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Saturday, January 23, 2010

MthEd 117 Blog 3

In Erlwanger's article "Benny's Conception of Rules and Answers in IPI Mathematics", he presents evidence that Individually Prescribed Instruction Mathematics, or IPI, is not as effective as the designers of the program would have hoped. Erlwanger uses Benny, a sixth grade student, as an example for how the program has actually hindered the progress of students rather than helped them. As Erlwanger describes the interviews that he had with Benny, he brings up the main flaws of the IPI mathematics program. First of all, IPI mathematics does not do a good job of evaluating the understanding of the students, but rather evaluates correct answers that students give based on rules and examples; it rewards correct answers only, regardless of the way they were obtained. Second, IPI mathematics develops learning habits and views about math that actually hinder progress later. And third, IPI greatly detaches the teacher from their role of for understanding how the student learns and thinks by giving a very rigid and inflexible structure of learning. Benny's example and Erlwanger's study shows that IPI was a good experiment, but it was vastly ineffective.

One of the most important roles a teacher has is to understand how the student learns and thinks. Teachers must find a way of evaluating not just right answers that students give, but also their overall understanding of mathematic concepts. It actually reminds me of a concept that is taught in Preach My Gospel in the chapter on teaching skills: "Teach for Understanding". It is the teachers responsibility to not just teach the material, but to teach it in a way that the students understand relationally, and not just how to give correct answers. IPI mathematics was not able to do this at all, but rather gave students an idea of math as a guessing game, or a game of chasing right answers. This concept of teaching students so that they truly understand the mathematical concepts will always be important.


  1. Whoa, your post is so clearly written. You definitely have a solid topic sentence that everything else connects to. I really like your connection to Preach My Gospel. It isn't something I would think of, but it's applicable. I agree that the teacher has responsibility in evaluating how the student learns and thinks. A much more complete learning can take place if that happens. I don't really have any suggestions. I might include direct ideas from Erlwanger to support the second paragraph, but it wouldn't be necessary. You did a really good job.

  2. I enjoyed reading Paragraph 1. It was well structured. The topic sentence was strong and located at the beginning. Numbering the flaws helped me find them. The content accurately reflected Erlwanger's thinking. The only suggestion I have is that a little more description for points 2 and 3 would have been helpful. For example, when you discuss unproductive beliefs and learning habits, an additional sentence that provided examples of these would have strengthened your description.

  3. I loved your connection to "Preach My Gospel!" It made the concept of teaching and relational understanding reach farther than just the classroom, and that is important as well. Nice job. Your entry was very clear and connected; my only suggestion is maybe a more detailed answer to Dr. Siebert's question of "Does the author provide a compelling argument for the validity of the idea for teaching mathematics today?" (in particular the teaching mathematics part). Overall, great entry!