Blog #3

Erlwanger's main point in the article about Benny was that IPI was failing to teach Benny correct math principles and not only that was impeding Benny's future understanding and enjoyment of mathematics. In the opening paragraphs Erlwanger emphasizes the weakness that are in IPI. He talks about the how IPI weakness stems from how it is taught. Elwanger goes on in the article to mention more then once that in the IPI system the teacher is removed from the his or her role as a guide to students leaning mathematics. Erlwanger feels this is a mistake and almost puts the student and teacher at opposition. The student like Benny gets frustrated at the teacher for only ever following a key of answers. Erlwanger also mentions that Benny learned incorrect math principles from going through the IPI program. Benny made his own reasoning for how math works because there was nobody in the IPI program to tell him differently. As long as his answers were right, he got to move on in the program. Erlwanger felt that the IPI program was important step in education understanding but ultimately fails to teach children mathematics.

One of the most important things Erlwanger taught was importance of the teacher. The IPI program was designed to remove the teacher from the teaching process, and Erlwanger showed that this was a mistake. This is very applicable today because teachers have a huge influence on students attitudes toured subjects, especially math. In my experience, I used to really like chemistry, but I had a horrible teacher a few years ago and it completely ruined the whole subject for me. I still have a bitter taste in my mouth from that class and its subject. On the other hand. I have had great teachers in math that have helped me see the beauty of mathematics.

Blog #2

There are many things that unify and separate Skemp's idea's for relational and instrumental understanding. One of Skemps main ideas about relational understanding is that someone who knows the purpose and the method for the math they are doing. Instrumental is understanding the method, or in other words the process to get the right answer, but without knowing why they are doing it, or why it works. Even though Skemp highly favored relational understanding, he did note that they are not mutually exclusive. To truly understand a principle in mathematics, or to have a relational understanding, one must have the instrumental as well. One must know the method in which to get the answer. Skemp knew that a student must know the method and the purpose to truly have a relational understanding. Some of the main advantages Skemp talked about in regard to relational understanding is that it was easier to remember, it was easier to go from one problem to another, it gave students motivation to learn more. Instrumental understand however, could give more visible positive outcomes. Or in other words, it is easier and faster to see a page full of right answers with instrumental understanding. However, usually if the problems change a little bit, it will be harder for one with instrumental understanding to adapt. Overall there are many reason why a teacher would choose to teach for relational or instrumental understanding. However, Skemp felt that relational understanding would best serve all who learned it.

Blog Entry #1

What is mathematics?



I think mathematics is the study of numbers and relationships between those numbers.



How do I learn mathematics best?



I think I learn mathematics best by examples. I usually need to be shown how to do a math problem before I can understand it. I also learn by repetition, though I probably don't do enough of that. I do not do as well when I have to try and learn math principles out of a book. I do really well when the math problems I am given build upon one another to teach greater principles.



How will my students learn mathematics best?


I think it is important to cover all the learning styles when you teach mathematics. Or at least all the ones that are possible or prudent to the lesson being taught. That way, every student will be able to learn the concepts and not just those students that happen to learn best by a particular style. I also feel it is important to understand how each student learns so that when they ask questions you will be able to tailor your response to that student and help him or her the most.



What are some current practises in school mathematics classrooms that promote students' learning of mathematics?


I feel one of the best current practises is being able to work in groups on math problems. This allows many students to ask questions of each other and learn at a faster rate. I also feel that math games help students learn, because it provides a fun atmosphere and students learn when they are having fun.

What are some current practises in school mathematics classrooms that are detrimental to students' learning mathematics?


I honestly don't know a lot of the current school practices. I do remember that I hated it when a teacher would put the students name on the board who got the highest grades on tests. I felt it led to unhealthy competition and isolationism.