Mathematics Education: Taking a Clue
From the Recent Technological Revolution
Taking a Clue: Introduction
I really appreciate the opportunity to talk about Technology and Mathematics Education. I am fascinated with the one and concerned about the other. Of course, as a parent, I have something to say about them both. I am also an educated person, a former professor of mathematics, and the developer of a popular Web site. For the past 10 years or so, I worked in software development. Shortly, I'll argue that the modern methodology of software development may have bearings on the education reform. I'll do my best to be objective.
Once I came across a link to my site that, in particular, said:
Interactive Mathematics Miscellany and Puzzles
A compendium of puzzles, speed tips, definitions, editorials, philosophical meanderings, and more related to mathematics. The author is a working programmer, rather than educator, so his perspective is different.
The credit is due to somebody at Valencia Community College, Orlando, Florida. Although the page offers no opinion to differ from (and since disappeared), I saw the sign. In the talk, some degree of objectivity may serve as a safety net.
So, let me say something up front. I do not claim expertise in either mathematics education or complete understanding of possible applications of technology in that process. I do not think that is necessary in order to gain an insight into the issue of the reform. In software development, programmers and analysts work together with domain experts to establish understanding and, eventually, create software. Bankers do not write banking software, laboratory robots are controlled by software written by people who might have known nothing about robots or chemistry. (I know, I did it.) There is a whole process of interaction at the end of which the programmers (who originally knew nothing about "what is it for") deliver a software tool that the domain experts (who originally did not know "how to get it") will use to their heart's content.
The process is iterative and often torturous. But it is common knowledge that the more time is spent on each stage preceding actual software development, so much easier is the implementation phase and so much more satisfactory is the end result.
One of the first steps in interaction between people with different backgrounds is to establish a data dictionary.
So proceeding a step at a time, I shall quote domain experts and try to sort out information thus obtained.
Thus, we are talking of Mathematics, Education and Technology. What are these? It's hopeless to give a satisfactory definition of Mathematics. Let's, for now, just say that Mathematics is a body of knowledge. It's easier to say what is education. Here's a dictionary entry (The American Heritage Dictionary):
ed·u·ca·tion n. 1. The act or process of educating or being educated. 2. The knowledge or skill obtained or developed by a learning process. ..
Education is a process. Unlike evolution or inertia, this process is deliberate and, as such, has goals. The goal of education is to educate. Is it possible to be more specific? Sure. We may gaze into the future and try to predict what kind of education will best serve an educated man 10 - 20 years from now. We may also look back and ask
"Was a similar problem stated in the past? (
Remember Polya?) And, if it was, how was it approached and with what
If we are lucky, we may find something that applies to the current situation; for, although some things change, some things do not change and may be true today as much as they were in the past, and then probably will be true in the future. After all, every past had its future and faced problems that had to be resolved with the view of adapting better to the demands of the evolving society.
So far, I mentioned mathematics and education. I'll talk of technology later. For now, let's agree that technology plays a certain role in the deliberate process which is education.
So, you see, my intention is to fill in for a programmer-analyst who attempts to grasp the meaning of the education reform which, as we all know, is currently under way. Sometimes, however, I shall take up a second role - that of a domain expert (a parent, I mean) - to express my personal views. This is permissible.
- American Heritage Dictionary
- J.Rumbaugh et al, Object-Oriented Modeling and Design, Prentice-Hall, 1991