How Interval and Fuzzy Techniques Can Improve Teaching

Introduction: Need for Interval and Fuzzy Techniques in Math and Science Education.-Part I How to Motivate Students.-How to Motivate Students? .-Need to Understand the Presence of Uncertainty: Emphasizing Paradoxes as a (Seemingly Paradoxical) Way to Enhance the Learning of (Strict) Mathematics .-Uncertainty-Related Example Explaining Why Geometry Is Useful: Geometry of a Plane .-Uncertainty-Related Example Explaining Why Calculus Is Useful: Example of the Mean Value Theorem .-How to Enhance Student Motivations by Borrowing from Ancient Tradition: Egyptian Fractions .-How to Enhance Student Motivations by Borrowing from Ancient Tradition: Mayan and Babylonian Arithmetics .-How to Enhance Student Motivations by Borrowing from Ancient Tradition: Babylonian Method of Computing the Square Root .-How to Enhance Student Motivations by Borrowing from Ancient Tradition: Russian Peasant Multiplication Algorithm .-How to Enhance Student Motivations by Borrowing from Modern Practices: Geometric Approach to Error-Less Counting .-How to Enhance Student Motivations by Borrowing from Modern Practices: Can We Learn Algorithms from People Who Compute Fast.-How to Enhance a General Student Motivation to Study: Asymmetric Paternalism .-Financial Motivation: How to Incentivize Students to Graduate Faster.-Part II In What Order to Present the Material.-In What Order to Present the Material.-Spiral Curriculum: Towards Mathematical Foundations.-How Much Time to Allocate to Each Topic?.-What is Wrong with Teaching to the Test: Uncertainty Techniques Help in Understanding the Controversy.-In What Order to Present the Material: Fractal Approach.-How AI-Type Uncertainty Ideas Can Improve Inter-Disciplinary Education and Collaboration: Lessons from a Case Study.-In What Order to Present the Material Within Each Topic: Concrete-First vs. Abstract-First .-Part III How to Select an Appropriate Way of Teaching Each Topic.-How to Select an Appropriate Way of Teaching Each Topic .-What is the Best Way to Distribute the Teacher's Efforts Among Students .-What is the Best Way to Allocate Teacher's Efforts: How Accurately Should We Write on the Board? When Marking Comments on Student Papers? .-How to Divide Students into Groups so as to Optimize Learning .-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 .-A Minor but Important Aspect of Teaching Large Classes: When to Let in Late Students? .-Part IV How to Assess Students, Teachers, and Teaching Techniques.-How to Assess Students, Teachers, and Teaching Techniques.-How to Assess Students: Rewarding Results or Rewarding Efforts?.-How to Assess Students: Assess Frequently.-How to Assess Students: Surprise Them.-How to Assess Individual Contributions to a Group Project.-How to Access Students's Readiness for the Next Class.-How to Assess Students: Beyond Weighted Average.-How to Assess a Class .-How to Assess Teachers.-How to Assess Teaching Teachniques.-How to Assess Universities: De?ning Average Class Size in a Way Which Is Most Adequate for Teaching Effectiveness.-Conclusions .