-
FUNCTIONAL IN'CORPOBATICN Ql!'
LEARNING THEORY:
MATHEMATICS AND THE
BASIC LANGUAGE
Honors College Thesis
February 24, 1984
.1ill Lynn Deller
~f'Cc Ii
-r he "
-
'j
,>-
,
J
In sincere appreciation
to
Dr. Alice I. Robold
whose pat1ence and encouragement
have reflected both personal and profess1onal excellence.
-
TABLE OF CONTENTS
INTRODUCTION
· . '. . · . . . •
'
MOI'IVATION • • • • • • • • • • • • • • • •
Personalization. • •
Goal Setting • • •
·•
·•
1
• • • • • •
• • • • • • •
• • • • • • •
·
2
-
2
- 3
4
4
· · • · • • • • 4 - 12
· . . · . • • · . . • 12 - 13
• •
· . • • • • • 14 - 15
LEARNING • • • • • • • • •
THE TEACHER'S ROLE •
BIBLIOGRAPHY • • • •
APPENDIX I (Listing of the Program) • • • • 16 - 21
APPENDIX II (Sample Run of the Program) •• 22 - 30
DfTRODUCTION
"A plan in the heart of a man is like
deep water,
But a man of understanding
draws it out."
Proverbs 20:5
"Many exciting, potentially powerful, and valid educational ideas
have gone unused" simply because the task of inventing methods and
creating materials for any new educational idea is enormous (13).
Such is the case of the computer.
Teachers in today's elementary
school have many methods (or plans) for teaching children mathematics.
To "draw out" such plans and revise them so that they may be programmed
successfully into a computer takes examination and insight on the
part of the teacher with regard to his or her own theories and
practices in education.
"All of us must cross the line between
ignorance and insight many times before we truly understand."
(7)
As teachers, motivation and learning are constant perplexities, and
many theorists have attempted to illustrate how to motivate children and
how children best learn.
Not every teacher does or should teach with
respect to the same theory; however, many well-known theories are
incorporated into the majority of classrooms.
This writing proposes
to delve into some of the well-known aspects of learning theory in
the area of Mathematics, and illustrate how these aspects may be
incorporated functionally into a computer program in the BASIC
language.
2
-,
MarIVATICN
What motivates children? What causes them to act? Since children
are stimulated by objects and events as sundry as the children themselves,
the teacher's task of moving each child into productive action is
monumentali however, it is this motivation that sets the quality
of learning which takes place, and which may also heighten perception
(9).
According to Seidel (1974), the experience of learning on a
computer usually is, in itself, motivating (17).
Successful experiences
allow a child to learn without feeling the need to employ the self-centered,
self-protective avoidance of disapproval, which so often children feel
is necessary even in non-threatening classroom environments (6).
Unsuccessful experiences may lead to dislikes of the computer and the
unique and valuable methods of teaching it offers.
In order to establish
and maintain motivation in computer instruction, a teacher may use
several t.echniques in his/her programming.
Personalization
Through the use of interactive computing and properly Phrased
comments which are individualized, a child can be referenced, personally
and by name in each activity he/she does on the equipment.
Students'
names may easily be inserted into the context of a program by using an
INPUT statement, proper prqmpts, and PRINT statements which include
the child's name.
10
20
PRINT "WHAT IS YOUR NAME?"
INFUT NAME$
30
PRINT "HELLO, "iNAME$;".
YOU ARE HERE TODAY.
I AM GLAD THAT
-
-
By inserting the string variable into any PRINT line in the form above,
the child's name may be repeated throughout the program.
-
Personalization of content area may also be established in computer
programs.
After the student has typed his or her name as the string
variable, the computer may be directed to find the string variable
within a set of DATA statements containing all of the students'
names and levels of difficulty on which they are to work.
30
GCSUB 999
..
998
HEM D = NUMBER OF STUDENTS
999 FOR D = 1 TO 4
1000 READ STUDENT$, L
1.010 IF STUDENT$
1011 NEXT D
10000
10010
10020
10030
DATA
DATA
DATA
DATA
= NAME$ THEN
1015
JILL, 1
LISA, 2
RICK, 3
TOM, 4
Problem complexity and/or type may easily be changed s·imply by
re-typing a single DATA statement which will direct the program to
instigate problems on a different level.
When the program controls the
function of choosing problem difficulty according to pretest scores or
teacher discretion rather than allowing the learner to select his or
her own level of difficulty, achievement has been proven to be at
higher levels (11).
Success strengthens learning and helps to motivate
students toward further learning.
Thus, programming the computer to
present challenging problems with reachable solutions on the level of
-
the student will enhance motivation.
4
-
Goal Setting
Setting· a goal for the student, and being sure that he or she is
aware of the goal is an important aspect of motivation (9).
can be involved in setting goals for themselves.
Students
Not only does this
allow the st.udent, and not the computer, to control the activity (an
important aspect of programming for motivation suggested in an
editorial in The Arithmetic Teacher (October, 1983)), but also makes the
goal an intrinsic one rather than one placed on a student through
extrinsic means.
In support of this theory, allowing a student the
opportunity to choose the number of problems that he/She wants tosolve can establish a personal goal for each child.
One programming
line accomplishes this task:
1015 PRINT "HELLO, ";NAME$;",. HOW MANY MATH PROBLEMS
DO YOU WANT TO SOLVE TODAY?'";:
INPUT C
After each problem is correctly solved, the computer may also update
the number of problems that the student must complete in order to
meet his/her goal.
This "awareness of progress toward the goal
strengthens learning and motivates further learning." (9)
48 PRINT lOWLY "; C - E;" PROBLEMS TO GO!!"
(NOTE
E is number of problems solved)
LEARNING
The process of learning is one of active involvement.
Such
involvement, wheather physical or not, is always mental, and always
-
should be meaningful to the student involved (11).
Organization of
5
learning is very important.
Cognitive processes are as important for
computer assisted instruction as they are for effective and efficient
teacher instructed lessons; therefore, creating educationally sound
computer instruction is a difficult and time-consuming task (12).
Mathematical concepts are most successfully formed according to the
developmental processes of a child.
Since children grow in. mathematical
thought from concrete phases through symbolic phases, organization which
follows a continuum from manipulatives to abstracts is deemed most
appropriate and comprehensible for mathematics instruction (3).
The
computer cannot be, itself, a manipulative form of mathematical instruction,
but it certainly can illustrate mathematical concepts in several
capacities.
For the purpose of illustration, I have chosen the operation of
multiplication and developed four different methods of teaching the
concept.
Each method corresponds to a different level of difficulty,
which the computer is directed to execute when the DATA statements are
read (see Motivation section).
up to his own capacity to learn.
"Each pupil will be expected to work only
He should master what he does at his
own level of maturity so that he can do things at that level of
efficiency and can have a sense of having achieved success." (9)
Level one can be accessed by using the name "Jill."
Jill has not
yet grasped the meaning of multiplication and is struggling with
basic multiplication facts.
computer (line 10).
Upon request, Jill types her name into the
Her DATA statement is read (line 1000); she is
greeted (line 1015); she chooses her own goal (l1nel015); and the
.-
computer is then directed to develop that number of basic multiplication
6
-
problems from random numbers.
The first problem is printed, and the
computer waits for an answer.
40
*42
44
46
=
FOR E
1 TO C
LET A
INT (1 0 * BND(1)) + 1
LET B
INT(10 * RND(1)) + 1
PRINT A;" X It ;B; It
It;: INPUT ANS
=
=
=
* RND(1) Randomized the random numbers
After the answer is punched into the computer, a subroutine is used to
check the problem.
If the problem is correct, the child is reinforced,
and the next problem is given.
48
GOOUB 2000
49
NEXT E
2000
2010
2020
Q
2080
ImrURN
5000
5010
5020
5030
* RND(1)) + 1
ON R Goro 5020, 5030, 5040, 5050, 5060
PRINT "WAY TO GO, ";NAME$; "!": RETURN
PRINT "WOW, WHAT A WHIZ!!! KEEP IT UP, "
;NAME$; "!": RETURN
PRINT "YOU'RE DOING VERY 'WELL, ";NAME$;".
I AM PR CUD OF YOU.": RETURN
5040
5050
5060
=0
IF
IF
R
ANS
ANS
=A *
=A *
B THni
B THEN
GCliUB 5000
GOTO 2080
.
= INT(5
PRINT "SUPER, SUPER JOB!!!!! MICKY MOUSE
WILL CHEER YOU ON, ";NAME$; "!": RETURN
PRINT "THAT'S THE RIGHT ANSWER. GOOD WORK!":
RETURN
If the answer is incorrect, the counter, initiated at line 2000, is increased
by one and the problem is printed again on the screen.
answer is entered and checked.
given.
Once again, the
If correct, a reinforcing statement is
7
2030
2060
2070
Q = Q + 1
= ";
PRINT A;" X "; B;"
INPUT ANS: Goro 2010
On the third presentation of the problem, which
occur~
after the
second incorrect response, a strategy is used which gears the child
toward mastery and success.
Each level, after this point, differs since
algorithms for higher-level mathematics become more abstract.
For the
first level, Jill's level, a program which uses a pictorial algorithm
has been written as follows:
2035
IF Q = 2 THEN GOOUB 4000
4000
4001
4002
4005
4008
4009
4015
4016
4017
4018
4019
4020
4021
4022
4024
IF L < )1
4070
REM CLEAR SCREEN
HOME
PRINT "LET'S LOOK AT THE FOLLOWING DIAGRAM."
P
0
P
P + 1
FOR R
1 TO A
FOR CO = 1 TO B
PRINT" * ";
NEXT CO
PRINT
PRINT
NEXT R
PRINT : IF P
2 THEN 4035
PRINT "HOW MANY ROWS ARE THERE IN THE DIAGRAM?"
: INPUT RO
PRINT "HOW MANY COLUMNS? ": INPUT COL
PRINT "DID YOU SAY THAT THERE ARE ";A;" ROWS
AND ";B;" COLUMNS? IF S0, YOU ARE RIGHT!!
IF Nor, TRY COUNTING THEM AGAIN. (PRESS
RETURN WHEN YOU ARE DONE COUNTING ROWS AND
COLUMNS. )"
INJ?UT R$
Gar04009
PRINT "THE NUMBER OF '*' IS EQUAL TO "IA;" X "
;B;" • HOW MANY 1*' ARE THERE? ": INPUT S
PRINT "THE ANSWER IS ";A * B;". DID YOU GET IT
RIGHT?
RETURN
4025
4031
4032
4034
4035
4037
4050
THEN
=
=
=
=
8
-
Lines 4023 - 4031 and line 4035 guide the child toward understanding
the algorithm.
At line 40)4, the array is reprinted since some of
the asterisk marks may have been scrolled off of the screen as PRINT
statements were typed.
The answer is given at line 4037, and the
same problem is then repeated to reinforce the learning of the basic
fact.
The pictorial array model "will serve as a natural extension
to prior work in making and naming rectangles using cubes, geoboards,
or graph paper." (10).
As illustrated above, the computer can "draw"
arrays to assist children in developing early multiplication concepts.
level two is accessed in the program by using the name "Lisa."
Lisa's level of skill is somewhat more advanced.
Form (problems
contain o~e-d1git multipliers and two-digit multiplicands); complexity
(same regrouping is required); and algorithm expla1nation (the distributive
property is used) all reflect Lisa's increasing mental competency in
the area of multiplication.
The program runs in the same basic foremat as the level one program
. does until the algorithm clarification section begins.
Of course, the
multiplicand now has changed to a number between ten and ninety-nineinclusive.
62
63
64
66
67
=
LET A
INT (100 * RND(l))
. IF A < 10 THEN 62
LET B
INT (10 * RND(l)} + 1
PRINT A; It X ";B;" = ";: INPUT ANS
=
GOSUB 2000
Again, two chances to correctly solve the problem are given to the
student before she studies the new algorithm.
I f Lisa misses the
9
problem twice, the multiplier (A) must first be split 1nto partial
sums (tens (T) + ones (0)) so that the distributive property can be
illustrated effectively.
4080
4090
LET T
LET 0
= INT
=A
(A
- T
*
.1)
*
10
We divide the problem • • •
4100
PRINT A;" X "; B;" = "; B; ,,( " ; T ;" + "; 0; " )"
then print the partial products.
4110
PRINT "(";B;" X ";T;")-+ (";B;" X ";0;")"
Individually, we ask for the solutions to the two partial products, and
the student punches the answers 1nto the computer.
=-
4120 PRINT B;" X ";T;"
n;: INPUT ANS
4130 PRINT B;" X "; 0;" = ";: INPUT AS
Finally, we explain how these answers correlate with the original
problem and ask for the sum.
4140 PRINT "DID YOU FIND THE CORRECT PARrIAL PRODUCTS?
IF SO, THEIR SUM IS -THE ANSWER TO THE
PROBLEM A;" X " ; B; " •
4150 PRINT ANS;" + ";AS;"
= ";:
WHAT IS THEIR SUM?"
INPUT AP
The Child, checks herself by comparing her answer to the correct one.
4160 PRINT "WAS YOUR ANSWER";A
*
B"'?
IF SO, YOU ARE
RIGHT! "
And the problem is repeated, once again
be entered.
So that the correct answer may
10
-
The distributive property helps children to realize the relationship
between addition and multiplication, and is necessary at this point
since higher-level multiplication problems require repeated application
of this procedure (2).
On level three, Rick, our level three student, again follows the
same basic outline as he solves even more advanced multiplication
problems.
His program is adjusted so that both the multiplicand and the
multiplier are double-digit numbers.
Both numbers are broken down
by the student into tens and ones, and new vocabulary is introduced.
4220
PRINT "HOW MANY TENS IN THE FIRST NUMBER
4230
PRINT "HOW MANY ONES m THE MULTIl'LIER'? " :
INRJT 0
PRINT "HOW MANY TENS IN THE SECCfiD NUMBER
(THE MULTIPLICAND) 1 ": D1PUT. TS
PRINT "HOW MANY oms IN THE MULTIPLICAND? ":
mPUT a3
PRINT as;" ONES X ": 0;" 0N]5 = WHAT NUMBER'? "
;: mPUT AO
PRINT a3;" 00llS X "; T ;" TENS
WHAT NUMBER? "
;: mJ?UT AD
PRINT TS;" TENS X "; 0;" ONES = WHAT NUMBER?
";: nr.PUT AU
PRINT TS;" TENS X "; T;" TENS = WHAT NUMBER'? "
(THE MULTnLIER )1"
4240
4250
4252
4255
4260
4265
":
INPUT T
=
;: mJ?UT AS
4270
4280
4330
PRINT: PRINT: PRINT "IF YOU MULTIPLIED ALL OF
THE NUMBERS CORRECTLY, THEIR SUM SHOULD
BE EQUAL TO THE ANSWER TO THE PROBLEM "
;A;" X "; B; " • LET'S ADD YOUR ANSWEBS TOGETHER TO SEE IF YOU ABE CORRECT."
PRINT: PRINT: PRmT"
";AO;" + ";AD;" + "
;AU;" + ";AS;"
INPUT SU
PRINT" IF YOU SAID THAT THE SUM OF ALL OF THE
NUMBERS IS ";A * B;" YOU ABE CORRECT!
THIS IS AISO THE ANSWER TO THE PROBLEM
= ";:
"jAjU
4340
X n;B;"."
RETURN
By writing all of the partial products down, the child can gain greater
insight into expanded notation and its usefulness, as well as repeatedly
11
apply the distributive property.
When each partial product is added
individually as this program illustrates, development of the more
standard, shortened form of partial product addition will be accesse:d (2).
"In more complex multiplication problems, the principles of place
value are applied and the basic algorithm is extended (2)."
This is the
goal of the fourth level of multiplication accessed by using the
name "Tom."
level four, like the other levels preceeding it, follows
the same basic procedure until the algorithIn must be developed.
At
this point, the multiplicand is split into its component parts, and
each part is then multiplied individually by the multiplier.
The
hundreds part of the multiplicand is found first • • •
4400
LET PH
= niT
(:8
*
.01)
*
100
then the tens • • •
4410 LET PI'
= niT
«:8 - PH)
*
.1)
*
10
and finally, the ones.
4420
LET PO
= :8
- PH - PI'
We print the expanded" form of the problem,
4430
PRINT A;" X ";:8;"
PO;" )"
= ";A;"(";:EH;"
+ ";Pr;" + ";
and give instructions and partial product problems.
4440 PRINT
4470 PRINT
4480 PRINT
4490 PRINT
"FmD THE PARTIAL PRODUCTS."
A;" X ";PH;"
mPUT PI'
A;" X "; PI' ;"
mPUT m
A;" X "; PO;" = ";: INPUT PI'
= ";:
= ";:
12
-,
Finally, the algorithm is explained, and the solution is calculated.
4500 PRmT "THE SUM OF THE PARTIAL PRODUCTS YOU JUST
COMPUTED SHOULD BE THE ANSWER TO THE
PROBLEM "; A;" X "; B; " • ADD THEM TOGETHER
TO SEE IF YOU .ARE CORRECT. WHEN YOU ARE
DONE ADDING THE PARTIAL PRODUCTS TOGETHER,
ENTER YOUR ANSWER AND PRESS RETURN."
4510 INPUT TP
As in the three previous levels, the calculated answer is compared with
the actual answer, and the correct product is entered as the solution.
As exemplified above, the computer is a unique and valuable
teaching method which allows a child to pace himself/herself,
repeat parts of lessons that he/she does not understand, and skip
what he/she knows (14).
In addition, immediate feedback can be
provided upon successful completion of a problem as illustrated in
lines 5000 - 5060, and guidance can be administered at appropriate levels
of mathematical maturity when "trouble spots" emerge.
More difficult
algorithms may be developed which directly relate to previous algorithms
and make learning logical.
Careful planning on the part of the
teacher, which allows students time to guess, test their guesses,
and develop abilities to estimate, helps students to test the
reasonableness of their answers and not to acquire the erroneous
conclusions which often lead to unreasonable answers (1).
THE TEACHER'S ROLE
The person who is instrumental in providing the classroom with
-
quality computer assisted instruction is the teacher.
"Those who would suggest that the computer can
replace the teacher and those who would suggest
13
that the computer will somehow depersonalize the
classroom have never seen a competent teacher using
the strengths of the computer to do those things
it does best and leaving the teacher free to do
those things which can be done only by a teacher."
(5)
Only the teacher, says :8. F. Skinner, can function through "intellectual,
cultural, and emotional contacts of the distinctive sort which testify
to (his/) her status as a human being. (5)."
In using qualities that
are uniquely human, a teacher "operates on a frontier of educational
knowledge--thinking up new ways to implement new knowledge (13), and
places the new technology into the classroom.
Opportunities are
thus created for learning to take place which goes beyond the subject
matter and extends into new areas.
Good teaching is not merely
transmission of information and skills, but the encouragement of zest
for further study.
Computers are here to stay.
They are not "electric
teachers," (15) but rather a general purpose tool to be utilized both
in teaching subject areas and as a subject area themselves (8).
Teachers
need only use their knowledge of effective teaching to create quality
softw~e
from which children can learn not only the subject matter,
but how technology can enhance their lives.
14
BIBLIOORAl'HY
1.
Ashlock, Robert B. Error Patterns in Computation: A Semiprogrammed Approach. Columbus, Chio: Charles i. Merrill
Publishing Company, 1976.
2.
Ashlock, Robert B. Guiding Each Child's learning of Mathematics:
! Diagnostic ApProach to Instruction. Columbus, Chio:
Charles E. Merrill Publishing Company, 1983.
3.
Copeland, Richard W. ~ Children learn Mathematics: Teaching
Implications of Pieget' s Research. New York: MacMillan
Publishing Company, 1979.
4.
Driscoll, Mark J. Research Within Reach. Elementary School
Mathematics. Reston, Virginia: National Council of
Teachers of Mathematics, 1980.
5.
Hofmeister, Alan. Microcomputer Applications in the Classroom.
New York: CBS College Publishing, 1984.
6.
Holt, John. How Children Fail. New York:
Company, Incorporated, 1964.
Holt, John. How Children learn. New York:
Company, Incorporated, 1967.
8.
Dell Publishing
Dell Publishing
Morsund, Iavid. Teachers' Guide to Computers .!E. the Elementary
School. Ellgene, Oregon: International Council for Computers
in Education, 1980.
National Council of Teachers of Mathematics. The learning of
Mathematics, Its Theory and Practice. Washington, D.C.:
The National Council of Teachers of Mathematics, Incorporated,
1953.
10.
Reys, Robert E, Marilyn N. Suydam, and Mary M. Lindquist.
Helping Children learn Mathematics. Englewood Cliffs, New
Jersey: Prentice-Hall, Incorporated, 1984.
11.
Ross, S.M. and E.A. RaItov. "learner Control vs. Program Control as
Adaptive Strategies for Selection of Instructional Support on
Math Rules." Journal of Educational Psychology, October 1981,
pp. 745-753.
12.
Scandura, J .M. "Microcomputer Systems for Authoring, Diagnosis,
and Instruction in Rule-Based Subject Matter." Educational
Technology, January 1981. pp. 13-19.
15
--
13.
Smith, James A. Setting Conditions ~ Creative Teaching in the
Elementary School.
Boston: Allyn and Bacon, Incorporated,
1966.
-
.
14.
Spencer, Mirna, and Linda Baskin. "Computers in the Classroom."
Childhood Education, March/April 1983, pp. 293-6.
.
15.
Stecy, Edward M. "Students: Handle with C.A.R.E. (Computer
Assisted Remediation and Enrichment)." American Annual of
the Deaf, September 1982, pp. 617-24.
-
16.
Steffe, Issl1e P., ed. Research.2!! Mathematical Thinking of Young
Children. Reston, Virginia: National Council of Teachers of
Mathematics, 1975.
17.
Wall, S.M., and N.E. Taylor. "Using Interactive Computer Programs
in Teaching Higher Conceptual Skills: An Approach to
Instruction in liriting • " Educat ional Technology, February
1982, pp. 13-17.
-
16
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APPENDIX I
Listing of the Program
,-
17
J
JLIST
42
PRINT "WHAT IS YOUR NAME?"
INPUT NAME$
GOSUB 999
PRINT
FOR E = 1 TO e
LET A = INT (10 lK RND ( 1) ) +
44
LET E:
10
20
30
32
40
1
==
INT 00
1
it6
PRINT A;" X
II ;
E:;
RND
lK
II
I~NS
=
II
+ •
t •
(1»
INPUT
62
GOSUE: 2000
PRINT "ONLY ";e - E; .. PROE:LEM
S TO GO! ! ..
PRINT
PRINT
NEXT E
STOP
FOF.: E = 1 TO C
PRINT
LET A = INT (100 lK RND ( 1) )
63
64
IF A .( 10 THEN 62
LET 8 = INT (10 lK
47
if8
49
50
51
60
61
+
RND (1» +
:l
69
70
80
81
82
PFUNT A; .. X
= t • INPUT
ANS
GOSUE: 2000
PRINT "ONLY ";e - E; " F'F.:OE:LEM
S TO GO! !
NEXT E
STOP
FOR E = 1 TO e
PRINT
LET A = INT (100 lK RND (1 »
83
84
IF A :> 99 THEN GOTO 82
LET E: = INT (100 lK RND ( 1 ) )
66
67
68
II ;
E~; II
II • •
II
+ 10
8t::"
+ 10
IF E: ). 99 THEN GOTO 84
B6
PFUNT A; .. X .1; E: ; II = t +• INPUT
ANS
..-q7 GOSUE: 2000
38 PRINT "ONLY "te - E;" PROE:LEM
S TO GO! ! "
89 NEXT E
90 STOP
100 FOR E = 1 TO e
101 PRINT
102 LET A = INT (1000 lK RND ( 1
,j
II •
) )
lu3
104
IF A .( 100 THEN GOTO l()Z
LET B = INT (1000 )I( F:ND ( 1
))
IF B .::: 100 THEN GOTO 104
PRINT At" X II;E:;11 = t •+ INPUT
ANS
- 07 GOSUB 2000
108 PRINT "ONLY "C - E;" PROE:LEM
S TO GO!!"
109 NEXT E
110 STOP
999 FOR 0 = 1 TO 4
1000 READ STUDENT$tL
1010 IF STUDENT$ = NAME$ THEN 10
:1.05
II •
:1.06
15
1011
1015
NEXT 0
.
PRINT "HELLO, ";NAME$;" HOW
MANY MATH PROBLEMS DO
YO
U WANT TO SOLVE TODAY?";: INPUT
C
=1
1020 IF L
1030 IF L =
1040 IF L =
1050 IF L
:t. 09 0 l:::ETURN
2000 Q = 0
2010 IF ANS
5000
=
2020
THEN 40
2 THEN 60
3 THEN 80
4 THEN 100
=A
IF ANS = A
)I(
B THEN
GOSUB
lK
E: THEN
GOTO 2
080
2025 PRINT
2030 Q = Q + 1
2032 PRINT
203~5
IF Q - 2 THEN
2040 IF Q - 3 THE!'·!
2055
2060
2070
2075
2080
4000
4002
4005
GOSUE: 4000
PF~INT "I'M T
IRED OF THIS PROBLEM, AREN'T
YOU, ";NAME$;"."
PRINT
PRINT A;" X ";E:;" = ";
INPUT ANS: GOTO 201~
PRINT
RETURN
IF L < >:1. THEN 4070
HOME
PRINT "LET'S LOm< AT THE F
OLLOWING DIAGfMM."
4008 F' = 0
4009 LET P
F' + 1
4010 PRINT: PRINT : PRINT
4015 FOR R
:I. TO A
4016 FOR CO = 1 TO E:
4017 PRINT" )I( " ;
4018 NEXT CO
4019 PRINT
4020 PI=\:INT
4021 NEXT R
4022 PRINT
IF P
2 THEN 4035
=
=
=
PRINT "HOW MANY ROWS ARE TH
ERE IN THE DIAGRAM? ": INPUT
RO
4025 PRINT "HOW MANY COLUMNS? "
t INPUT COL
4031, PRINT "DID YOU SAY THAT THE
RE ARE "; A;" ROWS, AND
";B
;" COLUMNS? IF SO,YOU ARE R
IGHT!! "
~024
---.---
--
---
18
l-'h.J..r""il
'""(\).:)L
"li-
r'lUT
fRY
t
CUUNTING
THEM AGAIN. (PRESS RETURN
WHEN YOU ARE DONE COUNTING "
PRINT "ROWS AND COLUMNS.)"
INPUT RS: PRINT : GOTO 4009
4033
4034
-.
.035
19
PRINT "THE NUMBER OF ')I(' IS
EQUAL TO "; A; X "; E:; " • HO
W MANY 'lK' ARE THERE? u: INPUT
11
S
4037
PFUNT "THE ANSWER IS "; A )I(
B;". DID YOU GET IT RIGHT?"
RETURN
IF L > 2 THEN 4200
PRINT
LET T = INT (A lK .1) )I( 10
LET 0 = A - T
PRINT A;" X ";B;" = ";B;"("
;T;II + ";0;") ="
4105 PRINT
4106 PRINT
'+1 1 0 PRINT "(";B;" X ";T;") + ("
4050
4070
4075
4080
4090
4100
H::;" X ";0;")
4115
4120
4125
4130
4135
4140
"
PRINT
PRINT B;" X ";T;" = ";: INPUT
ANS
PRINT
PRINT E:;" X "; 0;" = ";: INPUT
AS
PRINT
PRINT "DID YOU FIND THE CO~:
RECT PARTIAL
PRODUCTS
? IF SOt THEIR SUM IS THE"
PRINT "ANSWER TO THE P~:OE:LE
M ";A;" X ";E:;". WHAT
I
S THEIR SUM?"
4:L4~5
PRINT
4150 PRINT ANS;" + ";AS;" = ";: INPUT
AP
4155 PRINT
4:l.60
PRINT "WAS your.: ANSWER " ; A
>X E:;"?
IF SO, YOU Ar\E
RI
GHT!"
4:1.65 PRINT
4170
liETURN
4200 IF L > 3 THEN 4400
4210
PRINT
4220 PRINT "HOW MANY TENS IN THE
FIRST NUMBER (THE
MULTIPL
IER)? ": INPUT T
4230 PfUNT "HOW MANY ONES IN THE
MULTIPLIER? ": INPUT 0
'+240
PRINT "HOW MANY TENS IN THE
SECOND NUMBER (THE MULTIPLI
CANO)? ": INPUT TS
~250
PRINT "HOW MANY ONES IN THE
MULTIPLICAND? ": INPUT OS
425:l.
PRINT
4252 PRINT OS;" ONES x ";0;" ONE
S = WHAT NUMBER? ";: INPUT
AO
4253 PfUNT
4255 PRINT OS;" ONES X u;T;" TEN
----.--------- - ------- --- -._----------_._--_
4142
....
..
-
...
...-~---.------
...
...
~'!HH I
;;) :::
4257
4260
-4262
+265
4266
'+267
4270
I\Wlvlt:!::J<~;
" ;;
.iNr'UT
AD
PRINT
PRINT TS;" TENS X ";0;" ONE
S = WHAT NUMBER? ";: INPUT
AU
PRINT
PRINT TS;" TENS X ";T;" TEN
S ::: WHAT NUMBER? ";: INPUT
AS
PRINT
pr~INT
PFUNT: PRINT : PRINT "IF Y
OU MULTIPLIED ALL OF THE NUM
BERS
CORRECTLY, THEIR SU
M SHOULD E:E EQUAL TO "
4272 PRINT "THE ANSWER TO THE PR
OE:LEM "; A; X "; B; " •
LE
T'S ADD YOUR ANSWERS TOGETHE
R TO SEE
4275 PRINT "IF YOU ARE CORRECT."
11
II
PRINT
PRINT: PRINT
;AO;" + ";AD;" + ";AU;" + ";
AS;" ::: ";: INPUT SU
4290
PRINT
431()
PRINT
IF YOU SAID THAT TH
PRINT
4330
E SUM OF ALL OF THE NUMBERS
IS ";A lK e:;11 YOU ARE CORRECT
4280
11
11
11
11
4340
'+400
RETURN
LET PH:::
INT (e:
*
.01)
lK
1
00
4410
LET PT::: INT «8 - PH) lK •
lK 10
LET PO = e: - PH - PT
PRINT A;" X 1I;e:;" = II;A;"(II
;PH;" + II;F'T;" + ";PO;")"
PRINT
PRINT "FIND THE PARTIAL PRO
DUCTS."
PRINT
PRINT
PRIP·!T AI t• X ";PH;" ::: +t •• INPUT
10)
4420
4430
4435
4440
4450
"+'+60
'+470
II
II
F'P
4475
4480
4485
'+490
4495
4~50 0
.-4502
PRINT
PRINT A;" X ";PT;" = t •+ INPUT
PS
PRINT
PRINT A; X ";PO;" ::: t • INPUT
PT
PRINT
PRINT "THE SUM OF THE PARTI
AI_ PF:ODUCTS YOU JUST COMPUTE·
D SHOULD e:E THE ANSWER TO TH
E "
F'RINT "pr~OBLEM "; A; X II; E:;
"
ADD THEM TOGETHER TO SEE
IF YOU ARE CORRECT. WHEN Y
OU ARE
PRINT IIDONE ADDING THEM TOG
ETHER t PUNCH IN YOUR ANSWER
AND PRESS RETURN."
INPUT TP
PRINT
PRINT : PRINT IIWAS
II ..
II
II
4505
4510
452(\
....
II
20
YOUR ANSWER "; A :« E:;" '? IF S
0, YOU ARE RIGHT!"
4525 RETURN
5000 R =INT (5:« RND (1»
+ 1
5010 ON R GOTO 5020,5030,5040,50
50,5060
PRINT IIW.AY TO GO, II;NAME$;"
!"t RETURN
5030 PRINT "WOW, WHAT A WHIZ!!!
~{EEF' IT UP, "; NAME$; " ! .. t RETURN
)020
PRINT "YOU'RE DOING VEF~Y WE
LL t " ; NAME$; " • I AM
PR
OUD OF YOU."t RETURN
5050 PRINT "SUPER, SUPER "JOE:!!!!
MICKEY MOUSE WILL CHEER YO
U ON,
";NAME$;"."t RETURN
5040
PRINT "THAT'S THE RIGHT ANS
WER. GOOD WOR~(!" t RETURN
10000 DATA JILL, 1
10010 DATA LISA, 2
10020 DATA RICK, 3
10030 DATA TOM, 4
:L50 00 END
5060
-
21
22
APPENDIX II
A Sample Run of the Program
-
23
:J
JRUN
WHAT IS YOUR NAME?
?JILL
HELLO, JILL HOW MANY MATH PROBLEMS DO
7 X 7 = ?.tt9
WAY TO GOt JILL!
ONLY 3 PROBLEMS TO GO! !
YOU WANT TO SOLVE TODAY??4
9 X 6 ::: ?55
9X 6 = ?5.tt
THAT1S THE RIGHT ANSWER.
ONLY 2 PROBLEMS TO GO! !
GOOD WORK!
5 X 6 ::: ?32
5 X 6 = ?40
LET'S
LOOK AT THE FOLLOWING DIAGRAM.
JI(
:«
)!(
:«
:«
:.1(
)K
)I(
:«
:I(
:«
lK
:«
)I(
lK
:«
lK
lK
)It
lK
lK
:«
lK
lK
:«
~l(
)I(
:«
:«
lK
HOW MANY ROWS ARE THEF:E IN THE DIAGPAt1?
?5
~OW
MANY COLUMNS?
6
DID YOU SAY THAT THERE ARE 5 ROWS AND
6 COLUMNS? IF SO, YOU ARE RIGHT!!
IF NOT, TRY' COUNTING THEM AGAIN.
(PRESS RETURN WHEN YOU ARE DONE COUNTING
ROWS AND COLUMNS.)
?
._----------------_.-------_._--------.---------------
-- ---- -- ----- _._-
._-----------------------
24
lK
)t(
lK
lK
lK
lK
THE NUMBER OF ' . ' IS EQUAL TO 5 X 6.
HOW MANY 'lK' ARE THERE?
?30
THE
ANS~ER
5 X 6
IS 30.
DID YOU GET IT RIGHT?
= ?30
WAY TO GO, JILL!
ONLY 1 PROBLEMS TO GO! !
2 X 8
= ?15
~~
= ?17
X 8
LET'S
LOOK AT THE
HOW MANY
.....
RO~S
FOLLO~ING
DIAGRAM.
ARE THERE IN THE DIAGRAM?
?'"'
HOW MANY COLUMNS?
?8
DID YOU SAY THAT THERE ARE Z RO~S AND
8 COLUMNS?
IF SO,YOU ARE RIGHT!!
IF NOT, TRY COUNTING THEM AGAIN.
(PRESS RETURN WHEN YOU ARE DONE COUNTING
ROWS AND COLUMNS.)
?
THE NUMBER OF ')1(' IS EQUAL TO 2 X 8.
HOW MANY'.' ARE THERE?
?l6
THE
ANS~ER
IS 16.
DID YOU GET IT RIGHT?
1. X 8 = 116
THAT'S THE RIGHT ANSWER.
ONLY 0 PROBLEMS TO GO! !
E:REAI{ IN 51
GOOD WORK!
25
J
JRUN
WHAT IS YOUR NAME?
?LISA
HELLO, LISA HOW MANY MATH PROBLEMS DO
54 X 10 = ?540
THAT'S THE RIGHT ANSWER.
ONLY 3 PROBLEMS TO GO! !
67 X 6
= ?408
67 X 6
= ?404
67 X 6
= 6(60
(6 X 60)
+7)
YOU WANT TO SOLVE TODAY??4
GOOD WORK!
=
+ (6 X 7)
6 X 60 = ?360
6 X 7
= ?42
DID YOU FIND THE CORRECT PARTIAL
ANSWER TO THE PR08LEM 67 X 6. WHAT
360 + 42
PRODUCTS? IF SO, THEIR SUM IS THE
IS THEIR SUM?
= ?702
WAS YOUR ANSWER
402?
IF SO, YOU ARE
RIGHT!
67 X 6 = 1'+02
WAY TO GO, LISA!
ONLY 2 PROBLEMS TO GO! !
24
X 6
= ?142
2'+ X 6 = ?144
SUPER, SUPER JOB! !!! MICKEY MOUSE WILL CHEER YOU ON,
ONLY 1 PROBLEMS TO GO! !
-
5 X 6
15
X 6
15 X 6
= ?30
=
180
= 6(10
+ 5)
=
LISA.
(6 X 10) + (6 X 5)
6 X 10
-
6 X 5
26
= ?60
= ?30
JID YOU FIND THE CORRECT PARTIAL
ANSWER TO THE PROBLEM 15 X 6. WHAT
60 + 30
= ?90
WAS YOUR ANSWER
90?
IF SOt YOU ARE
15 X 6 = ?90
WOW t WHAT A WHIZ!!! KEEP IT UP t LISA!
ONLY 0 PROBLEMS TO GO! !
8REA~(
--
PRODUCTS? IF SOt THEIR SUM IS THE
IS THEIR SUM?
IN 70
RIGHT!
27
JRUN
QHAT IS YOUR NAME?
?RIC~{
HELLO, RICK HOW MANY MATH PROBLEMS DO
YOU WANT TO SOLVE TOOAY??4
73 X 14 = ?1022
SUPER? SUPER JOB! !!! MICKEY MOUSE WILL CHEER YOU ON t
ONLY 3 PROBLEMS TO GO! !
65 X
= ?3050
47
65 X 47
:=
?3055
YOU1RE DOING VERY WELL, RICK.
ONL Y 2 PROBLEMS TO GO! !
19 X
1.9 X
RICI< •
F'F,OUD OF YOU.
= ?345
47
.tt7
I AM
?895
:=
HOW MANY TENS IN THE FIRST NUMBER (THE
?1
HOW MANY ONES IN THE MUL TIPLIEF.:?
MULTIPLIER)?
'?9
HOW MANY TENS IN THE SECOND NUME:ER (THE MULTIPL.ICAND)?
?.tt
HOW MANY ONES IN THE MULTIPLICAND?
?
?REENTER
';>• '7
I
;" ONES X 9 ONES
:=
WHAT NUMBER?
?63
7 ONES X 1 TENS
:=
WHAT NUMBER?
?70
4
TENS X
9
ONES = WHAT NUMBER?
4 TENS X 1 TENS
:=
WHAT NUMBER?
?360
?400
-l:F YOU MULTIPLIED ALL OF THE NUME:ER~)
HE ANSWER TO THE PROBLEM 19 X 47.
IF YOU ARE CORRECT.
63 + 70 + 360 + 400
:=
CORRECTLY, THEIR SUM SHOULD BE EQUAL T(
LET'S ADD YOUR ANSWERS TOGETHER TO SEE
?893
IF YOU SAID THAT THE SUM OF ALL OF THE NUMBERS IS 893 YOU ARE CORRECT!
19 X ~7 = ?893
WOW, WHAT A WHIZ! !! KEEP IT UP t RICK!
ONLY 1 PROBLEMS TO GO! !
93 X
50
28
= ?~550
~
93 X 50
= ?~570
HOW MANY TENS IN THE FIRST NUMBER (THE
MULTIPLIER)?
79
HOW MANY ONES IN THE MULTIPLIER?
?3
HOW MANY TENS IN THE SECOND NUMBER (THE MULTIPLICAND)?
~~
!~
HOW MANY ONES IN THE MULTIPLICAND?
?O
0 ONES X 3 ONES
0 ONES X 9 TENS
5 TENS X 3 ONES
~
~
TENS X 9 TENS
= WHAT
= WHAT
= WHAT
= WHAT
NUMBER?
?O
NUMBER?
?O
NUMBER?
?150
NUMBER?
?4500
IF YOU MULTIPLIED ALL OF THE NUMBERS
THE ANSWER TO THE PROBLEM 93 X 50.
IF YOU ARE CORRECT.
o
+ 0 + 150 + 4500
CORRECTLY, THEIR SUM SHOULD BE EQUAL T
LET'S ADD YOUR ANSWERS TOGETHER TO SEE
= ?~650
IF YOU SAID THAT THE SUM OF ALL OF THE NUM8ERS IS 4650 YOU ARE CORRECT!
93 X 50
= ?5650
I'M TIRED OF THIS PROBLEM, AREN'T YOU, RICK.
93 X 50
= ?4650
SUPER, SUPER J08!!!! MICKEY MOUSE WILL CHEER YOU ON,
ONLY 0 PROBLEMS TO GO!!
BREAK IN 90
RICK.
29
]RUN
WHAT IS YOUR NAME?
?TOM
HELLO, TOM HOW MANY MATH PROBLEMS DO
589 X 685 = ?403465
THAT'S THE RIGHT ANSWER.
ONLY 3 PROBLEMS TO GO! !
YOU WANT TO SOLVE TODAY??1
GOOD WORK!
262 X 150 = ?117910
262 X 450 = ?117900
THAT'S THE RIGHT ANSWER.
ONLY 2 PROBLEMS TO GO! !
569 X 150
= ?56900
569 X 150
= ?57500
569 X 150
= 569(100
GOOD WORK!
+ 10 + 10)
FIND THE PARTIAL PRODUCTS.
569 X 40
= ?56900
= ?22760
569 X 10
= ?5690
569 X 100
THE SUM OF THE PARTIAL PRODUCTS YOU JUST COMPUTED SHOULD BE THE ANSWER TO THE
PROBLEM 569 X 150. ADD THEM TOGETHER TO SEE IF YOU ARE CORRECT.
WHEN YOU ARE
DONE ADDING THEM TOGETHER, PUNCH IN YOUR ANSWER AND PRESS RETURN.
?85350
WAS YOUR ANSWER 85350?
IF SO, YOU ARE RIGHT!
569 X 150 = ?85350
SUPER, SUPER JOB! I!!
MICKEY MOUSE WILL CHEER YOU ON t
ONLY 1 PROBLEMS TO GO! !
230 X 571
= ?10065
230 X 571
= ?18056
= 230(500
230 X 571
FIND THE PARTIAL
+ 70 + 1)
P~ODUCTS.
TOM.
230 X 500
)0
= ?16100
230 X 70
230 X 1
= ?115000
= ?230
SUM OF THE PARTIAL PF.:ODUCTS YOU JUST COMPUTED SHOULD E:E THE ANS~ER TO THE
230 X 571.
ADD THEM TOGETHER TO SEE IF YOU ARE CORRECT. WHEN YOU ARE
DONE ADDING THEM TOGETHER, PUNCH IN YOUR ANS~ER AND PRESS RETURN.
--'--IE
~R08LEM
?:1.31330
WAS YOUR
230 X 571
ANS~ER
131330?
= ?131330
IF SOt YOU ARE RIGHT!
YOU'RE DOING VERY WELL t TOM.
ONLY 0 PROBLEMS TO GO! !
E:REM{ IN 110
-
I AM
PROUD OF YOU.