John Hopcroft on the teaching of today and tomorrow

John Hopcroft is an ACM A.M Turing Award laureate, which he won in 1986 together with Robert E. Tarjan for fundamental achievements in the design and analysis of algorithms and data structures. He distinguished himself by his excellent and inspiring teaching. I talked with him about it during last year’s 7th Heidelberg Laureate Forum.

Mr. Hopcroft. People who are enthusiastic about teaching generally have a role model from their own school days. Is that also the case for you and if so, who was it?

I was very lucky because I had a lot of inspiring teachers. Not only in primary and secondary school, but also at the university. For example, I had a very good primary school teacher who taught me algebra at the time. But he was also a football coach and he was good in both subjects. He left his mark in my life, which led me to want to have such an influence on other people. I think what he did was to show the students how important their success was to him. And that hit home! It is important that students realize that the teacher really cares about their future.

How should a student feel in class?

It doesn’t matter whether the lecturer has a lot of experience and whether he knows a lot. How he designs the class or the lecture is not the crux of the matter. While this is important, it is far more important that he passes on his passion to the students. That is what makes a good lecturer. Because if you have that in mind, then the first two properties are automatically added. If students do not understand a topic, then the experience of the teacher or the design of the class will not help. But that the lecturer cares about his students does.

How can you make students feel comfortable in class?

It has to come from yourself. It must be a matter of course for you to want to achieve this. If a student has a problem with homework, this is not the problem, but that the student did not understand the subject matter. Then I try to explain this topic to him from the start and take the appropriate time. You have to do that in every situation. You have to ask yourself how you can help this person. And if you have a lot of students in a course, you can’t really help everyone personally. That’s a problem. But then you have the opportunity to make the whole team of lecturers aware of the need to take special care of the students.

Do you change a lecture when you notice that student feedback is not good?

Yes. I actually always prepare my lectures and I always know what I’m going to say and if after 15 minutes I notice that it doesn’t work, I have to change it. There is no way out. That is another reason why you should not use presentations or similar stuff in class. It has a negative impact on the lecture because you cannot adapt to the circumstances. You are stiff. There is nothing better for teaching than using a blackboard.

 What do you think about unorthodox, newer teaching methods? Do you use them?

I don’t use them. But that doesn’t mean that they’re not valuable. Some say that you shouldn’t actually teach, but rather take care of captivating the students. Every tool is valuable for this. But you also have to be aware of the fact that you have to invest a lot of time in such methods. It must also be clear beforehand what the goal of university-level education actually is so that these methods act towards this goal. Unfortunately, this is not always clear.

What do you mean by that?

Young people do not study to get a job, but to shape their entire future life. They shouldn’t take a job for salary, because the job is a fundamental foundation of every life. And you want to be a winner. You shouldn’t have the feeling that you go to work every day, but that you have fun every day. Pick what you enjoy. At the university, you not only learn the subject matter but also other things, such as interacting with other fellow students. The greatest lessons are found outside of lectures, not during them. In this sense, it is particularly important as a lecturer to pass on knowledge and wisdom to the students even outside of the subject matter. That should be important to every lecturer. For example, if there are electives, students have to pay particular attention to what is expected of the course. You also have to project into the future and be aware that many decisions made during your time at university affect your whole life. You shouldn’t pay attention to the demands you get from the curriculum, but your own demands on life. 

You gave one of the first computer science courses. What do you have to do if you want to teach a new subject and have to design a curriculum for it?

It depends a lot on the area. As an example, I would like to use deep learning, which is particularly popular today. But the main results are based on experimental approaches. And how do you teach that? There is no mathematical theory that justifies why deep learning works (yet). So if you teach something new like this, you have to put together everything you have available and over time you expand it and include new topics. But whenever you teach something new, you have to develop a theory about it. That is the most important thing for me. 

You are introducing measures and policies in the academic field in China to improve teaching there. But what can you do on a smaller scale to improve teaching?

If a system doesn’t work, you have to ask the honest question why it doesn’t work. What we did in China was to make it attractive for universities to improve their teaching work. They should have motivation, especially in the financial area, to focus on it. The important thing here is that support for this venture came from above. This is the only way to initiate such changes. I have taught in many countries and have supported everyone who is committed to such changes. However, neither I nor the individual had an actual influence because the attempt was nipped in the bud. The government must support such an idea, have an honest interest in it, and set an example. This is the only way to change something in the long term.

How do you think teaching will change in the future?

That is difficult to say. But we can do it differently. It is said nowadays that we are in the middle of an information revolution. So if we look at other major changes in the past, it may help us. The first really fundamental change in human history was probably the agricultural revolution. This led to societies developing because in order for agriculture to thrive, you need a hard-working force. Until then, however, education was not as important because it is not as important in the country as other skills. Then came the industrial revolution, which abolished physical labor in factories and changed everything on a large scale. Nowadays you need at least a school leaving certificate because no matter where you work, you have to be able to deal with numbers and above all, you have to be able to communicate properly with others. That changed the way of education. Until a few decades ago, in the heyday of the industrial age, energy sources and raw materials helped powerful states achieve their status. It is believed that this will change again in the information revolution because it will then be available to every country. Countries will then stand out for their ability to develop talent, which can be achieved primarily through education. So it is the countries that will adequately improve their educational policies that will take the leading positions in the world in the future.

One of the other issues I work on in this context is early childhood. I talked to a lot of scientists who study and analyze them and they all agree that if you invest in education at the earliest possible time, you will get the greatest possible payoff. By “earliest possible time” I mean the first two years in life. That is amazing. My question was whether there really is research to back this up and indeed there have been an incredible number of studies in the last 25 years that show that a peaceful and stable environment during growth is important for the optimal development of an infant’s brain. Children develop more and more skills until they are around 20 and are fully mature, but in the first two years children learn how to learn and that is the important thing here. You have to tackle this successfully so that the children can excel in elementary school later on. But it goes one step further. If you really invest in the earliest possible upbringing, it is also proven to be one of the best investments that can be made in the financial area. But no politician does that, because that would be long-term measures and they only think about the next 5 years. 

How can you make society aware of the importance of talent?

I often think about strategic opportunities to make society aware of this. People need to be aware that we only live once and that we have to enjoy it. You have to search for what is really fun in life and then invest time in it. I’ve had many PhD students in my life, and only one of them never got his PhD. He came to me once to explain that he wanted to be a ski instructor. And of course it was the right decision. If he had stayed in the academic field, he would certainly not enjoy his work as much as he does today and that is certainly particularly important for his students. It will have a positive impact on their lives and there is nothing better than that. That’s why I try to get people to do what makes them happy. If you do a job that you really enjoy and you have a colleague who may be more brilliant and talented but doesn’t enjoy it as much as you do, you will surely do the better job.


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Demian Nahuel Goos is a half-German, half-Argentinian assistant instructor and PhD student in mathematics at Universidad Nacional de Rosario in Argentina, where he also does research in its nuclear research institution. Moreover, he is a teacher in German as a foreign language and a soccer referee. In search of ways to communicate mathematics in a more appealing way, he does artwork about math and mathematicians.   Demian Nahuel Goos ist ein deutsch-argentinischer Assistant Instructor und Doktorand in Mathematik an der Universidad Nacional de Rosario, Argentinien, wo er auch an dessen Kernforschungsinstitut in der Forschung tätig ist. Des Weiteren unterrichtet er Deutsch als Fremdsprache und jobbt als Fußball-Schiedsrichter. Auf der Suche nach Wegen, Mathematik auf eine attraktive Art und Weise zu vermitteln, setzt er sich gerne künstlerisch mit Mathematik und Mathematikern auseinander.

1 comment

  1. Citation:

    He [John Hopcroft] distinguished himself by his excellent and inspiring teaching.

    Hopcroft’s lectures want to reach the audience and they do. So Hopcroft is a good teacher. But when I look at Hopcroft’s HLF lecture “Research in Deep Learning”, for example, I notice something else about Hopcroft’s approach: Hopcroft presents examples that seem to be taken from real life, but he does not stick to it, he tries to uncover the mathematical structure behind the example. Others do that, but Hopcroft seems to me to be more mathematically oriented than other computer science teachers.
    Perhaps good teaching is always like that: it needs to convey the desire to teach, but it needs a certain view of the thing to be taught. And this particular view must be convincingly represented by the teacher to reach the audience.

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