Impact of Engineering Students' Attitudes on Achievement in Statistics: A Structural Model

We created, tested, and revised a structural model interrelating undergraduate engineering students’ previous academic success, their attitudes toward statistics, and their achievement in a required introductory statistics course. Our model was based primarily on Eccles and colleagues’ application of expectancy-value models of behavior to mathematics achievement. In the original Saturated Model, students’ previous academic success (Previous Success) was an exogenous latent variable. It was followed, in order, by the endogenous latent attitude variables of students’ perceptions of the difficulty of statistics as a domain of study (Difficulty), their self-concept about their statistical knowledge and skills (Cognitive Competence), their feelings toward statistics (Affect), and their perceptions of the value of statistics (Value). All of these latent variables were allowed to impact the outcome latent variable of Achievement both directly and indirectly through all possible downstream paths. Although this model fit the data reasonably well, several paths (including the path from Value to Achievement) were not statistically significant and so were eliminated to create the Pruned Model. The Pruned Model represented the data in a more parsimonious manner with no fit degradation. The amount of variance in each of the latent constructs accounted for by their upstream latent predictors was sizable. About two-thirds of the shared variance in Achievement was associated with the impact of Previous Success, while the remaining one-third was associated with the impacts of the upstream latent attitude variables of Difficulty, Cognitive Competence, and Affect. Our results support a model in which both prior academic achievement and attitudes toward statistics impact engineering students’ achievement in introductory statistics courses. Attitude-achievement model 3 Impact of Engineering Students’ Attitudes on Achievement in Statistics: A Structural Model Successful completion of at least one statistics course is a requirement in many post-secondary programs. Students often view these courses as overwhelming learning and survival tasks that cause a great deal of stress (e.g., Onwuegbuzie and Daley 1999). Instructors and students alike believe that students’ attitudes toward statistics impact their statistics achievement and even their willingness to try to complete these courses. Attitudes toward statistics affect a large number of students in their college (and eventually professional) careers (Young and Nelson 1994; Gordon 1995; Potter 1995; Green and Carney 1997; Loftsgaarden and Watkins 1998; Wilson 1998; Parker, Pettijohn and Keillor 1999). Until recently, most studies exploring attitudes toward statistics have focused on a small part of the complex relationships between attitudes and achievement. These studies often have explored these relationships by correlating attitude and achievement scores. Most studies report small to moderate correlations between attitudes toward statistics and statistics course achievement with better attitudes associated with higher achievement. At least some of the variability in findings is due to differences in samples (e.g., community college, undergraduate, or graduate students), attitude instruments (a variety of surveys), attitude component measures (e.g., anxiety toward statistics, statistics’ value), achievement measures (usually test scores or course grades), and measurement timing (beginning, middle, or end of the course). See Gal, Ginsburg, and Schau (1997) and Harris and Schau (1999) for brief summaries of this research. However, two groups of researchers have created structural models representing possible causal relationships among these variables. The models generally have addressed the impact of attitudes toward statistics on success in statistics courses and were tested using structural equation modeling (SEM) techniques. Lalonde and Gardner (1993) developed and tested a model of introductory statistics achievement based on Gardner’s theory of second language learning. Tremblay, Gardner, and Heipel (2000) then revised that model and tested it with 166 Canadian students enrolled in five sections of a required introductory course in psychological statistics. Their achievement outcome variable was students’ scores on the final exam. Their final model included five exogenous variables: the global construct of aptitude (previous achievement in math and psychology) and scores on four variables (attitude toward the professor, attitude toward the course, interest in psychology, and interest in math). Three endogenous constructs included statistics anxiety and valence (value of statistics) and score on a variable of motivational intensity (effort). The model did not include a direct effect from valence to achievement or between valence and anxiety. The fit of the model was acceptable. This model included two variables specific to psychology and so cannot be applied directly to students who are not enrolled in psychological statistics courses. However, the results suggested some potentially generalizable findings. Aptitude exhibited the expected strong positive direct impact on achievement and a small negative direct impact on anxiety. Anxiety showed a moderate negative direct effect on achievement. The direct effect from motivational intensity to achievement was positive but quite small. Wisenbaker and colleagues (e.g., Wisenbaker and Scott 1997; Wisenbaker, Scott and Nasser 1999; Wisenbaker, Scott and Nasser 2000) also created, tested, and modified structural models of statistics achievement. Their models always included achievement and four components of students’ attitudes toward statistics (students’ feelings about statistics, their self-concept about their statistical knowledge and skills, the value they attributed to statistics, and the difficulty of statistics) assessed twice (pre and post). Some of their models also included mathematics achievement, anxiety, and attitudes as exogenous variables. In their models, the structure interrelating the attitude components differed depending on time of measurement. Participants came from the Attitude-achievement model 4 U.S. and Israel and were enrolled in undergraduate or graduate introductory statistics courses taught either in a one-semester format or during summer school. Their largest sample consisted of 136 U.S. undergraduates. In general, Wisenbaker and colleagues reported that attitude components measured at the end of the course predicted final course achievement; those measured at the beginning of the course did not. The purpose of our study was to examine possible causal relationships among undergraduate engineering students’ previous academic success, their attitudes toward statistics, and their achievement in a required introductory statistics course. We created, tested, and revised a structural model interrelating these global constructs. METHODOLOGY Theoretical Framework The model created in this study was based primarily on Eccles and colleagues’ application of expectancy-value models of behavior to mathematics achievement (e.g., Eccles, Adler, Futterman, Goff, Kaczala, Meece, and Midgley, 1983, Eccles and Wigfield 1995). They posited an important influence of three expectancy-value factors on math achievement. These factors included: (1) students’ expectancies for success, (2) their perceptions of task difficulty, and (3) their perceptions of task value. The factor of expectancies for success concerned students’ self-concepts regarding their ability to do math successfully. The factor of task difficulty, as its name suggests, referred to students’ perceptions of the difficulty of math. The factor of task value reflected students’ perceptions of the value of doing math successfully (Eccles and Wigfield 1995). Perceptions of past academic performances influenced each of these three factors. Statistics Attitudes-Achievement Structural Model Our Statistics Attitudes-Achievement Saturated Model included six latent constructs (see Figure 1). Statistics achievement (called Achievement in the Model) was the outcome latent variable. Students’ reports of their previous academic achievement (called Previous Success), the exogenous variable, represented their perceptions of outcomes from prior learning experiences. The four endogenous attitudes’ latent constructs were based on our application and modification of Eccles and colleagues’ three expectancy-value factors. The first attitudes’ construct, Difficulty, represented the factor of task difficulty. Eccles and colleagues assessed task difficulty as the student’s perception of the difficulty of math for that specific student; we, however, asked for students’ attitudes about the difficulty of the domain of statistics for most people. The second attitudes’ construct, Cognitive Competence, represented the factor of students’ expectancies for success in statistics. Cognitive Competence represented students’ perceptions regarding whether they possessed the knowledge and skills needed to learn statistics. The third attitudes’ construct, Affect, represented students’ positive and negative feelings about statistics. Although Eccles and colleagues included affective perceptions within the factor of task value, we included it in our model as a separate construct for three reasons. First, conceptually, students’ affective feelings toward statistics are not the same as their attitudes about the value of statistics. In fact, Eccles and Wigfield (1995) indicated that students’ affect influences their perceptions of task value through classical conditioning mechanisms. Second, measures of attitudes toward statistics historically have included this component (often in the form of statistics anxiety). Third, statistics instructors and students believe that students’ affect toward statistics is important in its own right. Our fourth attitudes’ construct, Value, represented the factor of task value: s