Ego orientation and task involvement in mathematics achievement: A three year follow-up Shirley M. Yates The Flinders University of South Australia Gregory C. R. Yates University of South Australia Paper presented at the Joint Conference Educational Research Association, Singapore Australian Association for Research in Education Singapore, November, 1996 Ego orientation and task involvement in mathematics achievement: A three year follow-up Paper presented at the ERA/AARE Conference Singapore, November, 1996 Student performance at school has been found to be related to prior achievement, attitudes to specific aspects of school learning, and to motivational factors (Keeves, 1972). Reviewers in the area of motivational psychology have emphases the importance of self-efficacy (Schunk, 1996), self regulation (Pintrich & Garcia, 1991; Zimmerman, 1990), self determination (Deci & Ryan, 1991), and causal attributions (Graham, 1991). In particular, goal theory has been advanced to explain the relationship between students' beliefs about the causes of school success, and their engagement and persistence in academic learning. Within the field of mathematics, achievement has been examined in relation to school-type factors, curriculum considerations, student characteristics and background, and gender differences. However, few studies have examined the relationship between goal oriented beliefs and achievement in mathematics (Bong, 1996). The present study is part of a larger data set concerned with motivational variables in mathematics over a period of almost three years. The present analyses were concerned with the extent to which achievement gain could be predicted using measures which involved goal orientation beliefs. In an earlier report (Yates, Yates & Lippett, 1995), it was found that ego and task goal orientation measures failed to correlate significantly with concurrently measured achievement. Within academic motivation research, the focus on adaptive and maladaptive motivation has lead to the emergence of goal orientation theory (Dweck, 1986) Adaptive patterns of achievement orientation have been variously termed mastery oriented goals (Ames, 1992), learning goals (Dweck, 1986) or task involvement (Nicholls, 1984). Maladaptive motivation has been termed performance-oriented goals, performance goals , or ego orientation. The terms task involvement and ego orientation were used in this paper to exemplify goal orientation. Task-involvement goals have been distinguished from ego oriented goals in terms of students conceptions of success, different reactions for approaching and engaging in achievement activity, and different ways of thinking about the self, the task and the task outcomes (Ames, 1992: Nicholls et al., 1989). Goal theory researchers have suggested that learning and performance goals were not opposing ends of a continuum, but were orthogonal (Maehr & Pintrich, 1991; Meece & Holt, 1993; Miller et al., 1993). Four dichotomous goal configurations were thus possible, as any given student may have been high on both dimensions, low in both or high on one and low on the other. Task involvement and ego orientation are not necessarily fixed characteristics, as they have been shown to be influenced by conditions in school environments (Ames, 1992). Dweck (1986, 1989) has suggested that the nature of achievement goal orientation may have changed in relation to subject-matter areas, but Duda and Nicholls (1992) have found that high school students' causal explanations of success were generalised across subject areas. Factor analytic studies have determined that task involvement and ego orientation were independent dimensions of both personal academic goals and beliefs about the causes of school success (Nicholls et al., 1989; Nicholls et al., 1990), with the third dimension of work avoidance being found in investigations of students' beliefs of mathematics achievement (Nicholls et al., 1990). All three dimensions have been found to be only slightly correlated with perceived ability (Nicholls et al., 1990). Task involvement goals are akin to "motivation to learn" as students have been found to be focussed on mastery and understanding content and have demonstrated a willingness to engage in the process of learning. Ames (1992) has postulated that effort and outcome covaried within a mastery goal, with this attributional pattern leading to stronger achievement directed behaviour over time. Students' attention was more likely to be focussed on the intrinsic value of learning (Nicholls, 1984; Butler, 1988; Meece & Holt, 1990), and on effort utilisation, with the belief that effort lead to success and that mastery was intrinsic to self-efficacy. Such students were oriented towards the development of new skills, trying to understand their work, improving their level of competence or achieving a sense of mastery based on self referenced standards. Within this mental frame, students perceived ability as being improvable and incremental. They were more confident in expending or investing effort (Schunk, 1996). Ego orientation, however, entails a focus upon ability as a fixed attribute which determines a sense of self-worth (Covington, 1984; Dweck, 1986; Nicholls, 1984). Ability could be evidenced by doing better than others, by surpassing normative-based standards, or by achieving success with little effort (Covington, 1984). Ames (1992) has suggested that central to ego orientation was the need for public recognition of being better than others, or performing in a superior manner. In this orientation, learning was viewed as a way to achieve this desired goal, with attention being directed towards achieving normatively defined success. Effort became a double-edged sword as the self concept could be threatened if trying did not lead to immediate success (Covington & Omelich, 1979b). Over time, effort could be seen as counterproductive, with increased effort interpreted as an indication of lack of ability. Differences between ego oriented and task involved students have been found in the amount of time students spent on learning tasks, persistence in the face of difficulty, in the quality of engagement in learning, and in the use of adaptive mental strategies (Butler, 1987; Elliott & Dweck, 1988; Meece et al., 1988; Nolen, 1988; Nolen & Haladyna, 1990; Graham & Golan, 1991). Task involvement goal orientation appears to be implicated also in failure tolerance. Task involved students have responded to impending failure by remaining task focussed (Dweck & Leggett, 1988). By contrast, in the face of failure, ego oriented students chose simpler tasks, used inefficient strategies, or adopted an attitude of academic alienation so as to preserve their self image (Dweck & Leggett, 1988). Clearly then, the adoption of task involvement goals could be expected to lead to long term achievement motivation in students. However the extent to which this source of achievement motivation related to actual achievement was not clearly defined within the existing literature. This project was undertaken to investigate the nature of this relationship. The data base enabled the examination of mathematics achievement in primary school aged students over a period of almost three years. Measures of ego orientation and task involvement in attitudes towards mathematics were also available for analysis. Method Subjects The study commenced in term 1, 1993, with 328 students from Years 3, 4, 5, 6, and 7 in two primary schools in metropolitan Adelaide. Both schools were selected on basis of an invitation from the school principals who were interested in factors influencing the mathematics achievement of their students. In the first school students from six classes in Years 4, 6 and 7 took part in the study, while in the second school all students from Years 3-7 took part. In 1995 these students were traced to 26 primary schools and 24 secondary schools in both the government and nongovernment sectors. When the 1993 and 1995 were compared, it was that found that complete data were available for 243 students. The analyses of the Feelings in Mathematics Questionnaire was thus conducted on the total population who took part in the study, with the sample of 243 being used for the relational analyses. The age of each student was calculated in completed months. Instrumentation: Progressive Achievement Tests in Mathematics: Tests 1, 2, 3 (ACER, 1984.) The Progressive Achievement Tests of Mathematics were adapted by the Australian Council for Educational Research (ACER) from the Progressive Achievement Tests: Mathematics developed by the Test Development Division of the New Zealand Council for Educational Research. The series, which utilised a multiple choice format, consisted of three tests at different levels of difficulty with each covering a range of general mathematics topics. Within each test, the items were arranged in content groups with the items increasing in difficulty within each content area. The item difficulty order had been determined by the Rasch analysis of the responses from the standardisation sample tested in November, 1983, and the scores on the three tests were provided by the ACER on a single Rasch scale. Test 1 designed for Years 3, 4, and 5 contained 47 items which measured number, computation, fractions, measurement and money, statistics and graphs, and spatial relations. The same areas with logic and sets added were covered by the 57 items in test 2, which had been designed for Years 5, 6, 7, and 8. Test 3, designed for Years 6, 7, and 8, contained 55 items which sampled the areas of number, computation, measurement and money, statistics and graphs, spatial relations, relations and functions, and logic and sets. Feelings in mathematics questionnaire. This questionnaire, designed to measure task involvement and ego orientation, was a variant of the Motivation Orientation Scales developed by Nicholls (Nicholls et al., 1990; Duda and Nicholls, 1992). It was composed of 25 items which commenced with the stem "Do you really feel pleased in maths when ..." followed by a statement reflecting either task involvement or ego orientation, with some filler items in random order. The students were required to rate each statement on a five point scale ranging from strongly agree to strongly disagree. Administration of test and questionnaire At the commencement of the study in Term 1, 1993, one of the two schools had already administered the Progressive Achievement Tests as part of their normal procedures for the start of the academic year. In the second school the tests were administered to intact classes by a male researcher. The Feelings in Mathematics Questionnaire was then administered to intact classes in both schools by a male researcher. When the students were traced in 1995, the test and the questionnaire were administered in term 4 either by a male or female researcher. In most instances the test and questionnaire were administered individually. Test 1, 2 or 3 of Form A was administered once in accord with the standardization procedures, with 45 minutes plus administration time being allowed. The level of the test was chosen in accord with the year level of the student, with all students in year 9 taking Test 3. All responses were recorded by the students in pencil on the computer scoring response sheet purchased from the ACER. Results Achievement in mathematics The raw scores from the Progressive Achievement Test of Mathematics for 1993 and 1995 were converted to a scaled score, using the table from the Teachers Handbook (ACER, 1984). During the standardization process, the scaled scores had been calibrated for difficulty with the common-items linking procedure using the Rasch model calibration program BICAL3. The scores for the Forms 1, 2, and 3 were thus able to be placed on a single scale for both 1993 and 1995. The mean achievement scores were then calculated in relation to age and gender for 1993 and 1995 (see Table 1). Table 1 Mean mathematics achievement scores by year level and gender for 1993 and 1995 The comparison between the mean achievement scores, year level, and gender were then determined for both 1993 and 1995. When the scores were analysed with one way analysis of variance, a significant relationship between year level and achievement in both 1993 and 1995 was apparent (see Table 2). However there was no significant relationship between gender and mathematics achievement. The predictive relationship between achievement in 1993 and 1995 was substantiated with multiple regression using direct entry of the variables, although the year level and gender variables were not significant (see Table 3). Table 2 Analysis of variance for year level and gender in relation to mathematics achievement in 1993 and 1995 1993 mathematics achievement n = 243 df F Significance of F 1993 year level 4 51.66 <0.00 Gender 1 1.50 ns 1995 mathematics achievement 1995 year level 4 18.62 <0.00 Gender 1 1.93 ns Table 3 Multiple regression analysis of 1993 mathematics achievement, 1993 year level, and gender on mathematics achievement in 1995: n = 243 Beta r T Significance of T 1993 Mathematics achievement0.75 0.74 13.37 <0.00 1993 year level 0.20 0.43 1.42 ns Gender -0.32 -0.06 0.74 . ns Multiple R = 0.74 R square = 0.55 Standard error = 3.80 The Feelings in Mathematics Questionnaire Factor analysis. Principal components analysis and the oblimin rotation revealed that the questionnaire contained two major factors. However items 2, 7, 11 and 25 which had been inserted as filler items did not contribute to the two major factors. The oblimin factor correlations were 0.36 in the 1993 data and 0.16 for the 1995 data. Rasch analysis As the questionnaire was clearly composed of two separate factors, the requirement for unidimensionality for Rasch analysis was met. The Feelings in Mathematics Questionnaire was analysed with the QUEST program (Adams & Khoo, 1994), using the rating scale model for the analysis (see Table 4). All items were retained for the analysis, although it was already evident, on the basis of the factor analysis, that items 2, 7, 11, and 25 would be deleted as they did not meet the criteria of unidimensionality. The data from the 328 students who were administered the questionnaire in the two primary schools in 1993 were used for the analysis. Items 11 and 25 were deleted because their infit mean square values were outside the acceptable range of -0.83 to 1.20. Although items 2 and 7 appear to be fitting, they had been deleted on the basis of the factor analysis as not meeting the criteria of unidimensionality. For the purposes of the subsequent analyses the questionnaire was divided into two separate subscales, with the task involvement scale being composed of 15 items and the ego orientation scale being composed of six items. Table 4 Rasch analysis of the Feelings in Mathematics Questionnaire for 1993 Order Item no. Type of item Infit Mean Sq DiscrIndex Del items 1 item 1 task 0,98 0.44 2 item 2 filler 1.03 0.36 deleted 3 item 3 task 0.85 0.50 4 item 4 ego 0.94 0.52 5 item 5 task 0.95 0.44 6 item 6 task 0.92 0.52 7 item 7 filler 1.11 0.33 deleted 8 item 8 ego 0.92 0.53 9 item 9 task 0.98 0.51 10 item 10 task 1.00 0.40 11 item 11 filler 1.41 0.25 deleted 12 item 12 ego 0.99 0.47 13 item 13 task 0.92 0.46 14 item 14 ego 1.27 0.29 15 item 15 task 0.82 0.59 16 item 16 task 0.79 0.60 17 item 17 task 0.89 0.51 18 item 18 task 0.88 0.53 19 item 19 ego 1.15 0.38 20 item 20 task 0.93 0.53 21 item 21 task 1.13 0.41 22 item 22 task 0.88 0.49 23 item 23 ego 1.01 0.47 24 item 24 task 0.86 0.46 25 item 25 filler 1.53 -0.11 deleted Task involvement in mathematics. The 15 items that composed the task involvement scale were then further analysed with Rasch analysis using the data from the 1993 administration of the scale to 328 subjects from Years 3 to 7 (see Table 5). Table 5 Task involvement in mathematics Item analysis of the 15 item 1993 rating scale Items 16, 20 and 21 were deleted as their item infit mean square characteristics were outside the acceptable range of 0.83 to 1.20. The final scale for task involvement was thus composed of 12 items. Estimated scores for each student were then calculated on the basis of these 12 items, with the case estimates being derived by the concurrent equating method. The raw scores for 1993 and 1995 were initially pooled, the case estimates determined from the 486 cases and the estimated scores calculated for each subject for the two occasions. Concurrent methods have been found to yield stronger estimates than equating based on common difference or anchor item equating procedures anchoring (Mohandas, 1996). Ego orientation in Mathematics. The six items that composed the ego orientation scale were then further analysed with the Rasch procedure using the data from the 1993 administration of the scale to 328 subjects from years 3 to 7 (see Table 6). Table 6 Ego orientation in mathematics Item analysis of the 1993 rating scale The final scale for ego orientation was thus composed of five items. Estimate scores for each student were then calculated on the basis of these five items, with the case estimates being derived from the concurrent equating method, in which the scores for 1993 and 1995 were pooled. Stability of the task involvement and ego orientation measures. When the stability of both task involvement and ego orientation between 1993 and 1995 were measured with intraclass and interclass correlations, it was apparent that while neither measure was particularly stable, the task involvement scale was more robust over time (see Table 7). Table 7 Intraclass correlations between task involvement and ego orientation in 1993 and 1995 n = 243 F p r Task orientation 1.92 0.32 0.34 Ego involvement 1.45 0.18 0.20 The relationship between mathematics achievement and goal orientation in 1993 with achievement in and goal orientation in mathematics in 1995 The relationships between the measures of achievement and attitudes to mathematics in 1993 were examined by bivariate correlations (see Table 8), and by multiple regression (see Tables 9 and 10). Table 8 Correlations between achievement, task involvement and ego orientation in mathematics in 1993 and 1995 n = 243 2 3 4 5 6 1 1993 Maths achievement0.74***0.13* • • • 2 1995 Maths achievement 0.18** 0.13* • • 3 1993 Task involvement 0.39*** • • 4 1995 Task involvement 0.27***0.26*** 5 1993 Ego orientation 0.20** 6 1995 Ego orientation - * p <.05, ** p <.01, *** p <.001 , • correlation not significant There was a weak correlation between the mathematics achievement and task involvement measures for both 1993 and 1995. There was also a relationship between the task involvement and ego involvement measures for both 1993 and 1995. The relationship between achievement, task involvement and ego orientation was then examined with direct entry multiple regression for both 1993 and 1995 (see Table 9). Mathematics achievement was most strongly predicted by prior performance in 1993, but neither task involvement nor ego orientation measured in 1993 significantly added to the prediction of achievement in 1995. Table 9 The influence of mathematics achievement, task involvement, and ego orientation in 1993 on mathematics achievement in 1995 n = 243 Beta T Significance of T 1993 Mathematics achievement0.73 16.39 0.00 1993 Task involvement 0.08 1.78 ns 1993 Ego orientation 0.51 0.51 ns Multiple R = 0.74 R square = 0.55 Standard error=3.79 The data were then analysed by multiple regression to determine the effects of the three measures in 1993 on both task involvement and ego orientation respectively in 1995 (see Table 10). While there was no significant relationship between mathematics achievement and the two indices of goal orientation, there was an interesting relationship between the measures of task involvement and ego orientation. Specifically, there was a significant relationship between task involvement and ego involvement in 1993 with task involvement in 1995, while ego orientation in 1995 was predicted by ego involvement in 1993 only. Table 10 The influence of mathematics achievement, task involvement and ego orientation in 1993 on task involvement in 1995 and ego orientation in 1995 1995 Task involvement Beta T Significance of T 1993 Mathematics achievement 0.02 0.39 ns 1993 Task involvement 0.29 4.70 0.00 1993 Ego orientation 0.20 3.31 0.00 Multiple R = 0.39 R square = 0.15 Std. Error = 1.09 1995 Ego orientation 1993 Mathematics achievement-0.04-0.64 ns 1993 Task involvement -0.06-0.87 ns 1993 Ego orientation 0.19 2.93 0.00 Gender 1.45 2.29 0.02 Multiple R = 0.24 R square = 0.06 Std. Error =1.44 Discussion The major findings can be summarised as follows: 1. Mathematics achievement. Achievement in mathematics in 1993 was strongly predictive of achievement in mathematics in 1995. Analysis of variance indicated that achievement in both 1993 and 1995 was significantly related to the year level of the students but not to their gender. 2. Goal orientations and achievement in mathematics: Weak but significant correlations were found between task involvement and concurrent achievement (r =0.13 in both cases). Ego orientation did not correlate with achievement in either 1993 or 1995. Overall, goal orientation in mathematics as measured by the task involvement and ego orientation constructs was not related to year level or gender except in the case of ego orientation 1995, where a significant gender difference was evident. In this case boys were found to endorse ego goals more readily than the girls. 3. The influence of achievement in mathematics, task involvement and ego orientation in 1993 on achievement in mathematics, task involvement and ego orientation in 1995 Once prior achievement was included in the regression equation, it was found that task involvement failed to add to the prediction of subsequent achievement. Task involvement in 1995 was predicted by both task involvement and ego orientation in 1993 . By contrast, ego involvement in 1995 was predicted only by the same measure in 1993. Overall further evidence was found for the remarkably strong impact of past achievement on current achievement, a relationship borne out despite the fact that the majority of students were tested on different forms of the Progressive Achievement Test of Mathematics, with the scores equated with the common Rasch-derived scale as published in the test manual. These data thus make a further contribution to the known validity of this mathematics achievement instrument. It should be noted that in the present data the students had been tracked from two original primary schools, with 110 of the 243 being tracked into Years 8 and 9 in their high schools Goal orientation data, in the form of task involvement and ego orientation questionnaire measures, failed to add to the prediction of achievement over time. Task involvement significantly correlated with achievement across both time phases, but failed to account for additional variance in the 1995 achievement data once the effect of prior achievement had been accounted for in the regression analysis. The notion that goal orientation measured by task involvement, would facilitate actual achievement gain across time was not supported. The second goal dimension, that of ego orientation, similarly did not add to the prediction of achievement gain over time. In hindsight was apparent that the measure of ego orientation was inadequate, as it was based on only five items, and possessed a weak level of stability. It should be noted that the two goal orientation measures used in this project were based on a trait theory assumption: that it was possible to assess goal orientations at one point in time in order to tap into enduring dispositions. This assumption was supported by other research using similar measures (see Ames, 1992), but it should be recognised that many of the researchers in the goal theory tradition have regarded the goal dimensions as situationally induced states. The extent to which students can be meaningfully assigned to dispositional categories such as "ego oriented" and "task involved" is unknown. In a further set of analyses, not reported above, quartile splits were used on the goal orientation measures to contrast students extremely high and low on the goal dimensions. In relation to achievement, none of these analyses were significant, thus paralleling the results reported above. Hence, overall, the current data suggest that it would be unwise to make predictions of future performance changes in achievement domains from simple questionnaire measures of dispositional goal orientation. It certainly is possible, and very likely that goal orientation measures relate meaningfully to achievement gain, but uncovering the nature of this relationship will require designs and measures more complex that the ones used within this study. As indicated in the introduction to this paper, past research been very productive in tracing relationships between goal orientation, achievement related indices, and other motivational variables. In the light of the existing literature it is possible that linkages between dispositional goal orientations and achievement gain could be mediated by environmental conditions such as classroom climate and perceived competitiveness which were not addressed in this study. Significance of the study: 1. The influence of prior performance was evident for mathematics over a three year period for students from years 3 to 9. 2. While task involvement did correlate with the contiguous measure of mathematics achievement in 1993, the evidence indicated that it did not predict subsequent achievement over and above the effects of prior achievement. Ego orientation failed to correlate with achievement at any point in time. This finding however, must be tempered by the evidence that the measures were only weak to moderately stable across time, and the ego measure in particular was based on only a small number of items. 3. The study has made a significant contribution to the goal orientation literature, particularly given the longitudinal nature of the design. 4. While the present findings failed to give strong support to the notion that dispositional goal orientations were predictive of achievement gain, there is a large body of evidence within the research literature indicating that goal orientations relate to many aspects of motivated achievement related behaviour. The extent to which goal orientation measures can be regarded as having trait-like qualities is a matter as yet undecided. References Adams, R. J. & Khoo, S. (1994). Quest: The interactive test analysis system. Melbourne: ACER. Ames, C. (1992). Classrooms: Goals, structure, and student motivation. Journal of Educational Psychology, 84, 261-271. Ames, C., & Archer, J. (1987). Mothers' beliefs about the role of ability and effort in school learning. Journal of Educational Psychology, 79, 409-414. Bong, M. (1996). 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Educational Psychology, 15, 28-34. Zimmerman, B. J. (1990). Self-regulated academic learning and achievement: The emergence of a social cognitive perspective. Educational Psychology Review, 2, 173-201. Acknowledgments This study was supported by a Flinders University of South Australia Research Board Establishment Grant to Shirley M. Yates in 1995. Thanks are extended to the staff and students in the 50 schools without whom the study would not have been possible. Thanks are also extended to Professor John Keeves for his kind patience, expert knowledge and encouragement throughout the project