Entry #3

In his article about Benny, Erlwanger is trying to convey the weaknesses of an individualized learning system and emphasize the importance for the teacher to initiate interaction with their students. Erlwanger describes the basic precepts of the IPI system to show the individualistic beliefs that underlie its method for students to learn mathematics. Since the IPI focuses on pupil independence, Erlwanger works to show the mishaps it has created within Benny's learning to point out the weaknesses of such an approach. He provides very specific examples of misconceptions Benny has developed such as how 0.3+0.4=0.07. Erlwanger describes how even when a student displays a supposed mastery of the content and skill, this does not necessarily mean that understanding is present. Erlwanger points out that a teacher could encourage Benny to ask questions, discuss, and reflect on his experience with mathematics if a close personal relationship with Benny and his understanding had been developed. Through IPI system, such a relationship does not exist. Benny feels no need to talk with his teacher, and due to the lack of teacher initiated interaction, Benny develops many faulty ideas and conceives math as being different rules for different problems, which creates a chase for the right answer.

One of the points that Erlwanger makes is the need for teachers to initiate interaction with their students. Teachers should provoke deeper thought, reasoning and justification from their students. I believe that this idea is still applicable today. I know that often times I will not even think about certain aspects of the material that I learn unless a teacher points them out to me through questions, examples and discussion. In fact, just this past semester in Abstract Algebra we were learning about elementary and invariant factors. I felt as though I understood the concept and thought I understood the process of how to find these factors. My method produced all of the right answers on my homework, and from an outsiders perspective, it would have looked as though everything was right. Yet even though the work I showed was correct, I did not fully understand. For when I was given a more complicated problem that wasn't quite like all of the rest, my method was not sufficient and did not produce the right answers. When I realized this mishap and learned the proper way of thinking about it, the correct procedure was not very difficult and so it was understandable why someone would assume that I properly understood. However, it was a matter of luck that I happened to spot this because the teacher hadn't asked for any reasoning beyond showing our computations, nor assigned any homework that would have led one to recognize such an error. Because of this experience, as well as others I have had/seen, I feel as though teacher initiated questions, discussion, and reflection can still be improved in classrooms today, even when it seems as though the students have mastered the concepts.