One-Hour Demonstration of

Prueitt's Teaching/Learning Methodology

September 6, 2002

Prueitt's Teaching/Learning Methodology

September 6, 2002

Teaching Objective (in one hour): Engage the audience in the question: In base-6 what is 1/3 + 1/4?

Anticipated Audience: Professors of mathematics, mathematics education and university administrators.

There are five “agendas”.

First: We ask the students to engage in the most elementary tasks found in basic arithmetic. Each student will appreciate the sophistication that is fundamental to arithmetic when arithmetic is fully comprehended. The switch to bases other than base-10 is used to expose the students to an extreme form of novelty while at the same time a series of problems that at first appear to be unlearnable. The first example is the question

In base-6 what is 1/3 + 1/4?

Second: We expose the student to what appears to be a series of very challenging problems. But the challenge of these problems is due simply to the students not be familiar with arithmetic in various bases. So a model of learning is taught to the students. This model is then used over and again to gain confidence in the new learning theory. It is in fact necessary to teach not only the mathematics slightly differently than in traditional courses, but to also teach the learning theory at least just enough to give the individual student the ability to see that the problem, of poor arithmetic skills, does not lie entirely with the student.

D/S Model of learning: Things-to-learn are difficult or simple, depending only on one’s experience. In case of counting and doing arithmetic in bases other than 10, experience can be developed by ANYONE over a period of between two or three weeks. The path to acquiring this experience is at first a private experience with a few students. If circumstances are proper, this experience becomes a re-enforced social activity. The author has observed that the novelty of the learning experience provides positive social attention to those who learn first. This positive re-enforcement can spread to those who pick up on the experience. The ease of the first learning tasks, counting, then addition and then multiplication represented significant personal achievements that can be shared between the class members. But these early tasks are followed by other tasks to lead directly into higher mathematics such as computer science, topology, number theory, and category theory.

Note on expectations: Positive social attention and increased interest in the new curriculum was observed (in previous teaching experiences at Hampton University, St Paul’s University and several community colleges (1989- 1994)). Given a period of two to three years, it is perhaps possible to make measurable differences in the University wide outcomes from mathematics training. We also expect to make contributions to statewide mathematics education programs and to the scholarly literature in cognitive science and mathematics education.

Third: We ask that the student come to understand one's own history regarding experience in mathematics classes. We have used writing across the disciplines (in vogue in the early 1990s) to ask that students write about personal feelings towards mathematics (and science) during the first week of class. At mid-term and then again at the end of the semester the student is asked to develop a private log of how they are feeling towards mathematics.

Fourth: We ask that the students realize that not every one will see the light at the same time and in the same way. So the Teaching/Learning Methodology puts some rules down in regards to grades.

Rule 1: Any test may be retaken given the student write an essay as to why the test was failed or done poorly.

Rule 2: Students may reject the notion of learning and then come to a private understanding of the importance of breaking out of the inhibition of his/her interest in arithmetic, science, economics, etc. When that moment occurs, everything should be negotiable.

Rule 3: Any activity that aids students in awaking interest in arithmetic, science, economics, etc should be supported.

Fifth: The last agenda is related to eternalizing the process of learning. Most students “learn” that math is to be memorized and that theory is unknowable. Ask the freshman class and they will tell you this. Use a polling instrument and one will find that, on average, on college campus that 60% - 90% of incoming freshman will say that mathematics theory should not be talked about outside of class and that good grades in math is merely a question of rote memorization. But, we hold that the only way to make arithmetic difficult is to deny the student a clear understand of how arithmetic works.

The author’s proposed developmental mathematics textbook creates learning tasks that:

1) Can be visualized as a student is walking to a friend’s house or to the store.

2) Can be rehearsed serendipitously.

3) Have a specific way to check the answer to problems that are made up randomly by the student.

This last agenda has a neuro-cognitive basis to suggest that if this agenda become effective within a student body that the students will positively change behaviors in mathematics, science, economics, etc classes. We are looking for this type of result.