Rigidity or Flexibility and Creativity

There was a viral posting on the social media regarding a school test paper on multiplication that has caused a stir including myself. See here as an example. Normally, I do not want to comment on it since people do not usually like having their work to be commented on; what more if it is coupled with many jeering remarks. This has become a trend in the social media. But then, I felt I had to comment at least to voice that one can have a different interpretation to this matter and the student who got two marks could have been given eight marks instead if I interpreted the answer boxes differently. The insistence to have one way of approaching the problem seems to me troubling. And this is not a matter of having good marks for the student or to see who wins the argument. It is the rigidity. Instead of commenting further on the issue, let me just comment on my own experience.

I tend to have issues with certain instructions that tell me how to do my own teaching in some classes. Some of these are cosmetic that in the end one just follows the instruction. But there are others that tend to limit my creativity and what I thought is best in teaching. Particularly with university students which I thought should be independent and critical at some level. For instance, when I teach, I do not like to follow any one single book for the subject I am teaching. I tend to draw my own experience in understanding the subject matter. I do a lot of internalising before I teach a topic and this could involve a wider reading beyond a single book. Again let me recall my own experience with Prof. Herbert Green which has shaped my thoughts. His style of approaching a topic can't actually be found in books and that let me study and form my own ideas in understanding the subject. The other lecturers that I had experienced in Adelaide, Cambridge and Durham are more or less the same in their approaches in teaching. All of them had their opinions on the subject matter for which one can compare these with one's own reading of books elsewhere. Here is a pic of the people at the Department of Mathematical Physics, University of Adelaide and Bert Green is in the middle, which I found recently.

There are of course exceptions like when one is sharing a course with another colleague and you need to standardise the contents to be taught with say from some textbook. Even here, we do not interfere with each other's teaching method and we only meet to agree on the contents that needs to be covered. When developing tests and exam, we just need to agree what can be examined. When we are evaluating the exam scripts, we welcome alternate solutions than the solutions we have prepared for the exams. In fact, we often take note of the students who do so and they are often rare, of course. In the Math Competitions too, they may even award such students who produce original solutions.

I sincerely believe teaching, learning and of course research are activities that involve creativity and thus one should be flexible in ways of approaching them. There is no one standard way of teaching and the students that can come to us are not like factory products to be homogeneously shaped into one style of thinking. As such is my experience, I think the same applies in school. We need to rethink some of the approaches of teaching and workbooks that tend to flood the school students nowadays that have the tendency to remove creativity and joy in learning. Of course, this is only my personal opinion.

But let us see what some studies have said about great teaching:

These practices have evidence in improving learning:

• teachers' content knowledge and their ability to understand students' understanding and misconceptions
• strategies in effective questioning and assessment
• challenge students to understand reason behind a lesson
• large number of questions and response evaluation
• space out study and practice on a given topic
• test them or let them generate answers before they learn a topic

On the other hand, these practices have no evidence in improving learning:

• lavish praising
• students discover ideas by themselves
• group students by their abilities
• presenting materials according to learners' style.

The whole report can be read here. Even with this, one should not take this as unquestioned gospel. Allow flexibility of ideas and approaches to see what works in the circumstance one is in.

In the end, we will be partly responsible on what we teach students and how they are affected.