comparative achievement with departmentalized and self-contained classroom organization

Comparative achievement with departmentalized and self-contained classroom organizationAuthor(s): EDETTE B. PRICE, ARTHUR L. PRESCOTT and KENNETH D. HOPKINSSource: The Arithmetic Teacher, Vol. 14, No. 3 (MARCH 1967), pp. 212-215Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187270 .

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Comparative achievement with departmentalized and self-contained classroom organization EDETTE B. PRICE, ARTHUR L. PRESCOTT, and KENNETH D. HOPKINS

Miss Price and Mr. Prescoti are professors at the University of Southern California, Los Angeles, California, and Mr. Hopkins is a professor at the University of Colorado, Boulder, Colorado.

L he most advantageous organizational structure for elementary classrooms has been the subject of much discussion in educational literature. Departmentalization was common practice through the twenties and thirties, declined during the forties, and then returned in popularity.1' 2 The departmentalized classroom organization provides a "teacher-specialist" for each of the subjects taught. In the self-contained classroom, one teacher instructs a class of children of a given grade in all the curricular areas. The advocates of departmentalization have emphasized the superiority in having a specialist teaching each subject, the implication being that greater learning would accrue.

A review of the available research on achievement under elementary classroom departmentalization yielded few carefully designed studies, with considerable inconsistency in findings. Hosley found significantly greater grade placement gains for the self-contained organizational pattern in most achievement areas.3 Jackson found

no differences in arithmetic achievement of sixth-graders under departmentalized and semi-departmentalized classroom organization.4 Gibb and Mátala found higher achievement for departmentalized science but not for arithmetic.5 Gerberich and Prall reported significant differences in certain achievement areas, but with inconsistency in direction, favoring both patterns of classroom organization.6 Other studies have yielded inconclusive results due in part to the absence of statistical treatment of their data.

It is apparent from the review of the literature on departmentalization that no general conclusion can be drawn regarding its relative instructional efficiency in arithmetic or in other curricular areas. The present investigation attempted to employ a more comprehensive statistical approach in analyzing elementary school achievement in arithmetic reasoning, arithmetic concepts, and arithmetic computation under departmentalized and self-contained classroom organization.

1 R. C. Anderson, "The Case for Teacher Specializa- tion in the Elementary Schools," Elementary School Journal, LXII (1962), 253-60.

2 J. J. Goodlad, "Classroom Organization," in Ency- clopedia of Educational Research, ed. C. W. Harris and Marie Liba (3rd ed.; New York: The Macmillan Co., 1960), pp. 221-26.

3 C. T. Hosley, "Learning Outcomes of 6th Grade Pupils Under Alternate Grade Organization Patterns" (Unpublished Ed.D. thesis, Stanford University, 1954).

4 J. Jackson, "The Effect of Classroom Organization and Guidance Practice upon the Personality Adjust- ment and Academic Growth of Students," Journal of Genetic Psychology, LXXXII (1953), 159-70.

5 E. Glenadine Gibb and Dorothy C. Mátala, "Study on the Use of Special Teachers of Science and Mathe- matics in Grades 5 and 6," School Science and Mathe- matics, LXII (1962), 565-85.

8 J. R. Gerberich and C. E. Prall, "Department Organization Versus Traditional Organization in the Intermediate Grades," Elementary School Journal, XXXI (1931), 671-77.

212 The Arithmetic Teacher



Procedure

The investigation used two neighboring Los Angeles City elementary schools for the experimental and control samples. Both schools had three full classes of fifth-grade pupils, with an overflow into a fifth-sixth combination class. These pupils placed in the combination classes were eliminated from t;he study because of the contaminat- ing effect of the additional variable of multigrade grouping and the inconsistency in selection criteria. The four departmentalized teaching assignments were social studies, reading, English and science, and arithmetic and art. Each teacher also taught physical education on a rotating schedule. Each school attempted to make teacher assignments on the basis of special competence and interests.

All subjects were administered the Cali- fornia Test of Mental Maturity (1957 S-Form) and the California Arithmetic Tests (Form W) in October 1963 as part

of the regular testing program. In June 1964 the three SRA Arithmetic Tests (Form A) were given to all pupils in the experimental and control classes. Usable results on 173 subjects were obtained. 97 and 76 for experimental and control schools respectively. In addition to the test data, the participating teachers and administrators of the two schools were given questionnaires in order to elicit rele- vant nontest factors.

The statistical design utilized a 2 X 2 X 2 (classroom organization, by level of intelligence, by sex) multiple analysis of covariance. Before testing for significance was done, this model statistically equated the groups on each of these variables: age, language IQ, nonlanguage IQ, total IQ, and the pretests (the CAT Arithmetic Reasoning Test and the CAT Arithmetic Fundamentals Test). The statistical equat- ing was indispensable, since the control school had somewhat lower pretest per- formance. The comparative data for the

Table 1

Unadjusted raw score means and standard deviations of dependent variables and covariants

Control Experimental _(JV = 76) (N = 97) X s Us

DEPENDENT VARIABLES*

SRA Achievement Series

Arithmetic reasoning 26.29 9.32 31.23 7.56 Arithmetic concepts 12.36 4.71 14.78 3.25 Arithmetic computation 22.78 8.84 26A9 5Ì94

COVARIANTSt

Age (in months) 123.76 4.06 123.00 4.39

California Test of Mental Maturity

Language IQ 104.76 17.48 117.21 15.35 Nonlanguage IQ 103.07 21.47 116.51 18 22 Total IQ 104.04 17.69 117.03 14.39

California Achievement Tests

Arithmetic reasoning 25.63 7.40 32.16 4.94 Arithmetic fundamentals 30.26 8.60 36.36 7.42

* Tests administered in June 1964. t Tests administered in October 1963.

March 1967 213



Table 2

F-ratios from covariance analyses on the SRA Achievement Series*

SRA Achievement Series Arithmetic

Source of variation Reason- Compit- ai ing Concepts tation

Classroom organization (CO) 1 1.04 c 3.45 Intelligencet 1 ct 2.16 c Sex lece CO X intelligence 1 e 10.45§ e CO X sex 1 2.26 c 1.97 Intelligence X sex lece CO X intelligence X sex Ice 1.98 Error MS 159 31.42 7.37 26.73

166

* F-ratios, degrees of freedom, and error mean squares only are given; all other desired data can be reconstructed from these, since a fixed-effects analysis-of-covariance model was employed.

t Intelligence was used as a covariant, therefore no significant intelligence main effect would be expected; intelligence levels were above and below IQ 110.

te = F <1.0 § P < .01

experimental and control subjects on the SRA Arithmetic Reasoning, Concepts, and Computation Tests were analyzed using the BIMD 14 computer program, which allows inequality of cell frequencies. The IBM 7094 computer at the Western Data Processing Center performed the statistical analysis, for which gratitude is expressed.

Results

The unadjusted means and standard deviations for the experimental and control group on the SRA Arithmetic Tests, Cali- fornia Arithmetic Tests, and the California Test of Mental Maturity (CTMM) are found in Table 1.

Since the groups differed significantly in IQ and pretest achievement, only after the groups were equated on critical variables such as IQ and pretest scores through the use of multiple analysis of covariance could a meaningful comparative evaluation be made. The requirements of parallel regression lines and homogenous variances were tested and satisfied. The results from such analyses of covariance are given in Table 2.

Only one of the twenty-one comparisons reached the .05 level of significance; an interaction of minor consequence was ob-

served between organizational pattern and intelligence level on arithmetic concepts. This interaction resulted from relatively less achievement differential between high and low intelligence groups under departmentalization, although total group means did not differ.

A fifteen-item questionnaire was returned by five of the six personnel in- volved in each of the schools. The items pertained to teacher load, learning time, pupil interest, scholarship, teacher knowl- edge of pupils, classroom control, subject- matter emphasis, teacher responsibility, teaching specialization, supervision, and equipment use. Both groups tended to favor the purported "logical advantages" of departmentalized approach in relation- ship to each of the above factors. Differ- ences between the two groups' responses were not statistically significant.

Summary The findings of this investigation in-

dicated that departmentalization with its "teacher-specialists" was not associated with higher achievement in the three areas of arithmetic skills measured by the SRA Arithmetic Reasoning, Concepts, and Com- putation Tests, even though the teachers

214 The Arithmetic Teacher



viewed it as being advantageous. A clear implication from the study is that classroom organization is no panacea and does not, per se, increase pupil achievement in arithmetic at the intermediate grades, at least during its initial year. Perhaps, with additional experience, the "logical advantages" of departmentalization can be tapped

to allow superior arithmetic achievement. It should be noted that the experimental

school used the same curricular scope-and- sequence guides as the control school. A differing organizational pattern, such as departmentalization, may necessitate curricular revision to take full advantage of any unique feature it offers.

The mathematics of supermarket shopping (Continued from page 211)

one can build up over a. period of years with constant revision and addition to those that have already proved successful!

An interesting activity is provided by comparative shopping. For example, which is the better buy - three one-pound cans of Red Feather brand tomatoes for 49¿ or one one-pound-twelve- ounce can of the same brand for 31^?

Surprisingly enough, the larger can (usually thought to be more economical) is, in this instance, more expensive. These are actual fig- ures taken from cans on a supermarket shelf; only the brand name is fictitious.

This problem becomes compounded when you taken into account the numerous different brands and methods of packaging. Bathroom tissue, for example, comes in rolls of 350, 500, or 1,000 sheets. Some of the rolls, however, are single- ply, while others are double-ply. Different brands are sold in units of three, four, five, six, or even ten rolls per package. Could you make an in- stantaneous decision as to which choice gives the best return for the purchase price? Soda pop offers another interesting challenge, for it comes packaged in ten-ounce, twelve-ounce, and four- teen-ounce bottles, which can come in four- or six-pack cartons of either throwaway or re- turnable bottles.

To implement this activity, the teacher can gather plenty of supermarket prices with which the students can practice directly; or the students themselves, after sufficient introduction to the problem, can be given the assignment of collecting the data. Some students might be charged with investigating the price-weight ratios of various brands of canned vegetables or fruits. Others might inquire into the relative costs of soap powders, or of meats, or of any of the many commodities on the shelves. If possible, however, the most impressive introduction to this problem would be a pre- arranged trip to the neighborhood supermarket by the class as a whole. A field trip of this type may often add just that flavor of being "different" that can stimulate interest. Perhaps an affable supermarket manager might be prevailed upon to say a few words or to conduct a guided tour of behind-the-scenes areas where meats and produce are cut, weighed, packaged, and priced.

In addition to the wealth of mathematical computation inherent in this activity, there are the budgeting, moral, and social implications as well. No one can question the practicality of such an exercise for the development of the citizen consumer. - William Kosicki.

March 1967 215



comparative achievement with departmentalized and self-contained classroom organization

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