Computing DevicesMathiputer Cybernetic Systems, Inc.Review by: Lowell Leake Jr. and Thomas E. RowanThe Mathematics Teacher, Vol. 69, No. 5, [Individualization] (MAY 1976), pp. 422-423Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27960518 .

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PRODUCTS

PUBLICATIONS

NEW PRODUCTS

Edited by Lowell Lea ke, Jr., University of Cincinnati, Cincinnati, Ohio:

computing devices Thomas E. Rowan, Montgomery County Public Schools, Rockville, Maryland:

models, games, devices Albert P. Shulte, Oakland Schools, Pontiac, Michigan:

audio-visual materials

Audio Tapes Mini-Courses in Mathematics: Trigonometry. Audio

cassette tapes with accompanying response man

uals. Robert C. Steinbach. Educulture, P.O. Box

1932, Santa Monica, CA 90406. $247.50 for twelve

response manuals and two audio cassette tapes for

each of the nine modules; $27.50 for individual

modules; $17.50 for separate cassettes; $10.20 a

dozen for manuals for a given module. Reorders or

replacement, $4.00 a cassette, $8.16 a dozen for

manuals. Senior high, community college.

The review is based on excerpts from module 1,

dealing with a review of functions and an introduction

of the unit circle, and from module 3, dealing with

techniques for solving identities. The development is

smooth and well paced, the mathematics is both cor

rect and well presented (much in the form of "helpful hints"), and the voices (Ann Davenport and Steve

Johnston) are pleasant. The modules are grouped into two categories. The

ory includes modules 1-4: "Circular Fractions";

"Graphs of Circular Functions"; "Identities and

Proof"; "Inverse Functions and Conditional Equa tions." Applications includes modules 5-9: "Right

Angle Trigonometry"; "The Solution of Right

Triangles"; "Polar Coordinates and Parametric Equa tions"; "Vectors"; "Complex Numbers."

The modules contain several aids, including a skill

review and teacher's diagnostic test to assess prerequi site skills, posttests, self-tests, and back-up frames (to

supplement the development in the regular frames). The materials may be used in either group or individ

ualized situations. Educulture welcomes questions, ac

cepting collect calls to (213)-393-3792. These materials merit examination and consid

eration for purchase.?Shulte.

Computing Devices

A programmable calculator for lesa than $80

National Semiconductor is marketing a program mable calculator (4615) for $79.95 that offers the

buyer another option, but at a price that is quite reasonable. The programmable Hewlett-Packard 65

($795) was reviewed in the May 1975 issue of this

journal and the programmable Hewlett-Packard 25

($195) in the February 1976 issue. The National

Semiconductor 4615 should be compared with the

H-P 25, keeping in mind that it costs less than half

as much as the H-P 25.

The National Semiconductor 4615 is a solidly con

structed, compact unit with a clear display and a well

engineered keyboard layout. It is rechargeable and

comes with the charger, a carrying case, and an in

struction guide. Its capacity is ?9,999,999, and this

limitation needs to be considered very carefully by a

purchaser, since the H-P 25 has a capacity of110" and

can display ten significant digits. The 4615 uses Re

verse Polish Notation (RPN), as do Hewlett-Packard

calculators. Incidentally, National Semiconductor has

quite wisely used RPN in its scientific and program mable calculators, and it has just as wisely used alge braic logic in its more basic instruments. The 4615 has

double function keys and can handle trigonometric

functions, common and natural logarithms, ex, yx,

square root, reciprocal, degree-radian conversion,

memory storage and recall, x2, and memory + x2. It

also has an ?- y interchange key and a key for . In

short, it is roughly comparable to many scientific cal

culators in its keyboard provisions. Unlike most scientific calculators, however, the 4615

is programmable in that it can store several different

422 Mathematics Teacher

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functional equations and display f(x) for any accept able input. This means, for example, that f(x)

= x3 ?

2 + + 1 and g(x) = 3/x2

- 5/3 JF + cos can both

be stored (it is not limited to two functions) and both

f(a) and g(a) can be displayed, one by one, for any

sequence of values of a. The limits are that the 4615

can store up to 100 steps for the various programs

(H-P 25 can store 49 steps), and a "skip" key allows

the user to enter any program at its starting point. One

hundred steps seem to be completely adequate for

most situations. The 4615 does not have any decision

keys or a "go to" key (such as the H-P has), and this

makes it less programmable than the H-P 25. How

ever, the instruments do show the user how to build in

DO-loops and branching that can be handled by press

ing appropriate keys to loop through part of a pro

gram before going on. The instructions illustrate this

usage with some examples dealing with statistical com

putations of means and variances for a given set of

data. No looping or branching is done automatically, however. In summing up its programming ability, the

instructions speak of "learn-mode programming," which is then defined as "essentially automatic key

pressing." This seems to be a good description of what

can be done.

Anyone looking for a scientific programmable cal

culator should give the National Semiconductor 4615

serious consideration because of its remarkably low

cost. The H-P offers much more, but the National

Semiconductor 4615 would be a good choice for some

one who simply cannot afford more than $80 and can

live with the limitations of the 4615.

Other National Semiconductor calculators

The calculator described in the preceding review is

paired with a companion costing $29.95, designed for

mathematicians and containing all the features of the

4615 except the "learn mode" keyboard capability. National Semiconductor markets three other such

pairs designed primarily for statisticians, scientists, and financiers. These cost somewhat more than the

4615 and the 4510, but purchasers should look at all

trie possibilities. They also market a model designed for metric conversion that has standard functions for

the international and business user. In addition, Na

tional Semiconductor has many other models aimed at

a wide variety of users. These include, for example, a

model that fits in a checkbook and a very inexpensive model that works in a computer-assisted instruction

mode. The user punches in a problem and an answer.

If the answer is right, a green light goes on; if wrong, a

red light goes on. There is no display. This particular model is now selling in department stores and else

where as an educational toy. The checkbook model and the CAI model are inter

esting from another viewpoint?they suggest that cal

culators are likely to pervade our lives in a variety of

ways. What about a model built into a transistor radio

so students can really be close to their music while they do their homework??Leake.

Mathiputer. Cybernetic Systems, Inc., Albuquerque, NM 87123. $249.50. (For comparison, see Digitor review, March 1976, p. 249.)

Virtually everything that was said for the Digitor can be said for the Mathiputer, The Mathiputer has

one additional feature, and one additional disadvan

tage. The Mathiputer can present the inverse opera tion format of an exercise as well as the direct sentence

(8 + 6 = ? can be presented as ? -6 = 8). This is a

very useful extension to the device's potential. On the

other hand, this extension leads to a slight dis

advantage. When an exercise such as 0 X 7 = ? is

on the screen and the inverse is called for the machine

produces ? X 0 = 7. The latter is obviously not

solvable, but the machine is programmed to accept 0 -r 0 = 7 as the correct answer. While it is very un

likely that students would encounter this example

during routine use of the Mathiputer, this writer would

certainly feel better if Cybernetic Systems found a

better way to handle this problem. Teacher selection

of the mode for the student can completely negate the

possibility of this example appearing.?Rowan.

Computing Notes

For teachers interested in sophisticated simulations, a bulletin outlining new developments in hybrid

(analog/digital) computer hardware and program

ming is available from Whit Downer, Electronic As

sociates, Inc., West Long Branch, NJ 07764.

Statistical applications of H-P calculators are de

scribed in a new booklet, "Are You Drawing the Right Conclusions?" available from Inquiries Manager, Hewlett-Packard Company, 1501 Page Mill Road, Palo Alto, CA 94304.

Most of the new low-priced, ultrasmall calculators

don't perform more than the standard four functions.

Here's one billed as the "World's Smallest Electronic

Calculator" (5 cm X 7 cm X 1 cm; 57 g) with 8 digits, % key, floating decimal, constant, and lead zero depres

sion, priced at $19.95. Available only by mail (Stock No. 1945) from Edmund Scientific Co., 380 Edscorp

Bldg., Barrington, NJ 08007.

As Japan's inflation continues to rise, look for the

lower-priced calculators to come from other parts of

Asia?probably South Korea.

Casio makes a calculator that works on any of five

different voltages. Now you can compute anywhere in

the world.

Look for more colleges and high schools to move

toward free-access computing. Computing time should

be as freely available as books from the library. For the man who has everything, one company now

markets a ball-point pen with a full five-function elec

tronic calculator mounted in its barrel. Can the

disposable calculator be just around the corner??

George Christoph, Finneytown Public Schools, Finney town, Ohio.

May 1976 423

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