Are we learning from mistakes in math

Mistakes can be your greatest teacher. But only if you understand what went wrong, and what you might do to fix it. In math education, a lot of feedback is binary. You are correct, or you are not. And if you are wrong, the only feedback you get is that you are wrong. We believe that understanding a mistake takes dynamic feedback, and that math education has a lot to learn from the way feedback is provided in games.

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Visual feedback in math

If two different values are presented as equations, understanding them takes knowledge, time and processing. If the same values are presented visually, seeing the difference between them is instinctual and easy. When we give the player feedback on their mathematical choices that they perform in our game, we strive to make this feedback visual and dynamic. If the value 6 is increased by 50%, we visually animate this action. So that the player can see that 9 is 50% bigger than 6, and that 6 is 66,6% of 9. And when mistakes are made, the player has visual data connected to the mistakes. If your goal was to get to 8, instead of 9, you can see that 50% was just a bit too much. And if your goal was 12, you can see that 50% only took you half the way there.  

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Who decides that a mistake has been made?

In our game Cal & Bomba, the player get to make a lot of mistakes. And the interesting thing is that the game will not tell you that you have made a mistake. The game will simply let you make any available mathematical choice, and the game will show you the consequence of that choice. 

The player gets to decide if they are happy with the outcome of their choices, meaning that it is the player who is deciding what is a mistake, and what is not. And when this decision is made by the player, the motivation for correcting the mistake comes much easier.

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Mistakes needs context

Students with a poor understanding of math make a lot of mistakes in math. But they are not learning from their mistakes. We think that a mistake can be a positive learning opportunity. At the same time, mistakes can make you doubt your abilities, and kill your motivation. Merely stating that a mistake has been made is far from enough. We need systems that present mistakes with relevant context so that students can understand what they have done wrong, and give them ideas about how to fix the mistakes. Our approach is dynamic visualizations of mathematical actions.