Journal of Educational Psychology 2003, Vol. 95, No. 3, 604 – 616
Copyright 2003 by the American Psychological Association, Inc. 0022-0663/03/$12.00 DOI: 10.1037/0022-0618.104.22.1684
A Model of Statistics Performance Based on Achievement Goal Theory
Deborah L. Bandalos
University of Georgia
Sara J. Finney
James Madison University
Jenenne A. Geske
University of Nebraska Medical Center
Structural equation modeling techniques were used to test a model of statistics performance based on achievement goal theory. Data were collected after the midterm and final examinations in an introductory statistics course, and models were fit at each time point. Learning goals were positively related to the use of deep-processing strategies and to self-efficacy and were negatively related to test anxiety. Performance goals were positively related to disorganization in study strategies and to test anxiety. Both learning and performance goals affected achievement indirectly through study strategies, self-efficacy, and test anxiety. Use of deep-processing strategies was positively related to effort but displayed an unexpected negative relationship to achievement. Disorganization was a positive predictor of test anxiety. Implications of these findings for teaching and learning statistics are discussed.
The recent emphasis in the educational psychology literature on the effects of cognitive skills on achievement offers promise to educators in that there is evidence that such skills can be taught to students, resulting in increased performance. Such findings are of particular interest in the area of statistics for two reasons. First, the numbers of students taking such courses at both the graduate and undergraduate levels is increasing (Garfield, Hogg, Schau, & Whittinghill, 2002). Second, study strategies of students in statistics courses are often ineffective (Derry, Levin, Osana, & Peterson, 2000; Gardner & Hudson, 1999). Although there is some evidence that certain skills, such as categorizing statistics word problems according to the type of analysis needed, can be taught more or less successfully (Quilici & Mayer, 1996), superficial understanding and compartmentalized knowledge is probably more the norm than the exception in introductory statistics courses. One reason for the lack of a deeper understanding may be related to Cobb’s (1997) argument that quantitative reasoning involves an integration of four very different kinds of thinking. He describes these as computational–algorithmic, logical– deductive, visual– dynamic, and verbal–interpretive. Given the essentially incongruent nature of these types of thinking and the disparate skills required by each, it is not surprising that students have difficulty devising study strategies to address what Cobb referred to as the “cognitive emulsion” of quantitative reasoning. Wild and Pfannkuch (1999) made similar points in the context of learning statistics. Adding to the difficulty of strategy use in statistics courses is the fact that the relationship between strategy use and achievement is
Deborah L. Bandalos, Department of Educational Psychology, University of Georgia; Sara J. Finney, Center for Assessment and Research Studies, James Madison University; Jenenne A. Geske, Department of Family Medicine, Research Division, University of Nebraska Medical Center. Correspondence concerning this article should be addressed to Deborah L. Bandalos, Department of Educational Psychology, University of Georgia, 325V Aderhold, Athens, Georgia 30602. E-mail: firstname.lastname@example.org 604
not clear-cut but has been found to be part of an intricate web of motivational and affective factors. Although this is true of the strategy use–achievement relationship in general, motivational and affective factors may be particularly salient in learning statistics. For example, the strong negative relationship between test anxiety and achievement in math-related courses has been a pervasive finding in both the math and statistics achievement literature (Bandalos, Yates, & Thorndike-Christ, 1995; Benson, Bandalos, & Hutchinson, 1994; Pajares & Miller, 1994; Schutz, Drogosz, White, & DiStefano, 1998; Veenman, Kerseboom, & Imthorn, 2000). More generally, researchers in the area of statistics education have emphasized the role of such affective factors as loss of confidence and subsequent disengagement in the “cycle of failure” in statistics courses (Gal & Ginsburg, 1994; Gordon, 1995). One way in which the interrelationships among study skills, affective and motivational factors, and achievement can be understood is through the organizing framework provided by achievement goal theory (Ames, 1992; Dweck, 1986, 1990; Dweck & Leggett, 1988; Midgley et al., 1998; Pintrich, 2000). These researchers posit two basic goal orientations that affect students’ approaches to responses to achievement situations. Those with learning goals, also called taskinvolved or mastery goals, generally seek to improve their knowledge and abilities, whereas those with performance goals (also referred to as ego-involved goals) are more focused on demonstrating their abilities through high performance on academic tasks.1 It should be noted, however, that learning and performance goals are not thought to be mutually exclusive. On the contrary, “adaptive individuals effectively coordinate performance and learning goals” (Dweck & Leggett, 1988, p. 260).
More recent perspectives on goal theory differentiate between approach performance (demonstrating one’s ability) and avoidance performance (avoiding the appearance of incompetence) goals. Because we did not make this distinction, we do not address this issue further.
A MODEL OF STATISTICS PERFORMANCE
In his review of the research on achievement goal theory, Urdan (1997) stated that “goal theorists are generally in agreement that goals provide an organizing framework through which a variety of cognitive and affective responses to achievement situations can be interpreted” (p.101). Achievement goal orientations are posited to influence affective reactions through their role in the creation of a context in which individuals interpret their successes and failures. Students with performance goals tend to interpret success and failure as evidence of their ability or lack thereof, whereas those with learning goals are more likely to interpret outcomes in terms of the information they provide about the effectiveness of one’s learning strategies (Bandura, 1993; Dweck & Leggett, 1988). These differences in interpretation are most salient to students’ reactions to failure situations. Because students with learning goals tend to believe that ability can be increased through effort, they are more likely to respond to failure by trying harder. In contrast, students with performance goals are less likely to believe that ability can be increased through effort and are more likely to perceive failure as an indication of their own lack of ability, leading to feelings of frustration, shame, or anxiety. As indicated previously, relationships such as these may be particularly relevant to studies of statistics achievement, in which failure is, unfortunately, sometimes experienced by otherwise high-achieving students. In the present study, we include test anxiety in our model as a possible mediator between achievement goals and performance. Another important part of the achievement goal–performance relationship is self-efficacy (Bandura, 1986, 1993; Zimmerman, Bandura, & Martinez-Pons, 1992). Dweck and Leggett (1988) studied how self-perceptions of ability mediate the relationship between goals and achievement. Because self-perceptions of ability are similar to self-efficacy beliefs, relations of the two constructs with other variables should be comparable. Dweck and Leggett explicated the mediating effects of self-perceptions of ability in the following manner. Students with a performance goal orientation tend to be concerned with how competent they appear to others. If students with such an orientation judge their abilities
to be satisfactory, they will be motivated to expend the effort necessary to do well on academic tasks and thus demonstrate their abilities. If, on the other hand, these students perceive that their abilities are not up to the task, they are likely to withdraw rather than risk failure and humiliation. Although studies reported by Dweck and Leggett support this conceptualization, it has not received unequivocal support. For example, Elliot and Church (1997) found no difference in the grades of high- and low-selfefficacy performance-oriented students. However, if supported, this mediating relationship may be particularly salient to content areas such as statistics in which students often have little confidence in their abilities. Under the scenarios described previously, we posited that goals would affect performance indirectly through their effects on effort. Another outcome to which researchers have more recently linked goals is the cognitive and metacognitive strategies used in studying (Elliot, McGregor, & Gable, 1999). Study strategies have been of particular interest to educators because there is evidence that such skills can be taught to students, resulting in increased performance. However, only a few studies in the area of mathematics or statistics have addressed the influence of cognitive skills or use of study strategies on achievement (Pokay & Blumenfeld, 1990; Schutz et al., 1998; Veenman et al., 2000). Subject-specific research on the effects of study strategies is important because there is evidence that different learning strategies are more or less efficacious depending on the type and complexity of the material to be learned (Pintrich & de Groot, 1990; Pokay & Blumenfeld, 1990; Schutz et al., 1998). Because the process of learning statistics involves what O’Connell (2002) has called a “multiplicity of competencies” including statistical language and procedures as well as statistical reasoning, the matching of strategies to material may be particularly critical in this area. In the present study, goal theory is adopted as a framework for a comprehensive model of achievement in an introductory statistics course. This model is shown in Figure 1 and hypothesizes that students’ goals affect course performance indirectly through their
Hypothesized positive ( ) and negative (–) paths model of statistics achievement.
BANDALOS, FINNEY, AND GESKE
effects on self-efficacy, test anxiety, effort, and study strategies. Although models involving cognitive, motivational, and affective predictors of statistics achievement have been proposed in the statistics education literature (Garfield et al., 2002), such a model has not been tested previously. Because of the particular salience of model components such as test anxiety and self-efficacy in statistics learning, such a model is of considerable interest. The various components of the present model are elaborated separately in the following sections.
Bandura (1986) stated that “given appropriate skills and adequate incentives . . . efficacy expectations are a major determinant of people’s choice of activities, how much effort they will expend, and of how long they will sustain effort” (p. 194). He went on to describe how self-efficacy both influences and is influenced by effort, with success based on small amounts of effort leading to greater appraisals of ability than success resulting from greater effort. Dweck and Leggett (1988) have hypothesized that selfperceptions of ability serve a mediating role in the relationships of learning goals with both effort and affect. Under this paradigm, students who are performance oriented and have positive perceptions of their abilities may choose to expend a greater amount of effort in the belief that this will lead to the desired high levels of performance. On the other hand, performance-oriented students with more negative ability perceptions may feel that, even if an increase in effort were to lead to some increase in learning, they may still ultimately fail. Because high-effort expenditure that results in failure is usually interpreted by these students as evidence of low ability, students may choose to withdraw from the task rather than risk being seen as lacking in ability. A different but not incompatible view is that, because those with performance goals tend to view failure as indicating a lack of ability, it is difficult for these individuals to maintain high levels of confidence in the face of failure. In contrast, those with learning goals are less likely to associate failure with ability deficits and are therefore less likely to lose confidence in their abilities under failure conditions. Studies reported by Dweck and Leggett showed that high levels of learning goals are associated with greater persistence and more positive affect regardless of self-perceived ability levels. Similar results were reported by Wood and Bandura (1989; as cited in Bandura, 1993) from a study of performance on managerial tasks. The mediating relationship of ability perceptions has not been found consistently, however. For example, results from a recent study by Pintrich (2000) indicated no significant differences in levels of self-efficacy or negative affect for math students with different combinations of mastery and performance goals. Self-efficacy has been found to be positively related to achievement in several studies in the areas of mathematics and statistics (Pajares & Miller, 1994; Randhawa, Beamer, & Lundberg, 1993; Schutz et al., 1998; Zohar, 1998). However, other studies have failed to find such a relationship (Bandalos et al., 1995; Benson et al., 1994; Norwich, 1987). The latter results may be due to the inclusion of both self-efficacy and self-concept in these three studies. As Pajares and Miller (1994) have pointed out, the inclusion of both self-concept and self-efficacy measures in the same study may result in nonsignificance of one or both of these variables due to the typically high correlations between them. Bandura
(1986) distinguished self-efficacy from self-concept by pointing out that the latter is a more generalized form of self-image that is affected by levels of self-efficacy, among other things. He argued that, because of its greater task specificity, self-efficacy should be a better predictor of behavioral outcomes. In addition to its relationship with achievement, self-efficacy has been found to have a strong negative association with test anxiety (Bandalos et al., 1995; Benson et al., 1994; Zohar, 1998). Zohar (1998) found that when both self-efficacy and test anxiety were included as predictors of achievement, only the former was significant. He suggested a mediational model in which selfefficacy affects test anxiety, which in turn affects achievement, but noted that self-efficacy might also have a direct effect on achievement. Such a mediated path was supported in the study by Benson et al. (1994), although the direct path was not. In the present study, both direct and indirect (through test anxiety, effort, and study strategies) effects of self-efficacy on achievement are tested.
One way in which goals are thought to affect performance is through their relationship with strategy use. Several studies have examined the link between goals and strategy use (Ames & Archer, 1988; Schraw, Horn, Thorndike-Christ, & Bruning, 1995) or between strategy use and achievement (Pintrich & de Groot, 1990; Pokay & Blumenfeld, 1990; Schutz et al., 1998; Veenman et al., 2000). Ames and Archer (1988) found that 8th- to 11th-grade students who perceived their classroom environment as being learning oriented were more likely to use information processing, self-planning, and self-monitoring strategies. No significant relationship between perceived performance goal emphasis and these learning strategies was found. In the study by Schraw et al. (1995), significant positive correlations of learning goals with both strategy use and metacognitive knowledge (as measured by selfreports) were found for a sample of college undergraduates. Pokay and Blumenfeld (1990) found that self-reported use of general metacognitive strategies was negatively related to high school geometry achievement early in the semester but positively related to achievement later in the semester. However, because the zero-order correlations of metacognitive strategy use and achievement were close to zero at both time periods, it seems likely that the observed relationships were due to suppressor effects. Pintrich and de Groot (1990) found that strategy use was significantly positively related to performance on both exams and essays for a sample of seventh-grade students in science and English classes. In the study conducted by Schutz et al. (1998), no relationship between use of elaboration strategies and exam grades in a graduate statistics course was found when strategies were measured by using items from the Motivated Strategies for Learning Questionnaire (MSLQ; Pintrich, Smith, Garcia, & McKeachie, 1991). However, when these researchers analyzed interviews with low- and high-performing students, they found that high-performing students reported using more self-monitoring and elaboration strategies when studying. In the study by Veenman et al. (2000), metacognitive ability was measured through the use of think-aloud protocols and systematic observations that focused on mathspecific strategies such as “paraphrasing what was asked for” and “estimating a possible outcome.” These researchers found that metacognitive ability was positively related to math achievement
A MODEL OF STATISTICS PERFORMANCE
for two samples of Dutch high school students. A possible explanation for the conflicting results of these four studies may be the differences in procedures used to assess strategy use. Veenman et al., referring to earlier studies conducted in this area, reported that “research revealed that students’ self-reported study behavior on questionnaires hardly corresponded to their actual study behavior in a learning situation” (p. 394). Only one study, not in the area of statistics, was found in which the mediational role of goals on the strategy use 3 achievement relationships was investigated. In this study, based on two samples of college students in introductory psychology classes, Elliot et al. (1999) examined the effects of two types of learning strategies using self-reports of strategy use. Deep-processing strategies were defined as “challenging the veracity of information encountered and attempting to integrate new information with prior knowledge and experience” (p. 549), whereas surface processing included such things as rehearsal and memorization. Disorganization was defined as “difficulty in establishing or maintaining a structured, organized approach to studying” (p. 549). Although learning goals were found to be positively related to self-reported deep processing of information, they were not related to exam scores. Thus the mediational role of deep processing in the learning goal 3 achievement relationship was not supported. Performanceavoidance goals were significantly negatively related to both selfreported use of deep-processing strategies and exam scores, supporting the mediating role of deep-processing strategies for the performance avoidance 3 achievement relationship. Performanceavoidance goals were also significantly positively related to selfreported use of surface-processing strategies. Finally, although performance-approach goals were positively related to exam scores, they were not significantly related to self-reports of any type of study strategy, thus failing to support this mediational path.
analysis of the same data, Schutz et al. found that one cluster of low-performing students was characterized by both high test anxiety and high use of elaboration study strategies, suggestive of Naveh-Benjamin et al.’s (1987) Type 2 students. Discrepancies in the results of these studies could be due to differences in the measurement of strategy use, as discussed earlier. Finally, although relationships between goals and test anxiety have been posited (Dweck & Leggett, 1988; Elliot, 1997), little empirical research has been done in this area. According to Dweck and Leggett (1988), students with performance goals are more likely to react to failure situations as a threat to their ability, engendering test anxiety, whereas those with learning goals would be more likely to view failure as a signal that more effort is required. However, Pintrich (2000) found no significant relationship of test anxiety with either learning or performance goals in a study involving eighth- and ninth-grade students in math classes. In contrast, Skaalvik and Rankin (1995) found a significant negative relationship of anxiety in math classes with performanceavoidance goals. The relationships of learning and performance goals to test anxiety in statistics classes has not been studied previously.
Overview of Present Study
On the basis of the literature cited previously, we formulated a model of achievement in statistics, which is shown in Figure 1. Specifically, the following relationships were posited: (a) Learning goals will positively impact self-efficacy, effort, and use of deepprocessing strategies and negatively impact test anxiety. Learning goals are also hypothesized to affect achievement indirectly through these four variables. (b) Performance goals will positively influence self-efficacy and deep processing, but these relationships will be weaker than those of learning goals with these variables. Performance goals will also be positively related to disorganization in study strategies and to test anxiety and will affect achievement indirectly through these variables. (c) Self-efficacy will have direct positive relationships with deep-processing strategies, effort, and achievement, and will have negative relationships with disorganization in study strategies and test anxiety. In addition to its direct effect on achievement, self-efficacy is also expected to affect achievement indirectly through study strategies, test anxiety, and effort. (d) Disorganization in study strategies will affect achievement negatively and test anxiety positively. In addition, disorganization will affect achievement indirectly through its effect on test anxiety. (e) Use of deep-processing strategies will impact positively on effort and achievement and will also affect achievement indirectly through its effect on effort. (f) Test anxiety will influence achievement negatively and effort positively. However, the increase in effort will result in lower, rather than higher, achievement scores, so that effort is expected to impact negatively on achievement. These relationships are expected to be manifested at both the middle and the end of the semester. In addition, because data were collected at two times during the semester, we included previous (midsemester) achievement in the model for end-of-semester achievement in order to investigate the effects of the study variables while controlling for prior achievement. This study extends the research base by incorporating a comprehensive set of cognitive, motivational, and affective predictors of achievement in a
The negative relationship between test anxiety and achievement in math-related classes has been a consistent finding in the literature (Bandalos et al., 1995; Benson et al., 1994; Pajares & Miller, 1994; Schutz et al., 1998; Veenman et al., 2000). In the present study, we were particularly interested in study or metacognitiveskill deficits as a mediator of this relationship as found in the study by Veenman et al. (2000). Naveh-Benjamin, McKeachie, and Lin (1987) have described two ways in which such mediation is manifested. Type 1 students lack effective study and/or cognitive skills, and this deficit leads to poor performance and test anxiety. In contrast, Type 2 students have adequate skills but are unable to benefit from them in testing situations because test-irrelevant worry drains their cognitive resources. In the Veenman et al. study, support for both of these typologies was found. We felt that both of these patterns were relevant to statistics achievement because of the typically high levels of test anxiety and often ineffective study strategies of students in statistics courses. Other studies, although not investigating the mediating effect of study strategies, did examine the link between strategy use and test anxiety. Pintrich and de Groot (1990) found that neither use of self-regulation strategies nor general cognitive strategies was significantly related to test anxiety, whereas Schutz et al. (1998) were unable to support a relationship between use of elaboration strategies and test anxiety in a statistics course. However, in a cluster
BANDALOS, FINNEY, AND GESKE was measured by such items as “It is important for me to get a better grade than my classmates” and “I like others to think I know a lot.” Strategy use. The MSLQ (Pintrich & de Groot, 1990) includes two scales designed to measure cognitive strategy use and self-regulation in study behaviors. Items on these scales were answered using a 7-point Likert-type format. Students were administered these items immediately after their midterm and final examinations with instructions to “answer in terms of how you have studied for this class and this test in particular.” We attempted to replicate the two-factor structure described by Pintrich and de Groot (1990) using principal-axis factoring. However, the structure and pattern matrixes obtained did not support the factor structure described by those authors. Instead, we obtained two factors. One of these factors, labeled deep processing, included seven items, four of which were very similar to those on the Elaboration scale from the revised version of the MSLQ (Pintrich et al., 1991). The other three items on this scale were worded similarly to items on the Self-Regulation scale of that instrument. The second factor was labeled disorganization and contained items that were very comparable with those on the disorganization scale used by Elliot et al. (1999). A complete listing of the items used to measure deep processing, disorganization, and self-efficacy is in the Appendix. We obtained values of coefficient alpha of .78 and .71 at Times 1 and 2 for the deep-processing scale and .73 and .68 for the Disorganization scale. These values are comparable with those reported by Pintrich et al. (1991) and Elliot et al. for similar scales. Test anxiety. Test anxiety was assessed by the Worry scale of the Test Anxiety Inventory (TAI; Spielberger, 1980). The Worry scale, rather than the entire instrument, was used because worry, rather than emotionality, is the aspect of test anxiety that is hypothesized to result in decrements in performance, and this has been demonstrated in several studies. This instrument was administered to students immediately after they had taken a course exam in their statistics class with instructions to answer according to how they had felt while taking the exam. The TAI consists of 20 items with a 4-point Likert-response format, of which 8 items form the Worry scale. Worry items include questions about how worrying might affect one’s test performance. In the present study, alpha values of .92 and .93 were obtained for the Worry scale at Times 1 and 2, respectively. The correlation between Worry scores at the two time periods was .80. Self-efficacy. Perceived self-efficacy was measured by eight efficacy items adapted from the MSLQ (Pintrich & de Groot, 1990), using a 7-point Likert format. These items are very similar to those in the revised MSLQ (Pintrich et al., 1991). The wording of some items was changed slightly from its original format to refer specifically to statistics. In addition, the scale was augmented by the inclusion of two items used in a previous study (Bandalos et al., 1995): “I think I am naturally good at statistics” and “Learning statistics is easy for me.” The items were administered twice, following the midterm and final exams. Pintrich and de Groot (1990)
content area in which they have not previously been studied and in which these factors may be particularly salient.
Method Subjects and Procedures
Subjects in the study were 355 students in nine sections of an undergraduate course in an introductory statistics course taught during the spring and fall semesters of 1998 at a large, public, midwestern university. During the first week of class, students completed an instrument that included the Goals Inventory (Roedel, Schraw, & Plake, 1994), an instrument designed to measure goal orientation. Students were also surveyed at two times later in the semester, immediately after the midterm and final course exams in the statistics class. The surveys administered at these two times included measures of test anxiety, self-efficacy, and strategy use as well as questions about the amounts of time spent on such activities as reading the textbook, working on end-of-chapter exercises, and studying for exams. Students were also asked for permission to obtain their exam scores from their course instructor. Descriptive statistics for the scales at both time points for the final sample are shown in Table 1. Although all students who enrolled initially volunteered to participate in the study, attrition and absences during the course of the semester resulted in missing data on at least one variable for approximately 50% of the students. Because we wanted all results to be based on the same group of students, only those with complete data at all three data collections were included in analyses. Deletion of cases with missing data resulted in a sample size of 176. Independent sample t tests of students with and without missing data on the study variables revealed only one significant difference between the two groups. Students with missing data had significantly lower scores on the final examination than did students with complete data (t 3.174, p .002). However, in terms of effect size the difference is not large (d .34).
Goal orientation. The Goals Inventory (Roedel et al., 1994) consists of 25 items measured on a 5-point Likert scale. Roedel et al. (1994) reported that a two-factor structure representing learning and performance goals resulted from an orthogonal principal-axis factor analysis. These authors also reported estimates of test–retest reliability of .73 and .76 for the Learning and Performance subscales, respectively, over a 2-week period. Values of coefficient alpha were .80 for the Learning scale and .76 for the Performance scale. In the present study, alpha values of .79 and .72, respectively, for the Learning and Performance scales were found. Examples of learning items are “I enjoy challenging school assignments” and “Personal mastery of a subject is important to me,” whereas performance
Table 1 Descriptive Statistics and Values of Coefficient Alpha for Scale Scores at Times 1 and 2 (n
Time 1 Scalea Self-Efficacy (11) Test Anxiety (Worry; 8) Effortb Deep Processing (7) Disorganization (4) Exam score (standardized) M 57.2 13.7 86.1 31.1 10.3 0.2 SD 13.0 5.2 93.0 7.6 3.9 0.9 Skewness 0.9 1.1 2.4 0.2 0.7 1.1 Kurtosis 0.6 0.7 6.7 0.1 0.1 1.3 .95 .92 .78 .73 M 58.2 13.3 89.0 30.3 10.2 0.1
Time 2 SD 13.9 4.9 156.6 6.7 3.8 0.9 Skewness 1.1 1.1 8.0 0.4 1.1 1.6 Kurtosis 0.9 0.8 82.5 0.1 1.3 1.3 .95 .93 .71 .68
Note. For the Learning Orientation Scale (12), M 45.9, SD 5.1, skewness 0.1, kurtosis 0.6, and .79; for the Performance Orientation Scale (5), M 17.4, SD 3.6, skewness 0.5, kurtosis 0.2, and .72. a Numbers in parentheses indicate number of items on the scale. b Effort scores indicate average numbers of minutes per week.
A MODEL OF STATISTICS PERFORMANCE
Table 2 Covariance Matrix for Model of Statistics Achievement (n
1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Ach1 Ach2 Learn Perf Deep1 Deep2 Disorg1 Disorg2 SE1 SE2 Anx1 Anx2 Eff1 Eff2 0.743 0.424 0.249 0.186 0.703 0.653 1.059 1.103 5.302 6.639 1.105 1.138 0.083 0.107 2 0.747 0.909 0.274 0.459 0.511 1.647 1.703 6.312 6.979 1.652 1.677 0.065 0.035 3 4 5 6
7 8 9 10 11 12 13 14
25.998 4.637 10.639 6.406 5.845 6.040 27.300 24.051 6.342 6.451 0.173 0.492
13.183 0.961 1.700 0.080 0.293 11.232 10.711 3.411 2.771 0.272 0.331
57.802 32.701 3.386 3.080 7.665 2.858 0.784 0.884 2.105 2.104
44.969 0.022 2.722 7.126 2.471 0.119 1.268 1.244 1.487
15.416 10.797 27.909 29.382 11.225 9.237 0.684 0.037
14.358 24.868 25.754 8.591 9.217 0.041 0.373
170.401 154.151 32.462 25.004 2.258 0.461
193.151 31.584 26.294 2.153 0.361
27.304 20.942 1.664 0.915
23.561 0.858 0.550
Note. Ach1 achievement, Time 1; Ach2 achievement, Time 2; Learn learning orientation; Perf performance orientation; Deep1 deep processing, Time 1; Deep2 deep processing, Time 2; Disorg1 disorganization, Time 1; Disorg2 disorganization, Time 2; SE1 self-efficacy, Time 1; SE2 self-efficacy, Time 2; Anx1 test anxiety, Time 1; Anx2 test anxiety, Time 2; Eff1 effort, Time 1; Eff2 effort, Time 2.
reported a coefficient alpha value of .89, based on a sample of 173 seventh-grade students. Coefficient alpha values of .95 for the 10-item scale used in the present study were obtained at both time points. The test–retest coefficient across the 5-week time period was .86. Effort. Following the two course exams, we assessed effort by asking students several questions regarding the amounts of time they spent engaging in the following activities: studying for the exam, reading the textbook, completing homework assignments, reviewing material or working on practice problems, and working in a study group. Although we originally intended to create a scale from these items, we found that their intercorrelations were not sufficiently high to support such a scale. This may have been due to a lack of variability, as many students reported spending 0 min on the majority of these activities. Because time spent doing homework assignments displayed the greatest amount of variability, we used this as our single indicator of effort. This item was “So far this semester, about how many minutes have you spent on homework assignments?” Exploratory analyses using other of the effort questions confirmed that these did not add additional explanatory power to our models. Achievement. Students’ midterm and final examination scores were obtained from their course instructors and were used as our measures of achievement. Exams were essentially the same across the nine class sections, and amounts of variability and percentage correct scores were comparable across sections. However, exams differed somewhat in numbers of questions, because the instructor of two of the sections included extra questions on her exams. For this reason, exam scores were standardized within classes, and the standardized exam scores were used in all analyses. Questions on the exams were designed to focus on conceptual understanding of the material but also included computational and definitional problems.
one minus the reliability of the measure times the variance of the variable to take into account the lack of perfect reliability. Similar procedures were used to correct for the presumed lack of perfect reliability of the exam scores and students’ self-reports of time spent on homework. Reliabilities for these variables were estimated at .8 and .9, respectively.2 As can be seen from Table 1, distributions of the hours spent on homework were highly nonnormal. These distributions were therefore log transformed prior to analyses. Because all other variables displayed relatively small levels of skewness and kurtosis and because the relative multivariate kurtosis estimate given by PRELIS was 1.2, indicating no serious deviations from multivariate normality, maximum-likelihood estimation was used. Separate models were analyzed for data collected at the midterm and the final exams. These models will be referred to as the Time 1 and Time 2 models, respectively. Both models included the goalorientation data collected at the beginning of the semester, but all other measures were collected immediately after either the midterm (for Time 1) or final (for Time 2) exams. In addition, previous achievement, as measured by scores on the midterm exam, was included as a predictor of achievement and self-efficacy in the Time 2 model in order to investigate the effects of the study variables when prior achievement was controlled.
Time 1 Model
Overall model fit. The Time 1 model is shown in Figure 2. Standardized path coefficients are shown for paths that were statistically significant; dashed lines indicate hypothesized paths that were not significant. Although not shown in Figure 2 for
2 Because these values are admittedly arbitrary, we conducted a sensitivity analysis, as suggested by Bollen (1989), to determine whether the use of lower values would have changed our results. We varied both reliability estimates as low as .60 (in increments of .05) and found no changes in standardized parameter values greater than .09. Most changes were much smaller, and none resulted in a change in statistical significance for any path in either of our two models.
Structural equation models based on our hypotheses were analyzed using LISREL Version 8.51 (Joreskog & Sorbom, 1993), ¨ ¨ with a covariance matrix generated by PRELIS Version 2.3 (Joreskog & Sorbom, 1996). The covariance matrix used is in¨ ¨ cluded as Table 2. Because of the relatively small sample size, analyses were not run at the item level. Instead, the covariance matrix was based on total scores for test anxiety, deep processing, disorganization, self-efficacy, and performance and learning goals. The measurement error variances for these variables were set at
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Figure 2. Time 1 model with standardized path coefficients shown. Dashed lines indicate hypothesized paths that were nonsignificant.
simplicity, the disturbance terms for deep processing and disorganization were allowed to correlate, consistent with the fact that these are subscales of the same instrument. The overall fit of the model was good, 2(6, N 176) 8.29, p .22, root-meansquare error of approximation (RMSEA) .05, standardized root-mean-square residual (SRMR) .03, normed fit index (NFI) .97, comparative fit index (CFI) .99. These values exceed those recently recommended by Hu and Bentler (1999) as indicative of good model fit. However, the parsimonious normed fit index (PNFI .21) indicated that fit was obtained to some extent at the expense of parsimony. Values of the standardized path coefficients for both direct and indirect paths are shown in the left-hand side of Table 3, which also includes the t values and values of R2. Values of direct paths. Most, but not all, of the hypothesized direct paths were statistically significant. Both learning and performance goals positively predicted self-efficacy, although learning goals had the stronger path value, as expected. Learning goals was also the only significant predictor of deep processing. Values of the paths from performance goals and self-efficacy to deep processing were not significant, but path values from these two predictors to disorganization and test anxiety were significant and the expected directions. The path value for the learning goals 3 test anxiety relationship, although in the expected negative direction, was not significant. Disorganization was a strong positive predictor of test anxiety, as expected. Effort was a positive predictor of test anxiety and deep processing, as anticipated, but did not significantly affect learning goals or self-efficacy. Finally, the only significant predictors of achievement at Time 1 were selfefficacy and deep processing. However, although the relationship between self-efficacy and achievement was in the expected positive direction, the path value from deep processing to achievement had an unanticipated negative sign. Values of indirect paths. Indirect path and t values for the Time 1 model are shown in the second column of Table 3. As
anticipated, learning goals had a significant, positive, and indirect effect on achievement through their influences on selfefficacy and deep processing. However, because of the negative direct deep processing 3 achievement effect, the positive value of the indirect learning goal 3 achievement path was weakened somewhat. Performance goals also affected achievement indirectly through self-efficacy. However, none of the other expected indirect effects on achievement were found to be statistically significant. Although not hypothesized, both learning and performance goals, it was interesting to note, had significant, negative, and indirect effects on disorganization. Learning goals and self-efficacy also displayed significant, indirect effects on test anxiety in a negative direction. Finally, selfefficacy negatively affected effort through its effect on test anxiety. R2 values. Although substantial amounts of the variance in test anxiety (.51) and disorganization (.45) were explained, these R2 values were primarily due to one or two very strong relationships in each case. The explained variance for achievement (.33) was more modest, and the model was able to explain very little of the variance in deep processing, self-efficacy, or effort.
Time 2 Model
Overall model fit. The hypothesized model at Time 2 was the same as that for Time 1, except for the inclusion of Time 1 achievement as a predictor of Time 2 achievement and selfefficacy. This model is shown in Figure 3. As in Figure 2, standardized path coefficients are shown for statistically significant paths, and nonsignificant hypothesized paths are indicated by dashed lines. This model did not fit as well as the Time 1 model, with 2(11, N 176) 25.03, p .009, RMSEA .08, SRMR .05, NFI .94, CFI .96, but values of the fit indices do exceed recommendations for good model fit (Hu & Bentler, 1999). As with the Time 1 model, however, the PNFI value of .29
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Table 3 Standardized Path Coefficients, t Values, and R2 Values for Models at Times 1 and 2
Time 1 Direct Path To Effort from: Learning Orientation Performance Orientation Achievement Time 1 To Deep Processing from: Learning Orientation Performance Orientation Self-Efficacy To Disorganization from: Learning Orientation Performance Orientation Self-Efficacy To Test Anxiety from: Learning Orientation Performance Orientation Disorganization Self-Efficacy To Effort from: Learning Orientation Performance Orientation Text Anxiety Deep Processing Disorganization Self-Efficacy To Achievement from: Learning Orientation Performance Orientation Text Anxiety Disorganization Deep Processing Self-Efficacy Effort Achievement Time 1 Note. Values significant at p coefficient. PC 0.38 0.14 0.39 0.12 0.05 0.16 0.69 0.07 0.26 0.50 0.21 0.05 0.30 0.33 0.03 t 5.33 2.00 .13 4.37 1.36 0.49 2.13 8.95 1.04 3.87 4.52 2.00 0.58 3.31 3.62 0.33 0.04 0.01 0.02 0.02 0.00 0.00 0.00 0.00 2.70 2.86 .33 0.01 0.03 0.21 0.54 0.06 0.07 0.17 2.17 4.52 0.71 2.29 1.82 0.69 0.09 0.69 0.22 0.03 0.43 0.12 0.12 0.10 0.44 0.35 3.31 1.65 1.06 1.54 4.56 0.02 0.00 0.00 0.00 0.00 0.02 0.25 2.24 0.05 1.14 0.17 1.26 3.82 4.18 path 0.02 0.01 0.18 0.09 0.21 0.00 0.14 0.00 0.01 0.49 0.48 .45 4.61 1.95 .51 4.38 0.00 4.04 .21 0.36 0.66 0.09 0.16 0.23 0.05 0.86 1.73 2.37 0.51 0.03 0.01 1.61 1.71 .71 0.01 0.00 0.71 0.32 0.16 0.28 0.51 0.11 1.89 3.36 4.37 1.05 0.15 0.02 0.11 3.57 0.23 3.81 .08 0.11 0.64 1.23 7.58 0.14 0.06 3.87 1.35 .45 0.32 0.16 0.06 2.76 1.43 0.58 0.02 0.01 0.57 0.54 .39 PC Indirect t R2 .20 0.32 0.10 0.61 4.45 1.38 8.87 .09 PC Direct t PC Time 2 Indirect t R2 .71
.05 are indicated by boldface; because of the directional nature of our hypotheses, all tests are one-tailed. PC
indicates that the model lacks parsimony. The standardized path values, t values, and values of R2 for this model are shown in the right-hand side of Table 3. Values of direct paths. Similar to the results at Time 1, many, but not all, of the hypothesized direct relationships were supported in the Time 2 model. In addition, most of the path values were quite similar to those obtained at Time 1, with the following exceptions. Performance goals were not found to be significant predictors of disorganization at Time 2, although the direction of the relationship remained negative. Paths from learning and performance goals to test anxiety displayed the expected negative and positive values to test anxiety at Time 2; at Time 1 only the latter value was statistically significant. However, contrary to our findings at Time 1, self-efficacy did not have a significant negative impact on test anxiety at Time 2. Deep processing and test anxiety maintained their significant positive paths to effort at Time 2. Achievement at Time 1 has positive direct effects on both self-efficacy and achievement at Time 2. The paths from selfefficacy and deep processing to achievement, significant at
Time 1, were no longer significant in the Time 2 model. It may be that these two predictors are spuriously related to Time 2 achievement through prior achievement, resulting in nonsignificant relationships when prior achievement is included in the model. Values of indirect paths. Although two of the variables that predicted achievement at Time 1 were nonsignificant at Time 2, it was interesting to note that learning goals and self-efficacy maintained the significant, indirect relationships with achievement they exhibited at Time 1.With the exception of the indirect path from performance goals to disorganization, all other indirect paths that reached significance at Time 1 were also significant at Time 2. Values of R2. Values of R2 for self-efficacy and achievement at Time 2 were noticeably higher than at Time 1, probably because of the inclusion of Time 1 achievement as a predictor of these variables. The R2 values for all other variables were roughly comparable across the two time periods, with the exception of that for effort. At Time 2, the R2 value for this variable was .08, compared with .21 at Time 1.
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Figure 3. Time 2 model with standardized path coefficients shown. Dashed lines indicate hypothesized paths that were nonsignificant.
The results of this study offer support for the role of achievement goals as predictors of self-reported strategy use, self-efficacy, and test anxiety. These results are consistent with previous research, as summarized in a recent review of the goal theory research (Urdan, 1997). Specifically, although both learning and performance goals positively predicted self-efficacy at both time points, learning goals displayed the stronger relationship. These results are also consistent with those summarized by Skaalvik (1997) is his review of the self-concept literature. The positive relationship found between learning goals and deep processing of information is consistent with the results of Elliot et al. (1999). In the present study, however, the relationships of goals with selfefficacy and strategies were maintained even when a measure of prior achievement was included in the model, thus strengthening support for these relationships. Although both Elliot et al. and we measured study strategies through the use of self-reports, in the present study the measure of deep processing included mainly elaboration items, whereas the items used in the Elliot et al. study were characterized by Pintrich et al. (1991) as measures of critical thinking. The present study thus extends this relationship to different types of higher level study strategies. Another difference between the two studies is that Elliot et al. categorized performance goals as performance avoidance or performance approach, whereas only the former were related to disorganization in study strategies. In the present study, performance goals included only performance-approach items, but a significant, positive relationship with disorganization was still found. Finally, although many of the relationships investigated in the present study have been
examined in other content areas, the present study is unique in that it has examined these relationships in the context of a statistics class. Given the documented increases in the number of students enrolled in statistics courses (Garfield et al., 2002) and the importance of understanding quantitative information (Cobb, 1997), it seems clear that a better understanding of performance in statistics courses is an important area of study for the new millennium. Although careful inspection of Figures 2 and 3 reveals few significant direct paths to achievement, several hypothesized indirect paths have been supported. These indirect paths are of particular interest because previous studies have been restricted to investigating only direct effects. Self-efficacy was found to affect achievement both directly and indirectly, through its influences on self-reported strategy use and test anxiety. The mediational role of test anxiety in the relationship between self-efficacy and achievement suggested by Bandura (1986) and Zohar (1998) has also been supported in the Time 2 model. The hypothesized indirect relationship between goals and effort through self-efficacy was not supported. Although learning goals did positively predict selfefficacy as hypothesized, self-efficacy did not have a significant direct effect on effort at either time point. However, both learning and performance goals were indirectly related to achievement through their relationships with self-efficacy, self-reported strategy use, and test anxiety at Time 1. At Time 2 only the indirect effects of learning goals were maintained. The Time 2 findings are of particular interest in that at this time point the indirect relationships of learning goals and self-efficacy to achievement remained significant even after the effects of prior achievement had been taken into account.
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Finally, the positive relationship of disorganization to test anxiety found in this study partially supports the profile of the Type 1 test-anxious student suggested by Naveh-Benjamin et al. (1987). For these students, a lack of effective study strategies is thought to lead to poor performance, which in turn results in test anxiety. In the present study, test anxiety was positively related to disorganization at both time points but was not significantly related to achievement. However, at Time 2 disorganization affected both achievement and test anxiety, suggesting the possibility of a spurious relationship between test anxiety and achievement due to a common cause: deficits in study strategies. This result is consistent with the “deficits” model of test anxiety (Tobias, 1985) in which a lack of adequate encoding and organizing skills is thought to result in both test anxiety and decreased test performance. Although the results of the present study provide strong evidence for such a causal path, it must be emphasized that demonstration of causality in the absence of an experimental design is beyond the capabilities of the methodology used here. As with all posited paths in the present study, any conclusions with regard to causality can be only tentative. A model in which test anxiety “causes” decrements in both study strategies and exam performance cannot be ruled out on the basis of the present findings. The results of the present study offer some insight into the difficulties students often experience in understanding statistics. One intriguing result of this study is the negative relationship of deep processing with achievement. Although a similar relationship was found in the study by Pokay and Blumenfeld (1990), this appears to have been the result of a suppressor effect. The present result cannot be explained in this way because the bivariate relationship between the two variables was itself negative, though weak. It is the case that other studies have found mixed results in this area. Elliot et al. (1999) found positive relationships between deep processing and achievement in introductory psychology classes, but Schutz et al. (1998) failed to find any relationship between the two variables in graduate statistics classes. However, when a cluster analysis was performed in the Schutz et al. study, one cluster of students reporting high use of elaboration strategies but low test performance was found. Although differences in the method of measuring deep processing is one possible explanation for these results, Schutz et al. hypothesized that use of deepprocessing strategies may only be useful for students after they have developed a basic understanding of the concepts. Similarly, with regard to strategy use in geometry, Pokay and Blumenfeld speculated that “it might be the case that students who are poor learners or new at the subject need to experiment with more concrete strategies before they can make use of metacognitive planning and implementation” (p. 47). A related possibility is suggested by Elliot et al.: “One intriguing possibility is that deep processing does not have a strong influence on immediate performance outcomes (independent of ability) but that it facilitates the long-term retention of material that has been learned” (p. 559). In the present study, short-term rather than long-term retention was assessed. We feel that there is some support for the hypothesis that the negative relationship may have to do with inefficacious use of deep-processing strategies. As stated by Pintrich and de Groot (1990), “students must be able to understand not only the ‘what’ of cognitive strategies but also how and why to use strategies effectively” (p. 38). Successful learning may therefore depend more on
one’s ability to choose efficacious study strategies as on one’s ability to use any specific strategy. The use of deep-processing strategies before one has developed a basic understanding of the material may, in some cases, do more harm than good. This may be especially true in the area of statistics, where students often find their usual study strategies ineffective and struggle to find strategies that will work. In this area it may be the case that the use of memorization and rehearsal strategies is quite effective at the beginning stages of study and that use of elaboration and other deep-processing strategies at this stage simply leads to confusion for many students. Some support for this position can be found in a recent study by Rittle-Johnson and Alibali (1999) in which elementary school students were given instruction focusing on either procedural or conceptual knowledge in the context of mathematics. Results indicated that the relationship between the two is bidirectional, with instruction in procedures resulting in gains in conceptual knowledge and conceptual instruction resulting in increases in correct use of procedures. Although this study was conducted with elementary school rather than college-aged students, the results were of interest in that previous studies had suggested a more one-sided relationship, with conceptual knowledge driving procedural skill. In the present context, the results are of interest in that they suggest that increases in conceptual knowledge may not necessarily result in increased procedural skill. As Rittle-Johnson and Alibali suggested, the bidirectional effects found in their study may have been due to the fact that the procedures being taught were not overly complex for students. These authors noted that “it is possible that conceptual instruction may facilitate procedure generation only under these conditions” (p. 187). In the present study, many of the procedures taught were quite complex. Completing these procedures may therefore have exhausted all of the mental resources students had available, and attempts to incorporate more abstract conceptual knowledge may have proved counterproductive. This would be especially true if the examinations did not incorporate many questions in which conceptual knowledge was called for. In light of this hypothesis, it is interesting to note that some researchers in statistics education have pointed out that learning in the majority of classes in this area is concentrated on knowing formulas and working out numerical problems, tasks that do not necessarily require students to develop a deep understanding of the concepts involved (e.g., Gal & Garfield, 1997). Although we had worked hard in the statistics courses studied here to create learning experiences and exams that emphasized a deeper understanding of concepts over memorization of formulas, we are aware that we were not completely successful in our efforts. For example, a subsequent review of our exams revealed that less than 40% of the questions required higher level thinking, with most questions focusing on simple comprehension or applications. We may thus have inadvertently penalized students striving for a deeper understanding of the material. These results emphasize the importance of teaching students not only content but also how to use strategies, when to use them, and how to determine their effectiveness. In the statistics classes with which we are familiar, such instruction is rare, and although it may be the case that the area of statistics is unusual in this regard, we fear that it is not. We urge instructors of mathematics and statistics courses to provide instruction in the use of cognitive strategies and to encourage in-class discussions of strategies that students have
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found to be particularly efficacious. In light of our earlier hypothesizing about the relative efficacy of different types of strategies during different phases of learning, it is important that students consider whether a particular strategy will be helpful given their current level of understanding. It may not be the case that the use of deep-processing strategies should always be encouraged. In particular, use of these strategies may not be efficacious when students have only a rudimentary understanding of a topic. We have often heard students remark that, although while taking a statistics course they had thought they understood the material, it was not until they had completed the course and gone on to the next that they “really” understood the topics. It may be that it simply takes many students longer to process statistical material than is typically allowed in a semester-long course. If this is the case, encouraging students to use deep-processing strategies before they are ready to do so may actually do them a disservice. Instructors may better serve students by using activities designed to make the material more accessible to them. This could be accomplished through a variety of methods such as relating the material as much as possible to students’ experiences and to concepts with which they are already familiar, providing heuristics that help students to see similarities and differences among procedures (as suggested by Quilici & Mayer, 1996, as well as Gardner & Hudson, 1999), and making the material more concrete for students through projects and realistic applications. Although students will certainly vary widely in terms of which strategies help them to learn, we feel that simply hearing about a wide variety of strategies that could be used and seeing these modeled in class has the potential to affect students’ strategy use. Future research in this area could fruitfully address the relative efficacy of different strategies at different times during the learning process so that educators can make more informed decisions about the types of strategies to teach their students. The points made by Cobb (1997) and Wild and Pfannkuch (1999) regarding the difficulty of integrating the very different types of thinking required in statistical and numerical reasoning are also relevant to teaching and learning in the area of statistics. Cobb describes these types of thinking as computational– algorithmic, logical– deductive, visual– dynamic, and verbal– interpretative. The skills and abilities required for these types of thinking are clearly very different and may therefore require different types of study strategies. In addition, most students are not equally skilled in all areas and will most likely tend to rely more heavily on the abilities in which they are stronger. Students are therefore likely to approach statistics learning from very different perspectives, relying on different abilities and using different strategies. Without guidance, students may develop an over reliance on one set of skills to the detriment of their development of another, thus limiting their capacity to fully develop and integrate all of the capacities necessary for sophisticated statistical reasoning. Instructors should therefore emphasize the importance of cultivating and integrating all of the types of thinking needed in statistical reasoning. Students should be encouraged to use their statistics courses as opportunities to develop new skills and strengthen those on which they are weak. Of course, this would require that students operate outside of their “comfort zone.” Creation of an environment in which students feel safe and supported in doing so is therefore essential. One component of such an environment might be a focus on formative forms of evaluation in which students are allowed to
redo assignments as they acquire more competence in using unfamiliar skills. Other limitations of the present study should also be noted. Although the students participating in this study represent a variety of major areas, all were students at one midwestern university, and to the extent that they are different from other students with regard to the relationships among the variables studied, the generalizability of our results is limited. With the exception of the exam scores used as our achievement measure, all data were obtained from self-reports, and students may not have been entirely accurate in their reporting. Although the large samples used in this study precluded the use of such methods, future research should explore the comparability of information obtained from self-report and observational and/or think-aloud techniques. However, the fact that the results of this study substantiated many of the relationships previously reported in the literature gives us some confidence that our results might be generalizable beyond the specific subjects and measures we used.
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Appendix Items Used in the Study
“I asked myself questions to make sure I knew the material I had been studying.” “When I studied, I put important ideas into my own words.” “I used what I learned from old homework assignments and the textbook to do new assignments.” “Before I began studying, I thought about the things I would need to do to learn.” “When I studied a topic, I tried to make everything fit together.” “When I was reading, I stopped once in a while and went over what I had read.” “When reading, I tried to connect the things I was reading about with what I already knew.”
“Compared with other students in this class, I expect to do well.” “I’m certain I will be able to understand the ideas taught in this course.” “I expect to do very well in this class.” “Compared with others in this class, I think I’m a good student.” “I am sure I can do an excellent job on the problems and tasks assigned for this class.” “I think I am naturally good at statistics.”a “I think I will receive an excellent grade in this class.” “Compared with other students in this class, I think I know a great deal about statistics.” “I know that I will be able to learn the material for this class.” “Learning statistics is easy for me.”a Note. All items, except for those marked with superscript a, are from “Motivational and Self-Regulated Learning Components of Classroom Academic Performance,” by P. R. Pintrich & E. V. de Groot, 1990, Journal of Educational Psychology, 82, p. 40. Copyright 1990 by the American Psychological Association. Reprinted with permission of the author.
“It was hard for me to decide what the main ideas were in what I read.” “When work was hard, I either gave up or studied only the easy parts.” “I often found that I had been reading for class but didn’t know what it was all about.” “I found that when the teacher was talking, I thought of other things and didn’t really listen to what was being said.”
Received May 24, 2002 Revision received January 24, 2003 Accepted February 3, 2003