Mistake Centered Active Exploration

Mistake Centered Active Exploration puts students in the center of an exploration process to uncover what they don’t know and how to learn it.

Most people hate making mistakes. We want to be good at things. But, remember, none of us started out good at anything.

All of us were once wriggly babies who couldn’t walk, much less do math. Not only was the process of acquiring our capabilities littered with mistakes, we depended on those mistakes for critical information about what to do differently.

“Mistake Centered Active Exploration” formalizes the practice of mindfully engaging with our mistakes to guide learning. A mistake exploration cycle involves 4 steps...

1) Make Mistakes

To get anything out of our mistakes, we have to make some first. At minimum, this means finding the right test for what it is you’re trying to master. But taking a test to make mistakes is different from taking a test to prove your skill. Here’s how to put yourself in a position to gain the most insight from your mistakes.

First, pick a test that is comprehensive enough to reveal your trouble spots. Second, while taking it, do more than just write down the answer. Keeping careful, neat scratch work will make it possible to go back and analyze exactly what you did. Finally, pay attention to how each question feels as you go. Getting something right doesn’t always mean we completely understood it. So as you go, make a quick meta note alongside questions you guess on or find particularly hard so you can learn from those too.

2) Analyze Mistakes

Alright, you missed a question. Now what? Treat your mistakes like treasure. Or at least, a treasure map. Because they are the key to figuring out the learning path from where you are to where you’re trying to go. For this step, you’ll make a log of each question you missed and why. (This is where you thank your past self for all that neat, careful scratch!) Once finished, look through your log for patterns in what you’re missing to determine what you need to learn or practice to move forward.

Your goal here is to find broad patterns, so don’t focus too much on the specifics of the question itself. Instead, try to articulate the underlying reason why you missed it. For example, if you mistakenly found 1 + 2 x 3 equals 9, you probably didn’t use order of operations. Logging this as “I added 1+2 instead of multiplying 2x3” would be too specific to the question. It doesn’t get at the underlying issue that would help avoid this kind of mistake in future. A more useful analysis would be “I didn’t know to use order of operations.” Keep in mind not all mistakes have to do with missing knowledge, like this one. Other common mistakes result from issues with problem solving strategy or careless execution.

3) Learn from Mistakes

Once you’ve found the patterns in your mistakes, you’ll need to find targeted instruction and/or practice for the trouble spots you’ve identified. An instructor or mentor can be really helpful here in helping you source the right material. Keep in mind, you don’t need to learn everything at once. Start with one small concrete goal that you can get done this week. After you’ve mastered it, you can move on to another.

4) Remember Mistakes

Learning something once is no guarantee it’ll be there to use forever after. We have to circle back and refresh things to keep them from fading. How do you make sure you’re regularly doing this? Mistakes to the rescue again. After choosing material to learn based on your mistake log, your log automatically turns into a list of everything you’ve learned. So set a time each week to come back and retry 10 of your logged problems. If you don’t remember how to do one, you know you need to go back and refresh that knowledge. Just keep track of the date you last got each problem right and you’ll always know which mistakes are most due for a retry.