Erlwanger's main point is the necessity for reasoning behind mathematical rules. He stresses the need to understand the concepts underlying the procedures. Benny's main problem was that he was not able to derive his rules from mathematical concepts. When Erlwanger questioned Benny's rules, many of them had shaky reasoning. Benny had no idea why his own "rules" were correct, he simply used them. Erlwanger's paper is pointing out that had Benny been taught mathematical concepts, his rules would have made sense to him, and Benny could have enjoyed mathematics.

This goes back to the difference between relational and instrumental understanding. Benny thought math had no reason. He called it magic and he said it didn't make sense, however he was doing very well on his exams and homework assignments. This is a little warning sign to teachers that good grades do not always mean the student understands. Sometimes in math classes we are pressured into working more for the grade and less for the understanding. This is a problem teachers need to try and avoid because as we were shown in Benny's case it is detrimental to actual learning.

This goes back to the difference between relational and instrumental understanding. Benny thought math had no reason. He called it magic and he said it didn't make sense, however he was doing very well on his exams and homework assignments. This is a little warning sign to teachers that good grades do not always mean the student understands. Sometimes in math classes we are pressured into working more for the grade and less for the understanding. This is a problem teachers need to try and avoid because as we were shown in Benny's case it is detrimental to actual learning.