Different Thinking

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Throughout my time working with students and peers in mathematics I have noticed that many students tend to somehow think differently when attempting a problem; they may work through the problem differently or try different measures to solve the problem. Being a future teacher, I have been pondering how to teach with this in mind. Can we as teachers instruct so that all students may be able to reason through the mathematics differently?


I posed this question to myself due to the fact that I have been a tutor for many years, and I desire to connect my experiences as a tutor to how I teach in the future. Being a tutor, I work with a lot of students one-on-one and I am able to see how they think through a problem. When I finally see what comes to mind when they see a certain math problem, I am able to help them think through either a mistake or through confusion. Therefore, I shift how I think to help students learn the best. Sometimes, though, I have multiple students at once, some of whom may be in a different class, and I have less time to be as personal and on the same page as I previously described. So, my initial thought was that it would be impossible to really become personal and on the same wave-length with a whole classroom of students who think at least somewhat differently.

After more thought, I did not come up with a solution to this problem, but I did find some plausible actions that I can take to do my best to help students understand the math personally. First, I must realize that if all I do is lecture on one way to do a problem, then students will think there is only one way and disregard the connections their brains make. For example, two days ago I was working with a student where I was helping her with the problem. When I went to do it one way she said she didn't do it that way. My first reaction was that the way she was doing it was either wrong or extra work. After looking at it a little more, I decided to try the problem her way. In the end, I recognized that her method worked, though a little more work needed to be done. So, I told her that if this was the way she learned then she should do it that way, not my way because I understand the problem better. Thus, we as teachers must let the students try some of their methods and see if they work without forcing them to do things our way.

The second thing I thought that I could implement is that I could allow more time for in class work on the problems and less lecturing. By having the students working on the problems after a brief introduction, I would be able to help them do the problem, rather them helping or watching me do the problems. This way they would have time to try what they think and I could be there to encourage their work and help with confusions and mistakes.

Now, I am not completely sure if these two ideas are the most idealistic practices in the classroom because I have yet to fully be in charge of a classroom, but I want to at least try to implement them to see if they will work. So, my question to all of you reading this: Do you think mathematics needs more personalization to help students who may think differently?