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How Interval and Fuzzy Techniques Can Improve Teaching

Processing Educational Data: From Traditional Statistical Techniques to an Appropriate Combination of Probabilistic, Interval, and Fuzzy Approaches

  • Book
  • © 2018

Overview

Authors:
  1. Olga Kosheleva

    1. Department of Teacher Education, University of Texas, El Paso, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Karen Villaverde

    1. Department of Mathematics, New Mexico State University, Las Cruces, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Includes the latest research on processing educational data
  • Presents traditional
  • Written by leading experts in the field

Part of the book series: Studies in Computational Intelligence (SCI, volume 750)

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Table of contents (38 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction: Need for Interval and Fuzzy Techniques in Math and Science Education

    • Olga Kosheleva, Karen Villaverde
    Pages 1-8

  3. How to Motivate Students

    1. Front Matter

      Pages 9-9
      Download chapter PDF

    2. How to Motivate Students: An Overview of Part I

      • Olga Kosheleva, Karen Villaverde
      Pages 11-14

    3. Need to Understand the Presence of Uncertainty: Emphasizing Paradoxes as a (Seemingly Paradoxical) Way to Enhance the Learning of (Strict) Mathematics

      • Olga Kosheleva, Karen Villaverde
      Pages 15-26

    4. Uncertainty-Related Example Explaining Why Geometry is Useful: Geometry of a Plane Rescue

      • Olga Kosheleva, Karen Villaverde
      Pages 27-31

    5. Uncertainty-Related Example Explaining Why Calculus Is Useful: Example of the Mean Value Theorem

      • Olga Kosheleva, Karen Villaverde
      Pages 33-50

    6. How to Enhance Student Motivations by Borrowing from Ancient Tradition: Egyptian Fractions

      • Olga Kosheleva, Karen Villaverde
      Pages 51-63

    7. How to Enhance Student Motivations by Borrowing from Ancient Tradition: Mayan and Babylonian Arithmetics

      • Olga Kosheleva, Karen Villaverde
      Pages 65-72

    8. How to Enhance Student Motivations by Borrowing from Ancient Tradition: Babylonian Method of Computing the Square Root

      • Olga Kosheleva, Karen Villaverde
      Pages 73-85

    9. How to Enhance Student Motivations by Borrowing from Ancient Tradition: Russian Peasant Multiplication Algorithm

      • Olga Kosheleva, Karen Villaverde
      Pages 87-95

    10. How to Enhance Student Motivations by Borrowing from Modern Practices: Geometric Approach to Error-Less Counting

      • Olga Kosheleva, Karen Villaverde
      Pages 97-105

    11. How to Enhance Student Motivations by Borrowing from Modern Practices: Can We Learn Algorithms from People Who Compute Fast

      • Olga Kosheleva, Karen Villaverde
      Pages 107-115

    12. How to Enhance a General Student Motivation to Study: Asymmetric Paternalism

      • Olga Kosheleva, Karen Villaverde
      Pages 117-124

    13. Financial Motivation: How to Incentivize Students to Graduate Faster

      • Olga Kosheleva, Karen Villaverde
      Pages 125-130

  4. In What Order to Present the Material

    1. Front Matter

      Pages 131-131
      Download chapter PDF

    2. In What Order to Present the Material: An Overview of Part II

      • Olga Kosheleva, Karen Villaverde
      Pages 133-134

    3. Spiral Curriculum: Towards Mathematical Foundations

      • Olga Kosheleva, Karen Villaverde
      Pages 135-145

    4. How Much Time to Allocate to Each Topic?

      • Olga Kosheleva, Karen Villaverde
      Pages 147-151

    5. What Is Wrong with Teaching to the Test: Uncertainty Techniques Help in Understanding the Controversy

      • Olga Kosheleva, Karen Villaverde
      Pages 153-159
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Keywords

About this book

This book explains how to teach better and presents the latest research on processing educational data and presents traditional statistical techniques as well as probabilistic, interval, and fuzzy approaches. Teaching is a very rewarding activity; it is also a very difficult one – because it is largely an art. There is a lot of advice on teaching available, but it is usually informal and is not easy to follow. To remedy this situation, it is reasonable to use techniques specifically designed to handle such imprecise knowledge: the fuzzy logic techniques.

Since there are a large number of statistical studies of different teaching techniques, the authors combined statistical and fuzzy approaches to process the educational data in order to provide insights into improving all the stages of the education process: from forming a curriculum to deciding in which order to present the material to grading the assignments and exams.

The authors do not claim to have solved all the problems of education. Instead they show, using numerous examples, that an innovative combination of different uncertainty techniques can improve teaching. The book offers teachers and instructors valuable advice and provides researchers in pedagogical and fuzzy areas with techniques to further advance teaching.

Reviews

“The book is an attempt to present a unifying view of the papers on fuzzy techniques in different aspects of education … Given that the references come from conference proceedings on computational intelligence, fuzzy systems, or informatics and publications like IEEE Transactions on Education, academics who attend such conferences seem to be the most likely readers, as well as any mathematicians interested in potential, if somewhat theoretical, applications of fuzzy sets and interval techniques.” (Annie Selden, MAA Reviews, December, 2017)

Authors and Affiliations

  • Department of Teacher Education, University of Texas, El Paso, USA

    Olga Kosheleva

  • Department of Mathematics, New Mexico State University, Las Cruces, USA

    Karen Villaverde

Bibliographic Information

  • Book Title: How Interval and Fuzzy Techniques Can Improve Teaching

  • Book Subtitle: Processing Educational Data: From Traditional Statistical Techniques to an Appropriate Combination of Probabilistic, Interval, and Fuzzy Approaches

  • Authors: Olga Kosheleva, Karen Villaverde

  • Series Title: Studies in Computational Intelligence

  • DOI: https://doi.org/10.1007/978-3-662-55993-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag GmbH Germany 2018

  • Hardcover ISBN: 978-3-662-55991-8Published: 02 November 2017

  • Softcover ISBN: 978-3-662-57256-6Published: 04 September 2018

  • eBook ISBN: 978-3-662-55993-2Published: 23 October 2017

  • Series ISSN: 1860-949X

  • Series E-ISSN: 1860-9503

  • Edition Number: 1

  • Number of Pages: X, 362

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Computational Intelligence, IT in Business, e-Commerce/e-business

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