S. H. Erlwanger's paper Benny's Conception of Rules and Answers in IPI Mathematics has many main points that are important to learning mathematics and that are pertinent to the way Benny himself learned math. Yet, the most important idea I feel Erlwanger keeps throughout his paper is the idea of teaching the "how's and why's" to concepts in mathematics. This is what relational understanding is. Through the IPI system, children are learning the processes of different concepts and are just learning how to do or accomplish specific problems given them. This is instrumental learning. This style of learning only teaches children the surface of mathematics. In Benny's experience, because he didn't understand why he was doing these certain processes, he created his own rules and reasons for accomplishing problems the way given him. In examples throughout Erlwanger's paper, he showed how detrimental this can be to a child's life. They begin creating ideas and rules on their own, and don't truly understand the reasons why they are going about mathematics and that specific way.
This main importance throughout Erlwanger's paper of learning relationally instead of instrumentally is still quite valid in today's society. It is still very important for children in the long-run to learn relationally the different concepts in mathematics. The children need to learn why they are using each process and how specifically it relates to the different problems, as well as problems OUTSIDE of what they are doing. This idea is very important in the world today. In learning more than just the process, the child can then connect what they are doing to problems outside the classroom. They will be able to use what they've learned in everyday problems and also be able to connect the different concepts they've learned to past and future education. They will understand how prior knowledge is pertinent to the concepts they are learning in the classroom today, and also remember the processes more in order to apply them to math they learn in the future. Learning relationally, as Erlwanger kept as a main idea throughout his paper, is still as important and valid today as it was when he was researching and studying Benny, a child who didn't have the best mathematics learning experience to help him throughout the rest of his life.
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I agree with you completely. I wrote about the same thing in my post. Though, from reading most of the other students' posts I've also discovered how much the article stressed the importance of teacher-student relationships. I definitely think these are perhaps the two most important points in the article.
ReplyDeleteI really liked how you connected the idea of relational understanding to this paper. I think it explains Erlwanger's stress on Benny's problem. I wonder if Benny didn't feel like he had relational understanding. From my interpretation of the article, Benny felt like he understood what he was doing and why he was doing it.
ReplyDeleteI agree that the importance of relational understanding is a point Erlwanger was trying to make.
ReplyDeleteI felt that a lot of time was spent summarizing the article and ideas, but not a lot time was spent providing evidence of why this is a main point of the article. I would go into a few more details of why IPI did not provide a relational understanding and why this was harmful.