Benny Article

In Erlanger's paper about Benny and the self taught math program, his main point was that it doesn't work and that teachers are necessary to guarantee a certain level of success. Benny was clearly a bright child since he managed to make up math rules that made sense to him and they worked for him about 80% of the time. His teachers didn't notice how much he was struggling because in comparison with the rest of the class, Benny was doing quite well with the program. His teachers had no reason to work individually with him unless he asked for help, and even he thought he was doing well so there was no reason to ask for help.

I think it's ridiculous to think that teaching mathematics principles can be done without the guidance of a real live teacher. If you don't know the correct math rules as a student, and you don't build upon those rules, you will not be able to progress very far. The high school student that I tutor had a very "hands off" math teacher last semester. Now she has a new teacher, and when I come to help her with her homework, most of it is finished ahead of time becomes she's gaining relational understanding at school just because her new teacher is involved with his students.

Skemp's Article

Skemp's article discusses the differences between relational understanding and instructional understanding. Relational understanding involves knowing the proper way to solve a problem, including how you would set it up, and why you would set it up in that manner. Instructional understanding is knowing which algorithm to apply without knowing the reasoning behind it. From these definitions, you can tell that instrumental understanding is included within relational understanding just like the diagram that we drew in class. Each of these has different advantages. While instrumental understanding is relatively simple and just takes memorization, relational understanding provides long term benefits because when you understand the "why" of a problem, you can easily replicate the "how". Instrumental learning can provide results fast, and when a student gets the right answer quickly it can give them confidence. However, when teaching new information, relational understanding can be applied more readily. A student wouldn't always see which numbers to plug into an equation without having a relational understanding. When a student understands relationally they are less likely to seek external rewards and they are also more likely to seek relational understanding in different areas of life.

First Post

1. Mathematics is the study of numbers and their practical application in our daily life.
2. I learn mathematical concepts best when they are explained to me and then I have time to try it by myself, make mistakes, try to fix my mistakes, and then ask for additional help. In high school, math came easily to me so I never had to branch out and try other methods of learning.
3. I think my students will learn best visually. I have found that it's easier for me to explain things when I have a picture or diagram or something to show.
4. Student have more tools and resources in the classroom than there used to be. Technology has played a huge roll in that. I know growing up that math based computer games not only helped me learn, but made it something that I enjoyed and wanted to spend my time doing.
5. I tutor a high school student. I asked her what the square root of 100 was and she pulled out her calculator. I was in shock. In her defense, her mother said that when my student was in the 4th grade, "they" (I don't know who "they" is, the people who make decisions I'm assuming) had decided that they were no longer teaching times tables and that mental math was a thing of the past. Just watching my student struggle through basic math shows me how detrimental that is.