subject: Mistakes In Math - A Vehicle Of Learning [print this page] We accept that making mistakes is part of learning and growing up, but this is overlooked in math education as a valuable tool for student development. Just like learning to ride a bike, learning math requires taking risks and being prepared to do things wrong. Children need to be encouraged to step out of their comfort zones and take on problems they are uncertain of. Doing so will give them increased confidence both through learning theory and gaining experience in taking those risks. This will help them not only with their math but with their overall education.
One indication of a child's preparedness to venture into unknown territory with confidence in math is the appearance of their workbook. Generally, the child who is prepared to leave a mistake on the page and tackle the same problem again will be a child who is more confident in their work. This child views the attempt at the question as valid work, worth keeping. If the child has a greater awareness, he or she will understand that the process of making the mistake and then correcting it with another attempt is the key to learning in this subject.
A child with a narrower, less flexible approach to math will have a workbook that contains only correct work with all mistakes completely removed. This child views the answer as the aim of the exercise as opposed to learning a method. Tackling unknown or difficult questions is frightening for this child, since there is a large possibility of complete failure in the form of an incorrect answer. A child with this view of math will prefer to hand in a test that is blank rather than risk getting a question wrong.
Some time ago I taught a grade 7 student who made a particularly strong impression on me. The first time I collected his homework book I noticed that it was filled with nonsense. This child had strung together the numbers, letters and symbols we had been using in class into what resembled sums. This child was a recent migrant with almost no prior schooling and a non-English speaking background. Despite barely being able to add, this child had tried to emulate the work being done in class. He knew he had little knowledge of the subject. But he was prepared to take those risks in order to achieve in the subject.
That was an outstanding effort. This child knew he did not have enough understanding of the topic, but he tried his best and was prepared to be wrong. He was even prepared to risk ridicule in order to learn about the topic. That same child made outstanding progress in math throughout the year and by its end he had almost reached the standard of the other students in the class that had been at school for up to seven years longer than him.
Risks need to be taken by children and they need to be rewarded, regardless of the outcome. Math students need to be told frequently that since they are doing unfamiliar work they must expect to make mistakes, and that these mistakes are an essential part of their learning. If a child hears this often enough and is regularly rewarded for attempting work they are unfamiliar with, they have the opportunity to develop a positive approach to risk taking in the classroom.
