Tuesday, August 09, 2005

"Calculators: Vital Tool or Crutch?"

This Article first appeared in the Spring 1975 issue of the Babson Alumni Bulletin.


What ever happened to the slide rule?

What has happened to it, on campuses across

the country, is the emergence of the hand-held

calculator, a remarkable pocket-sized gadget which is

affecting teaching-and learning-from first grade to

graduate school.

Is it a good thing?

On the whole, yes. But most educators are convinced

that it should never be given to a child who has not

mastered the basic four functions. For some students,

this mastery can be achieved in elementary school. For

others, it takes years longer.

Calculators are widely used on the Babson campus

-in the classroom, for homework, and, when per-

mitted, in exams. No college-wide policy has been set,

and most professors lay down their own rules, some-

times after discussion with their students.

"If even one student does not have a calculator,"

says Asst. Prof. Margaret Weinblatt of the math division,

"I allow no one to use them in exams."

Prof. Earl Bowen, on the other hand, allows calcula-

tors in exams even though some students may not have

one. If two students want to swap a calculator back and

forth during an exam, this is permitted provided the

student who is about to pass a calculator to a friend first

raises his hand so Prof. Bowen can be sure that the

machine is clear and that the answer has not been left

on it.

In all, 27 Babson teachers permit the use of calculators

in exams, while six do not.

Recently the Bulletin distributed a questionnaire to all

Babson faculty members, including teachers in the

evening MBA program, soliciting their views on the

calculator. Almost universally, they agree that it is a

convenient, time-saving tool, but some of them warn

that overdependence on it can lead to the loss of basic

math skills.

"I can't turn the tide," says Asst. Prof. Robert Maciel,

"but I do warn the students against overdependence.

They recognize themselves how easy it is to forget

arithmetic."

On the positive side, the calculator speeds up the

computation of problems and eliminates a lot of drudg-

ery. The chairman of the math division, Prof. John

Saber, believes "it can help in the sense that the student

is not overburdened by messy calculations, so he can

concentrate more on concepts."

"Educationally, it is an aid," Prof. Bowen says,

"because more realistic numbers can be handled.

Traditionally, texts have used simple numbers such as

integers, easy fractions, square roots that can be taken at

sight such as .j25 = 5, and so on. Equations used to

look like this:

x2 + x - 2 =0

Now we can use:

3.752x - 21.43x + 17.962 =0

"The second equation is taken from a real situation,

while the first is easy to handle without a calculator."

Several professors expressed the opinion that, by

saving time with the calculator, the student has more

time to consider and learn the theory. Asst. Prof. Gordon

Roberts of the finance division finds that the calculator

enables a student to "consider more possibilities than

he/she could in hand calculations." In science classes,

Prof. Bryce Prindle says the calculator makes it possible

"to check experimental results before laboratory sessions

are over and take corrective action if necessary."

At the University of Southern California, Prof. Russell

Hardwick, who supervises freshman chemistry courses,

says that students who use the calculator in examina-

tions have a ten-minute advantage over those who

use slide rules. For this reason, he will not allow calcula-

tors in exams until every student has one.

That day may not be far away. A simple calculator

can be bought today for $30 or less, and the New York

Times reported recently that, by 1977, the price may

drop to $10. Some educators predict that schools may

eventually build calculators into school desks, just as the

old-fashioned desk had a built-in inkwell.

The Babson bookstore carries a Japanese-made cal-

culator priced at $39, but very few students buy their

calculators on campus. "They can get them cheaper at

Lechmere Sales or Jordan Marsh," says Charles

Maccini, the bookstore manager.

Slide rules have virtually disappeared from the cam-

pus. The simplest calculator does not do all that a slide

rule can-logarithms and square roots, for example.

But a good calculator goes up to eight or ten digits,

while the slide rule is limited to three-digit accuracy.

For younger students, a basic calculator can be

mastered in a few minutes, while a slide rule is more

complicated to use.

The Bulletin questionnaire revealed that, while there

is little disagreement about the value of a calculator to a

college student who has mastered the basic skills, Bab-

son prof~ssors differ sharply about the use of calculators

in elementary and secondary schools.

"Elementary school-absolutely not!" says Prof.

Weinblatt. 'They will never learn to add."

Prof. Maciel thinks that the calculator should not be

used until college. Prof. Joseph Alexander, chairman of

the economics division, would not allow calculators until

high school, and then he feels that "students with serious

deficiencies in math should be discouraged from using

them."

Assoc. Prof. David Drinkwater of the accounting

division believes, on the other hand, that the calculator

should be mandatory after the fourth or fifth grade. "I

have both my third and fifth graders use them for their

homework." Both, he says, can already perform the

basic four functions.

Another point on which Babson teachers disagree

concerns the quality of math skills which today's students

possess. Asked whether Babson students are better

prepared in math than were the incoming students of a

few years ago, four faculty members said that students

today are better, five felt that they are about the same,

and eight consider them poorer math students. A dozen

others did not comment because they have not been at

Babson long enough to judge.

Comments varied from "Yes, students today are

better prepared" to "No, they are much worse; a large

proportion cannot handle elementary algebra" -the

latter statement from an economics professor.

Prof. Bowen takes the view that most Babson students

have demonstrated aptitude in math by their college

board scores, but that they fall down in applying that

ability in college courses. He does find that incoming

freshmen tend to be weak in algebraic fractions and log-

arithms, which should have been mastered in high

school.

"We tried offering a special review section, without

cost, to any calculus student who wanted it," Prof.

Bowen says, "but it didn't work. After the first session or

two, the group dwindled to a half dozen who didn't

really need it. These six all received good grades in

calculus, but they would have gotten good grades with-

out the review sessions."

In teaching any mathematical process, Prof. Bowen

first gives small problems with easy numbers. Students

do these with pencil and paper, repeating if necessary

until they understand what they are doing. 'Then," he

says, "I give real-world problems, with nasty numbers

that drive you up a wall, and students can do these

either with a calculator or with the computer. This is

the approach of the entire math department."

Prof. Bowen believes that the danger with both cal-

culators and computers is that "the world becomes a

series of black boxes. That is the thing we have to avoid.

If a student knows which buttons to push, but doesn't

really understand what he or she is doing, that is not

education at all."

Prof. Saber says that "if anything, the calculator hurts

the students' mathematical ability in that they are too

dependent on it." Furthermore, he thinks that the stu-

dent who can afford an expensive, more sophisticated

calculator has an advantage unless the instructor

chooses both exam and homework questions carefully.

Following are the questions which Babson teachers

were asked, a tabulation of their answers, and some

typical comments:

Do you encourage students to use the calculator as

much as possible, or do you warn them against over-

dependence?

17 -encourage its use

8-warn against overdependence

l2-give no advice

"After all, we are overdependent on the automobile,

but it wouldn't do much good to be warned about it."

"I ask them to use pencil and paper for a time or two

until they understand the operation, then use the

calculator for repetitive solving."

"I warn them about losing their math skills."

Do you permit the use of calculators in the classroom?

In exams?

33-permit it in classroom

27 -permit it in exams

6-do not allow it in exams

"If the exam has a lot of computation on it, yes."

"Yes, in classroom, but I discourage it."

"Do not permit on exams because some students

do not have them."

If you have established rules about the use of the cal-

culator, have these rules been set by you individually?

Or by agreement between you and your students?

lO-individually

6-in consultation with students

l3-no rules




"No rules except no use of the Hewlett-Packard 80,

which does finance calculations internally."

"The math/science division is considering requiring

that all students have a calculator."

Does the calculator enable an average or below average

student to do better work, or is it merely a convenience

and time saver?

5-students can do better work

20-it is merely a time saver

"Depends on which calculator he/she is using."

"It may prevent errors in computation which anyone

could make."

"It enables the average or below-average student to do

more accurate work and so develop confidence."

"Like the slide rule, it is a time saver."

Does the availability of so many kinds of calculators give

an advantage to the affluent student who can afford to

buy a model which performs more functions?

14-yes

20-no

"There might be a slight advantage, but I do not want

to reduce the entire class to the lowest common

denominator in the name of misguided democracy."

"If the student uses a fancy calculator exclusively and

then takes a test where he is required to use tables for

logs or annuities, then he is in trouble."

Does ownership of a calculator sometimes increase a

student's interest and encourage him to undertake more

difficult projects?

17 -yes

10-no

6-not sure

"Yes. A student is more likely to want to solve a com-

plicated problem if he has access to a number-crunch-

ing machine."

"Don't think so. Remember, everyone can use the

computer, which is much more powerful, for nothing."

"No. It is like a security blanket for Linus."

Are the students who come to Babson today better pre-

pared in math than were the incoming students of a few

years ago?

4-yes

8-no, they are worse

5-their ability is unchanged

"New math appears to have been a flop."

"They are inadequate in most basic operations of

grade school levels."

"Students today are better prepared."

"No. If anything, the calculator hurts in the sense that

the students are dependent on it."

"Math quality is not better; in fact, I fear too early

dependence on the calculator reduces mathematical

abilities."

To what extent do you think calculators should be per-

mitted in elementary school? In junior high or high

school?

Elementary school:

15-yes

15-no

Junior high school:

16-yes

ll-no

High school:

21-yes

4-no

"I think students should be taught to think and reason

first. "

"The calculator should not be allowed until the stu-

dent has mastered arithmetic."

"I would encourage their use at all levels."

"They should be mandatory after the fourth or fifth

grade."

"The calculator should not be used until college.

Students should develop their basic skills first."

"No to elementary and junior high. A possible intro-

duction as a senior in high school."

"At the high school level, students with serious

deficiencies in math should be discouraged from

using them."

"I see nothing but good from the use of calculators.

Slide rules were once common in both college and

high school. The only reason their use was limited in

the earlier grades was because of their complexity.

Now a simple tool is available for students of all ages."

Thus the debate goes on. Meanwhile, as the price of

calculators continues to drop, this remarkable tool is

finding its way into the pockets and briefcases of more

and more students. It is estimated that between 12 and

15 million hand-held calculators were sold in the United

States last year.

"Calculators are like television; they have their pro-

ponents and opponents," says Edgar T. Canty, director

of the Babson Computer Center. "Nevertheless, as with

television, they are a fact of life and have to be used

constructively."

Assoc. Prof. Richard Bruno, chairman of the account-

ing division, is one faculty member who favors the use of

the calculator at all school levels.

"The most expensive adding machine in the world,"

he says, "is a yellow 'E. Faber' or 'Ticonderoga' with an

eraser at one end." -

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