Benny

Erlwanger's main point was to show that students can progress through the mathematical IPI program without a complete and adequate understanding of previous work. Benny, a 12 year old boy, who is involved in the IPI program was the subject of study for this paper. Benny's scores on homework and tests were quite high. Then during the interview, Benny couldn't compute simple mathematical equations correctly; such as converting between fractions and decimals. Benny thought he understood the concepts when in fact he did not.

After reading Erlwanger's paper, it got me thinking about when i become a teacher. If Benny was one of the highest scoring kids in the IPI program in his class and he had very little to no understanding of the concepts of mathematics, then when i am a teacher i need to be aware that even the students with the highest scores in my class may not have a complete understanding of the material.

In Skemp's paper titled 'Relational Understanding and Instrumental Understanding' Skemp addresses two types of mathematical teaching, those being relational and instrumental. Relational understanding is a way of teaching where students understand both how to do a math problem and why they did it that way; where instrumental understanding is a way of teaching just the how. Instrumental teaching would be much easier and faster, making it possible to cover more material than if teaching in a relational way. But if students are taught only in an instrumental fashion will they be able to apply what they have learned to other similar problems? Probably not. While both methods of teaching get the teaching done and both methods help the student's pass their tests; one method, relational, is better for the students in the long run.

Assignment #1

1. What is mathematics?

Mathematics is a study of numbers. It is a broad topic encompassing many aspects. Ranging from adding and subtracting numbers to solving multivariable equations. Mathematics is used in everyday lives from research to grocery shopping. Mathematics is used by everyone!

2. How do I learn mathematics best?

I best learn mathematics by doing examples. Doing them repeatedly, over and over again. I personally like to watch the teacher explain it then work on my homework right away while it is fresh in my head. I usually don't have enough time to get it all done right away so I then have to return to it later to test my memory. It works for me!

3. How will my students best learn mathematics?

I am thinking they will best learn similar to how I learn. I will show them how to do the subject making sure to have plenty of examples. Also making sure to use plenty of different ways of explaining the topic so as to best help everyone in the class. Then i will give them homework to practice what they have learned. after all... practice makes perfect.

4. What are some current practices in school mathematics classrooms that promote students' learning of mathematics?

Mathematics classrooms are equipped with several devices to help enhance the learning experience. The basics include marker boards and overheads, calculators, computers, books, etc... but now we have even more ways to help such as smartboards, overhead calculators, etc. I believe personally that if the teacher has a love for math and a great desire to teach it that students can tell and are more open to learning. so i personally believe the greatest tool a teacher can have is their attitude.

5. What are some current practices in school mathematics classrooms that are detrimental to students' learning of mathematics?

As i mentioned before, the teachers attitude. If the teacher is being negative and not willing to help, the student in turn is not going to want to be an active participant nor will they be willing to put the time necessary to learning mathematics into they schedule.

I think another practice would be to only teach in a way that you understand. It is important to remember everyone has their own unique learning style. It is important as a teacher to try and teach things several different ways so as to try and reach each of those learning types.