Teacher-Computer Interaction in Teaching a Mathematics Lesson

Teacher-Computer Interaction in Teaching a Mathematics LessonAuthor(s): Lyle E. Andersen, Glenn D. Allinger and Jean P. AbelSource: The Arithmetic Teacher, Vol. 36, No. 2 (October 1988), pp. 42-46Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193469 .

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Teacher-Computer Interaction in Teaching a

Mathematics Lesson By Lyle E. Andersen, Glenn D. Allinger, and Jean P. Abel

Elementary school teachers are being encouraged to use the computer for mathematics instruction (NCTM 1980). Many are seeking appropriate methods for integrating the computer into their mathematics lessons. Un- fortunately, much of the present software must be altered or creatively adapted before it can be incorporated into teacher presentations. The lack of computers in individual classrooms and the lack of regular access to computer laboratories are other stumbling blocks that discourage the use of computers in a regular lesson. These state- ments are supported by a survey con- ducted in Minnesota (Andersen 1984) that showed fewer than 5 percent of the K-8 teachers who responded had ever used the computer for teaching mathematics.

This article suggests ways to com- bine the strengths of both the teacher and the computer to yield effective lessons. Certain multiplication concepts and an algorithm for whole- number multiplication are taught in a sample lesson. These topics might be taught effectively with manipulatives; however, the computer is used as an electronic chalkboard to teach at a semiconcrete level because it is fast

Lyle Andersen and Glenn Allinger teach at Montana State University in Bozeman, MT 59717. Their responsibilities include teaching content and methods involving elementary and secondary school mathematics curricula. Andersen's special interests include problem solving and the integration of the calculator and computer into instruction. Allinger' s interests include computation, estimation, and men- tal arithmetic, particularly using percent. Jean Abel teaches at Berry College, Mount Berry, GA 30149. She is interested in using computers to improve mathematics instruction.

and accurate, sometimes reaching students who are not motivated by con- ventional approaches. The computer program used in this article is not the focus of discussion but serves as a vehicle to assist in modeling a teacher-directed presentation using one computer in an elementary school classroom.

The Teacher Is the Instructional Leader Computer programs designed to sup- plement instruction have a place in

the elementary school curriculum, for example, drill-and-practice software for mastering the use of an algorithm. The computer can create exercises tailored to correct students* deficien- cies. However, the computer does not recognize when a student is obtaining a correct answer without understand- ing the concepts involved, nor does the computer react in any special way toward an unmotivated student who is not paying attention. Teachers using the computer in their class presentations soon gain the experience needed to interject appropriate questions.

42 Arithmetic Teacher



They learn to control the quantity and difficulty level of illustrative prob- lems, sensing when to direct students to paper-and-pencil practice.

Important teacher-computer-student interactions will be illustrated in the next section. The array concept of multiplication and an associated multiplication algorithm are the lesson topics.

Teaching a Multiplication Algorithm The following presentation to a fourth-grade class indicates a possible sequencing of the content and the potential for interaction among twenty to twenty-five students, one teacher, and one computer terminal. One computer per classroom con- nected to a twenty-one-inch classroom monitor or wired to two twelve- inch monitors by video cable has been found to be adequate for involving the entire class simultaneously (Phillips 1983).

The computer is used to teach at a semiconcrete level because it is fast and accurate.

A computer program called MULT (see the Appendix) is used to support the teaching of multiplication of a two-digit number (between eleven and nineteen inclusive) by a nonzero one- digit number. The program graphi- cally depicts a marching band as the motivating application. The band is created by annexing a fixed number of trombone (T) players (between one and nine inclusive) to each row of ten drummers (D). The number of rows (of drummers and trombonists) is between one and nine inclusive.

Teacher: [Loads the program MULT] Lucille, enter the number of trombone players to be added to each row of ten drummers and press RE- TURN. Now, enter the number of rows and press RETURN again.

The total number of drummers (D) and trombone (T) players is displayed on the screen, row by row, in rectan- gular formation. For example, ten

Fig. 1 . Computer display

HOW MANY TROMBONISTS WOULD YOU LIKE TO ADD TO EACH ROW OF 10 DRUMMERS? 7 HOW MANY ROWS? 3

10 DRUMMERS 7 TROMBONISTS

DDDDDDDDDDTTTTTTT 3 ROWS DDDDDDDDDD TTTTTTT

DDDDDDDDDDTTTTTTT

3 ROW(S) OF 17

HOW MANY ARE IN THE BAND?

Fig. 2. The teacher displays this drawing on the chalkboard.

10 7

3 | 3 x 10 = 30 | 3 x 7 = 21

Fig. 3

10 DRUMMERS 7 TROMBONISTS


DDDDDDDDDDTTTTTTT

3R0W(S)0F17


10 DRUMMERS + 7 TROMBONISTS x 3 x 3 ™3(f +"""£? = 51

drummers and seven trombone players are pictured in each of three rows < for a total of fifty-one players. (See i fig. 1.)

Teacher: How do we find just the i number of drummers?

Student: 10 + 10 + 10 = 30 or 3 x 10 = 30.

Teacher: Now find the number of trombone players.

Student: 7 + 7 + 7 = 21 or 3x7 = 21.

Teacher: What is the total number of players in the band?

Student: 30 + 21 = 51 total players.

Teacher: Let's represent the band on the chalkboard without drawing the individual members. [She or he draws two adjacent rectangles. (See fig. 2.)]

How many drummers in each row? (answer: 10)

How many rows of drummers? (answer: 3)

How many total drummers? (answer: 30)

How many trombone players in each row? (answer: 7)

How many rows of trombone play-

October 1988 43



ers? (answer: 3) How many total trombone players?

(answer: 21)

Let's see what the computer has to say. [She or he presses any key. (See fig. 3 for monitor presentation.)] This is just another way to write the arithmetic for computing the total number of players without using capital letters or boxes.

At this point, since the algorithm

2 17

x 3

51

is not shown, the teacher can choose to terminate the sequence of new ideas prematurely and repeat more examples with the aid of the computer. To do so, she or he presses CON- TROL and RESET simultaneously and then types RUN. However, if continuing the program, the teacher explains the final algorithm, using the chalkboard or overhead. Next, the teacher pushes any key to show the algorithm displayed by the monitor to solidify the association of boardwork with the band on the monitor. (See fig. 4.) She or he selects other students to type in values, each time pausing and asking questions before activating the computer display. Students are asked to indicate the total number of players determined both by some counting process and by the final multiplication algorithm.

As the students experience success, the teacher can cover part of the monitor with a piece of paper (see fig. 5) that shields information from the students, thus encouraging them to ab- stract and to determine a way to find the number of band members. Lead- ing questions can also be posed before the computer confirms an answer as being correct. Questions that might be typical of accompanying paper-and- pencil exercises are illustrated in figure 6.

Conclusion This article focuses on the teacher as the essential ingredient in the presentation of the lesson, with the software

Fig. 4


DDDDDDDDDDTTTTTTT

3 ROW(S) OF 17


10 DRUMMERS + 7 TROMBONISTS x 3 x 3

To" T Sì ~™7T~ 2 17

x 3 51

Hg. 5 is.

^^TTTTT

The teacher and computer can be very effective as an instructional team.

being subordinate to the teacher. The MULT program is used in this simu- lated lesson to support the elementary school teacher's presentation of a selected topic in multiplication. The teacher plays the key role in the instructional process.

Still, the main thesis is that the teacher and computer can be very effective as an instructional team when working with the entire class. The following reminders may prove helpful:

1 . Develop questions to be used at key points in the computer-teacher presentation. The computer program cannot anticipate all the interest and ability levels present among students. This is the teacher's strength.

2. Use the flexibility of the computer. With adequate software, the computer displays graphics, creates exercises, and performs calculations

quickly and accurately. These are the computer's strengths.

3. Help students differentiate between inappropriate and appropriate uses of the computer. The student who masters the multiplication fact 3x7 can mentally calculate the prod- uct 30 x 7 much more quickly than someone generating the answer on the computer. However, knowing that 3 x 7 = 21 will usually not allow an elementary school student to beat a machine when calculating the solution to the problem, "If Maria can earn $13 per day for 7 days, what are her total earnings?" Still, students need to realize that the computer cannot interpret the problem, determine what operation to use, or automatically at- tach the correct units to the answer.

References Andersen, Lyle E. "Survey of Selected K-8

Minnesota Teachers [1984]." Montana State University, Bozeman.

National Council of Teachers of Mathematics. An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, Va.: The Council, 1980.

Phillips, Wayne R. "How to Manage Effec- tively with Twenty-five Students and One




Fig. 6

1 . For the band pictured:

row1 DDDDDDDDDD TTTT row 2 DDDDDDDDDD TTTT row 3 DDDDDDDDDD TTTT

Number of drummers? 10 Number of trombonists? 4 _x 3 x 3

Total number of players: Number of drummers = Number of trombonists = +

Total =

14 By the algorithm: X__J?-

2. For the band pictured:

row 1 DDDDDDDDDD TTT Number in row 1 = row 2 DDDDDDDDDD TTT Number in row 2 = row 3 DDDDDDDDDD TTT Number in row 3 = row 4 DDDDDDDDDD TTT Number in row 4 =

Total number of members in the band =

Then 4x13= and 13 x 4__

3. Draw a band using D for a drummer and T for a trombonist. There are 16 players in each row and each row has exactly 10 drummers. Draw the band if there is a total of 80 players.

row 1 row 2 row 3

•

4. Compute using paper and pencil; then check with the computer.

a) 16 b) 19 c) 12 d) 17 __x__5_ _ x 6 x 8 __2i-9__.

October 1988 45



Computer." Computing Teacher 10 (March 1983):32.

Appendix MULT is written in Apple BASIC for the Apple family of computers. 100 PRINT "THIS PROGRAM GROUPS

DRUMMERS AND TROMBONE PLAY- ERS INTO ROWS AND COLUMNS. "

110 PRINT 120 PRINT " YOU WILL BE ASKED TO DE-

TERMINE HOW MANY TROMBONE PLAYERS SHOULD BE ADDED TO ROWS ALREADY CONTAINING 10 DRUMMERS. " : PRINT : PRINT : PRINT

130 PRINT "YOU WILL THEN DECIDE HOW MANY OF THESE ROWS WILL MAKE UP YOUR BAND.11

140 PRINT : PRINT : PRINT : PRINT 11 PRESS ANY KEY TO CONTINUE. " 150 CALL - 756 160 HOME 170 V1 = 8 180 C1 = 0 190 H1 = 0 200 C2 = 0 210 C3 = 0 220 INPUT "HOW MANY TROMBONISTS

WOULD YOU LIKE TO ADD TO EACH ROW OF DRUMMERS? " ;T1

230 IF T1 < 1 THEN HOME : GOTO 220 240 IF T1 > 9 THEN HOME : GOTO 220 250 INPUT " HOW MANY ROWS? " ;R1 260 IF R1 < 1 THEN HOME : GOTO 250 270 IF R1 > 9 THEN HOME : GOTO 250 280 HOME 290 PRINT " » 300 FOR K = 1 TO 10:S = PEEK ( - 16336):

NEXTK 310 VTAB V1: HTAB 11: PRINT

"DDDDDDDDDD" 320 FORK = 1 TO 10:S = PEEK (- 16336):

NEXTK 330 HTAB 22 + H1 : VTAB V1 : PRINT " T " 340 REM USE 285 AS A BELL IF YOU

WISH. DO THIS BY TYPING PRINT, OPEN QUOTE, CONTROL G.CLOSE QUOTE

350 PRINT " " 360 C1 = C1 + 1 370 H1 = H1 + 1 380 IF C1 < T1 THEN 330 390 VTAB 18: HTAB 9: PRINT C2 + 1 "

ROW(S) OF " 10 + T1: PRINT 400 FOR Z = 1 TO 300: NEXT Z 410 C1 = 0 420 V1 = V1 + 1 430 C2 = C2 + 1 440 H1 = 0 450 IFC2<R1 THEN 310 460 A = T1:B = R1 470 VTAB 6: HTAB 8: PRINT "10 DRUM-

MERS "T1" TROMBONISTS" 480 VTAB 20: PRINT " HOW MANY ARE IN

THE BAND?" 490 VTAB 8 + R1 / 2: PRINT R1 " ROWS" 500 VTAB 22 51 0 PRINT " PRESS ANY KEY TO CONTIN-

UE": CALL -756 520 VTAB 22 " 530 PRINT " 540 VTAB 22 550 PRINT " 10 DRUMMERS + "A"

TROMBONISTS" 560 PRINT "X "B" X "B 570 PRINT " ":SUM = 10*B + A*B 580 IFA*B>9THEN600 590 PRINT" "10*B" + "A*B" =

"SUM: GOTO 610 600 PRINT" "10*B" + "A*B" = "SUM 610 PRINT: PRINT 620 VTAB 23: PRINT " PRESS ANY KEY" :

CALL - 756: VTAB 23: PRINT " " 630 HTAB 18

640 IF A * B > 9 THEN PRINT " " INT ((A*B)/10)

650 HTAB 18 660 PRINT " "10 + A 670 HTAB 18 680 PRINT "x " B 690 HTAB 18 700 PRINT " " 710 HTAB 18 720 IF (10 + A) * B > 99 THEN GOTO 760 730 HTAB 18 740 PRINT " "(10 + A)* B 750 GOTO 780 760 HTAB 18 770 PRINT " "(10 + A)* B

780 PRINT : PRÍNT " PRESS ANY KEY TO TRY ANOTHER PROBLEM": CALL - 756

790 GOTO 160

A copy of an Apple program that uses graphics to illustrate the trombonists and drummers can be obtained by sending a blank disk and $1 for postage to Glenn Allinger at the Department of Mathematical Sciences, Montana State Uni- versity, Bozeman, MT 59717. m




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Teacher-Computer Interaction in Teaching a Mathematics Lesson