Writing Assignment #3

Erlwanger attempts to show that IPI was a system designed to allow students to learn math on their own without the aid of a teacher or discussion with others, and that it failed miserably. The card system allowed each student to work at their own pace. As long as the student was passing the assessment tests each time there was no need to discuss any of the material with anyone else. Benny was doing well and was ahead of most his class. Because of this he never talked to his teacher about his ideas of math. When Erlwanger spoke to him he discovered that because Benny had been working on his own he had invented a million rules about math that had no reasoning behind them except that they sometimes got him right answers on the assessments.
Even today there are classrooms where there is very little teacher student discussion. As long as a student can do well on tests it is assumed they know what they are doing and there is no need for the teacher to interact with them. I think it is important that as I get ready to become a math teacher that I am worried about the individual learner. A teacher needs to know more than what sort of grades their students are achieving. Teachers and students need to build relationships.

Writing Assignment 2

Knowing about rational understanding and instrumental understanding is vital if you want to become the best math teacher you can. Rational understanding is knowing the why behind math. If you have a rational understanding of math then you know where your formulas come from and how to apply them to problems and life. Having an instrumental understanding of math means you know how to plug numbers into formulas in order to get right answers. Instrumental understanding is within rational understanding. You can't truly have a rational understanding of math without knowing the instrumental part of it. Teaching a student an instrumental understanding of math does have its benefits though. Students get more immediate feedback, therefore there is less frustration. Instrumental understanding is also just simply easier to grasp at first. But, without a rational understanding all math is is numbers. Change the situation in a problem and suddenly students with an instrumental understanding can't get right answers any more, whereas those with rational understanding can apply their knowledge to multiple situations. Rational understanding also helps you keep math over time. When a student does finally gain a rational understanding then they have greater satisfaction than when they simply were able to find right answers. Instrumental understanding is important, but it can become useless without gainging a rational understanding.

Writing Assignment 1

Mathematics is a whole new language. It proves how the world works, or at least that is what I have always been told. To me mathematics is organized. There is a right answer to what you are working on. The solution is always there, you just have to find it. Except, sometimes you don't.

I learn mathematics best when there is an unnatural amount of structure. This is obviously not the best method for everyone but it works for me. I need a teacher to make me feel like their class is the most important class I will ever take. Now this may seem silly but if all my teachers make me feel like this then I put in my very best effort in every class.

It has been my experience that when my teachers give me the opportunity to work out problems with them I learn the most. When a teacher makes me feel like they want me to come ask them every one of my questions then I learn more.

In my high school math classes, weekly quizzes were a good thing. They let me know if I needed to work harder and what I was missing. Examples were also crucial. I have a hard time applying theorems without lots of examples guiding me through.

I think that one of the negative aspects of high school math is the negative outlook everyone has towards it. There is this idea in high school that you'll never need the math you are learning. Students lose interest fast and stop trying. You can't stop trying in a math class.