Page 2 - Specific problems with conventional calculators; without reporting an error
decimal point, when not in an error condition . . . ). Furthermore, as users may make slips — pressing the wrong button, omitting a press, or pressing a button twice in succession by accident — the intermediatedisplays of the calculator should confirm progress and, where an error occurs, help the us...
Page 3 - lb; lu
All might be harmless design variation, except manufacturers’ claims suggest otherwise, as the following typical example from a market leader makes clear: “Thanks to V.P.A.M. (Visually Perfect Algebraic Metho d) calculations have become a lot easier.It may sound confusing, but all it means is that t...
Page 4 - Variations in syntax for combinations.; is simply entered as; the simplest to the most complex equations.”
Model 4 × − 5 ; 1 − 5 % ; 1 + 5 % Notes Canon WS-121H − 1 − 80 † 1 . 05 † 1 + 5 ± % calcu- lates 0 . 95. Casio MS-70 l − 1 − 80 1 . 0526315 Casio MS-270 l − 1 − 80 1 . 05 ‡ ‡ 1 . 0526315 displayed in a 2 decimal digit mode. Casio JW-8L − 1 0 . 95 1 . 05 Casio fx-85 vh − 1 − 80 120 Casio fx-P401 − 20...
Page 5 - Systematic problems; Numerical problems
This suggests 2 − π might be worked out by 2 y x − π or perhaps 2 y x ( − π ) . Neither approach works. It is sensible to do some experiments, to see how a calculator works, and then, understanding it, proceed to the real problem. Once we can do the right sort of thing, we should be able to substitu...
Page 6 - Rearrangement; same; Chain calculations
marketted for at least ten years and its serial number suggests it has been revised many times. 4 Calculators have inadequate constants (recall the inconsistent use of π ). The precision of conversions may be unnecessarily different to other calculations on the same calculator. All the calculators t...
Page 7 - Modes; does; that; No undo, and feeble correction
3.4 Over-functionality Buttons mean lots of different things. Button with four meanings, depending on the mode, are common.Many of the calculators (especially the Texas Instruments and Casio mo dels) have low legibility andpoor colour coding schemes, which exacerbate problems with overloaded buttons...
Page 8 - Poor manuals; require; Hyperbole; Summary of problems, and a new approach; more a
evidently means 4 − 5. But if there is a ‘correction rule,’ it does not generalise: 8 3 √ √ takes a 6th. root, not a square root; and 2 + + 3 creates an ‘add 2’ mode ( § 3.5). Understo od like this, operator correction is just another feature intro ducing spurious complexity and still failing to sol...
Page 9 - The basic solution
according to the rules of arithmetic .” [24] The purp ose of a calculator is to do correct calculations, and to do so efficiently. It is clear thata calculator should relieve the user of the need to do mental operations and of the need to rely onpaper, so far as possible. Calculators (and their manu...
Page 11 - Worked examples
Key press Display after each key press 4 × − 5 ∆ = − 20 ⇐ 4 × − ∆ 5 = − 20 DEL 4 × ∆ 5 = 20 = 4 × 1 . 25 = ∆ 5 8 4 × 21 . 25 = 8 ∆ 5 ⇒ 4 × 21 . 25 = 85 ∆ DEL 4 × 2 = 8 ∆ DEL 4 × 1 = ∆ 4 Figure 4: Example of editing a simple calculation. The changes to the display occur immediately, on every key pres...
Page 12 - Elements; Temperature conversion; any; Other features; ‘Scientific’ functions
you can, and what’s more you only need to input the formula once, thereafter you can just fillin the knowns and the calculator works out the unknown. So then he says: “WHY AREN’TALL CALCULATORS BUILT LIKE THAT?” [25] Showing a key-by-key description is tedious and obscures the clarity of this calcul...
Page 13 - Calculators with a large screen; kπ
Key press Display after each key press 33 . 8 ∆ = 1 × 1 . 8 + 32 − − ∆ − 33 . 8 = 1 × 1 . 8 + 32 4 − 4 ∆ = − 20 × 1 . 8 + 32 0 − 40 ∆ = − 40 × 1 . 8 + 32 Figure 5: Converting Fahrenheit and Celsius. We continue with the calculation (described in the text) just after deleting the 100 and 212, so the ...
Page 14 - Preferences for powerful calculations; exactly as if it
Problem New calculator Casio fx -82 lb ‘fraction’ calculator 4 / 3 =? 4 / 3 = 1 + 1 / 3 4 a bc 3 = , answer: 1 1 3 1 . 1 =? 1 . 1 = 11 / 10 = 1 + 1 / 10 cannot handle decimals (4 / 3) 2 =? (4 / 3) ↑ 2 = 16 / 9 cannot handle squares Figure 6: Calculating with fractions. The user can obtain more detai...
Page 15 - Constants and standard formulæ; Sound and errors; beep if pressing a key does not cause
An important property of RCL is that whenever the memory is used its value can be seen (this is not the case on any other calculator reviewed here). The two immediately successive key presses S T O RC L when the cursor is in a correction have a combined effect identical to FIX , though also changing...
Page 16 - Undo and editing; write; Arbitrary limitations; far
or to b eep and not change the display? 9 (The keyboard has a key e so that large numbers can be entered exactly as they are displayed.) The prototype calculator takes the approach that, if possible, no user action should b e discarded. Thus we get the longer correction to huge factorials. The appro...
Page 17 - Other important design details; Also; Possible ob jections to the new calculator; The display changes too much; doesn’t
7.9 Other important design details Current calculators can be criticised on their non-technical design. A good calculator would b e ruinedby p oor design. The following points may seem obvious when they are stated explicitly, but severalcalculators get details wrong. The keys will have a firm resp o...
Page 18 - The calculator as a ‘chalk board.’; The display is not big enough
log 10 (3) + log 10 (4) = log 10 (12) 10 ↑ log 10 (42) = 42 71 × log 10 (10) = log 10 (10 ↑ 71) 2000 = 3 + log 10 (2) Figure 7: The calculator as a ‘chalk board.’ The user can edit the equations and see the numerical identities, even when the base of the logarithm is changed. Note the effective use ...
Page 19 - Non-specific complaints; what; Possible developments; and indeed one that the user
8.6 Non-specific complaints My final resp onse to ob jections is that the new design is mathematical. It is mathematical in twoimportant ways that no other calculator is. It is declarative. It is general. Mathematics itself is declarative, meaning its notation is used to express (declare) facts whos...
Page 20 - exactly; Going b eyond the handheld paradigm
It may be desirable to introduce mo des for working in degrees, changing the logarithm base, or setting other preferences. This can be done consistently with the rest of the design, though the prototype uses menus for this purp ose. We might introduce a button m and a status (mode) line in the displ...
Page 21 - Conclusions; key is a case in point.; References; , Approved translation of
into algebra rather than numerical coincidences, would cause more educational damage than the cal-culators we are trying to supercede. (That wouldn’t stop it selling.) Compare our brief exploration ofEuclid ( § 6.1) with Euclid’s own exposition of 300 bc . Euclid proves a proposition is true for all...
Page 22 - Acknowledgements
[11] P. Latham and P. Truelove (1983) Nuffield Maths 3, Pupil’s Book , Longman. [12] R. E. Mayer and P. Bayman (1981) “Psychology of Calculator Languages: A Framework for De- scribing Users’ Knowledge,” Communications of the ACM , 24 (8), pp511-520. [13] G. Polya (Combined Edition, 1981) Mathematica...
Page 23 - and
' & $ % 22 / 7 ∆ − π = 0 . 001264 → ⇐ F I X DE L ⇒ ( √ π ) 7 8 9 ÷ 4 5 6 × 1 2 3 − 0 • = + Figure 8: The new calculator — example key layout. The calculator has a protective flip cover with a quick reference list, explaining, in particular, the buttons FIX , DEL , ⇐ , ⇒ , the display’s ∆ symbol ...