Psychological Reports, 1990, 66, 531-538
@ l'sychological Reports 1990
STRUCTURE O F LEARNING ENVIRONMENT VARIABLES UNDER TWO INSTRUCTIONAL CONDITIONS ' BIKKAR S. RANDHAWA University of Saskatchewan Summary.-The present study investigated the congruence between the factor structures of the learning environment and cognitive variables for mathematics and English courses in Grade 10. T h e e common factors were obtained in each course. Procedural characteristics and cognitive factors in mathematics were highly similar to the corresponding factors in English. However, the formative characteristics factor identified in mathematics was not congruent to the corresponding factor in English. Learning environment variables produced two factors. These factors resembled the congruent factor properties for the two courses when the learning environment and cognitive variables were factor analyzed together. Implications for learning and instructional research are mentioned.
I n discussing theoretical, methodological, and practical issues it has been concluded that perceptions of learning environments are useful as independent, mediating, and dependent variables (see Moos, 1979; Randhawa & Fu, 1973; Shulman & Tamir, 1973; Walberg, 1974). Academic courses have shown reliable differences on a variety of social-psychological environment variables (Anderson, Walberg, & Welch, 1969; Moos, 1979; Randhawa & Michayluk, 1975; Walberg, 1969). However, the structural similarity of these variables across different academic courses has not been investigated. Great dissimilarity among variables is unlikely because pedagogical practices in various academic courses have much in common. Structural similarities in the general procedural dimension are expected, as are differences among those characteristics representing unique properties of the academic courses. Different requirements, expectations, levels of difficulty, precision, competition, and speed of two courses might be perceived differently by the same students. These properties of courses are either inherent or emerge as a function of the instructional approaches and are called here formative characteristics (Randhawa & Hunt, 1976). O n the other hand, classroom organization, material resources such as manipulatives, library materials, and audiovisual aids, students' own interests and satisfaction are not subject to as much variability as the formative characteristics across courses. These perceived properties of classrooms are referred to as procedural characteristics (Randhawa & Hunt, 1976). Schools in general have common operational procedures for discipline, attendance, and other opportunities.
'Address re uests for reprints to B. S. Randhawa, Department of Educational Psychology, Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OWO. University
07
532
B. S. RANDHAWA
Hypothesized course-specific differences on emerging formative characteristics of perceived learning environments may also be expected in different grades. With development individuals become more discerning and exhibit more critical differentiation of preferences (Reese & Lipsitt, 1770). In fact, Randhawa and Hunt (1976) reported relative stability across grades on the procedural dimension of the learning environment of classrooms, whereas the formative characteristics factor for the two grades showed poor congruence. The present study was designed to investigate the factor analytic congruence of the structures of learning environment variables in mathematics and English courses.
METHOD
Sample Three hundred seventeen students in Grade 10 from three high schools in a small city of about 20,000 inhabitants in a midwestern province in Canada were subjects. Students were enrolled in Grade 10 mathematics and English courses. All Grade 10 students enrolled in a parochial girls' high school (71) and in a parochial boys' high school (80) participated in the study. There were three classes at each school. From the secular high school six of the 14 Grade 10 classes were selected randomly and from these six classes 8 1 girls and 85 boys provided complete and usable data. It can be assumed that subjects represented the socioeconomic and sex mix of the grade population in that city.
Procedure The students from each school were randomly assigned to two groups. The Learning Environment Inventory (Anderson, 1971), the Otis-Lennon Mental Abllity test (Otis & Lemon, 1768), and the Sequential Tests of Educational Progress (Educational Testing Service, 1771) in reading, spelling, capitalization, English expression, mathematics computation, and mathematics basic concepts were administered in five different sessions to students assembled in a large room within each school. However, the students in one group (157), mathematics course, were told to complete the inventory to reflect as accurately as possible perceptions of the learning situations of their mathematics class while the other group (160), English course, completed the inventory for their English class. The inventory consists of 105 Likert-type items comprising 15 scales of seven items each. These scales are identified as cohesiveness, dversity, formality, speed, environment, friction, goal direction, favoritism, difficulty, apathy, democratic, cliqueness, satisfaction, disorganization, and competitiveness. Reliability and vahdity data on the Learning Environment Inventory are given by Anderson (1971).
533
LEARNING ENVIRONMENT TABLE 1 PEARSON CORRELATION MATRICES OF RESPONDENTS IN MATHEMATICSA N D ENGLISH* Variable 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Reading Spelling Capitalization English Expression Math Computation Math Basic Concepts Otis-Lennon Cohesiveness Diversity Formality Speed Environment Friction Goal Favoritism CLiqueness Satisfaction Disorganization Difficulty Apathy Democratic Competitiveness
1. Rea&ng 2. Spelling 3. Capitalization 4. English Expression 5. Math Computation 6. Math Basic Concepts 7. Otis-Lennon 8. Cohesiveness 9. Diversity 10. Formality 11. Speed 12. Environment 13. Friction 14. Goal 15. Favoritism 16. Cliqueness 17. Satisfaction 18. Disorganization 19. Difficulty 20. Apathy 21. Democratic 22. Competitiveness 'The lower triangular matrix is
1
2 53
50 54 70 52 54 78 -11 -13 -05 -15 -12 -35 00 -28 -22 09 -20 04 04 23 -15 11 08 04 04 09 10 13 06 01 14 -22
65 60 39 27 50 -13 -00 -03 -07 -19 -15 -06 -11 -08 -09 -01 07 08 15 -15 -15 -14 -20 -14 -03 -04 -14 -08 24 13 28 -12
3 59 67 72 58 46 60 -02 13 -06 -18 -07 -14 -09 -25 -05 02 -05 06 10 23 -17 -04 06 06 07 -08 -12 -05 21 10 31 -21 30 -17
-09 29 -18 -09 26 -32 -10 61 -18 33 -10 31 -22 36 -42 -10 -15 -02 -17 27 -37 03 -25 20 09 45 05 for mathematics
4
5 73 63 73
55 53 75 -05 -04 -00 -10 -12 -22 -07 -19 -10 -01 -09 08 10 18 -16 -16 -22 -29 -20 -15 -18 -19 09 -14 -01 22 -24 18 -23
6
7
58 43 58 59
43 37 51 48 68
64 65 -09 04 -11 -20 -09 -15 04 -27 -03 02 -07 08 15 24 -02 06 07 -01 07 07 11 08 -08 14 -07 07 -07 44 -23 10
63 04 06 -02 -21 08 -16 -04 -22 -04 13 -07 -02 02 24 03 03 10 10 03 -02 -04 02 08 -03 02 -35 41 -40 41 -35 -37
8
9
75 05 50 13 62 11 72 03 74 -01 61 11 -01 -07 -06 09 -02 06 -15 -10 -10 19 -27 09 -03 -03 -24 08 -13 -12 07 06 00 -16 11 -26 12 -02 27 -14 -08 03 -21 -22 -31 -18 -17 -08 -20 -00 09 -12 32 -33 52 -37 35 36 -54
01 -09 -02 02 13 22 06 05 08 29 31 -08 18 -16 12 09 -35 25
1 09 19 14 17 -03 10 06 02 20 -10 22 13 07 -00 14 02 12 -01 -10 22 16 05 -14 -11 -01 07 04 01 -20 -13 -10 24 -25 34 -34 29 25 -53 45 24
0
1 -07 -07 -13 -07 -11 -01 -15 03 18 12 19 03 25 09 05 14 19 14 24 02 23 05 06 10 05 06 07 14 -01 -12 02 -22 34 -30 25 -44 -23 44 -38 27 -28
1 -00 -04 -11 -04 10 10 -01 -11 08 14 13 -05 -18 11 -02 -32 07 45 -04 -I8 06 -02 -14 -02 -02 03 05 05 05 25 15 15 03 34 -03 09 28 -17 19 18 10 -17
18 -31 -11 33 32 -48 -16 -07 -30 04 13 25 -28 37 05 -43 -20 17 -19 02 13 14 33 02 11 -02 10 -01 and the upper triangular matrix is for English.
B. S. RANDHAWA
Analysis For the analysis of data from the Sequential Tests of Educational Progress and the Learning Environment Inventory, raw scores were used, but for the Otis-Lennon, raw scores were converted into the corresponding deviation IQs. The correlation matrices of the mathematics and English contexts for the 22 variables were computed and are given in Table 1. The mathematics context correlation matrix was analyzed by the method of iterative principal components (Harman, 1967). Three principal components with eigenvalues greater than 1.0 were retained. This decision was checked by Cattell's (1966) scree test. These principal components were transformed to a simple structure using the normalized varimax procedure (Kaiser, 1958). The English correlation matrix was also analyzed using the methods of analysis given above. As before, three principal components were retained and then orthogonally rotated by employing the normalized varimax procedure. The three English course components were again orthogonally rotated to make this factor solution as sirmlar as possible to the varimax factor structure obtained for the mathematics course. The procedure used was developed by Cliff (1966), and results in an orthogonal transformation which, when applied to the matrix of interest, produces a matrix which is maximally similar to the criterion matrix. The coefficient of congruence produced for a pair of maximally similar factors indicates the extent of their similarity. These coefficients are evaluated only subjectively because no statistical test of significance is available. Evans (1970) suggests coefficients of .90 or higher indicate "good" correspondence, coefficients from .80 to .90 show "fair" correspondence, coefficients from .70 to .80 indicate "poor" correspondence, and coefficients lower than .70 show no correspondence between a pair of factors. An analysis similar to the one reported above was also made for the 15 variables in the inventory. This 15 x 15 matrix produced two common factors for each course context for which an orthogonal congruence transformation was found.
RESULTSAND DISCUSSION The communalities for the variables and the factor structures for the mathematics and English courses are given in Table 2. Three common factors in the mathematics course accounted for 38.6% of the total variance in 22 variables. The corresponding variance accounted for in the English course was 41.3%. For the two courses a clearly distinct and specific common factor, Factor I, with significant loadings on the Sequential Tests and the -
-
-
'A cable of means and standard deviations is on file in Document NAPS-04760. Remit $7.75 for photocpy or $4.00 for fiche to Microfiche Publications, POB 3513, Grand Central Station, New York. NY 10017.
535
LEARNING ENVIRONMENT
Otis-Lennon Mental Ability test, emerged. Factor I was defined as the cognitive environment or intellectual climate factor. This factor in the two courses was highly sirmlar, with a congruence coefficient of .97. TABLE 2 CRITERIONFACTORLOADING WTRM ( M A ~ A T I C AND S) CONGRUENT ORTHOGONAL FACTORA ~ T R L (ENGLISH) X* Subtests/Scales
Mathematics
English I1
hZ
I
I1
111
h2
I
67 42 61 72 56 50 76 05 10 07 22 26 69 35 27 43 49 48 15 30 20 22
78 61 78 83 74 69 87 -07 03 -08 -25 -09 -22 -04 -31 -08 09 -11
-10 12 06 06 01 -08 -03 -07 -05 -21 17 -42 50 -58 41 46 -61 68
62 45 66 71 61 46 76 03 23 30 22 24 48 41 27 23 63 57 22 41 31 25
78 67 81 84 77 67 87 06 14 -09 -02 13 -15 00 -27 07 06 -26 05 -04 11 01
03 -09 -10 01 12 12 05 -12 04 -12 43 -44 53 -56 43 44 -79 71 37 63 -54 24
-07 -01 -05 00 -04 08 -07 11 46 53 17 19 42 31 -07 18 -03 09 29 -11 -09 44
Total Variance 849 Congruence Coefficient *Decimal points are ommitted.
909
461 97
332 94
155 50
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Reading Spelling Capitalization English Expression Math Computation Math Basic Concepts Otis-Lennon Cohesiveness Diversity Formality Speed Environment Friction Goal Direction Favoritism Chqueness Satisfaction Disorganization Difficulty Apathy Democratic Competitiveness
03
11
13 32 -11
53 -32 14
-21 -18 -03 -15 04 14 -11 19 30 12 -36 28 62 09 07 46 33 07 -37 06 01 43
462
244
144
I11
The other two common factors were defined by scales of the inventory. An examination of the absolute loadings which were largest on any single factor, gave Factor I1 (in the case of the mathematics course) defined by the formality, environment, friction, goal direction, favoritism, cliqueness, satisfaction, disorganization, apathy, and democratic scales. These scales seem mostly to pertain to procedural aspects of academic courses and are probably unlikely to be sensitive to group interactions. For the English course a highly similar factor was obtained. The formality scale, was an exception, having a very low communality but a small negative loading on Factor I1 in mathematics. I n contrast, it had an acceptable communality (.30) but did not load on Factor I1 in the English course. Another exception was that the difficulty
536
B. S. RANDHAWA
scale was included in Factor I1 for the English course but not in the mathematics course. I n spite of these exceptions, Factor II's coefficient of congruence was .94. This indicates that Factor 11, representing procedural characteristics, was similar in the two courses as expected. For the mathematics course friction, cliqueness, and competitiveness had factor loadings of .62, .46, and .43, respectively, on Factor 111. Cliqueness emerged as a complex variable, loading equivalently on both Factors I1 and 111. Also, the friction scale appeared somewhat complex because it produced the highest loading on Factor I11 but had a substantial loading (SO) on Factor 11. Four other scales of the Learning Environment Inventory, cohesiveness, diversity, speed, and difficulty, may be considered to define Factor 111 for the mathematics course because these scales had the highest (albeit small) loadings on Factor 111. These low loadings are not surprising because the scales had very low communalities. Therefore, Factor I11 could be defined as a weak formative characteristics factor. The formative nature of this factor is evident from the fact that most of the scales underlying this factor are sensitive to group rather than individual characteristics and the characterization of these behaviors is dependent upon the past experiences of the class groups. A weak formative characteristics factor was also obtained for the English course. For this situation, Factor I11 had significant loadings on diversity, formality, friction, and competitiveness. Friction again appeared to be a complex variable but it did not have the highest loading on Factor I11 as was the case with the mathematics course. Cliqueness and difficulty did not define this factor for the English course as they did in mathematics. These similarities and differences in this pair of factors for the two courses were confirmed by a very low coefficient of congruence (0.50). The factor structures of the 15 variables of the Learning Environment Inventory for the mathematics and English courses are given in Table 3. Two factors for the mathematics course accounted for 26.6% of the total variance, whereas for the English course the variance accounted for was 30.8%. This analysis was done to determine whether these variables would produce factor structures which were generally similar to the factors based on the Learning Environment Inventory for the two courses when the cognitive measures were also included with the inventory variables. As can be seen from the results in Table 3, the two factors were almost identical to the ones presented earlier in Table 2. As indicated by a congruence coefficient of .93 between the pair of Factor Is for the two courses, the procedural characteristics factor was similar. The obtained Factor 11s (formative characteristics) were not similar for the two courses. I t appears that the inventory's factors have a structural property which is unaffected by the cognitive variables of context but is sensitive to the instructional context.
LEARNING ENVIRONMENT TABLE 3 CRITERION FACTOR LOADING MATRIX(MATHEMATICS) AND CONGRUENT ORTHOGONAL MATRIX*(ENGLISH) FORLEARNING ENVIRONMENT INVENTORY SCALES FACTOR Scale
Mathematics b2
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Cohesiveness Diversity Formality Speed Environment Friction Goal Direction Favoritism Cliqueness
Satisfaction Disorganization Difficulty Apathy Democratic Competitiveness Total Variance Congruence Coefficient *Decimal points are omitted.
04 09 08 11 23 73 35 22 42 49 47 13 24 14 24 399
1 -01 -01 -16 15 -33 64 -54 47 54 -55 68 04 49 -37 24 258
I1 20 30 23 -30 35 56 23 04 36 44 -08 -36 -09 00 43 141
h' 02 21 26 21 26 48 39 22 22 63 54 20 39 32 26 462
English I -09 16 04 45 -39 64 -44 43 46 -77 73 41 57 -56 35
I1 13 43 51 04 32 25 44 -20 06 19 -13 17 -27 08 38
350 93
113 70
I n a large study involving 96 classrooms of Grades 8 and 11, Randhawa and Hunt (1976) reported that the factor structure stability of the Learning Environment Inventory and cognitive variables was dependent upon grade. They found, as in the present study, that the formative characteristics factor was less stable. I t seems that the procedural characteristics do not change across curricula, however a larger variety of curricula must be investigated before such results are generalized. Scales pertaining to the formative characteristics factor could provide useful data for evaluating instructional and curriculum interventions. Diversity, formality, speed, and competitiveness scales of the inventory may provide critical measures of formative characteristics for determining resultant changes from instructional and/or curriculum changes. Incongruity of the emerging properties of classes across grades (Randhawa & Hunt, 1976) and curricula (the present study) would render these characteristics sensitive to unusual effects. Instability of factor structure should not be interpreted to mean that scales defining the factor are themselves unstable. REFERENCES ANDERSON,G. J. (1971) The assessment of learning environments: a manual for the Learning Environment Inventory and the My Class Inventory. of Education.
Halifax, Canada: Adantic Institute
ANDERSON, G. J., WALBERG, H. J., & WELCH,W. W. (1969) Curriculum effects on the social
538
B. S. RANDHAWA
climate of learning: a new representation of discriminant functions. American Educational Research Journal, 6, 315-328. CATITELL, R. B. (1966) The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276. CLIFF, N. (1966) Orthogonal rotation to congruence. Psychometrika, 31, 33-42. TESTINGSERVICE.(1971) Teacher's manual for STEP Series II. Princeton, NJ: EDUCATIONAL Educational Test~ngService. EVANS,G. T. (1970) Congruence transformation: procedures for comparing the results of factor analyses involvm the same set of variables. (Unpublished manuscript, Ontario Institute for Studies in ~ ~ c a t l o n ) HAMAN, H. H. (1967) Modern factor analysis. (2nd ed.) Chicago, IL: Univer. of Chicago Press. KAISER,H . F. (1958) The varimax criterion for analytic rotation in factor analysis. Psychomeirika, 23, 187-200. Moos, R. H. (1979) Evaluating educational environments. San Francisco, CA: Jossey-Bass. O n s , A. S . , & LENNON, R. T. (1968) Otis-Lennon Mental Ability Test: manual for administration. New York: Harcourt. RANDHAWA, B. S., & Fu, L. W. (1973) Assessment and effect of some classroom environment variables. Review of Educational Research, 43, 303-32 1. RANDHAWA, B. S., & HUNT, D. (1976) Factors in classroom environment variables. Journal of Educational Psychology, 68, 546-549. RANDI-IAWA, B. S., & MJCHAYLUK, J. 0 . (1975) Learning environment in rural and urban classrooms. American Educational Research Journal, 12, 265-285. REESE, H . W., & LIPSITT, L. P. (1970) Experimentnl chiM pxychology. New York: Academic Press. SHULMAN, L. S., & T m , P. (1973) Research on teaching in the natural sciences. In R. M. W. Travess (Ed.), Second handbook of research on teaching. Chicago, IL: Rand McNally. Pp. 1098-1148. WALBERG,H. J. (1969) Social environment as a mediator of classroom learning. Journal of Educational Psychology, 60, 443-448. WALBERG, H. J. (Ed.) (1974) Evaluating educational performance: a sourcebook of methods, instruments, and examples. Berkeley, CA: McCutchen. Accepfed February 21, 1990.
@ l'sychological Reports 1990
STRUCTURE O F LEARNING ENVIRONMENT VARIABLES UNDER TWO INSTRUCTIONAL CONDITIONS ' BIKKAR S. RANDHAWA University of Saskatchewan Summary.-The present study investigated the congruence between the factor structures of the learning environment and cognitive variables for mathematics and English courses in Grade 10. T h e e common factors were obtained in each course. Procedural characteristics and cognitive factors in mathematics were highly similar to the corresponding factors in English. However, the formative characteristics factor identified in mathematics was not congruent to the corresponding factor in English. Learning environment variables produced two factors. These factors resembled the congruent factor properties for the two courses when the learning environment and cognitive variables were factor analyzed together. Implications for learning and instructional research are mentioned.
I n discussing theoretical, methodological, and practical issues it has been concluded that perceptions of learning environments are useful as independent, mediating, and dependent variables (see Moos, 1979; Randhawa & Fu, 1973; Shulman & Tamir, 1973; Walberg, 1974). Academic courses have shown reliable differences on a variety of social-psychological environment variables (Anderson, Walberg, & Welch, 1969; Moos, 1979; Randhawa & Michayluk, 1975; Walberg, 1969). However, the structural similarity of these variables across different academic courses has not been investigated. Great dissimilarity among variables is unlikely because pedagogical practices in various academic courses have much in common. Structural similarities in the general procedural dimension are expected, as are differences among those characteristics representing unique properties of the academic courses. Different requirements, expectations, levels of difficulty, precision, competition, and speed of two courses might be perceived differently by the same students. These properties of courses are either inherent or emerge as a function of the instructional approaches and are called here formative characteristics (Randhawa & Hunt, 1976). O n the other hand, classroom organization, material resources such as manipulatives, library materials, and audiovisual aids, students' own interests and satisfaction are not subject to as much variability as the formative characteristics across courses. These perceived properties of classrooms are referred to as procedural characteristics (Randhawa & Hunt, 1976). Schools in general have common operational procedures for discipline, attendance, and other opportunities.
'Address re uests for reprints to B. S. Randhawa, Department of Educational Psychology, Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OWO. University
07
532
B. S. RANDHAWA
Hypothesized course-specific differences on emerging formative characteristics of perceived learning environments may also be expected in different grades. With development individuals become more discerning and exhibit more critical differentiation of preferences (Reese & Lipsitt, 1770). In fact, Randhawa and Hunt (1976) reported relative stability across grades on the procedural dimension of the learning environment of classrooms, whereas the formative characteristics factor for the two grades showed poor congruence. The present study was designed to investigate the factor analytic congruence of the structures of learning environment variables in mathematics and English courses.
METHOD
Sample Three hundred seventeen students in Grade 10 from three high schools in a small city of about 20,000 inhabitants in a midwestern province in Canada were subjects. Students were enrolled in Grade 10 mathematics and English courses. All Grade 10 students enrolled in a parochial girls' high school (71) and in a parochial boys' high school (80) participated in the study. There were three classes at each school. From the secular high school six of the 14 Grade 10 classes were selected randomly and from these six classes 8 1 girls and 85 boys provided complete and usable data. It can be assumed that subjects represented the socioeconomic and sex mix of the grade population in that city.
Procedure The students from each school were randomly assigned to two groups. The Learning Environment Inventory (Anderson, 1971), the Otis-Lennon Mental Abllity test (Otis & Lemon, 1768), and the Sequential Tests of Educational Progress (Educational Testing Service, 1771) in reading, spelling, capitalization, English expression, mathematics computation, and mathematics basic concepts were administered in five different sessions to students assembled in a large room within each school. However, the students in one group (157), mathematics course, were told to complete the inventory to reflect as accurately as possible perceptions of the learning situations of their mathematics class while the other group (160), English course, completed the inventory for their English class. The inventory consists of 105 Likert-type items comprising 15 scales of seven items each. These scales are identified as cohesiveness, dversity, formality, speed, environment, friction, goal direction, favoritism, difficulty, apathy, democratic, cliqueness, satisfaction, disorganization, and competitiveness. Reliability and vahdity data on the Learning Environment Inventory are given by Anderson (1971).
533
LEARNING ENVIRONMENT TABLE 1 PEARSON CORRELATION MATRICES OF RESPONDENTS IN MATHEMATICSA N D ENGLISH* Variable 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Reading Spelling Capitalization English Expression Math Computation Math Basic Concepts Otis-Lennon Cohesiveness Diversity Formality Speed Environment Friction Goal Favoritism CLiqueness Satisfaction Disorganization Difficulty Apathy Democratic Competitiveness
1. Rea&ng 2. Spelling 3. Capitalization 4. English Expression 5. Math Computation 6. Math Basic Concepts 7. Otis-Lennon 8. Cohesiveness 9. Diversity 10. Formality 11. Speed 12. Environment 13. Friction 14. Goal 15. Favoritism 16. Cliqueness 17. Satisfaction 18. Disorganization 19. Difficulty 20. Apathy 21. Democratic 22. Competitiveness 'The lower triangular matrix is
1
2 53
50 54 70 52 54 78 -11 -13 -05 -15 -12 -35 00 -28 -22 09 -20 04 04 23 -15 11 08 04 04 09 10 13 06 01 14 -22
65 60 39 27 50 -13 -00 -03 -07 -19 -15 -06 -11 -08 -09 -01 07 08 15 -15 -15 -14 -20 -14 -03 -04 -14 -08 24 13 28 -12
3 59 67 72 58 46 60 -02 13 -06 -18 -07 -14 -09 -25 -05 02 -05 06 10 23 -17 -04 06 06 07 -08 -12 -05 21 10 31 -21 30 -17
-09 29 -18 -09 26 -32 -10 61 -18 33 -10 31 -22 36 -42 -10 -15 -02 -17 27 -37 03 -25 20 09 45 05 for mathematics
4
5 73 63 73
55 53 75 -05 -04 -00 -10 -12 -22 -07 -19 -10 -01 -09 08 10 18 -16 -16 -22 -29 -20 -15 -18 -19 09 -14 -01 22 -24 18 -23
6
7
58 43 58 59
43 37 51 48 68
64 65 -09 04 -11 -20 -09 -15 04 -27 -03 02 -07 08 15 24 -02 06 07 -01 07 07 11 08 -08 14 -07 07 -07 44 -23 10
63 04 06 -02 -21 08 -16 -04 -22 -04 13 -07 -02 02 24 03 03 10 10 03 -02 -04 02 08 -03 02 -35 41 -40 41 -35 -37
8
9
75 05 50 13 62 11 72 03 74 -01 61 11 -01 -07 -06 09 -02 06 -15 -10 -10 19 -27 09 -03 -03 -24 08 -13 -12 07 06 00 -16 11 -26 12 -02 27 -14 -08 03 -21 -22 -31 -18 -17 -08 -20 -00 09 -12 32 -33 52 -37 35 36 -54
01 -09 -02 02 13 22 06 05 08 29 31 -08 18 -16 12 09 -35 25
1 09 19 14 17 -03 10 06 02 20 -10 22 13 07 -00 14 02 12 -01 -10 22 16 05 -14 -11 -01 07 04 01 -20 -13 -10 24 -25 34 -34 29 25 -53 45 24
0
1 -07 -07 -13 -07 -11 -01 -15 03 18 12 19 03 25 09 05 14 19 14 24 02 23 05 06 10 05 06 07 14 -01 -12 02 -22 34 -30 25 -44 -23 44 -38 27 -28
1 -00 -04 -11 -04 10 10 -01 -11 08 14 13 -05 -18 11 -02 -32 07 45 -04 -I8 06 -02 -14 -02 -02 03 05 05 05 25 15 15 03 34 -03 09 28 -17 19 18 10 -17
18 -31 -11 33 32 -48 -16 -07 -30 04 13 25 -28 37 05 -43 -20 17 -19 02 13 14 33 02 11 -02 10 -01 and the upper triangular matrix is for English.
B. S. RANDHAWA
Analysis For the analysis of data from the Sequential Tests of Educational Progress and the Learning Environment Inventory, raw scores were used, but for the Otis-Lennon, raw scores were converted into the corresponding deviation IQs. The correlation matrices of the mathematics and English contexts for the 22 variables were computed and are given in Table 1. The mathematics context correlation matrix was analyzed by the method of iterative principal components (Harman, 1967). Three principal components with eigenvalues greater than 1.0 were retained. This decision was checked by Cattell's (1966) scree test. These principal components were transformed to a simple structure using the normalized varimax procedure (Kaiser, 1958). The English correlation matrix was also analyzed using the methods of analysis given above. As before, three principal components were retained and then orthogonally rotated by employing the normalized varimax procedure. The three English course components were again orthogonally rotated to make this factor solution as sirmlar as possible to the varimax factor structure obtained for the mathematics course. The procedure used was developed by Cliff (1966), and results in an orthogonal transformation which, when applied to the matrix of interest, produces a matrix which is maximally similar to the criterion matrix. The coefficient of congruence produced for a pair of maximally similar factors indicates the extent of their similarity. These coefficients are evaluated only subjectively because no statistical test of significance is available. Evans (1970) suggests coefficients of .90 or higher indicate "good" correspondence, coefficients from .80 to .90 show "fair" correspondence, coefficients from .70 to .80 indicate "poor" correspondence, and coefficients lower than .70 show no correspondence between a pair of factors. An analysis similar to the one reported above was also made for the 15 variables in the inventory. This 15 x 15 matrix produced two common factors for each course context for which an orthogonal congruence transformation was found.
RESULTSAND DISCUSSION The communalities for the variables and the factor structures for the mathematics and English courses are given in Table 2. Three common factors in the mathematics course accounted for 38.6% of the total variance in 22 variables. The corresponding variance accounted for in the English course was 41.3%. For the two courses a clearly distinct and specific common factor, Factor I, with significant loadings on the Sequential Tests and the -
-
-
'A cable of means and standard deviations is on file in Document NAPS-04760. Remit $7.75 for photocpy or $4.00 for fiche to Microfiche Publications, POB 3513, Grand Central Station, New York. NY 10017.
535
LEARNING ENVIRONMENT
Otis-Lennon Mental Ability test, emerged. Factor I was defined as the cognitive environment or intellectual climate factor. This factor in the two courses was highly sirmlar, with a congruence coefficient of .97. TABLE 2 CRITERIONFACTORLOADING WTRM ( M A ~ A T I C AND S) CONGRUENT ORTHOGONAL FACTORA ~ T R L (ENGLISH) X* Subtests/Scales
Mathematics
English I1
hZ
I
I1
111
h2
I
67 42 61 72 56 50 76 05 10 07 22 26 69 35 27 43 49 48 15 30 20 22
78 61 78 83 74 69 87 -07 03 -08 -25 -09 -22 -04 -31 -08 09 -11
-10 12 06 06 01 -08 -03 -07 -05 -21 17 -42 50 -58 41 46 -61 68
62 45 66 71 61 46 76 03 23 30 22 24 48 41 27 23 63 57 22 41 31 25
78 67 81 84 77 67 87 06 14 -09 -02 13 -15 00 -27 07 06 -26 05 -04 11 01
03 -09 -10 01 12 12 05 -12 04 -12 43 -44 53 -56 43 44 -79 71 37 63 -54 24
-07 -01 -05 00 -04 08 -07 11 46 53 17 19 42 31 -07 18 -03 09 29 -11 -09 44
Total Variance 849 Congruence Coefficient *Decimal points are ommitted.
909
461 97
332 94
155 50
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Reading Spelling Capitalization English Expression Math Computation Math Basic Concepts Otis-Lennon Cohesiveness Diversity Formality Speed Environment Friction Goal Direction Favoritism Chqueness Satisfaction Disorganization Difficulty Apathy Democratic Competitiveness
03
11
13 32 -11
53 -32 14
-21 -18 -03 -15 04 14 -11 19 30 12 -36 28 62 09 07 46 33 07 -37 06 01 43
462
244
144
I11
The other two common factors were defined by scales of the inventory. An examination of the absolute loadings which were largest on any single factor, gave Factor I1 (in the case of the mathematics course) defined by the formality, environment, friction, goal direction, favoritism, cliqueness, satisfaction, disorganization, apathy, and democratic scales. These scales seem mostly to pertain to procedural aspects of academic courses and are probably unlikely to be sensitive to group interactions. For the English course a highly similar factor was obtained. The formality scale, was an exception, having a very low communality but a small negative loading on Factor I1 in mathematics. I n contrast, it had an acceptable communality (.30) but did not load on Factor I1 in the English course. Another exception was that the difficulty
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scale was included in Factor I1 for the English course but not in the mathematics course. I n spite of these exceptions, Factor II's coefficient of congruence was .94. This indicates that Factor 11, representing procedural characteristics, was similar in the two courses as expected. For the mathematics course friction, cliqueness, and competitiveness had factor loadings of .62, .46, and .43, respectively, on Factor 111. Cliqueness emerged as a complex variable, loading equivalently on both Factors I1 and 111. Also, the friction scale appeared somewhat complex because it produced the highest loading on Factor I11 but had a substantial loading (SO) on Factor 11. Four other scales of the Learning Environment Inventory, cohesiveness, diversity, speed, and difficulty, may be considered to define Factor 111 for the mathematics course because these scales had the highest (albeit small) loadings on Factor 111. These low loadings are not surprising because the scales had very low communalities. Therefore, Factor I11 could be defined as a weak formative characteristics factor. The formative nature of this factor is evident from the fact that most of the scales underlying this factor are sensitive to group rather than individual characteristics and the characterization of these behaviors is dependent upon the past experiences of the class groups. A weak formative characteristics factor was also obtained for the English course. For this situation, Factor I11 had significant loadings on diversity, formality, friction, and competitiveness. Friction again appeared to be a complex variable but it did not have the highest loading on Factor I11 as was the case with the mathematics course. Cliqueness and difficulty did not define this factor for the English course as they did in mathematics. These similarities and differences in this pair of factors for the two courses were confirmed by a very low coefficient of congruence (0.50). The factor structures of the 15 variables of the Learning Environment Inventory for the mathematics and English courses are given in Table 3. Two factors for the mathematics course accounted for 26.6% of the total variance, whereas for the English course the variance accounted for was 30.8%. This analysis was done to determine whether these variables would produce factor structures which were generally similar to the factors based on the Learning Environment Inventory for the two courses when the cognitive measures were also included with the inventory variables. As can be seen from the results in Table 3, the two factors were almost identical to the ones presented earlier in Table 2. As indicated by a congruence coefficient of .93 between the pair of Factor Is for the two courses, the procedural characteristics factor was similar. The obtained Factor 11s (formative characteristics) were not similar for the two courses. I t appears that the inventory's factors have a structural property which is unaffected by the cognitive variables of context but is sensitive to the instructional context.
LEARNING ENVIRONMENT TABLE 3 CRITERION FACTOR LOADING MATRIX(MATHEMATICS) AND CONGRUENT ORTHOGONAL MATRIX*(ENGLISH) FORLEARNING ENVIRONMENT INVENTORY SCALES FACTOR Scale
Mathematics b2
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Cohesiveness Diversity Formality Speed Environment Friction Goal Direction Favoritism Cliqueness
Satisfaction Disorganization Difficulty Apathy Democratic Competitiveness Total Variance Congruence Coefficient *Decimal points are omitted.
04 09 08 11 23 73 35 22 42 49 47 13 24 14 24 399
1 -01 -01 -16 15 -33 64 -54 47 54 -55 68 04 49 -37 24 258
I1 20 30 23 -30 35 56 23 04 36 44 -08 -36 -09 00 43 141
h' 02 21 26 21 26 48 39 22 22 63 54 20 39 32 26 462
English I -09 16 04 45 -39 64 -44 43 46 -77 73 41 57 -56 35
I1 13 43 51 04 32 25 44 -20 06 19 -13 17 -27 08 38
350 93
113 70
I n a large study involving 96 classrooms of Grades 8 and 11, Randhawa and Hunt (1976) reported that the factor structure stability of the Learning Environment Inventory and cognitive variables was dependent upon grade. They found, as in the present study, that the formative characteristics factor was less stable. I t seems that the procedural characteristics do not change across curricula, however a larger variety of curricula must be investigated before such results are generalized. Scales pertaining to the formative characteristics factor could provide useful data for evaluating instructional and curriculum interventions. Diversity, formality, speed, and competitiveness scales of the inventory may provide critical measures of formative characteristics for determining resultant changes from instructional and/or curriculum changes. Incongruity of the emerging properties of classes across grades (Randhawa & Hunt, 1976) and curricula (the present study) would render these characteristics sensitive to unusual effects. Instability of factor structure should not be interpreted to mean that scales defining the factor are themselves unstable. REFERENCES ANDERSON,G. J. (1971) The assessment of learning environments: a manual for the Learning Environment Inventory and the My Class Inventory. of Education.
Halifax, Canada: Adantic Institute
ANDERSON, G. J., WALBERG, H. J., & WELCH,W. W. (1969) Curriculum effects on the social
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climate of learning: a new representation of discriminant functions. American Educational Research Journal, 6, 315-328. CATITELL, R. B. (1966) The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276. CLIFF, N. (1966) Orthogonal rotation to congruence. Psychometrika, 31, 33-42. TESTINGSERVICE.(1971) Teacher's manual for STEP Series II. Princeton, NJ: EDUCATIONAL Educational Test~ngService. EVANS,G. T. (1970) Congruence transformation: procedures for comparing the results of factor analyses involvm the same set of variables. (Unpublished manuscript, Ontario Institute for Studies in ~ ~ c a t l o n ) HAMAN, H. H. (1967) Modern factor analysis. (2nd ed.) Chicago, IL: Univer. of Chicago Press. KAISER,H . F. (1958) The varimax criterion for analytic rotation in factor analysis. Psychomeirika, 23, 187-200. Moos, R. H. (1979) Evaluating educational environments. San Francisco, CA: Jossey-Bass. O n s , A. S . , & LENNON, R. T. (1968) Otis-Lennon Mental Ability Test: manual for administration. New York: Harcourt. RANDHAWA, B. S., & Fu, L. W. (1973) Assessment and effect of some classroom environment variables. Review of Educational Research, 43, 303-32 1. RANDHAWA, B. S., & HUNT, D. (1976) Factors in classroom environment variables. Journal of Educational Psychology, 68, 546-549. RANDI-IAWA, B. S., & MJCHAYLUK, J. 0 . (1975) Learning environment in rural and urban classrooms. American Educational Research Journal, 12, 265-285. REESE, H . W., & LIPSITT, L. P. (1970) Experimentnl chiM pxychology. New York: Academic Press. SHULMAN, L. S., & T m , P. (1973) Research on teaching in the natural sciences. In R. M. W. Travess (Ed.), Second handbook of research on teaching. Chicago, IL: Rand McNally. Pp. 1098-1148. WALBERG,H. J. (1969) Social environment as a mediator of classroom learning. Journal of Educational Psychology, 60, 443-448. WALBERG, H. J. (Ed.) (1974) Evaluating educational performance: a sourcebook of methods, instruments, and examples. Berkeley, CA: McCutchen. Accepfed February 21, 1990.
