Week Five Prompt (2/7 - 2/11)

Week 5 Prompt:
Describe and discuss one mathematical error you have seen students make or one mathematical misconception that they hold that surprised you. How did you help students correct this error or misconception?

Describe and discuss one important mathematical connection that you have seen students make. What factors contributed to students’ success in making this connection?




One error I have seen a number of times in the Algebra class deals with students trying to add and subtract positive and negative numbers. They struggle when they are faced with adding or subtracting a positive and a negative number, adding two negative numbers, and subtracting two negative numbers. They could not understand how or why the answer would be positive or negative. I talked to several of the students individually during their work time and used the concept of money and debt to help them with this. If they were adding a negative number and a positive number (like -10 + 4) I would say, “having negative $10, is like being in debt or owing to me $10 dollars. Then if you pay me $4 your debt is going to be smaller and it would be -$6.” Putting this in terms of money seemed to really help these students grasp the concept.
Another way I tried to help them drawing a number line so they could visually see why the answer would be positive or negative. This really helped for one of the students I work with. She was able to get a better understanding with the concept of adding and subtracting positive and negative numbers.

There was one student in the same class that really surprised me on her connection with the two-step equations they were solving and the relations between dividing a number across the equation. My cooperating teacher and myself have been teaching them a certain way to solve these equations. If you were given an equation 12 = 2x + 4, and asked to solve for x, we taught them to subtract 4 from both sides and then divide by 2. While working with these a student asked me if you could divide by 2 first like she did on her paper. Before looking at her work I began to explain that if you do that you need to divide the 4 on the left side too. She showed me her paper and said she did. I apologized and told her that was correct.
This surprised me because we did not teach this concept. She saw the answer would be affected if she did not divide the 4 as well. That was really interesting to me because she was able to form that by herself. She was able to recognize this because she worked out the problem without dividing the 4 and realized that the answer she arrived at was too big and did not make sense. It was great to see a student look at her answer and see if it made sense for the problem she was working with.