Professor Zbigniew Michalewicz from the University of Adelaide visited our university and gave a seminar entitled “Puzzle-Based Learning” last Wednesday afternoon. The University of Birmingham’s new Learning and Teaching Strategy focuses on enquiry-based learning so I was keen to learn more.
During his presentation, Professor Michalewicz explained how and why the use of puzzles could be used to teach mathematics and develop students’ critical thinking and problem-solving skills. He gave numerous examples and seemed to like puzzles that involved a combination of mathematical techniques; however, he also demonstrated puzzles that illustrate the need to understand the problem and the pitfalls of intuition.
Based on my limited experience and knowledge, it is clear that Professor Michalewicz is a talented teacher. Right at the beginning of his presentation he acknowledged that the one-hour presentation was based on decades of work and I had to wonder how easy it would be for others to deliver a similar learning experience for their students. Fortunately, Professor Michalewicz has a new book just out entitled “Puzzle-Based Learning: An introduction to critical thinking, mathematics, and problem solving”.
When I ask myself whether I have a preference for being taught by an expert at teaching or by an expert in the subject then I would always go for the latter. If someone like Professor Michalewicz is not available then there is nothing like a bad teacher to promote critical thinking.
The beauty of Newton’s laws or motion and Einstein’s theories of relativity is that they provide a set of rules that explain the complexities of the universe. These rules have stood the test of time because of their ability to predict. Several years ago I asked myself whether the complexity of learning could be described more easily. Ever since, I have reflected on the following hypothesis:
Learning will always occur if the key ingredients are present; learning will not occur if any one of the key ingredients is absent.
In contrast with learning styles, this hypothesis emphasises the similarities between learners. Clearly we are not all the same, but everyone learns continuously throughout life. Regardless of whether you agree with this hypothesis, I believe it is worth while trying to identify candidates for the key ingredients.
Motivation has been suggested as a key ingredient by several people with whom I have discussed this hypothesis. However, I believe people can learn certain things without apparent motivation and therefore motivation cannot be a key ingredient.
My personal model has the following five key ingredients:
Information – Raw data is required for learning. Information can be presented in many ways and the learning can be an abstraction of that information. Prior knowledge and understanding is also included in this key ingredient.
Time – Learning is a process and processes take time. Often students do not dedicate as much time to learning as they should, but teachers should also allow time for learning when presenting information to students.
Aptitude – Skill, experience and raw intelligence place limits on what an individual can learn. Aptitude can be improved through learning but it is also dependent on intrinsic ability.
Consciousness – Some level of consciousness is always necessary for learning to take place. The type of consciousness needed for learning depends on what is being learnt. Consciousness is lost after a period of concentration. Learning cannot take place while totally unconscious, but a person can learn while asleep.
Set – A state of readiness or predisposition to learn is necessary for learning to take place. In contrast to motivation which implies a drive to do something, set is about being geared up to actually do it.
I will finish this post with a simple illustration. Write the word “Hello” in big letters on a piece of paper. Then ask a friend to close their eyes. Hold the piece of paper in front of their face and tell them that you will give them two million dollars if they can open their eyes, look at the paper in front of them and NOT learn the word written on the sheet.
A few years ago I participated in an online course on e-learning in higher education. During the course I reflected on the question: What to teach and what not to teach? I was reminded of this question last Friday during a two-hour conversation with a colleague at work. I will refer to my colleague as DH.
DH and I were discussing issues of course design and staff development for e-learning. We both agreed that more needed to be done and I think our views concurred on what staff needed to learn; however, we did not agree on what staff should be taught explicitly. I argued that staff who engaged in certain activities would automatically pick up some of the things DH wanted to teach.
Right now I am reflecting on two questions: Firstly, is there any point in teaching staff things they are going to learn anyway? Secondly, is situated learning always better?
To be fair, DH did not agree that staff would automatically learn all the things they needed to understand and street math illustrates the potential problem of overdependence on situated learning. Nevertheless, I still think it is important not to teach everything. Perhaps the ideal would be to combine situated learning with some kind of reflective activity designed to help plug remaining gaps in knowledge.
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geraint was here!!!!
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Well, I have edited it. The football match is about to start. After that I will submit another post.
