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

✍ Scribed by Olga Kosheleva, Karen Villaverde

• Publisher: Springer-Verlag
• Year: 2018
• Tongue: English
• Leaves: 347
• Series: Studies in Computational Intelligence 750
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Introduction: Need for Interval and Fuzzy Techniques in Math and Science Education (Olga Kosheleva, Karen Villaverde)....Pages 1-8
Front Matter ....Pages 9-9
How to Motivate Students: An Overview of Part I (Olga Kosheleva, Karen Villaverde)....Pages 11-14
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
Uncertainty-Related Example Explaining Why Geometry is Useful: Geometry of a Plane Rescue (Olga Kosheleva, Karen Villaverde)....Pages 27-31
Uncertainty-Related Example Explaining Why Calculus Is Useful: Example of the Mean Value Theorem (Olga Kosheleva, Karen Villaverde)....Pages 33-50
How to Enhance Student Motivations by Borrowing from Ancient Tradition: Egyptian Fractions (Olga Kosheleva, Karen Villaverde)....Pages 51-63
How to Enhance Student Motivations by Borrowing from Ancient Tradition: Mayan and Babylonian Arithmetics (Olga Kosheleva, Karen Villaverde)....Pages 65-72
How to Enhance Student Motivations by Borrowing from Ancient Tradition: Babylonian Method of Computing the Square Root (Olga Kosheleva, Karen Villaverde)....Pages 73-85
How to Enhance Student Motivations by Borrowing from Ancient Tradition: Russian Peasant Multiplication Algorithm (Olga Kosheleva, Karen Villaverde)....Pages 87-95
How to Enhance Student Motivations by Borrowing from Modern Practices: Geometric Approach to Error-Less Counting (Olga Kosheleva, Karen Villaverde)....Pages 97-105
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
How to Enhance a General Student Motivation to Study: Asymmetric Paternalism (Olga Kosheleva, Karen Villaverde)....Pages 117-124
Financial Motivation: How to Incentivize Students to Graduate Faster (Olga Kosheleva, Karen Villaverde)....Pages 125-130
Front Matter ....Pages 131-131
In What Order to Present the Material: An Overview of Part II (Olga Kosheleva, Karen Villaverde)....Pages 133-134
Spiral Curriculum: Towards Mathematical Foundations (Olga Kosheleva, Karen Villaverde)....Pages 135-145
How Much Time to Allocate to Each Topic? (Olga Kosheleva, Karen Villaverde)....Pages 147-151
What Is Wrong with Teaching to the Test: Uncertainty Techniques Help in Understanding the Controversy (Olga Kosheleva, Karen Villaverde)....Pages 153-159
In What Order to Present the Material: Fractal Approach (Olga Kosheleva, Karen Villaverde)....Pages 161-165
How AI-Type Uncertainty Ideas Can Improve Inter-Disciplinary Education and Collaboration: Lessons from a Case Study (Olga Kosheleva, Karen Villaverde)....Pages 167-178
In What Order to Present the Material Within Each Topic: Concrete-First Versus Abstract-First (Olga Kosheleva, Karen Villaverde)....Pages 179-187
Front Matter ....Pages 189-189
How to Select an Appropriate Way of Teaching Each Topic: An Overview of Part III (Olga Kosheleva, Karen Villaverde)....Pages 191-191
What Is the Best Way to Distribute the Teacher’s Efforts Among Students (Olga Kosheleva, Karen Villaverde)....Pages 193-204
What is the Best Way to Allocate Teacher’s Efforts: How Accurately Should We Write on the Board? When Marking Comments on Student Papers? (Olga Kosheleva, Karen Villaverde)....Pages 205-208
How to Divide Students into Groups so as to Optimize Learning (Olga Kosheleva, Karen Villaverde)....Pages 209-221
How to Divide Students into Groups: Importance of Diversity and Need for Intelligent Techniques to Further Enhance the Advantage of Groups with Diversity in Problem Solving (Olga Kosheleva, Karen Villaverde)....Pages 223-237
A Minor but Important Aspect of Teaching Large Classes: When to Let in Late Students? (Olga Kosheleva, Karen Villaverde)....Pages 239-244
Front Matter ....Pages 245-245
How to Assess Students, Teachers, and Teaching Techniques: An Overview of Part IV (Olga Kosheleva, Karen Villaverde)....Pages 247-248
How to Assess Students: Rewarding Results or Rewarding Efforts? (Olga Kosheleva, Karen Villaverde)....Pages 249-251
How to Assess Students: Assess Frequently (Olga Kosheleva, Karen Villaverde)....Pages 253-265
How to Assess Students: Surprise Them (Olga Kosheleva, Karen Villaverde)....Pages 267-277
How to Assess Individual Contributions to a Group Project (Olga Kosheleva, Karen Villaverde)....Pages 279-285
How to Access Students’s Readiness for the Next Class (Olga Kosheleva, Karen Villaverde)....Pages 287-293
How to Assess Students: Beyond Weighted Average (Olga Kosheleva, Karen Villaverde)....Pages 295-303
How to Assess a Class (Olga Kosheleva, Karen Villaverde)....Pages 305-318
How to Assess Teachers (Olga Kosheleva, Karen Villaverde)....Pages 319-334
How to Assess Teaching Teachniques (Olga Kosheleva, Karen Villaverde)....Pages 335-344
How to Assess Universities: Defining Average Class Size in a Way Which Is Most Adequate for Teaching Effectiveness (Olga Kosheleva, Karen Villaverde)....Pages 345-352
Conclusions (Olga Kosheleva, Karen Villaverde)....Pages 353-353
Back Matter ....Pages 355-362

✦ Subjects

Computational Intelligence