- Curriculum development --- Education --- Instructional systems --- Planning --- Math --- Science --- Curricula --- Design --- Mathematics—Study and teaching . --- Curriculums (Courses of study). --- Education—Curricula. --- Learning. --- Instruction. --- Learning process --- Comprehension --- Core curriculum --- Courses of study --- Curricula (Courses of study) --- Curriculums (Courses of study) --- Schools --- Study, Courses of --- Learning, Psychology of. --- Instructional Psychology. --- Study and teaching . --- Curricula. --- Learning --- Psychology of learning --- Educational psychology --- Learning ability --- Psychological aspects

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Mathematics --- #PBIB:2005.4 --- Math --- Science --- Study and teaching --- Standards --- Didactics of mathematics

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Two centuries ago, American teachers did not stand at the front of the room and teach, and most students—even those studying mathematics—did not own a mathematics textbook. Written examinations of any kind were not used. Most teachers of mathematics did not have formal qualifications in mathematics. The modern educator might well ask: “If all of that is true, then how were teachers expected to teach and how were students expected to learn mathematics?”

In this book Nerida Ellerton and Ken Clements argue that before 1840 mathematics was taught in North America via a cyphering approach that had been translated from Western Europe to the new settlements. This approach was based on a tradition that had endured since the thirteenth century, and depended heavily on students carefully writing their mathematics in cyphering books. After 1840, schools gradually adopted more teacher-centered whole-class pedagogies for mathematics instruction, and by the beginning of the Civil War, in 1861, the transformation was complete.

In his Foreword to this book, Jeremy Kilpatrick states:

“Ellerton and Clements show that the cyphering approach to learning mathematics has both an extensive history and a complex rationale. In the approach, the learner was to become an independent problem solver by learning to identify problems of various types, learning the rules for their solution, solving such problems, having each solution checked by a tutor or teacher and, only when the solution was correct, copying that solution into a cyphering book using exemplary calligraphy. The handwriting process was not meant to be only copying; it was to be an accompaniment to thinking. The learner was not simply inscribing the solution onto paper; he or she was inscribing it into memory. Cyphering books are a much neglected resource for understanding and appreciating the early history of North American mathematics education. The present book marks a major advance in putting that resource to effective use as well as in raising some challenging questions for subsequent research.”

This book provides the first history of early North American school mathematics in which the implemented curriculum—as seen in cyphering books—takes center stage, while the intended curriculum—as evident in textbooks—provides contextual background for the main argument.

Curriculum planning. --- Education. --- Mathematics. --- Mathematics --- Education --- Physical Sciences & Mathematics --- Social Sciences --- Education, Special Topics --- Mathematics Teaching & Research --- History --- Study and teaching --- History. --- Math --- Curriculums (Courses of study). --- Mathematics Education. --- History of Mathematical Sciences. --- Curriculum Studies. --- History, general. --- Curricula. --- Study and teaching. --- Science --- Curriculum development --- Instructional systems --- Planning --- Annals --- Auxiliary sciences of history --- Curricula --- Design --- Mathematics—Study and teaching . --- Education—Curricula. --- Core curriculum --- Courses of study --- Curricula (Courses of study) --- Curriculums (Courses of study) --- Schools --- Study, Courses of --- North America. --- Turtle Island

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Lerarenopleiding --- (vak)didactiek wetenschappen.

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