# Benny’s Math

**BENNY’S CONCEPTION OF RULES AND ANSWERS IN LPI MATHEMATICS’** [pdf]

*S. H. Erlwanger, Department of Secondary and Continuing Education,*

* University of Illinois, Urbana-Champaign Campus*

**My Response to the above article.**

The Magic of Mathematics. When I was in high school I was given a book by this name. It was full of very interesting examples of applying math to the real-world. It was very instrumental in my future interest in mathematics.

Mathematics without application is just numbers that have patterns, sequences and rules. The Individually Prescribed Instruction (IPI) program mentioned sounds like it could be a great way to learn the rules of mathematics. Using technology and assessment methods IPI attempts to teach mathematics by self-paced objectives. Benny, having been using the system for quite some time, began to develop his own pattern of giving correct answers. Benny basically outsmarted the system but in the process damaged his learning.

Learning tools, such as IPI, need to have checks and balances to prevent smart learners like Benny from going down the wrong path of learning for so long. The basic assumption of IPI, “that pupils can make progress in individualized learning if they proceed through sequences of objectives …. “, appears to be a solid assumption. From what I understood one of the downfalls of IPI was the “teacher-aide.” In correcting Benny’s answers the aide apparently was not trained sufficiently to accept an alternate, but correct, answer. Eventually, Benny thought he figured out ways around the aide, not knowing he was only hurting himself.

Also, I thought it was interesting that Benny decided his speed. I think there should have been some intervention points where a skilled teacher would have tested Benny’s knowledge and his process of determining his math solutions.

Mathematics is the language of the physical world. Teaching mathematics without relating the concepts to the real-world gives the learner a weak perception of the whole purpose of the “reason of mathematics”, that is, modeling the physical world.

**Filed Under**: Mathematics