I once taught a college algebra class at the local community college. "College algebra" is a misnomer of sorts: For many, the content of this course is covered in middle school or at least high school; rather than college-level algebra, this course is something of a minimum requirement for anyone's graduation.
Naturally, the course had been taught for years by others and had settled into a routine. A philosophy of teaching was selected long before I arrived, text books were vetted by the department, and the professors were well accustomed to teaching the way they teach. When I arrived, I stepped into their stream and was expected to go with the flow. I had significant freedom in how I taught and tested the students as long as I covered some minimum amount of material within the semester. I inherited a copy of the text book as well as a Texas Instruments graphing calculator...
One of the latest trends in mathematics education involves the incorporation of technology into the classroom. It was the department's philosophy---and requirement---that every student must have one of these newer model graphing calculators. The text book, written by the same calculator company, would naturally make extensive use of their calculator's functionality in the presentation of the material. The classroom was even equipped with a device that plugged into the calculator and sat above an overhead projector, allowing the class to see what the instructor was doing.
The principles of algebra are eternal, and the basics have been understood by different civilizations. For hundreds of years, the basic notation has been codified. The engineers who put man on the moon did so without graphing calculators. Hell, I learned algebra without a graphing calculator! What were these math education people thinking? How did they get into bed with a calculator company, requiring the students to buy these texts and expensive equipment as part of a core curriculum course?
At least once during the semester, the course coordinator sat in to evaluate my teaching. He was for the most part duly impressed: students were engaged, volunteering to solve problems at the board; and, I was animated, expanding old understanding and presenting new material in ways meaningful to the audience---but not once did I pick up my calculator, let alone plug it into the overhead projector.
That was clearly noted in the after-class discussion with my boss, and I took pride in it. When he mentioned my deficiency in incorporating technology into my teaching, I held up a piece of chalk, paused, turned to the blackboard, and drew three strokes---an X-axis, a Y-axis, and a parabola---and stated simply that this was all of the technology necessary for presenting this material.
I was proud of my enlightened understanding, and I was proud of my defiance. I would not teach my students to rely upon a calculator. As a matter of fact, my better students might even share and carry forward my understanding...
And that was my error.
What made my aversion to their "technology in the classroom" push preferable to their attachment to it?
What would happen to those students who went on in this college to take College Algebra 2 or the subsequent calculus curriculum? The calculator would be integral there too, and I would have failed to impart the necessary calculator skills to get them through...
No, it remains true that the calculator is decidedly not at the heart of college algebra; however, the calculator may be as useful as a blackboard or a stick drawing in the sand in teaching algebra. If I was as masterful or as enlightened as I thought I was, I would have moved beyond my own aversion and found a way to work within the department's system while still showing the students the heart of algebra---perhaps while still working to reform the department's choice to lock into one vendor and compelling an expensive purchase of each student.
Codified beliefs, rituals, doctrine, dogma, and so forth: These are the elements of religion, the tangible traces of spirituality when they are systematized. They are the elements that point to spirituality when used skillfully, but how often is the doctrine and ritual confused with the spirituality itself?
What if one day a Catholic decided that the crucifix was a distracting symbol, completely unnecessary to understanding the faith. As a result, he declared that, in his churches, the display of the crucifix is forbidden. Moreover, what if he decries the others' lack of understanding? With the best of intention, this fellow creates a new religion by virtue of his change of rule, and he pits his religion against the other.
Now what of his followers? Most may never share his spiritual insight; rather, they become the people who believe that the people with the crucifix are wrong... And vice versa.
Arguments over semantics, symbols, and so forth---the notions that exist only in our minds---become the things that separate us from each other and distract us from the underlying truth of the situation at hand.
If for a moment we strip away our notions of good and bad, right and wrong, black and white, me and you, and so forth, then what is it that remains?