Reading response

There are three things made me stop and go back to read this article again. The first one is when Skemp mentions the “understanding” problems in Math situation. Skemp brings out the difference between “understand instrumentally” and “understand relationally”. I go back and read the related context again is because I think may understand this situation and really faced before. When I was in high school study, I think there were some similar questions like the example Skemp gives in page 4 which showed up in my math exam. Teacher asked questions about area or volume, but they gave different units. Some of my classmates thought these questions aimed for applying area or volume formula, like for a ball, the Volume V = (4/3)πr³. But they lost some marks in the end, because the real purpose for these questions are not only to test students get the area and volume formula, but also to test if they understand how to change different units into the same one. And these pages in this reading really let me think more about relational understanding and instrumental understanding. The second thing that made me stop is Skemp mentions “faux amis” and “mathematics” together. He argues that “there are two effectively different subjects being taught under the same name, ‘mathematics’.” I stopped because I try to connect these two definitions in my mind first. I want to consider how to understand Mathematics as two different subjects. I think his opinion is related to the two different understanding. Then the third thing which made me stop is when Skemp gives the benefits of instrumental mathematics and relational mathematics. I feel it is really interesting for me to think Math teaching in this two different way. 
After reading, I think I agree with Skemp. I think instrumental mathematics teaching may help students get confidence for math learning in short term within a limited context, because it will be easier to understand. But just like Skemp mentions if we consider a long-term learning and understanding, instrumental mathematics teaching will not be helpful at all. Skemp also mentions that there will be many difficulties for an individual teacher to teach relational mathematics. But I agree with him that “Well is the enemy of better”. My teaching Philosophy is to help my students become life-long learners. I know it will be hard, but it is my dream. I grew up in China and based on my learning experience, many of my classmates are really good at school. They can get high marks in each exams and they know how to solve every questions on text books. But sometimes I wonder should marks be the only principle to test students. They are good at exams but they have no creativity. They can do best in Mathematics questions, but they have no interest in Math learning. I don’t think the purpose for all the students should only be get good marks. That is why I agree with Skemp. And I also think that even applying some new ideas will be difficult, we should try or we will have no chance to make it happen.