## Mathematics Education: Taking a Clue

From the Recent Technological Revolution

# Class and Classroom

Let's look up a few more dictionary entries. I am curious how well Drucker's prediction jibes with the current usage of the word *classroom*. If campuses are bound to disappear, so may be the classrooms.

From *The American Heritage Dictionary*

**class·room** n. **1.** A room or place especially in a school in which classes are conducted

From *Webster's New Collegiate Dictionary*

**class·room** n. **1.** A place where classes meet

A place where classes meet! People meet on the Web and converse in *chatrooms*. Formally then, the definition, being open to various interpretations, will stand even as the concept of meeting with other people changes. Surely, we do not mean this when we talk of bringing technology into the classroom. But let's look up another entry. What is a class?

**class** n. **b.** A group of students who meet at a regularly scheduled time to study the same subject.

This definition will also survive regardless of whether Drucker's prediction comes true or not. (Note in passing that the purpose of a class meeting is to study. It must not be a social event.)

As somebody has to conduct a class, the first definition of the *classroom* hints at the existence of the category of teachers.

**teach·er** n. One who teaches, especially one hired to teach.

And further, to **teach** means "To impart knowledge or skill." (As an aside, a very viable meme is spawned by teachers who do not know their subject. "Hmm. Do as I say - not as I do!?" If one can manage as a teacher without knowing the subject, surely in other walks of life this is also possible.)

I dislike the emphasis placed on the "hired to teach" part. Berating a professor who spent an entire semester on a proof of a single (Cauchy's integral) theorem, Ralph P. Boas, Jr. hesitated to call him a *teacher* (*Can We Make Mathematics Intelligible?*, Monthly 88(1981), 727-731). A rare teacher would settle for just being a hired hand. What are teacher organizations thinking? The entry is an insult to the profession.

Do you think I am nitpicking? I hope you are not, because word usage is a reflection of our culture. Looking into and agreeing on word usage helps separate essential from secondary. The question of a possible metamorphosis of the concept of the classroom is intimately related to what I believe is a more fundamental question: Where does the teacher go and what does he do there?

Off the top of my head, I can think of three scenarios in which mathematics as the subject matter will also play a role. In loose terms the scenarios can be formulated thus

- The teacher and the students meet over the network. Classroom becomes an association of learning and teaching individuals. Mathematics resides with the teacher. Residence may not be physical.
- The teacher is where the students are. Classroom remains a conventional classroom. Mathematics resides with the teacher. The teacher instructs.
- The teacher is where the students are. Classroom remains a conventional classroom. Mathematics resides elsewhere. The teacher facilitates.

For societal reasons, scenario #1 does not seem very probable, at least not in the short run. Scenario #2 raises a question "Where has technology gone?" Why, to instruct, the teacher uses audio and video supplements. Perhaps also the Web. The teacher must be very familiar with technology. Scenario #2 is quite plausible. This is the current format expanded by the use of technological gadgets. It's nice for the teacher to be knowledgeable, but one can get by preparing for individual class meetings.

Simplistically, in the third scenario, students gather information from the Web; the teacher helps them to do so. Assuming the material is available in a variety of ways, children benefit most: each gets mathematics in the manner best suited to one's mode of thinking. Requirements imposed on the teacher grow tremendously. As it may not be very predictable what a student will fish out from the Web, the teacher must be really knowledgeable to be prepared for every eventuality.

Which of the two will come true? I do not know. Probably neither. Chances are that, as the gadgets move into the class room (and they will), we shall get more glimpses of the latter scenario. It's likely that the two will somehow blend. Regardless of what actually happens, it is clear that technology will require more knowledgeable teachers. With technology in the classroom, students will ask more questions. If the questions startle the teacher, the effect will be the opposite of the expected: Hmm. Do as I say - not as I do!?

#### References

*A Century in Mathematics: Through the Eyes of the Monthly*, J.H.Ewing (ed), MAA, 1994

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