Making the connection research and teaching in undergraduate mathematics education 1st Edition by Marilyn Carlson, Chris Rasmussen ISBN 0883851830 978-0883851838

Making the connection research and teaching in undergraduate mathematics education 1st Edition by Marilyn P. Carlson, Chris Rasmussen  – Ebook PDF Instant Download/Delivery:
Full download Making the connection research and teaching in undergraduate mathematics education 1st Edition  after payment

Product details: 

ISBN 10: 0883851830 

ISBN 13: 978-0883851838

Author:  Marilyn P. Carlson, Chris Rasmussen

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. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics.

Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.

Table of contents: 

Part 1. Student Thinking
1a. Foundations for Beginning Calculus
On Developing a Rich Conception of Variable

Rethinking Change

Foundational Reasoning Abilities that Promote Coherence in Students’ Function Understanding

The Concept of Accumulation in Calculus

1b. Infinity, Limit and Divisibility
Developing Notions of Infinity

Layers of Abstraction: Theory and Design for the Instruction of Limit Concepts

Divisibility and Transparency of Number Representations

1c. Proving Theorems
Overcoming Students’ Difficulties in Learning to Understand and Construct Proofs

Mathematical Induction: Cognitive and Instructional Considerations

Proving Starting from Informal Notions of Symmetry and Transformations

Teaching and Learning Group Theory

Teaching for Understanding: A Case of Students’ Learning to Use the Uniqueness Theorem as a Tool in Differential Equations

Part 2. Cross-Cutting Themes
2a. Interacting with Students
Meeting New Teaching Challenges: Teaching Strategies that Mediate between All Lecture and All Student Discovery

Examining Interaction Patterns in College-Level Mathematics Classes: A Case Study

Mathematics as a Constructive Activity: Exploiting Dimensions of Possible Variation

Supporting High Achievement in Introductory Mathematics Courses: What We Have Learned from 30 Years of the Emerging Scholars Program

2b. Using Definitions, Examples and Technology
The Role of Mathematical Definitions in Mathematics and in Undergraduate Mathematics Courses

Computer-Based Technologies and Plausible Reasoning

Worked Examples and Concept Example Usage in Understanding Mathematical Concepts and Proofs

2c. Knowledge, Assumptions, and Problem Solving Behaviors for Teaching
From Concept Images to Pedagogic Structure for a Mathematical Topic

People also search for:

making the connections
    
making the connection meaning
    
making the connection conference
    
making the connections padias
    
making the connections pdf

Tags: Marilyn Carlson, Chris Rasmussen, Making the connection, research and teaching