Explore with us the Learning Benefits of Erroneous Examples

An erroneous example is a problem solution in which one or more of the steps are incorrect. For example:

Paul has a bucket of peaches weighing 10.63 pounds. He needs to use 5.3 pounds to make several peach pies. How much will the bucket of peaches weigh after Paul has made his pies?

Here is James' incorrect answer.

1 0 . 6 3
- 5 . 3
1 0 . 1 0   pounds

Why is this incorrect? Can you fix it?

Initial studies have shown that presenting students with errors is valuable, as long as students have a basic understanding of the problem domain. Erroneous examples encourage reflection and critical thinking. They also provide a different kind of problem solving opportunity than regular classroom math problems.

The AdaptErrEx project, funded by the U.S. Department of Education, has developed materials to support learning of decimals through erroneous examples. The main goals are to support deeper, more robust learning and to improve error-detection skills.

All the materials developed on the AdaptErrEx project will eventually be freely available through MathTutor (www.webmathtutor.org), a website that helps middle school students learn math. An example of an erroneous example problem is shown below.

The intelligent software tutors developed on the AdaptErrEx project are based on a long and rich history of research on intelligent tutoring systems and human learning. They were built at Carnegie Mellon University using the Cognitive Tutor Authoring Tools.