Students' Reasoning about Limit » książka
Students' Reasoning about Limit
ISBN-13: 9783639164640 / Angielski / Miękka / 2009 / 304 str.
Limit plays a vital role as a foundational concept in analysis. The vast majority of topics encountered in calculus and undergraduate analysis are built upon understanding the concept of limit and being able to work flexibly with its formal definition. This book describes a study conducted with the purpose of: 1) Developing insight into students' reasoning about limit in relation to their reinventing the formal definition, and; 2) Informing the design of principled instruction that might support students' attempts to reinvent the formal definition. In separate teaching experiments, two pairs of students successfully reinvented a definition of limit capturing the intended meaning of the conventional - definition. This book traces the evolution of the students' definitions over the course of two ten-week teaching experiments, and highlights thematic findings which point to what might be entailed in coming to reason flexibly and coherently about limit and its formal definition. This book should be especially useful for mathematics educators at the secondary and tertiary levels, particularly those who teach calculus and introductory analysis."
Limit plays a vital role as a foundational concept inanalysis. The vast majority of topics encountered incalculus and undergraduate analysis are built uponunderstanding the concept of limit and being able towork flexibly with its formal definition. This bookdescribes a study conducted with the purpose of: 1)Developing insight into students reasoning aboutlimit in relation to their reinventing the formaldefinition, and; 2) Informing the design ofprincipled instruction that might support studentsattempts to reinvent the formal definition. Inseparate teaching experiments, two pairs of studentssuccessfully reinvented a definition of limitcapturing the intended meaning of the conventionalε-δ definition. This book traces the evolution of thestudents definitions over the course of two ten-weekteaching experiments, and highlights thematicfindings which point to what might be entailed incoming to reason flexibly and coherently about limitand its formal definition. This book should beespecially useful for mathematics educators at thesecondary and tertiary levels, particularly those whoteach calculus and introductory analysis.
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