S. H. Erlwanger

In Erlwanger's article, he conducts a study with a 6th grade student, Benny, on what he has learned from the IPI program. His main argument is that in the IPI program, (Individually Prescribed Instruction), which is suppose to help students learn more effectively independently, has some flaws that create disadvantages in teaching children incorrect forms of mathematics. He states in the beginning that it was expected that a student could not succeed in the program unless he or she had a sufficient understanding of the concepts. However, throughout the study Erlwanger argues that although students may be "successful," as Benny was, does not mean that they have sufficient understand the concepts.

Erlwanger supports this in his study with Benny. Benny is one of the more successful students in the IPI program, but when Erlwanger interviews him he finds misconceptions that Benny developed through the program. Some of the evidence Erlwanger presents is Benny's understanding of adding fractions and multiplying decimals. Benny has different logic when it came to this and to him he was correct, even though he wasn't. Benny merely developed his own methods for explaining his answers to his satisfaction.

Erlwanger also argues that the IPI program places heavy emphasis on finding the answers rather than on the process or the understanding behind it. As a result the programmed form of IPI was making it a hunt for answers the teacher wants just to get them correct. Thus, in Benny's case Erlwanger states that a "mastery of content and skill" does not imply understanding.

One of the arguments Erlwanger presents that I think is beneficial to today is that the aim to teaching mathematics should be to "free the pupil to think for himself." He goes on to say that students should be provided with opportunities to discover patterns in numerical relationships, they should realize the independency of their actions in reasoning, seeking relationships, making generalizations, and verifying discoveries. One other support Erlwanger provides is that mathematiccs should be a subject in which rules come from concepts and principles.

I think that this is applicable to today because I believe that most of mathematics taught in school are very instrumental in that instead of deriving rules from mathematical concepts, students are taught the rule without the concept. I think if the students are allowed to experiement independently and then share with others their ideas about their discoveries, it will create more of a relational understanding between them.