Making the connection : research and teaching in undergraduate mathematics education / [edited by] Marilyn P. Carlson, Chris Rasmussen.

Format:

Book

Contributor:

Carlson, Marilyn P. (Marilyn Paula), editor.

Rasumussen, Chris, editor.

Series:

MAA notes ; no. 73.

MAA notes ; #73

Language:

English

Subjects (All):

Mathematics--Study and teaching (Higher).

Mathematics.

Mathematics--Research.

Physical Description:

1 online resource (xi, 319 pages) : digital, PDF file(s).

Edition:

[1st] ed.

Place of Publication:

Washington : Mathematical Association of America, 2008.

Language Note:

English

Summary:

The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any mathematics department or any individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem solving abilities, and students' understanding of fundamental ideas such as variable, and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice.

Contents:

On developing a rich conception of variable / Maria Trigueros and Sally Jacobs

Rethinking change / Bob Speiser and Chuck Walter

Foundational reasoning abilities that promote coherence in students' function understanding / Michael Oehrtman, Marilyn Carlson and Patrick Thompson

The concept of accumulation in calculus / Patrick Thompson and Jason Silverman

Developing notions of infinity / Michael A. McDonald and Anne Brown

Layers of abstraction : theory and design for the instruction of limit concepts / Michael Oehrtman

Divisibility and transparency of number representations / Rina Zazkis

Overcoming students' difficulties in learning to understand and construct proofs / Annie Selden and John Selden

Mathematical induction : cognitive and instructional considerations / Guershon Harel and Stacy Brown

Proving starting from informal notions of symmetry and transformations / Michelle Zandieh, Sean Larson, and Denise Nunley

Teaching and learning group theory / Keith Weber and Sean Larsen

Teaching for understanding : a case of students' learning to use the uniqueness theorem as a tool in differential equations / Chris Rasmussen and Wei Ruan

Meeting new teaching challenges : teaching strategies that mediate between all lecture and all student discovery / Karen Marrongelle and Chris Rasmussen

Examining interaction patterns in college-level mathematics classes : a case study / Susan Nickerson and Janet Bowers

Mathematics as a constructive activity : exploiting dimensions of possible variation / John Mason and Anne Watson

Supporting high achievement in introductory mathematics courses : what we have learned from 30 years of the emerging scholars program / Eric Hsu, Teri J. Murphy and Uri Treisman

The role of mathematical definitions in mathematics and in undergraduate mathematics courses / Barbara Edwards and Michael Ward

Computer-based technologies and plausible reasoning / Natalie Sinclair

Worked examples and concept example usage in understanding mathematical concepts and proofs / Keith Weber, Mary Porter and David Housman

From concept images to pedagogic structure for a mathematical topic / John Mason

Promoting effective mathematical practices in students : insights from problem solving research / Marilyn Carlson, Irene Bloom and Peggy Glick

When students don't apply the knowledge you think they have, rethink your assumptions about transfer / Joanne Lobato

How do mathematicians learn to teach? Implications from research on teachers and teaching for graduate student professional development / Natasha Speer and Ole Hald.

Notes:

Includes bibliographical references.

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

ISBN:

0-88385-975-0

OCLC:

923219593