Errors

Working with student errors has been one of the more interesting, frustrating and enlightening components of the Math Methods classroom. Its it amazing to see how logical student mistakes are.

Literally two days after we finished the Errors in class I experienced a real life example that cemented my understanding of how important it is to understand student errors. When you understand the error it becomes infinitely easier to correct the problem. I was grading papers before class with a student, this student is very bright and often comes in early to socialize with people who are at his level, teachers, and he was looking at the paper I was grading and commented that it appeared that the student seemed to think that the fraction with the largest denominator was the largest fraction. I studied the paper for a moment. He was right. I called that student up for a few minutes at the beginning of the class and allowed her to make correction on her paper. The second time around she only made a few computational errors. I pulled the young man aside and complimented him that he realized something that they teach in college courses, something that I still struggle with, he was very proud of himself, deservingly so.

This experience made me appreciate how much frustration, both for the teacher and the student, can be avoided when the teacher is knowledgeable about the types of mistakes that students make. Students generally make mistakes that are very logical, they confuse a rule or even make up their own, but generally their misunderstandings can be correctly if they are understood. One of the greatest dangers is when teachers include “short cuts.” Instead of simplifying the problem teachers add a new layer of rules and procedures. It actually becomes more confusing to the student. Sadly, teachers think that shortcuts are useful because they assign worksheets that ask the students to perform the same computations over and over again, creating a need for a quick solution. If teachers assigned work that focused on quality over content this wouldn’t be such an issue.

All in all I feel that I’ve learned a lot from seeing the wrong way to approach mathematics.