Today in the Classroom

Me: Instead of the sum of squares we can also try to minimize the maximal distance

\(f(c) = \max_\limits{1 \le k \le n} |x_k-c|\)

What would be the result, assuming we have the points in order

\(x_1 < \ldots < x_n\)

Silence …

After two painful minutes, Me: Okay, let’s make a sketch. If c is here


What is the value of f(c)?

Silence …

I can see from some faces that they know the answers, or at least have an idea about it. But still, silence.

Only after a long while with me impatiently waiting for any response, I can hear a whisper: In the middle.

So what is this? Are they afraid to show silliness? No posing? Is this problem so hard? I cannot say.

Currently, I assume that these Bachelor students are trained to passively absorb math. It starts in school, and continues, much worse, in University. How we can break through this I do not know. There are some legal problems involved. You can no longer enforce active participation. That was an illusion anyway. But we should generate a climate where students don’t feel bad about making mistakes. After all, learning math is not flight training. How to do that against the habits of all other classes is something I would love to learn.

09. November 2015 von mga010
Kategorien: English | 2 Kommentare

Kommentare (2)

  1. For many years I enjoy reading this site

    This is the Professor Felder home page. Among other things, the main subject of many „Random Thoughts“ is devoted to teaching methods and learning styles. I also like the Professors sense of humor too.

  2. Yes, that link is interesting.

    I am not so much in the school business to know exactly how many teachers feature active learning in their classes. I would bet that most try to do just that. They pose problems, let the kids work, partly in groups, and at least try to activate the sleepier ones. Most of them seem to fail, however. One of the reasons might be that there is simply not enough time to start activation in 45 minutes, and too many lessons. From what I see in the University, the attitude they bring from school is not towards active participation.

    Math at the University level has always included active learning in the form of problem sheets. Nowadays, we add tutoring to this to support the student. In the class, however, we still „teach“. I am yet unsure if we should change that or at least reduce the time the student is absorbing.

    But I am convinced that we should stop writing blackboard after blackboard in front of a sleeping group of students with deactivated brains and active pencils. It does not make sense anymore in times of the Web. If students do not learn anything in their time of attendance it is a wasted time.

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