10
115 Murnane, R. 'Seniority Rules and Educational Productivity'. American Journal of Education. 90 (1981), No. 1, pp. 14-38. Phelan, W. 'Governing Staff Productions: The Use and Abuse of Teacher Evalua- tions.' Education and Urban Society. 1983, 15, pp. 189-198. Roberts, R. '"Last Hired, First Fired" and Public Employee Layoffs: The Equal Employment Opportunities Dilemma'. Review of Public Personnel Administration. 2 (1981), pp. 29-48. Whelan, G. and Rubin, R. 'Labor Relations and Affirmative Action: A Tug-of- War'. Public Personnel Management. 6 (1977), pp. 149-155. TEACHING VARIABLES AND MATHEMATICS ACHIEVEMENT IN THE CONTEXT OF SIXTH GRADE CLASSROOMS IN TAIWAN This study examines elements of teacher behaviour and their relationship to student outcomes in Taiwan, the Repuhlic of China. Previously, the large field of studies of process-product research has found characteristics of teacher behaviour that are positively or negatively related to student outcomes (Medley, 1977). Some of these characteristics may be generic to all teacher settings while others are affected by con- text. The degree of generalizability of findings is dependent on the impact of context on the variables (Brophy, 1979). In the present study, the cultural context has per- mitted the examination of teacher behaviours for generic variables and allowed the study of variables that may not occur within American and European schools. Fur- thermore, this study has controlled some important teacher and classroom variables which frequently invalidate studies reported in the United States. The opportunity to control variables permits consideration of some of the concerns noted by Soar and Soar (1983), Berliner (1977) and Shavelson and Dempsey (1976). Intervening variables which were controlled in this study include (1) Teacher Selection: A random sample of teachers was used rather than a volunteer group, (2) Test Content Relationships: Criteria measures matching objectives, tests and teaching methods of the teacher's classroom and performance guidelines of the Re- public of China Ministry of Education were used in all classrooms, and (3) Teacher Behaviour Variations: Consistent teaching techniques from class to class were main- tained during the study, as a result of the cultural conformity guiding teacher hehaviour. lnternaüonai Research Findings Over the last ten years, research into teachers' effectiveness has reported consistent, overlapping and replicable results that have brought greater understanding of the teaching and learning process (Brophy, 1979). In America, process variables that measure teacher and student behaviours have been extensively examined, although precision has been difficult to develop (Good, 1979). These variables have been dif- ferentiated by experimenters through the use of previously identified variables from naturalistic or factor analysis procedures, or in the case of older studies, through a long history of recorded teacher and student behaviours. Although the list of variables is long and the relationships to learning are complex

Teaching variables and mathematics achievement in the context of sixth grade classrooms in Taiwan

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Murnane, R. 'Seniority Rules and Educational Productivity'. American Journal o f Education. 90 (1981), No. 1, pp. 14-38.

Phelan, W. 'Governing Staff Productions: The Use and Abuse of Teacher Evalua- tions.' Education and Urban Society. 1983, 15, pp. 189-198.

Roberts, R. ' "Las t Hired, First Fired" and Public Employee Layoffs: The Equal Employment Opportunities Dilemma'. Review of Public Personnel Administration. 2 (1981), pp. 29-48.

Whelan, G. and Rubin, R. 'Labor Relations and Affirmative Action: A Tug-of- War'. Public Personnel Management. 6 (1977), pp. 149-155.

TEACHING VARIABLES AND MATHEMATICS ACHIEVEMENT IN THE CONTEXT OF SIXTH GRADE CLASSROOMS IN TAIWAN

This study examines elements of teacher behaviour and their relationship to student outcomes in Taiwan, the Repuhlic of China. Previously, the large field of studies of process-product research has found characteristics of teacher behaviour that are positively or negatively related to student outcomes (Medley, 1977). Some of these characteristics may be generic to all teacher settings while others are affected by con- text. The degree of generalizability of findings is dependent on the impact of context on the variables (Brophy, 1979). In the present study, the cultural context has per- mitted the examination of teacher behaviours for generic variables and allowed the study of variables that may not occur within American and European schools. Fur- thermore, this study has controlled some important teacher and classroom variables which frequently invalidate studies reported in the United States. The opportunity to control variables permits consideration of some of the concerns noted by Soar and Soar (1983), Berliner (1977) and Shavelson and Dempsey (1976).

Intervening variables which were controlled in this study include (1) Teacher Selection: A random sample of teachers was used rather than a volunteer group, (2) Test Content Relationships: Criteria measures matching objectives, tests and teaching methods of the teacher's classroom and performance guidelines of the Re- public of China Ministry of Education were used in all classrooms, and (3) Teacher Behaviour Variations: Consistent teaching techniques from class to class were main- tained during the study, as a result of the cultural conformity guiding teacher hehaviour.

lnternaüonai Research Findings

Over the last ten years, research into teachers' effectiveness has reported consistent, overlapping and replicable results that have brought greater understanding of the teaching and learning process (Brophy, 1979). In America, process variables that measure teacher and student behaviours have been extensively examined, although precision has been difficult to develop (Good, 1979). These variables have been dif- ferentiated by experimenters through the use of previously identified variables from naturalistic or factor analysis procedures, or in the case of older studies, through a long history of recorded teacher and student behaviours.

Although the list of variables is long and the relationships to learning are complex

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(Medley (1977), for example, established a set of 613 relationships from 14 major studies), some consistent variables emerge across the studies. For example, substan- tial empirical support has been found for the amount and quality of academic time spent in schools (Fisher, et al., 1978, Stallings, et al., 1978). Furthermore, the effects of the relationship between learning and praise on students of varying levels of abili- ty (Brophy, 1981) and the negative relationship between learning and discipline and punishment have been demonstrated with a high level of confidence (Medley, 1977).

Studies in Europe and New Zealand support similar findings regarding teacher performance and its relationship to student learning. Early correlational studies by Wright and Nuthall (1970) established positive associations between teacher behaviour and student outcome for the percentage of questions requiring correct answers, praising students, and summarizing or reviewing lessons just completed. These studies also indicated that students who did not respond verbally to questions also attained lower test scores. Numerous relationships were not significantly cor- related, including the amount of teacher and student talk, and the amount of teacher refocusing or structuring of the lesson.

Later studies by Nuthall and Church (1973) and Hughes (1973) supported these findings and expanded them by concluding that teacher emphasis on content coverage was related to student learning more than to any particular teaching behaviour. Furthermore, by the seventh grade students may not need to participate in the learning overtly and can learn passively, although, a t the same time, evidence was found that a teacher's enthusiastic response to questions does relate to student performance on tests.

Studies in England established that the time spent actively involved in a particular subject increased student performance in that subject (Bennett, 1978). An extensive study by Rutter et al. (1979) indicated that teachers positively influence learning through high expectations related to student learning, as weil as through their em- phasis on the amount of time spent on academic- or achieve, ment-oriented activities. Teachers who spent more time interacting with the entire class and limited their behavioural interventions consistently outperformed teachers who spent time on discipline. Rutter (1979) found that praise was used very sparingly in all classrooms and no significant correlation with performance was etablished. On the other hand, punishment or negative atmosphere was negatively related to learning.

Also in England, Bennett, Desforges, Cockburn and Wilkinson (1981) found that low error rates in students are desirable and that it is important that errors should be limited when the students are attempting mastery of the material, although at the beginning of the lessons, when the learning is new and needs constant interpretation and review, errors may be more frequent.

In the literature, considerable attention to teaching variables has been focused on the practice of counting the number of occurrences of certain specified behaviours. However, this frequency counting has given only limited information about the im- pact on student learning, while other less frequently occurring teaching variables may be influential yet go unnotjced. A suggestion that 'high inference' variables be combined with the ' low inferen~e' variables to develop a more precise and complete picture of classroom activity and to reduce the dependence of research observation on merely counting behavioural occurrences was made by Brophy (1979).

Low inference variables are student and teacher behaviours whose occurrences may be counted. High inference variables are student and teacher behaviours or reactions from which an observer taust infer a result or condition (e.g., to what ex- tent is some teacher action towards a student perceived as punishment or reward).

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The discrete elements in an observed classroom can be quite extensive. Hence the observer's ability to perceive and record the distinctions is naturally limited (Berliner, 1977). It is with these limitations in mind that the present study concen- trated on a relatively small number of classroom variables, both of high and low in- ference, which have been determined from previous research to be the most likely predictors of effective mathematical instruction. In addition, another important determinant of the selected variables was the Chinese culture, which is manifest in certain teaching behaviours in mathematical instruction that are consistent from classroom to classroom.

Contextually, the problem of research into teacher effects relates to the generalizability of extending the results (a) beyond the grade level, (b) beyond the socio-eeonomic level of the sampled classrooms and (c) beyond the subject matter which is being taught in the classrooms sampled. The difficulty of generalizability has been previously documented for reading and mathematics subject matter in the work of McDonald (1975) and in the review of Medley (1977). The findings show that eontext is a substantial determinant of the teacher behaviour that is associated with student academic performance. The contextual variables, grade and subject matter, noted by Medley would be expected to be influential factors operating in any culture. It would seem reasonable for these contextual factors, if unvarying across cultures, to be strongly related to a set of generic teaching behaviours applicable to cultures having very similar educational goals. The present study sought to identify the extent to which a generic set of teacher and student behaviours, found to be highly associated with successful learning in mathematics in Western culture (the United States, Great Britain and Europe), would be as closely aligned with effective teaching in a Chinese culture.

In the study, the investigation of teacher effects on student performance in the Republic of China is not based on a wide and deep backdrop of information about classrooms and behaviours which has accumulated in the literature on Western educational practice. Rather, this study has drawn its variables not only from those presumed to be important in the West, but also from those suggested by scholars and teachers in the Republic of China.

Methodology

Sampling

Forty classrooms (with approximately 60 students in each) were randomly selected from all sixth grades (11- and 12-year olds) of the Kaohsiung City Schools in Kaoh- siung, Republic of China. Kaohsiung is a port city of over one million people in the southern region of Taiwan where schooling is compulsory for all students between the ages of six and 15 years. This population was chosen because 11- and 12-year olds were thought to be more consistent in their response patterns to the outcome measures to be used in the study, and because they would be likely to show greater variante in mathematical problem-solving and computational abilities than their younger peers. This latter eharacteristic was especially important for defining high and low performance groups, the independent variable.

Sampling difficulties encountered in European and American studies related to socio-economic factors contributing to differences in performanee have only limited impact in Taiwan. Neighbourhood schools are the rule in large cities and towns, but

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the concept of exclusive neighbourhoods or schools is limited, and major differences relate to urban, rural and mountainous settings, or exist between the limited number of private or parochial schools at the elementary level and their public school counterparts. Housing in any one city neighbourhood reflects the entire spectrum of Chinese society, as the location of dwellings has not until very recently been held as an indicator of wealth or status.

Income and wealth, another contributor to differentiation of performance in the United States and Europe, have limited influence on the placement of students in the elementary grades in Taiwan. Family incomes are not as varied among the Chinese as in the West. In general, the wealthiest family has only twice the yearly income of the average family. In addition, Chinese families are willing to invest a substantial percentage of their income in tutors and night schools [called 'bushiban'] to enhance their children's academic performance.

Practices within the school systems tend to reduce or eliminate placements of students in special classes or schools. Random assignment of students to classrooms in the first grade is the norm among schools, so as to reduce charges of favouritism against the principal from teachers or parents. These assignments remain unchanged up to the sixth grade. Reassignment at the junior high school level is also random, and is where competition for acceptance into elite high schools begins in deadly earnest.

Design

When defining teaching effectiveness in terms of student gains on tests, researchers have used regression or covariance as a technique to adjust for initial differences among the groups. This statistical procedure controls for some of the problems of variance and deviations of central tendency, but interpretations of subsequent com- parisons on post-measures remain dependent on the similarity of the groups in other salient characteristics - i.e., the groups taust be alike on all important variables. The previous discussion of sampling suggests the level of care used to select a sample that had limited differences among the students' background and school charaeter- istics.

The method of forming the comparision groups was similar to that of Good, Grouws and Ebmeier (1983). Each of forty classes was pre-tested on mathematics achievement in December. All teachers involved in the pre-test were observed for five hours over a period of four months during which time teacher and student behaviours were recorded. All classrooms were then post-tested on mathematics achievement.

Residual gains on mathematics achievement were used to determine high and low comparison groups. Classes which were more than half a standard error of estimate above the mean residual galn formed the high group, while the classes which were more than half a standard error of estimate below the mean formed the low group. This procedure placed nine classes in the high performance group and eleven in the low group.

The research question posed was: Do teachers of high mathematical performance classes manifest different levels o f high and low inference classroom behaviour as compared with teachers o f low mathematical performance?

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Instrumentation and Scoring

The mathematics performance for both pre-test and post-test was measured by the 1980 edition of the National Elementary Test ofMathematics Achievement, a com- monly used examination in the Republic of China. Based on studies of more than 2300 sixth grade students on Taiwan, the measures of reliability were acceptable with .90 on split-half tests, with a .91 Kuder-Richardson coefficient and a test-retest reliablility of .84. Predictive validity was determined from regression analysis with periodic (monthly) mathematics scores from classrooms over all student grade levels yielding r = .66 (M.O.E., 1980).

The two levels of mathematics performance were compared on two large classes of teacher behaviour variables. Fourteen low inference teacher behaviours and 12 high inference behaviours were observed by trained personnel using the Teacher Observation Scale (TOS) during the four month observation period. The TOS obser- vation scale for recording teacher behaviour in the classroom was pilot tested by a trained staff of undergraduates at Kaohsiung Teachers' College, who were employed to work with the study. The TOS measured the 14 low inference behaviours by frequency counts and the 12 high inference behaviours on Likert scales with rankings which indicate the degree of presence or occurrence of a behaviour. Table l contains a listing of the high and low inference variables (behaviours).

Table 1. Teacher and Classroom Variables

Low Inference High Inference

Off Task Confusion Praise Feedback Choral Response Individuai Response Seatwork Exercise Correction of Student Response Student Initiation Lecture Criticism Directions to Students Open Response Questions Closed Response Questions

Preparation Pronunciation Expression Classroom Climate Varied Teaching Methods Enthusiasm Clarity of Board Writing Classroom Management Punishment Reward

All observers had had three years of coursework in education, and trained for a period of thirty hours for one week before the first observations for the study. Observers were instructed in the use of the TOS, and using videotaped classes, prac- tice in its use was provided. Reviewing and criticizing the observers' practice sessions in applying the observation scale after one week of training resulted in inter-rated reliability ranging from .79 to .93. At the midpoint of the four week study a second check on reliability yielded a satisfactory range of .85 to .96 on inter-rater agree- ment.

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Results

High and low mathematical performance groups were compared on twenty-eight classroom variables. These variables included the twenty-six high and low inference classroom and teacher behaviour variables, as also teacher age and teacher ex- perience. The present study has recognized that 'behavioural problems are almost always multivariate in nature and cannot be solved with a bivariate approach' (Ker- linger, 1973, p. 149). Moreover, it is widely assumed that inter-relationships exist among teacher behavioural variables in a classroom and consequently complex cor- relations ought to be used to make adjustments in the analysis of the data. In addi- tion, since the purpose of this study included the simultaneous testing of hypotheses involving several dependent variables which are correlated, the multivariate analysis of variance (MANOVA) was used to protect against exaggeration of the probability of Type I error as weil as to acknowledge and account for the 'actual complexity of behavioural reality' (Kerlinger, 1973, p. 602).

A MANOVA provided the means, standard deviations and F-ratios for each of the dependent variables shown in Table 2. Also, since certain classroom characteris- tics were noted by Chinese scholars and teachers as being especiaUy important to their cultural expectations and values, these nine variables have been specially de- noted by an asterisk (*) in the table.

No statistical differences between high and low performance groups were found on the nine variables identified as being especially relevant to the Chinese classroom. This result suggests that these traits are found with consistency across the Taiwanese sixth grade classes and that they do not provide a reliable discrimination between high and low performance in mathematics.

The two performance groups were significantly different on two of the low in- ference variables, but not different on any of the high inference type (19 < .05). Off- task behaviour of students was lower for the high performance group than for the low performance group, with means of 2.24 and .62, respectively. Students' being on-task in the elassroom has been found to be an important trait which discriminates high and low performance in mathematics among American classrooms (Good, et al., 1983; Stallings, 1980), and being on-task is closely associated with high perfor- mance in the Taiwanese classroom.

Teacher age and teaeher experience generally go hand in hand, though statistieally the results of this study indicated that high performance was significantly associated with teacher age, while teacher experience was not (p < .05). However, the dif- ference of approximately six years' experience did occur in the same direction, with means of 26.9 years for teachers of the high performance groups and 20.6 for the low groups. At the same time it is important to note that significant differences in variances (F-max test, p = .05) were found between the high and low performance groups for teacher age, teacher experience and off-task behaviour. For each of these three variables, the low performance group had greater variante than the high group. The smaller variances in the measurements of these three traits among the high performance groups indieates greater homogeneity, which is frequently cited in Western educational literature as beilag important to academic performance.

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T a b l e 2. Means, Standard Deviations and Multivariate F-ratios for the High and Low Mathematical Performance Groups

High Low Total**

Variables X s X s X s F

Off Task (L) 0.62 0.91 2.24 2.02 1.52 2.09 5.55t Teacher Age (L) 48.6 3.27 39.3 12.94 44.3 7.51 4.851" Initiation (L) 4.54 4.38 14.50 15.18 8.99 10.29 4.01 Feedback (L) 13.32 7.71 22.56 12.26 18.4 10.47 3.44 Teaching Experience

(L) 26.90 4.12 20.61 10.85 23.21 7.21 2.99 Correction (H) 2.24 1.56 8.84 2.94 3.44 3.02 2.42 Classroom Manage-

ment (H) 3.9 0.43 3.63 0.51 3.70 0.64 1.78 Open Questions (L) 2.8 3.31 1.55 0.66 2.15 2.34 1.77 *Writing (H) 3.74 0.35 3.56 0.36 3.65 6.37 1.33 Closed Questions (L) 124.88 32.58 113.80 38.90 115.90 32.46 0.52 Lecturing (L) 307.80 81.70 282.05 87.31 281.37 36.41 0.49 Directions (L) 56.62 28.42 62.80 15.90 61.01 21.01 0.43 Confusion (L) 10.48 5.86 9.01 6.12 9.63 6.06 0.33 *Praise (L) 1.86 2.27 2.46 2.88 2.26 2.45 0.29 *Homework-New (H) 4.20 1.51 4.60 2.03 4.45 1.73 0.28 *Homework-Review

(H) 1.90 1.22 2.36 2.61 3.43 1.84 0.26 *Pronunciation (H) 3.30 0.51 3.40 0.46 3.34 0.48 0.26 Climate (H) 3.40 0.62 3,27 0,51 3.35 0,56 0.26 *Punishment (H) 0.01 0.25 0.15 0.20 0.01 0.21 0.26 Individual Response

(L) 74.62 40.72 82.81 46.37 77,44 41.31 0.25 Enthusiasm (H) 3.44 0.57 3.53 0.47 3.49 0.53 0.19 Seatwork Exercise (L) 69.16 33.78 76.50 50.93 74.40 42.76 0,15 Preparation (H) 3.52 0.40 3,56 0,35 3,54 0.39 0.15 *Choral Response (L) 123.20 38.78 126.66 55.31 124.98 48.51 0,07 Expression (H) 3.50 0,31 3,52 0.34 3.51 0.34 0.02 *Reward (H) 0.00 0.00 0.04 0.11 0.03 0.06 0.01 Teacher Method (H) 3.24 0.30 3.24 0.44 3.24 0,37 0.00 *Criticism (L) 2.14 2.97 2.21 2.45 2,18 2.36 0.00

* Variables indicated by Chinese educators as ** Number of groups = 40.

p<.05.

influential.

Discussion

T h e h o m o g e n e i t y o f t e a c h e r c l a s s r o o m b e h a v i o u r s in t h e R e p u b l i c o f C h i n a m a y be

a c c o u n t e d fo r b y a s t r o n g c u l t u r a l c o n s i s t e n c y a m o n g t e a c h e r s n o t f o u n d in m o s t W e s t e r n s c h o o l s y s t e m s . H o w e v e r , t h e t e a c h e r b e h a v i o u r s t h o u g h t b y C h i n e s e

e d u c a t o r s to be espec ia l ly g e r m a n e to a c h i e v i n g the i r a cade rn i c ob j ec t i ve s h a v e l i t t le to do wi th d i f f e r e n c e s in r n a t h e m a t i c a l p e r f o r m a n c e in the i r c o r n m o n l y u s e d Na- tional Elementary Test o f Mathematics Achievement. T h e f i n d i n g s o f th i s s t u d y h a v e i n d i c a t e d t h a t t i rne s p e n t o f f - t a s k by s t u d e n t s in s ix th g r a d e c lasses is de t r i rnen- ta l to m a t h e r n a t i c s a c h i e v e m e n t in t h e R e p u b l i c o f C h i n a . T h i s r e su l t s u p p o r t s p r e v i o u s f i n d i n g s in W e s t e r n e d u c a t i o n a l r e s e a r c h (Med ley , 1977). T h e m a i n t e n a n c e

o f o n - t a s k s t u d e n t b e h a v i o u r a p p e a r s to be a gene r i c t r a i t o f c l a s s r o o r n s h a v i n g h i g h m a t h e m a t i c a l p e r f o r m a n c e in b o t h C h i n e s e a n d W e s t e r n cu l tu r e s .

T h e f i n d i n g t h a t low a n d h i g h m a t h e r n a t i c a l p e r f o r r n a n c e c l a s s r o o m s d i f f e r in

122

terms of teacher age has several possible interpretations. It is not likely in this case that 'older' teachers, being more experienced, have learned to instruct at higher levels of effectiveness, since this would imply without any plausible rationale that in the Republic of China the spurt of effective teaching occurs between the twentieth and twenty-fifth years. A second possibility is that teacher assignments are subject to seniority status in the school system, with the result that high performing classes are assigned to the older teachers. However, in the Republic of China this practice is virtuaUy unknown.

The five teacher variables, which emerged in this study as most important, name- ly, off-task behaviour, teacher age, initiation, feedback and teaching experience were of the low inference type. With the exception of feedback, the high perfor- mance groups were significantly more homogeneous on these teacher variables than the low performance groups. This finding supports previous reports in the literature that the stability of these variables is positively associated with high performance in mathematics (Good, et al., 1983; Medley, 1977).

The variance in teacher behaviour in the Kaohsiung City Schools is much less on each of the low and high inference variables chosen for investigation in this study than one might expect in school systems of this size in Europe or the United States. For the most part, this relatively low variation in the manner and ways of conducting lessons in mathematics is due to a highly centralized school system. Teacher patterns for conducting classrooms in Kaohsiung follow a more narrow cultural consensus than those found in Western schools in cities of comparable size. In general, the findings of the present study do not indicate that most of the classroom teacher variables that have been used in research to predict academic performance in Western schools discriminate between low and high performance in sixth grade level mathematics in the Republic of China. Off-task behaviour of students and teacher age emerged as the only discriminators among the classroom variables commonly found also in Western research into teachers' effectiveness. Finally, none of the teacher and classroom characteristics identified by Chinese educators as particularly germane to their cultural values and emphasis was determined to be a predictor of mathematical performance. This is yet another instance of the low variation in these selected teaching practices of the sixth grade teachers in Kaohsiung.

YING-HAU CHEN, THOM B. CLARK and EUGENE C. SCHAFFER

Note

Dr. Tieh-hsiung Wu and Dr. P 'sha Hung contributed substantially to the training of observers and to the overall conduct of the research. They should be considered co-authors of this report.

References

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Bennett, N., Desforges, C., Cockburn, A., & Wilkinson, B. The Quality of Pupil Learning Experiences: Interim Report. Lancaster, England: Centre for Educational Research and Development, 1981.

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Stallings, J., Cory, R., Fairweather, J., & Needels, M. A Study o f Basic Skills Taught in Secondary Schools. Menlo Park, CA" S.R.I. International, 1978.

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StaUings, J. 'Allocated Academic Learning Time Revisited or Beyond Time on Task'. Educational Researcher. 8 (1980), No. 11, pp. 11-16.

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International Review of

Education FORTHCOMING - ISSUE 34/1988/2 Special Number

Vocational Education

edited by George Psacharopoulos

Art ic les and Notes

Mary J. Bowman, Walter M. McMahon, Claudio de Moura Castro, Mathew Zachariah, Alain Mingat/ Jee-Peng Tan, Christopher Dougherty, Jandhyala B.G. Ti lak, Andrew O. Urevbu, Yuan Qiu.

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