Mistakes are stigmatized in mathematics. Timed tests, answer-math curricula, questions from instructors that start with "What is the answer…?" all feed the perception that we are to do math right the first time, and any deviation from the correct path may be discouraged or labeled as wrong or inefficient.
While the quickest path might allow us to get through the material in class quicker in time, silent and lasting consequences sometimes take root. Being reluctant to experiment and think for oneself is one of these consequences, resulting in underdeveloped problem-solving skills, reliance upon external validation of solutions, and for some students a damaging self-image in math that is exposed by the sentence, "I'm no good at word problems."
What does Ed Burger do about this?
- 5% of course grades are based on the quality of student failure. In order to get an A in the class students must fail productively.
- Use specific activities to teach intentional mistake making as a positive strategy. An example of this strategy is to give a problem to students to work on. Their first task is to intentionally do the problem incorrectly and then share their mistake with a neighbor. Often learning why a strategy is wrong leads to deeper insights, and getting used to making mistakes forms a habit of mind in the spirit of experimentation.
- A related strategy is for the instructor to present an incorrect proof/solution, and then have the students discuss what insights we can learn from it.
Productive mistakes and experimentation are necessary ingredients of curiosity and creativity. A person cannot develop dispositions to seek new ideas and create new ways of thinking without being willing to make mistakes and experiment. Instructors can provide frequent, engaging in-class activities that dispel negative connotations of mistakes, and simultaneously elevate them to their rightful place as a necessary component in the process of learning.