Olga Kosheleva and Karen Villaverde How Interval and Fuzzy Techniques Can Improve Teaching Springer,Cham,Switzerland,2018

Teaching is difficult. In the old days, every elevator was operated by an operator. We learned how the elevators work, we automated them. In the old days, the only way to connect to someone over the phone was by using telephone operators. There were so many of them, and these numbers were growing so fast, that people half-seriously predicted that eventually, the majority of the world’s population will be telephone operators. But then we learned how the connections work, and we automated the connections.

In the old days, a pilot had to control the plane all the time. We learned how the planes work, now during the flight the autopilot does most of the work. Soon, driverless cars will become ubiquitous.

But there is one important area where, no matter how much we study it, we are still far from automation: the area of education. People have been predicting for a long time that automatic teachers will replace live ones: when phonographs appeared, they were supposed to be the teachers’ replacements, then the movies, then the computers – probably in Gutenberg’s time the books were also considered as the future replacement of teachers.

Recently, MOOCs – massive open online courses – were supposed to be the panacea, the magic bullet that would finally make teaching automatic – but it did not. In spite of all the technological advances, teachers are still needed. Why?

What is the main difference between teaching and all other applications. An elevator, a plane, a car are mechanical systems whose dynamics follows known equations. Once we learn these equations, we can find a good control.

In contrast, teaching is about “controlling” students, and their behavior cannot be described by easy-to-solve equations:-(

This does not mean that we have to give up. While we cannot fully automate teaching, we can still try to make it as efficient as possible. We do not know the equations, so we are back to the situations in the 1960s that motivated Lotfi Zadeh’s invention of fuzzy techniques: we want to control a system, we do not know the exact equations, but we have experts who control the system reasonable well. So let us use their recommendations.

Enter fuzzy. The problem is that these experts – in this case, skilled educators – cannot describe their recommendations in precise terms. Just like a skilled driver cannot describe for how many milliseconds he/she presses the break when the car in front slows down from 65 to 60 miles per hours, similarly a good teacher cannot tell exactly how many times we need to repeat a certain topic and exactly how many examples to show before students are able to solve them on their own.

However, in both cases, an expert can give imprecise (“fuzzy”) recommendations: e.g., “if a topic is hard, we need to repeat it more time and show more examples”. To describe this knowledge in precise terms, we can therefore use the same fuzzy techniques as Zadeh proposed for more traditional control situations.

This is what the book is about. The use of fuzzy techniques to improve teaching is the main topic of this book.

One may ask: if the situation is so straightforward, why do we need the whole book? Well, it is not that straightforward. In many aspects, teaching is indeed similar to control – in these aspects, the application of fuzzy techniques is indeed reasonably straightforward. However, in many other aspects, problems are very different – and thus, completely new tools and techniques are needed.

For example, the whole 100-page-long Part I is devoted to enhancing student motivations – we do not “motivate” an elevator or a plane, but an unmotivated student will not learn much.

Part II is about the order in which we present the material, Part III is about selecting the best way of teaching every topic, and Part IV is about the best assessment techniques – again, we do not need to think how to access a plane, we just easily measure its flight time, etc., but this is not so easy for students, when we need to gauge their knowledge of many different parts of the material.

For all these tasks, the authors use fuzzy techniques (and interval techniques, their particular case) to come up with recommendations for teachers.

Who this book is for. For teachers, of course, it will help teachers of all student levels to teach better – and thus, for researchers who are usually teachers as well. For students – it will help them learn better. And, of course, for researchers – this is an interesting topic in which there are still many open problems that need to be solved.