Right Angle

Visualising Pythagorean Theorem

When I first saw this animated gif, I was instantly attracted. It felt like a good tool when teaching the Pythagorean Theorem. When I looked at the comments accompanying the original post for this gif, I found an intriguing conversation about the difference between demonstrating and proving the theorem. In one of the comments, Tim Erickson shared the idea of getting preservice teachers to view several Pythagorean Theorem Youtube videos and then deciding if each one is a demonstration or an attempt to prove the theorem. I am intrigued by this.

In my recent Emergenetics workshops with students, I often get a reaction from students about one of the descriptors for the Analytical thinking style which states that those with a preference for this style would like mathematics and science. These students who have a preference for Analytical thinking did not like Mathematics nor Science classes in school. My guess is that the analytical nature in learning Mathematics and Science could be missing from most lessons in school. If they are largely rote learning, then it might be no wonder that these students did not enjoy these subjects as they ought to.

Just as when I was introduced to the Pythagorean Theorem as a teenager, what was important was to be able to identify the sides and also quote and use the formula correctly. And this was sufficient for doing well in the tests and examinations. Could I have understood or even been fascinated by the nature and properties of right-angled triangles? Would that have made a difference in my or any student’s learning?

We speak much about Bloom’s taxonomy in the field of education, and in Singapore, there is a clear desire to shift our examinations away from mere recall to more application-type questions, but I suppose there remains a tension for teachers that needs to be resolved about the needfulness and usefulness of helping learners dig deeper in most, if not all topics covered in school.

This not only requires a new approach, possibly more time, and furthermore it might not guarantee better performance in the current form of assessments. The claim and hope is that such an approach will build a firm foundation for more creative and productive learning for life. This concept also involves the question of what content should then form the foundational curriculum.

A very different angle, and might I suggest, the right angle at this point for looking at this might be to consider the thinking and behavioral skills needed and then build lessons around these skills using whatever content that might be of interest to the learners, such as suggested by the Habits of Mind. I think that technology today has certainly lowered the threshold and cost of exploring such a radically different way of learning. What might be holding us back?


About pauseability

An educator at large and learner at heart. Founder of Pauseability. Encouraging everyone to learn to pause, and pause to learn.
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