"I am told and I forget. I am shown and I remember. I do and I understand." -Chinese Proverb
Project Intuition seeks to revolutionize the way that mathematics is taught at the university level. At the core of our mission is the belief that knowledge is power only to the extent that its implications are understood by its bearer. Our series of interactive lab courses, designed to be taken alongside traditional math courses, offer the student concrete experience with concepts that frequently they may have had only abstract exposure to, in order to allow them to develop a real personal connection with the ideas taught. We believe this is necessary if we expect our students to be able to apply these ideas in new and nontrivial ways in the modern world. Since most tasks which simply require a basic knowledge of, or, straightforward application of, well-known mathematical concepts can be done by computers, the former skill is essential for students' future careers in today's society.
When confronted by a student bragging that he had learned the contents of an entire book of philosophy the Greek philosopher Epictetus replies: "Do you not know that the whole book costs only five denarii? Does then the expounder seem to be worth more than five denarii?" Epictetus wants the student to show him how he applied the knowledge gained from studying the text to improve his character and lead a more virtuous life rather than just recite its contents.
Project intuition emphasizes the concept of doing as an intermediate between the concepts of proving and applying. Our thesis is that there is a proof-application gap in university mathematics education wherein the student is shown how to prove but only required to apply. We think it may be useful to focus some of both instruction and assessment on an intermediate level (which we term doing). Doing requires an intuitive understanding (which is not required in applying) but not a formal understanding (as needed for proving). We believe that this middle ground is under-explored in part because it requires extensive interaction between the student and the system they are trying to understand. We believe that modern technology now makes such an interaction possible in mathematics. (Previously, such a learning environment was only possible in the physical sciences--and has taken the form of lab courses in sciences such as chemistry, biology, and physics.)
Project intuition lab courses typically do not cover all topics that appear in their associated math course. They cover topics carefully selected so that, even without the associated traditional course, the student can see the logical progression from one module to the next and end up with a solid knowledge ofthe most important concepts of the subject. By ensuring the student has a firm intuitive foothold on each stepping stone (module) we can be confident that the student will have the strength and confidence to required to maneuver to the next, even if the two stones are not perfectly adjacent.
© Copyright 2023 projectintuition.org