By Jonnelle Marte
Upbeat about stocks and the economy in general, investors were once again dumping U.S. Treasurys this morning — extending last week’s big sell-off. But are the recent moves the beginning of the end of the bond market’s long rally?
Last week, investors sold government bonds, pushing yields to their highest level since October (yields rise as prices fall). Yields on the 10-year Treasury hit 2.32% this morning, compared to 2.04% a week. Investors began to sell the bonds following the Federal Reserve’s mostly positive policy statement last week and its clean bill of health for most big banks. While most bond experts say the sell-off isn’t likely to accelerate, some predict investors will slowly abandon bonds in the coming weeks and months. “This is the start of a journey,” says David Kelly, chief market strategist for J.P. Morgan Funds.
In the near term, financial advisers say bond investors should brace themselves for losses as the drop in Treasury prices ripples over to high-quality corporate bonds, municipal bonds and mortgage bonds. High-yield bonds, which offer a substantive yield advantage over Treasurys, should hold up better than other types of bonds, says Kelly. And stocks may see some gains as bond investors shift some of their exposure to the market. Indeed, history shows that stocks tend to perform better as rates move up, says Sam Stovall, chief equity strategist for S&P Capital IQ.
To be sure, some experts predict the upward climb in bond yields to be short-lived. Anthony Valeri, fixed income strategist for LPL Financial, says it’s more likely that Treasury yields will trade in a range from 2.1% to 2.4% over the next several months as investors weigh a more confident Fed against threats stemming out of Europe and other economic reports, which may not be as bright down the road. And rising yields could in turn slow the economy by leading to higher mortgage rates, which would hurt an already weak housing market. “That tends to slow down the economy all else being equal,” says Valeri.
Either way, many advisers are recommending that investors start scaling back their fixed income holdings and increasing exposure to dividend-paying stocks in the U.S. and abroad, says Kelly. Within their bond portfolios, investors should stick to investment grade corporate bonds, high-yield bonds and mortgage bonds, which should have smaller losses than Treasurys. High-yield bonds may actually see gains while rates rise, says Kelly, if their yield advantage over Treasurys decreases.
By WebOsPublisher
U.S. Patent: 5638308 – Calculator with keys which can selectively be disabled – June 10, 1997
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United States Patent
5,638,308
Stokes
Stokes, ;, , , —
June 10, 1997
Calculator with keys which can selectively be disabled
Abstract
A portable, preferably pocket-sized electronic calculator includes
provision for disabling the use of certain keys on its keyboard. By
holding down a number key or certain of the function keys for a
predetermined period of time such as two to four seconds, the user can
disable the selected number or function. This allows the calculator to be
used effectively in teaching factoring and various mathematical properties
and leads the student to innovate in substituting different numbers and
functions in solving problems in the student’s own way. For discontinuing
all key disabling a reset key preferably is provided.
Inventors:
Stokes; William T. (1125 Robin Way, Sunnyvale, CA 94087)
Appl. No.:
361815
Filed:
December 22, 1994
Current U.S. Class:
708/131
Intern’l Class:
G06F 003/00
Field of Search:
364/709.01,709.14
434/201,202,365
References Cited
U.S. Patent Documents
4154007May., 1979Judd434/365.
4262337Apr., 1981Jones364/709.
4831569May., 1989Duriez364/709.
4836786Jun., 1989Wong434/365.
5020012May., 1991Stockberger et al.364/709.
5035502Jul., 1991Stokes434/365.
Primary Examiner: Mai; Tan V.
Attorney, Agent or Firm: Freiburger; Thomas M.
Claims
I claim:
1. An electronic calculator for teaching mathematics through the
performance of mathematical computations, comprising:
a calculator casing having a display means and a keyboard including
function keys and number keys,
internal processor means within the casing, for carrying out functions as
desired by a user operating the keyboard and for displaying the results of
operations, as well as indicating at least some of the functions as
selected by the user, on the display means,
means for supplying power to the internal processor means and display
means, and
disabling means for allowing the deliberate and selective disabling of one
or more of the keys of the calculator as selected by the user,
whereby the disabled keys must be bypassed in performing mathematical
computations.
2. The calculator of claim 1, wherein the disabling means comprises means
associated with the internal processor means for disabling a key as
selected by the user, upon the user’s depressing and holding the key for a
predetermined period of time.
3. The calculator of claim 2, wherein said predetermined period of time is
about two to four seconds.
4. The calculator of claim 2, wherein the disabling means further includes
means for displaying a number, when a corresponding number key is
depressed and held, for the duration of said predetermined time period,
and then for causing the displayed number to disappear from the display,
indicating the number key has been disabled.
5. The calculator of claim 1, wherein the disabling means includes means
allowing said selective disabling of each of the number keys.
6. The calculator of claim 1, wherein the disabling means includes means
for said selective disabling of at least some of the number keys and at
least some of the function keys of the calculator.
7. The calculator of claim 6, wherein the function keys capable of
disabling include addition, subtraction, multiplication and division keys.
8. The calculator of claim 7, wherein disabling means further includes
means for selective disabling of a square root key and a percent key.
9. The calculator of claim 1, further including a reset key on the
keyboard, and means connected to the reset key and the internal processor
means for discontinuing disabling of any keys which have been disabled,
upon the user’s pressing of the reset key, without changing the numerical
display on the display means.
10. The calculator of claim 1, wherein the display means and the internal
processor means include means for indicating on the display means that at
least one key has been selectively disabled on the calculator.
11. The calculator of claim 1, wherein the means for supplying power
includes a solar panel on the calculator casing.
12. The calculator of claim 1, wherein the display means comprises an LCD.
13. A method for teaching certain aspects of mathematics wherein the
student or students use electronic calculators, comprising:
providing each student with an electronic calculator having disabling means
for manually selectively disabling keys of the calculator’s keyboard,
instructing a student to disable one or more keys of the calculator, and
giving the student a problem or exercise involving mathematical
manipulations, which manipulations if accomplished in a most
straightforward way, involve the use of at least one of the keys which are
to be disabled,
the student’s disabling the key as instructed, using the disabling means,
and the student’s working through the exercise by performing calculations
on the calculator without the use of the disabled key or keys,
thereby teaching the student to devise alternative ways for carrying out
particular mathematical manipulations, and helping teach the student
substitution, factoring and the associative and distributive properties of
mathematics.
14. The method of claim 13, wherein the student’s disabling of the selected
keys is accomplished by pressing down and holding the particular keys to
be disabled, for a predetermined period of time which is received in the
processor of the calculator as an instruction to disable the key.
Description
BACKGROUND OF THE INVENTION
The invention relates to electronic calculators, specifically to a
portable, hand-held calculator, and more particularly to a student
calculator which includes a new feature useful in the teaching of
mathematics.
Small portable calculators are commonly used in the mathematics classroom
today. In many mathematics classes in high schools and elementary schools,
each student in a class uses a student calculator and is taught various
mathematical functions and manipulations by a teacher using a calculator
having similar functions. U.S. Pat. No. 4,154,007 introduced the overhead
projectible calculator, with a transparent liquid crystal display for
projection onto a screen. Using such a projectible calculator with
keyboard layout similar to the students’ calculators, the mathematics
teacher can show the solving of mathematical problems while instructing
students in the classroom. Further refinements have been developed with
U.S. Pat. Nos. 4,836,786 and 5,035,502, wherein not only the LCD of the
calculator but also the keyboard is transparent and projectible. Thus, the
students see not only the LCD as projected, but also the instructor’s
entries onto the keyboard.
Such projectible calculators have made great progress in furthering the use
of electronic calculators in the teaching of mathematics. However, in the
field of classroom calculators there has been a need for an effective
teaching tool which can be used to direct students in learning alternative
mathematical manipulations to achieve a given result, helping to teach
factoring and the associative and distributive properties in mathematics.
This is the purpose of the present invention described below.
SUMMARY OF THE INVENTION
The ability to teach students mathematics, while at the same time allowing
and teaching the use of calculators, is broadened by the new calculators
according to this invention. With the new calculators a mathematics
teacher can assign students a problem involving several of the common
functions–addition, subtraction, multiplication and division–then
instruct the students to disable one or more numbers or mathematical
functions. The students are thus forced to devise and learn alternative
manipulations to arrive at the same result.
As a very simple example, students may be instructed to disable the 8 key,
then to solve the problem 8+18. The student can mentally factor each
number in such a way as not to require use of the 8 key. The student thus
arrives at (2.times.4)+(2.times.9). The student can use the distributive
property to factor out the like 2s; 2.times.(4+9), which can be expressed
as 2.times.13=26. As another example, the teacher might assign a problem
6.times.3.times.12.div.4+48, the result divided by 78. If the students are
then instructed to disable the number key 8, several of these
manipulations will have to be performed in alternative ways. For example,
the division by 78 could be accomplished by factoring 78 into 6.times.13,
thus dividing by 6 and 13 successively. Alternatively, the student could
divide by 2 and 39 successively, or 3 and 26 successively. If the students
are instructed to disable the multiplication function key, they will have
to use addition in place of multiplication for several of the above
problem steps. Disabling of number keys, of numbers involved in an
assigned problem, can help teach the student the distributive property of
multiplication over addition.
The teacher can instruct students to disable the square root key, then
assign the students to find the square root of one or more numbers. The
student will learn to “bracket” the solution by squaring numbers
repeatedly, finally narrowing to the solution as confirmed by reviewing
the new squared product on each iteration. This exercise helps the student
appreciate what is done by the calculator in extracting square roots.
It is therefore seen that the calculator of the invention, with key
disabling, teaches the student to problem solve around the disabled key.
This actually holds true in the same way as in the case where no
calculator is used, but the student works out a problem on paper without
using certain digits or numbers. Whether or not a calculator is used by
the student, such an exercise is pedagogically sound in math education.
Calculators according to the invention are constructed generally similarly
to typical conventional classroom calculators having the same mathematical
functions. Key disabling, although it may be accomplished by simple dip
switches on the back of the calculator, in a more preferred embodiment of
the calculator is effected by holding down a key which is to be disabled,
for a pre-programmed duration which may be two to four seconds. The
internal microprocessor chip of the calculator has programming to switch
off any of the keys wherein disablement is provided, by sensing the
holding of such a key for the predetermined period of time. In the case of
the arithmetic function keys, e.g. addition, subtraction, multiplication,
division, square root and percent, the liquid crystal display of the
calculator preferably displays each of these functions when the
corresponding key is pressed. Similarly, the pressing of any numerical key
zero through nine will cause that numeral to be displayed on the LCD. To
confirm to the student that a key has been disabled, the LCD symbol
showing the number or function will appear on the LCD when the key is
initially pressed, but will then disappear after the predetermined
hold-down period for disabling of the key. The microprocessor is
programmed to control the display in this way.
It is therefore seen that calculators according to this invention present a
new approach and many new possibilities for the teaching of mathematics to
students while at the same time allowing and teaching the use of
electronic calculators. These and other objects, advantages and features
of the invention will be apparent from the following description of a
preferred embodiment, considered along with the accompanying drawings.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a frontal view of a calculator according to the invention, with
capability of disabling selected keys of the keyboard.
FIG. 1A is similar to FIG. 1 but with a variation in the calculator’s
display.
FIG. 2 is a flow chart outlining some of the logic which forms a part of
the programming of a microprocessor chip included in the calculator, for
the purpose of disabling and resetting keys.
DESCRIPTION OF PREFERRED EMBODIMENTS
FIG. 1 shows a calculator 10 of the type commonly known as a four-function
calculator, the calculator being designed for classroom use. The
calculator 10 preferably is of the typical pocket size, and may be about 5
to 8 centimeters in width by about 9 to 12 centimeters in height. The
calculator has a casing 12 which may be about 4 to 9 millimeters in
thickness. Dimensions may be smaller if desired, but the keyboard size
should be comfortable to use.
As is the usual case with a four-function classroom calculator, this
calculator includes a keyboard 14 with a division key 16, multiplication
key 18, subtraction key 20 and addition key 22, as well as a square root
function key 24. In addition, the calculator may include memory keys 26,
28 and 30, a percent key 32 and a +/- key 34 for changing sign. Although
the calculator 10 may be battery-powered, more preferably it includes the
typical array of solar cells 36 for powering its internal microprocessor
chip and LCD display 38. Thus, a clear entry/clear key 40 is included,
without the need for any “on” or “off” key.
In addition to these function keys, the keyboard 14 includes number keys 0
through 9 and the decimal point. An “equals” key 42 is provided, to cause
display of the last mathematical operation entered, or to use the
“constant” or squaring functions of the calculator.
As shown on the liquid crystal display 38, the calculator of the invention
preferably includes display of arithmetic icons at 44, for addition,
subtraction, multiplication and division. A particular icon will appear
when the particular operation is selected by depressing of the key. A two
by two square arrangement of the individual four functions is shown. Other
icon display formats for these functions can be used if desired, such as a
dot matrix, shown in FIG. 1A in the form of a five by five matrix 44a. The
display 38 also has an indicator or icon 46 which in this embodiment is
shown as a simple black dot. The indicator 46 relates to the key-disable
function of the calculator of the invention. When the black dot 46 (or
other appropriate icon) appears on the display, this indicates that at
least one numeral or function key has been disabled.
As described above, although manual switches could be used for disabling
selected keys, in the preferred embodiment disabling is accomplished by
the straightforward procedure of holding the key down for an
unconventionally long period of time. Since a user of a calculator will
normally hold down a numeral or function key for a period of considerably
less than one second, the disabling threshold may be about two seconds, or
it may be up to about four seconds. Any period of time which corresponds
to a deliberate effort to hold the key down is sufficient, but in a
preferred embodiment this period is about two to four seconds. The user
must hold down one key at a time for the threshold disabling period. That
will cause the number or function corresponding to the depressed key to be
displayed on the display 38 until the threshold time period is reached. At
that time the number or function symbol will disappear from the display.
Preferably all of the numeral keys of the calculator 10 are capable of
being disabled. In addition, at least the arithmetic function keys 16, 18,
20 and 22 should be capable of disabling. Like the numerals, these are
displayed (at 44) when pressed, then disappear when the time threshold is
reached. In one preferred embodiment all of the normal function keys can
be disabled, with the exception of the CE/C key 40, the memory keys 26-30
and the “equals” key 42, as well as the decimal point.
By disabling the [%] key, the student will be forced into changing 50%
value into 0.50 by mentally removing the percent sign and moving the
decimal point two places to the left (i.e. expressing 50% as 50
hundredths).
To restore the function of all keys, in the preferred embodiment a reset
key 50 is included on the keyboard. This will restore all functions and
numerals which have been disabled, and the black indicator dot 46 on the
display will disappear. This can in fact comprise a power off function
which sets all registers to zero. Although provision could be made to
accomplish this function through use of the CE/C key 40 (pressing twice),
without providing a reset key 50, it is preferred that the CE/C key
function in the normal way, clearing numbers for a new problem and not
resetting disabled keys.
The improved classroom calculator of the invention, in a preferred
embodiment, has a combination of additional specific operating features,
some of which have individually been included in higher-level calculators
in the past, and some of which are new with this calculator. These
features include the negative sign’s being displayed as a floating sign;
condensed numerals in the display being 8 to 9 mm in height; grouping of
each three digits by an apostrophe or caret; expressing percent as a
decimal, when the percent key is pressed after a number. Also, use of the
percent key for addition or subtraction of percentages will involve a
different display. Pressing [60] [+] [25] [%] first displays 15, then
pressing [=] yields 75. Further, with the square root function, if a
negative value is displayed, then the square root key is pressed, the word
“ERROR” will appear, centered in the display, without showing any
mathematical answer. Further, when the square root of a number is
calculated using the square root key, its root shall be returned to the
original number value using the [X] [=] keys (rather than returning to an
approximating decimal). As an example, if .sqroot.5 is extracted and
2.2360679 is displayed, then pressing [X] [=] will display 5.
When either memory key (26 or 28) is pressed, an “M” 52 will appear in the
upper left corner of the display.
Also, the processor will round off decimals. 2.div.3 will be displayed as
0.6666667. Upon clearing the calculator, the display shall show only a 0,
without decimal point. When a decimal number is then entered, it will be
shown as 0.[number]. Further, the decimal point may be fixed to a
designated number of places by holding down the decimal point key until it
disappears on the display, then by entering a digit for the fixed number
of places desired. This will fix the decimal point at the position desired
and will turn on a “FIX” icon 54. For example, if the decimal point is
pressed for three seconds, the decimal point will disappear in the
display, then the operator may press 2 for a two-place fix, thereby making
addition and subtraction of money problems easier. The display will show
0.00. If more than seven places are attempted to be fixed, then the
“ERROR” message will appear. To cancel the fixed decimal point and return
to a floating point, the user simply presses the “RESET” key.
Another preferred feature carried out by the internal processor of the
calculator 10 is that all basic operations (addition, subtraction,
multiplication and division) will automatically operate under conventional
algebraic logic, so that, as an example, 4+3.times.5 shall equal 19.
FIG. 2 indicates some of the logic of the internal microprocessor chip (not
shown) of the calculator 10, in simplified flow chart form, relating to
the key-disabling and resetting process.
The flow chart 55 of FIG. 2 is not comprehensive in showing the
interrelationship of the disable and reset functions with the normal
operation of the calculator. Normal operation is indicated at the block
56.
As shown in the flow chart 55, when a key is depressed, as indicated in the
block 60, if the key is not the reset key (decision block 62); and if the
key is not one of the keys not capable of disabling (CE/C, MR, M-, M+, =,
or decimal point), as shown in decision block 64; and if the display is
clear (block 66); and if that particular key is not currently disabled
(decision block 68), the character represented by the key is displayed, as
noted in the block 70. If the key is held down for the threshold period as
discussed above, shown here as three seconds in the decision block 72, the
process goes to the block 74, i.e. the screen is cleared of the displayed
character or icon, the disable dot 46 is displayed and the number is
disabled. The flow chart then shows return to “key depressed” 60,
indicating that another key will be depressed in carrying out mathematical
calculations, without use of the disabled key.
The chart 55 also shows that if, at decision block 62, the reset key is the
key which has been depressed (50 in FIG. 1), this will clear (reset to
operational) all disabled keys as indicated in the block 78. At the same
time, the disable dot (46 in FIG. 1) is turned off and all registers and
operations are cleared. As noted above, in a preferred embodiment the
reset key will also reset the decimal point, as no longer fixed. The chart
now flows back to the “key depressed” block 60, indicating that another
key will be depressed in the normal use of the calculator.
At the decision block 64, if the depressed key, which is held down for the
threshold period of time, is one of the keys not capable of disabling
(CE/C, MR, M-, M+, =, or decimal point), then normal operation involving
the depressed key will take place, as indicated at the block 56. The loop
returns to “key depressed” 60, indicating that the next step will be to
depress another key.
At the decision block 66, if the display is not clear, i.e. displaying zero
(or displaying nothing except the disable dot in the case another key has
just been disabled), then normal operation of the key continues, as
indicated by flow to the block 56. It is preferred that the processor
operate the disable function in this way, requiring a clear screen and no
numbers stored or calculations in progress. However, the processor could
have logic to operate at a slightly more sophisticated level wherein, if a
number and an arithmetic operation (+, .times., etc.) have been entered,
or a result has already been calculated and is displayed, a digit entered
and held at this point could be disabled.
At the decision block 68, if the key which has been depressed is a key
which has already been disabled, then there will be no display of this
depressed key, and the flow is back to “key depressed” 60, indicating that
the next step will be to depress another key.
At the decision block 72, if the depressed key is not held down for the
threshold period, then the flow indicates normal operation of this key at
the block 56, and returning to “key depressed”, indicating a further key
will be depressed.
It is therefore seen that the invention provides a function allowing the
user to disable one or more number or operation keys that will then
challenge the user to perform certain given algorithms in such a manner
that avoids the use of those disabled keys.
The above described preferred embodiments are intended to illustrate the
principles of the invention, but not to limit its scope. Other embodiments
and variations to this preferred embodiment will be apparent to those
skilled in the art and may be made without departing from the spirit and
scope of the invention as defined in the following claims.
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