Is a visual representation always beneficial?

Recently I’ve been inspired by Dan Meyer’s brilliant new site, 101questions, in which people put up a picture or video on the site to spark curiosity in a student. The main idea behind the site is that the visual stimuli makes the students ask the questions instead of the teacher providing the questions.

I’ve recently been working through the syllabus quite quickly with my year 8 students so I decided to do a few problem based lessons to consolidate some of the topics we’ve covered and get them thinking about some interesting mathematics.

I simply explained to the class that I was going to show them a short video without giving anything else away.

They were confused at first, but after a bit of discussion amongst themselves they started to ask the right questions and were quite easily able to arrive at a point in which they were convinced that the sum of these areas would never reach 2. On a very important note, they didn’t seem quite as surprised as most students do on first discovering this result. Don’t get me wrong, they were impressed by the result but maybe just not as much as I’ve come to expect. Was it because they saw it visually and it was therefore more intuitive for them to understand why it couldn’t reach 2? Maybe the video takes the mystery away from this problem?

What if I´d put the sum on the board: 1 + 1/2 + 1/4 + 1/8 + 1/16 + ….? Had I robbed the students of a way to represent this summation visually and at the same time made it easier for them to understand?

I have formed my own opinion on it now but I thought I’d throw it out there to see if anyone has any opinion on whether the video was a ‘more beneficial’ way to start the conversation or whether I should have gone with writing the summation out on the board?

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