The Effects of Large Class Procedures on AchievementAnd Attitude in a Mathematics CourseFor Prospective Elementary Teachers

Floyd Vest,B. G. Nunley,

and M. V. GarnerNorth Texas State University

Denton, Texas 76203

INTRODUCTION

Well known economic and administrative factors in both junior andsenior colleges suggest the utilization of large class instruction. Excellentsummaries of experimental research in this area are found in severalsources.2-5’6-7

THE PROBLEM

The purpose of this study was to compare a large class instructionprocedure with conventional small class instruction for a CUPM Level I,"Structure of the Number System" mathematics course for prospectiveelementary teachers. Such a course is offered by both junior and seniorcolleges. The treatments were compared on the basis of mathematicalachievement, and since it is often claimed that large class instruction isinadequate in terms of motivational and attitudinal learning outcomes,comparisons were also made on the basis of change in attitude towardarithmetic. This is a particularly important outcome for prospective ele-mentary teachers since there is evidence that a need for improvement ex-ists in this area, and teachers’ attitudes are likely to be perpetuated inchildren.3’4

PROCEDURE

For one semester, four small control classes (a total of 70 students)were taught by the conventional method�one teacher for each class,each class met three clock hours per week for the usual testing, lecture,and discussion procedure. One large experimental class of 98 studentswas taught by a large class procedure (LC treatment) in which they at-tended lecture with the same teacher for two clock hours per week in alarge classroom. The large lecture session was taught by the usual testing,lecture, and discussion as in small classes with perhaps somewhat lessdiscussion. The only teaching device used by the instructor in the largeclasses was a chalkboard. Each student in the experimental class also meta recitation session of about twenty students each for one clock hour perweek. All recitation sessions had the same teacher. The sessions discussedhomework and topics from the textbook.

607

608 School Science and Mathematics

The one large class and four small classes were all taught by differentexperienced teachers. One instructor conducted all the recitation ses-sions.

Experimental controls of teaching procedures were maintained. Allsubjects studied the first seven chapters in the same textbook.8 Home-work was assigned, graded, counted toward a course grade, and handedback in each class. The published policy on attendance was used in eachclass. All students were informed that the results of the administration ofthe evaluative instruments used in the experiment would not be used indetermining course grades.

All class meetings except recitation sessions were scheduled at 12 noon.An attempt was made to randomly assign students to treatments as theyappeared at the registration table. The analysis of the critical pre- andpost-data was conducted in terms of residualized gains.The evaluative instruments were:Mathematics Inventory I and II (MI)�multiple choice teacher-made

forms testing recall of the mathematical facts and principles of the coursewith a split-half corrected reliability coefficient of .87.LC Scale�a Thurstone type attitude scale which measures attitude to-

ward the experimental treatment with a reliability coefficient of .83based on the administration of two equivalent forms. Larger scores onthis eleven unit scale represent more positive attitudes toward the treat-ment.

Dutton Scale for Attitude Toward Arithmetic (D)�a Thurston scalefor measuring attitude toward arithmetic with a reliability coefficient of.94 based on test-and-retest. Larger scores on this eleven unit scale repre-sent more positive attitudes toward arithmetic 4.

Otis Quick-Scoring Mental Ability Test (Otis)�a commercial stand-ardized test of mental ability.

I Scale�a locally constructed evaluative scale based on the summativemodel providing student ratings of the teacher on critical items of teacherbehavior and management of the large class treatment. Larger scoresrepresent more positive attitudes toward the teaching behavior of the in-structor.

Questionnaire�a questionnaire for gathering personal and back-ground information from students.At the beginning of the semester, Mathematics Inventory I, LC Scale,

Dutton Scale for Attitude Toward Arithmetic, and the Otis Quick-Scor-ing Mental Ability Test were administered to all subjects. At the end ofthe semester, Mathematics Inventory II, LC Scale, Dutton Scale for Atti-tude Toward Arithmetic, and the personal information questionnairewere administered. The I-Scale was given to the experimental group atthe end of the semester.

Large Class Procedures 609

RESULTSA 2 x 2 analysis of variance was conducted with residualized gains re-

sulting from pre- and post-administration of Mathematics Inventory asthe dependent variable. As independent variables, students were strati-fied on the basis of two treatments consisting of experimental and con-trol and on the basis of two levels of mental ability (upper 50 per cent andlower 50 per cent as determined by the Otis Quick-Scoring Mental AbilityTest). The results of the analysis are reported in Table 1. As can be seenfrom this table the F ratio indicating differences in mathematicalachievement between the groups with high and low mental ability weresignificant as would be expected. The F ratio indicating difference inmathematical achievement between the treatments was not significant atthe .05 level. The F ratio indicating interaction between level of mentalability and treatment was not significant.

TABLE lSUMMARY OF ANALYSIS OF VARIANCE ON RESIDUALIZED GAINS

ON MATHEMATICS; TREATMENTS; AND MENTAL ABILITY

Source

TreatmentMental AbilityInteractionWithin Cells

Sum of Squares

113.24824.4730.49

7367.68

df

111

164

Mean Square

113.24824.4730.4944.92

F

2.5218.35***

.68

*** p<.001

Many would consider change in attitude toward arithmetic to be animportant dependent variable in content courses for prospective ele-mentary teachers. In order to study the effect of the treatments on thisimportant outcome, a 2 x 2 analysis of variance was conducted withresidualized gains resulting from pre- and post-administration of theDutton Scale for Attitude Toward Arithmetic as the dependent variable.As independent variables, students were stratified on the basis of experi-mental and control treatments and two levels of mental ability (upperand lower 50 per cent as determined by the Otis). The results are reportedin Table 2. From this table, one could conclude that the effect of treat-ment was not statistically significant at the .05 level in the area of changein attitude toward arithmetic.

TABLE 2SUMMARY OF ANALYSIS OF VARIANCE ON RESIDUALIZED GAINS ON ATTITUDE

TOWARD ARITHMETIC; TREATMENTS; AND MENTAL ABILITY

Source

TreatmentMental AbilityInteractionWithin Cells

Sum of Squares

1.18.64.37

154.40

df

111

164

Mean Square

1.18.64.37.94

F

1.25.68.40

610School Science and Mathematics

For all classes in the experiment, the mean resulting from the post-administration of the Dutton Scale for Attitude Toward Arithmetic wasgreater than from the pre-administration. Although these differenceswere not significant, one might conclude then that both treatmentstended not to have an adverse effect on students’ attitude toward arith-metic.

It seems reasonable that initial attitude toward the experimental treat-ment would have a significant effect on the mathematical achievementfor those in the experimental group. In effort to investigate this relation-ship, the upper and lower 50 per cent of the students in the experimentalgroup, as determined by scores resulting from the initial administrationof the LC Scale, were compared to see if they differed significantly inmental ability as determined by the Otis Quick-Scoring Mental AbilityTest. Since these groups were not significantly different at the .05 level,they were compared in terms of their mathematical achievement as mea-sured by residualized gains on Mathematics Inventory. See Table 3. Thedifference between the means was not significant at the .05 level indicat-ing that the initial attitude toward the experimental treatment did nothave an overriding differential effect on the mathematical achievementof the groups.

TABLE 3MEANS ON OTIS AND RESIDUALIZED MI OF GROUPS WITH HIGH AND LOW

INITIAL ATTITUDE TOWARD THE EXPERIMENTAL TREATMENT

OtisRes. MI

Upper 50% on Pre LCin Exp. Group

N = 49

Mean

55.22-.38

SD

7.327.34

Lower 50% on Pre LCin Exp. Group

N =49

Mean

54.82-.84

SD

8.695.86

t

.25

.34

The mean resulting from the post-administration of the LC Scale tothe large class (7.25) was greater than the mean resulting from its pre-ad-ministration (6.98). The scale was constructed in such a way that this dif-ference tends to indicate a more favorable attitude toward the experi-mental treatment at the end of the course than at the beginning. How-ever, this difference was not statistically significant (SD of difference =1.53,t = -1.76).The importance of the instructor as a determiner of students’ prefer-

ence for subsequent enrollment in classes taught by the experimental pro-cedure was demonstrated by replies to the following two items includedin the LC Scale:

Large Class Procedures 611

1. If I have the option next semester of enrolling in either a LC section or a convention-al section of a particular course, and if both sections are taught by the same in-structor (whom I like) and the sections are both given at desirable hours, I woulddefinitely prefer the conventional class.

2. If I had the option next semester of enrolling in either a LC section or a conventionalsection of a particular course, and the LC section is to be taught by an instructorwho has the reputation of being an excellent teacher, whereas I will have to take mychances on the instructor assignment in the conventional section, I would choose theLC section.

After a semester of large class instruction, 51 per cent definitely pre-ferred a conventional class when the instructor was constant; 84 per centindicated that they would rather be taught in a large class by an excellentinstructor than in a conventional class by an unknown instructor.

Since all of the students involved in the experiment attended class at 12noon, it was possible to study the often considered important relation-ship between achievement and the total number of hours spent in class inthe morning before attendance of the class in question. The range wasfrom zero hours in class to four hours in class before 12 noon. It is oftenconjectured that the student who spends as much as four hours in class isseverely handicapped in the fifth hour class. A simple correlation coeffic-ient between achievement as measured by residualized gains on MI andhours in class on a total of 168 students was .065 and not significant atthe .05 level.As a result of student unrest and complaints of depersonalization of

instruction, students’ view of the quality of personalization of the largegroup instruction was considered to be an important variable in thestudy. Several items on the LC Scale were addressed directly to the per-sonalization element of instruction. Students were asked to agree or dis-agree with the following three statements:

1. LC instruction procedures are too impersonal for me.2. I really don’t see any difference between the desirability of thetype of interpersonal contact with students and teachers in LCclasses and that in conventional classes.3. I think that the diminished contact with the instructor resultingfrom LC instruction could be a disadvantage.

It should be noted that these items were placed on the scale because ofdispersion of ratings by judges rather than their logical relationships toone another. The percentage of agreements with these statementsexpressed by the experimental group at the beginning and end of the se-mester are presented in Table 4. Those students who initially consideredLC instruction too impersonal were in the minority with even fewer indi-cating this feeling at the end of the term. From these responses, it seemsthat at least half of the subjects exposed to the large class instruction feltno strong objection to the level of personalization, and several subjectsraised their evaluation of the quality of personalization.

612 School Science and Mathematics

TABLE 4EXPERIMENTAL SUBJECTS’ EVALUATION OF PERSONALIZATION OF LC TREATMENT

Statement

LC Instruction too impersonalDon’t see any differenceDiminished contact with instructor a disadvantage

Per Cent Agreeing

PREN=98

364358

POSTN=98

205248

SUMMARY: FINDINGS AND CONCLUSIONS

On the basis of these findings and under the conditions of the study,the following general summary seems warranted:

1. For prospective elementary teachers taught by the experimental large classprocedure, achievement in the areas of mathematical knowledge and attitude towardarithmetic was not significantly different from that of those taught by conventionalsmall class procedures.

2. The large class experimental procedure and conventional small class procedure didnot seem to produce a differential effect or interaction with levels of mental ability,or levels of initial attitude toward the experimental treatment.

3. The majority preferred to be taught in large groups by a good teacher to being taughtin small groups by an unknown teacher. About half of the subjects expressed astrong preference for small class instruction when other conditions are equal.

4. At least half of the subjects did not mind the quality of personalization in large classinstruction.

Such findings as these tend to lead to the conclusion that althoughlarge class instruction comes under attack from time to time, bothaffective and cognitive learning outcomes can under appropriate condi-tions and in several ways be comparable to those of instruction in smallerclasses.

REFERENCES

1. COMMITTEE ON THE UNDERGRADUATE PROGRAMS IN MATHEMATICS, (1964). CourseGuides for the Training of Teachers of Elementary School Mathematics (Fourth Draft).Berkeley, Calif., Committee on the Undergraduate Programs in Mathematics, Mathe-matical Association of America.

2. DE CECCO, J. P. (1964). Class size and co-ordinated instruction, Brit. J. Educ.Psychol., 34, 65-74,

3. DUTTON, W H., (1954). Measuring attitudes toward arithmetic. Elem. Sch. J., 65, 24-31.

4. DUTTON, W. H., (1962). Attitude change of prospective elementary school teachers to-ward arithmetic, Arithmetic Teacher J., 418-424. (The scale used in this study is in Table1 on page 419).

5. GAGE, N. L. (Ed.), (1963). Handbook’ on Research in Teaching, Chicago, RandMcNally.

6. HARRIS, C. W. (Ed.), (1960). Encyclopedia of Educational research, 3rd Ed., NewYork, Macmillan.

7. NELSON, W. B., (1959). An experiment with class size in teaching elementaryeconomics, Educ. Rec. 40, 330-341.

8. PETERSON, J. A. and HASHISAKI, J., (1967). Theory of Arithmetic, 2nd Ed., New York,JohnWiIey. ____________