Motivation and performance in college students enrolled in self-paced versus lecture-format remedial mathematics courses.

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Students enrolled in a remedial mathematics course face an uphill battle to improve on their past performance. Prior attitudes, emotions and classroom experiences are often difficult to overcome. This is a comparison study of the psychological effects of learning and performance goal orientations, mathematics anxiety and confidence and the situational effects of self-paced versus lecture-oriented environments in a remedial mathematics course. While anxiety factors are well-documented as detrimental to mathematics performance, no studies have addressed the effects of both goals and anxiety on performance.

Dweck & Leggett (1988) identified two types of achievement goals that affect students' academic performance. Performance goals are as sociated with the desire to achieve favorable grades and social approval. Students with this orientation are typically concerned with the outcome rather than with the actual process of learning and are more likely to subscribe to an entity theory of intelligence, believing that intelligence is a fixed attribute. They tend to perform well on easier tasks where a positive evaluation can be achieved but when faced with difficult tasks, students with performance goals often become discouraged and give up easily, attributing their failure to a lack of ability, in contrast, learning-goal oriented students are interested in and enjoy mastering new material and tend to subscribe to the incremental theory that intelligence is malleable. These students display "mastery-oriented" behavior, showing more persistence on difficult tasks, using alternative strategies and attributing failure to a need to work harder rather than to a lack of ability (Heyman & Dweck, 1992).

Diener and Dweck (1978, 1980) tested this model by giving children a problem solving task to complete. Students could solve the first few problems easily but the last few problems were too difficult for children of their age. At the onset of the study, all of the children were equal in problem-solving ability but after experiencing failure on the difficult problems, children who exhibited a performance orientation focused their attention on their failure and blamed it on a lack of ability. They expressed feelings of defeat and depression, exhibiting the learned helplessness pattern that may be a factor in underachievement (Dweck 1975). In contrast, children exhibiting "mastery-oriented" responses did not perceive themselves as failing. These children tried new strategies, reported increased motivation, and some reported feeling invigorated by the challenge.

Early research on Dweck's model of motivation was focused on elementary school children. Henderson and Dweck (1990) examined the influence of goal orientation and confidence on students' adjustment to junior high school. Students with a learning goal orientation and an incremental theory of intelligence did well even if they initially had low confidence in their ability to succeed. In contrast, students who endorsed performance goals and who endorsed the entity theory of intelligence performed more poorly than expected regardless of confidence level.

Dweck's (1990) model has also been applied to college students (Beck, RotterWoody, & Pierce, 1991; Eppler, CarsenPlentl & Harju, in press; Eppler & Harju, 1997; Harju, 1997; Harju & Eppler, 1997; Hayamizu & Wierner, 1991; Hoyert & O'Dell, (2000a; b); Roedel & Schraw, 1995; Schraw, Horn, Thorndike-Christ, & Brunning, 1995), with sometimes contradictory results. Beck et al. (1991) found that grade orientation (similar to Dweck's performance orientation.) was negatively correlated with GPA and test scores while learning orientation was not significantly related to grades. Schraw et at. (1995), on the other hand, found that learning goals were associated with higher academic evaluations but that performance goals were unrelated to academic performance. Harju and Eppler (1997) found that GPA was not significantly related to goal orientation.

When Dweck first introduced the idea of learning and performance goals, they were considered to be a unidimensional variable (Dweck & Leggett, 1988). However, Roedel and his colleagues have suggested that learning and performance goals seem to be independent of one another (Roedel, Schraw, & Plake, 1994; Schraw et al., 1995). Thus, a person may be high in both learning and performance goals, low in both of the goals, or high in one mad low in the other. Eppler and Harju (1997), using Roedel's scale, divided college students into four categories of goal patterns: low on both learning and performance goals; high on both learning and perfomaance goals; high on performance goals while low on learning; and high on learning goals while low on performance. Students who endorsed learning goals and both learning and performance goals had significantly higher GPAsthanthe low goals group. Studies of college students, based on the instrument developed by Roedel et al. (1994), provide support for Dweck's notion that achievement goal orientation is predictive of academic success.

Based on Dweck's model, Hoyert and O'Dell (2000a) predicted that learning goal oriented students would appear to be quite similar to perfornaance goal oriented students except when faced with an academically challenging situation, such as failure on a test. They examined performance of introductory psychology students who had failed at least one examination. They found that students for whom learning goals were dominant responded by improving their grades on subsequent examinations. Students for whom performance goals were dominant earned much lower grades on subsequent tests. Similar results were reported by Hoyert and O'Dell (2000b). Goal orientation did not seem to influence the performance of students under normal conditions. But when faced with stress, namely failure on an examination, learning goal dominant students appear to persevere and to adopt more successful learning strategies, while performance goal dominant students per formed more poorly or engaged in irrational behavior, such as giving up but not dropping the class. Hoyert and O'Dell report that these results occur when looking at learning and performance goals as competing with each other, rather than continuous variable or independent variables.

Anxiety and self-efficacy have beer reported in numerous studies to influence academic performance, especially in mathematics. Vizek-Vidovic (19991) found that mathematics anxiety, perceived mathematics incompetence and mathematics self-efficacy contribute most to the total variance in mathematics grades of secondary students Pajares (1996) studied middle school gifted students and found that mathematics problem-solving was influenced by high self-efficacy in a model that controlled for the effects of mathematics anxiety, cognitive ability and mathematics GPA. Similarly, Bourquin (1999) found that mathematics self-efficacy was the best predictor variable of performance in college students. Anxiety is also/inked to the performance goal orientation. Dweck (1989) suggests that there are two especially detrimental expectancy patterns, evaluation anxiety and learned helplessness and that these are related to performance goals.

In the present study, we examined achievement motivation, anxiety and performance patterns of college students enrolled in remedial mathematics courses. This course is taught in one of two different class formats, a self-paced class and a traditional lecture class. Self-paced classes are typically found to be more more effective than traditional lecture classes in a variety of different subjects, including college-level chemistry, technical education courses and developmental reading courses (Canelos & Ozbeki, 1983; Eniaiyeju, 1983; Flippo & Terrell, 1984; Mausner, Wolff, Evans, DeBoer, Gulkus, D'Amore & Hirsch, 1983; Miller, Kohn, & Schooler, 19861). Students in the self-paced or personalized instruction 1 group expressed more positive attitudes and more confidence in their ability to perform t college work (Flippo & Terrell, 1984). Mausner et al. (1983) found that students did well in a self-paced college statistics course although anxiety and negative attitudes toward mathematics inhibited their performance. We were unable to locate any literature on self-paced versus lecture courses applied specifically to remedial mathematics courses.

The purpose of this study was to examine the influences of a) the two class formats, b) the four types of achievement motivation orientation (as measured by the Roedel scale) and c) attitudes toward mathematics (as measured by the Fennema-Sherman scale) on students' final grades in a remedial college mathematics class. Based on previous research, we predicted that students who endorsed learning goals or both learning and performance goals would perform better overall than students who endorsed only performance goals or neither. We also predicted that students in the self-paced classes would perform better than those in the traditional-lecture classes, and we examined whether one class format would benefit learning-goal students more than performance goal students. Finally, we believed that anxiety and confidence in mathematics ability might interact with goal orientation. Following Dweck's model, we predicted that performance goal oriented students would be more anxious and that low confidence would be more detrimental for performance-oriented students than for learning oriented students.

Method

Participants

Participants included 272 undergraduate students (66% women, 34% men) enrolled in 17 different sections of a remedial mathematics course at a large southeastern university. The sections were split into 10 self-paced and 7 lecture classes; 47% of the participants were in the self-paced class, 53% in the lecture class. While remedial course credits did not count toward graduation, the grades earned in these courses were computed into the students' GPA. In the self-paced class, there was some small group discussion and lecture but for the most part, students worked independently on assignments and exams. Because students could retake a test up to three times, they received more performance feedback and had more opportunities to improve their grade. Students in the lecture class had only one opportunity to take each exam. Students in all sections took a common final examination at the end of the semester. Participation in this study was voluntary and the students were given extra credit points on one examination for their participation.

Data from 51 of the participants were discarded from the analysis because these students did not indicate whether they gave permission to obtain their grades. (Based on patterns in previous studies, we believe that this was mainly due to oversight by the students filling out the consent form.) The majority of the students were 18 year olds who were enrolled in this course during summer orientation and thus most of the students had little or no information about the format of the class in which they were enrolling.

Measures

The Goals Inventory developed by Roedel et at. (11994) was used to measure learning and performance goal orientations. There are 12 statements relating to learning goals, e.g., "I try even harder when I fail at something." Five statements relate to performance goals, e.g., "it is important for me to get better grades than my classmates." One of the eight filler items, "I am willing to cheat to get a good grade." was discarded because we did not want students to be suspicious of the intentions of the study. A five point Likert scale (1 = not at all like me whereas 5 = very much like me) was used to rate each item. Cronbach's [alpha] = .81 for learning goals and. 74 for performance goals, comparable to those reported by Roedel et al. (1994).

Students also filled out a shortened version of the Fennema-Sherman Mathematics Attitudes Scales (Fennema & Sherman, 1976). We included six items each from the Confidence in Learning Mathematics ([alpha]= .43), Mathematics Anxiety ([alpha]= .85), Effectance Motivation in Mathematics ([alpha] = .71) scales.

Procedure

Participants were tested over a three week period of time, in groups of approximately 10 to 50 students. A few students with schedule conflicts were tested in an office in groups of one to four. Participants were given an informed consent form, a scan sheet and the following questionnaires in order: the Goals inventory, the FennemaSherman scales and three additional inventories that were not analyzed for this study. Participants were instructed that the testing was confidential and that there were no right or wrong answers but that they should be as candid as possible. At the end of the semester the mathematics test scores and final mathematics grade of each student were obtained as well as their SAT scores.

Results

Students were divided into four categories of goal orientation using a median split. The median score for learning goals was 3.67 while the median score for performance goals was 3.40. Scores above the median for each goal were classified as high and scores equal to or below the median were classified as low. The four categories were (a) low on both learning and performance goals, (b) low on learning but high on performance goals, (c) high on learning but low on performance goals, and (d) high on both learning and performance goals.

Final Examination and Final Course Grades

The means and standard deviations for final course grades are presented in Table 1. A 2 (Class Format) x 4 (Goal Orientation) ANOVA with final course grade as the dependent measure revealed no significant main effect for class format. The mean grade for the self-paced sections was 2.09 on a 4-point scale (SD = 1.23) and the mean grade for the lecture sections was 2.25 (SD = 1.23). A significant main effect was obtained for goal orientation, F (3, 2051) = 4.00, p <.009. The learning goals groups earned the highest grades (M = 2.73, SD = 1.20), while grades for the performance goals group and the students who were high in both were almost identical, (M = 2. ] 4, SD = 1.35 and 2. 15, SD = 1.23, respectively). The students who were below the median in both learning and performance goals scored the lowest (M = 1.86, SD = 1.08). Newman-Keuls tests (p < .05) revealed that the learning goals students performed significantly better in the course than the other three groups who did not differ from each other. This main effect is qualified, however, by a significant interaction between type of class and goal orientation, F (3, 205) = 3.01, p < .03. Paired comparison tests revealed that the students in the high learning goals group did significantly better in the lecture sections than in the self-paced sections (p < .003). The difference between performance in the self-paced vs. lecture sections was not significant for the other three groups.

A common final examination was administered to all students and, although an ANOVA revealed no significant effects, the pattern of results was similar to those for course grades. Students in the lecture class who were high in learning goals earned the highest grades on the final, averaging 83.86 (SD = 10.44), while the scores of the other three groups ranged from 67.64 (SD = 30.34) to 67.77 (SD = 26.07). Students in the self-paced section scored somewhat higher on the final examination if they endorsed performance goals (75.41, SD = 30.03) or both performance and learning goals (75.07, SD = 28.97) compared to the group who scored below average in both (69.40, SD = 32.701). Interestingly, the high learning goals group earned the lowest grades of all the students, averaging 66.31 (SD = 37.70) in contrast to similar students in the lecture section.

Response to Failure

Based on the findings of Hoyert and O'Dell, (2000a & b), we decided to examine the response of students in the traditional lecture sections to a challenging situation, namely failure on an examination. Students in the self-paced sections were omitted from this analysis since they had three opportunities to take tests and failure on a test did not represent the same level of challenge to them. Indeed, some self-paced students may have taken tests they were not yet ready to pass as a practice test. Similar to Hoyert and O'Dell (2000a), we classified students as either learning-goal dominant or performance-goal dominant by selecting the higher of their mean learning and performance goal scores. We then identified students in the lecture sections who had failed at least one test and looked at their score on the test subsequent to the one they failed to see if they had scored higher, lower or the same. Of the performance-goal dominant students who tailed a test (n = 20), 50% did the same or worse on the next test and 50% did better. For learning-goal dominant students (n = 37), however, 16% (n = 6) did worse and 84% (n = 31) did better on the next test. A chi-square test revealed that this difference was significant, [X.sup.2] (1) = 7.34,p < .001.

Attitudes toward Mathematics

We also measured mathematics anxiety, confidence, usefulness and effectance using a shortened version of the Fennema-Sherman Mathematics Attitudes Scales. All of these measures were significantly correlated with mathematics performance, especially for females. These correlations are presented in Table 2 Anxiety correlated the highest with mathematics performance, followed by effectance and confidence. Each of these variables correlated more highly with course grades than SAT-Quantitative Scores. These three measures were also highly correlated with each other. The correlation between confidence and anxiety was -.77, p < .001. The correlation between confidence and effectance was .52, p < .001 and between anxiety and effectance, -.52, p < .001. Thus, these scales appear to be measuring somewhat overlapping constructs, particularly confidence and anxiety.

Since Dweck's model predicts that anxiety is linked to achievement goal orientation, we performed a 2 (Class Format) x 4 (Goal Orientation) ANOVA with the Fennema Sherman Mathematics Anxiety Scale as the dependent variable. Only the main effect of goal was significant, F (3, 211) = 6.15,p < .001. Newman-Keuls tests (p < .05) revealed that students who endorsed learning goal s were significantly less anxious (M = .36, SD = .48) than the both low motivation, performance goals or both high motivation groups (M = .56, SD = .49; M = .63, 5/) = .48; and M = .52, 5/) = .50, respectively). Thus, students who focus on master), of material may experience less anxiety in mathematics courses and thus be able to achieve at a higher level, particularly under a traditional course structure.

To determine whether the effects of goal orientation on grades would be tempered by confidence in mathematics, we performed a 2 (Confidence Level) x 4 (Goal Orientation) ANOVA. Confidence had a significant effect on grades in the expected direction (F (1,2051) = 18.19,p <.001). Low confidence students earned a mean grade of 1.81 (SD = 1.17) versus high confidence students who earned a mean grade of 2.55 (SD = 1.181). The interaction between goal and confidence was not significant, however, the low confidence students who endorsed learning goals did perform better than the other groups, achieving an average grade of "C" compared to an average of "D" for the other low confidence students.

Discussion

This study addressed the question of how achievement orientation would influence students' grades in self-paced and lecture sections of remedial college mathematics. Consistent with previous research, students endorsing learning goals received higher grades than the other goal orientation groups. Students endorsing high learning goals were the only group to achieve a B average on both the final exam and their final course grade. The students who were low on both learning and performance goals earned the lowest grades overall, a D average. These results are similar to those of Eppler and Harju (1997) with the exception that they found that students who were high in learning goals were equivalent to students who endorsed both learning and performance goals in academic performance. In contrast, the mathematics students who endorsed both learning and performance goals did not perform as well as those students who were high in learning goals only. Concern about performance may have a detrimental effect on performance in remedial mathematics courses regardless of whether it is accompanied by concern for mastering the material. This concern for performance may take the form of mathematics anxiety, which we found to be related to performance goals. Students may he more likely to experience "math anxiety" than anxiety about other academic endeavors and thus it may explain why performance goals are detrimental to mathematics grades rather than to a students' overall grade point average. Indeed our results suggest that learning goal students not only performed better but were less anxious about mathematics than performance goal oriented students. Although the classes were taught differently, the final course grades were not different. This is contrary to earlier research (Canelos & Ozbeki, 1983; Eniaiyeju, 1983) which found an advantage for self-paced instruction. Previous researchers did not look specifically at remedial mathematics classes and this may be one reason for the difference in results. Another possible reason may be that the self-paced class in this study lacked one aspect often found in self-paced instruction: a mastery-oriented method. While these self-paced students had the opportunity to take the test several times and count the highest grade, there was no requirement that they achieve a certain level of achievement before advancing to the next level as the mastery method requires. Buskist, Cush, & DeGrandpre (1991) found the mastery criterion to be an important variable in the success of self-paced instruction.

Students who endorsed learning goals earned higher grades in the lecture sections than in the self-paced sections while the performance of the other achievement goals groups did not differ between the two types of classes. It could be argued that students' final course grades were influenced by the fact that the students in the self-paced class had more opportunities to take tests. However, the type of course should not affect performance on the common final examination. The pattern for final examination grades was similar, although the differences were not significant. Learning goal oriented students performed better than the rest of the students if they were in the lecture sections. The reasons for this are unclear but perhaps students in the lecture sections faced more academic challenges since they were not allowed to retake examinations to increase their grade. Dweck predicts that the differences between learning and performance goal students should appear under challenging circumstances, such as difficult subject matter or academic failure. Our results are consistent with this theory and match those of Hoyert and O'Dell (2000a; b). Students who endorsed predominantly learning goals were more likely than performance-goal dominant students to improve their academic performance subsequent to failing an exam.

Dweck's (199011 model was designed not to address achievement motivation and performance under different pedagogical models but to deal with the relationship between achievement motivation and confidence and how they influence performance and attributions. When we examined how mathematics confidence and achievement goals related to final course grades, it became apparent that the more confident students did better. Additionally, the students who were low in confidence but who endorsed learning goals performed better than other low-confidence students, averaging a course grade of "C" compared to a "D". Consistent with Dweck's model, learning goals seems to offset to some degree a lack of confidence about one's ability. Students with low confidence achieve better grades in a challenging course if they focus on mastering the material rather than on performance goals.

It is of particular interest to teachers of mathematics that anxiety and confidence predict mathematics performance better than standardized measures of quantitative ability. This knowledge may help instructors and students of mathematics to appreciate the significance of psychological factors in mathematics learning and to work towards change. Teachers can influence affective responses and, based on our data, one vehicle is goal attitudes. Rather than directly reassuring students to be less anxious or more confident, it is important for teachers to counter these emotions by building mastery attitudes. Teachers can continually remind students to narrow their focus to a step by step, systematic process, to persist and to acknowledge and reinforce persistence. When, for a variety of reasons, students do not use this mastery orientation, teachers can help students see how they lower their own achievement. This type of insight can help students either advance in their scholarly development or acknowledge their responsibility in maintaining their status quo. Perhaps this approach also can provide one more step in disabling a useless cultural weapon, "math anxiety".

Table 1
Final Course Grades for the Four Groups of Learning and Performance
Goal Orientations by Class (Lab vs. Lecture)

                           Lab                 Lecture
Goal Orientation    M       SD     n      M       SD     n

Both Low           1.92    1.19    37    1.82     .98    38
High Performance   2.29    1.21    17    2.04    1.46    25
High Learning      2.27    1.49    15    3.12     .82    26
Both High          2.10    1.18    30    2.29    1.33    24

Note. High indicates goal orientation scores above the median for the
entire sample of students (on a 5-point scale, 3.67 for learning goals
and 3.40 for performance goals). Low indicates goal orientation scores
equal to or below these medians.

Table 2
Correlations between Fennema-Sherman Mathematics Attitudes Scales and
Course Grades and Final Exam Grades

                      Course Grade          Final exam

anxiety           -.353    (p =. 001)    -.238    (p =. 001)
confidence         .334    (p =. 001)     .247    (p =. 001)
effectance         .345    (p =. 001)     .237    (p =. 001)
math usefulness    .291    (p =. 001)     .232    (p =. 001)
learning goals     .213    (p =. 002)     .098    (p =. 152)
SAT-Q              .201    (p =. 004)     .154    (p =. 004)

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Marsha Ironsmith (1), Jennifer Marva, Beverly Harju and Marion Eppler

(1) We would like to thank Katalin Szucs for her support and interest that made this project possible. Many thanks to the other mathematics instructors who helped us recruit students and collect data, including Ann Bellis, Bonnie Galloway, Lauren Oppenheimer and Kathy Wilkerson. Wendy Creasey also provided valuable assistance in analyzing the results.

Marsha Ironsmith, Jennifer Marva, Beverly Harju and Marion Eppler, East Carolina University.

Correspondence concerning this article should be addressed to Marsha Ironsmith, Department of Psychology, East Carolina University, Greenville, NC27858. E-mail: [e-mail]