Sunday, August 23, 2009

Let's Make Some Mistakes!

Too often, students see mistakes as tantamount to failure; however, mistakes are an inevitable and necessary part of the learning process. Marvin Minsky, the Toshiba Professor of Media Arts and Sciences at MIT has noted, “We tend to think of knowledge in positive terms—and of experts as people who know exactly what to do. But one could argue that much of an expert’s competence stems from having learned to avoid the most common bugs.”1 Innovation also hinges on making mistakes and learning from the errors, be it realizing that a process will not work, or examining how an unanticipated result could be used to solve another problem.

In education, the reliance on high stakes testing has created a climate of absolutism. Students tend to believe that for any problem, there is one correct answer, and to reach this answer, there must be one unique process. While this may be useful in developing easily scored standardized tests, it does little to promote discovery, creativity, and learning. Once outside of academia, very few problems have a unique path to a correct result. A simple example I use is choosing a route to a destination. The majority of people will stick to the main roads. It’s simple and usually relatively efficient; however, there are times, particularly when traffic is heavy, when taking some of the side roads can save time and aggravation. To learn where these side roads are requires either a willingness to experiment, to take risks and possibly get lost, or a guide to show the way. Even if the wrong road is taken, one can usually backtrack and try a different road. Once these paths are learned, the driver has a wider array of choices and can choose a course that increases efficiency.

The same concept of multiple paths to a solution often holds true in education. One of the goals I set for my students is to allow them to see there are multiple ways to solve problems. After showing my class several ways to approach a problem, I typically ask, “Which is the correct way to do the problem?” This generally provokes some discussion with some students selecting the first method and others selecting different methods. My answer is always the same. “The correct method is the one you can both understand and do efficiently.”

I also try to have my students realize that mistakes are part of the learning process, and that there is no failure until one stops trying. Many of my students are athletes, and I often use analogies from sports to illustrate this point. I may ask students, “If you were one on one against an opponent and he burned you on a play, would you guard him the same way next time? If he burned you again, would you keep trying different things until you could defend him? And, when you do manage to stop him, what happened?” Typically, the students will affirm that they would try different methods until they learned what worked. At this point, the connection usually hasn’t sunk in, and they need one more prompt, “So, you made a bunch of mistakes, and you didn’t think you failed. You experimented with new methods, learned from your mistakes, and ultimately succeeded. Do the same thing in this class, and you will succeed here. Do the same thing in life and you can be successful there, too.”

Ultimately, the goal of education is having students realize that the road to success has many paths; they will make wrong turns occasionally, but learning which routes work and which do not is what will allow them to reach their destination.



1 Marvin Minsky Essays, OLPC Project, http://wiki.laptop.org/go/What_makes_Mathematics_hard_to_learn%3F#Negative_Expertise

2 comments:

MariaD said...

Once in a while, I invite my students to make mistakes on purpose. Activities I've done so far:

- Make as many mistakes as you can in solving this problem!
Works better in groups, as a collaborative task. Leads to students analyzing "all possible" mistakes. Relies on the "catch them all" (collector) game mechanic for fun value.

- Make the silliest/weirdest mistake possible!
This relies on comparing mistakes. Again, it's a high order (creating/evaluating) task, because students have to compare their mistakes and judge which are silliest, and why.

An activity I want to try:
- Make mistakes that are hard to notice!
For example, the (in)famous proof that 1=2 has a relatively subtle mistake, at least for the beginning algebra level.

Pete Horne said...

Thanks Maria for the good ideas. Students often overlook the value in mistakes. Another useful excercise is to have students create a multiple choice test where the alternate answers represent common mistakes. This can also be done collaboratively with students voting on what they see as likely mistakes on a particular problem. Great practice before standardized tests.

Pete Horne
Bridgton Academy