Erlwanger's disaster study of Individually Prescribed Instruction, titled "Benny's Conception of Rules and Answers in IPI Mathematics," is a paper examining the IPI system. Erlwanger's paper is in support of having a strong foundation in mathematics, something we would call a relational understanding. Erlwanger explains that Benny would have done much better if he had been able to know why certain answers were correct and which processes truly worked. Erlwanger says that although Benny had a "master of content and skill," he did not have an understanding of concepts. A couple of the flaws in the system contributed to this lack of understanding. The first is that the key has only one correct answer so Benny was led to believe that his answers were correct just not in the correct form. Another flaw is that because the teacher is removed from instruction, evaluation of Benny's processes is missing. Instead of someone being there to see that he is doing something incorrectly and then helping him to fix mistakes, Benny is led to the false assumption that he is doing perfectly fine. The above issues go back to not having an instructor to help Benny, or any student, gain a relational understanding, an understanding where the rules make sense and weren't just made up by some guy who spent his entire life writing math rules.
Erlwanger's study supports the idea that there needs to be sufficient, personal relationships between instructor and student. In Benny's case he was working on his own and did not receive any guidance to correct his errors. I have tutored and helped in many classrooms. Most frequently the teacher asks me to be available to answer questions and just walk around the room to see how everyone is doing. I found that very rarely did students ask for help when they most needed it. As an aid in these classes, I had to learn to recognize the behaviors of the different students and see when they were struggling. This is something that a computer can not do in today's classroom. Only a human can see a look on someone's face and be able to recognize that as being a look of someone in need. Without getting to know each of the students it is difficult to help them progress. Since most students will not seek out help it is necessary for there to be a way for instructors to evaluate work done by students. After this evaluation takes place, it is crucial that the errors are discusses and corrected, otherwise like Benny, a student will believe that everything they have done is correct, because no one has told them otherwise.
