The results of Study IV were similar to those of Study I and Study III and again highlighted the importance of the application of knowledge component. The re- sults showed that performance in the application of knowledge task was signifi - cantly related to both the students’ study pace and fi nal grade. Students who had good procedural prior knowledge, that is, performed well in the application of knowledge task, were also likely to complete the course in pre-scheduled time. On the other hand, students whose performance was weak in the prior knowledge tasks were more likely to belong to the drop-out group or take a longer time to complete the course. This is in line with the fi ndings of Lewis & Lewis (2007) sug- gesting that low performance in the prior knowledge test was related to dropping out of the course. Furthermore, students who performed well in the application of knowledge task were also likely to get higher fi nal grades, even though the rela- tionship was moderate. There was also a signifi cant relationship between the fi nal grade and the ability to complete the course in pre-scheduled time.
Interestingly, the analysis revealed that the re-takers’ performance in the prior knowledge test was even weaker than that of the drop-outs’. Thus, low perform- ance in the prior-knowledge test might have served as a warning sign to which
explained by such factors as student motivation or persistence, which we have not included in our study. Further research is needed on the issue.
The results indicated that there indeed was signifi cant variation in prior knowl- edge in an introductory chemistry course, implying that inter-individual differ- ences in prior knowledge pose a heterogeneity that should be considered even in an introductory course. Furthermore, the major appears to be a factor that is clearly refl ected in prior knowledge performance at the beginning of the studies. Students who had a major other than chemistry scored signifi cantly lower in every prior knowledge task. The students’ major was also related to the fi nal grade, but prior knowledge overruled its infl uence when they were both included in the regression model. This means that the infl uence of major is only refl ected via the differences in the prior knowledge base. Gender did not have a signifi cant infl uence on prior knowledge test performance.
Moreover, the fi ndings are in line with Study I and Study III, which further af- fi rms to their success. While dropping out of the course may have been a function of prior knowledge, there may have been a variety of other reasons for leaving the course, ranging from personal reasons (see, for example, Mäkinen, Olkinuora & Lonka, 2004) to other aspects such as teaching and curriculum. However, the data do indicate that low performance in the prior knowledge test probably played a role in the decision.
5.3 The relationship between prior knowledge and academic self- beliefs
Study II explored the interplay of the variables that previous research has found to be strongly related to student achievement in mathematics: previous study success, academic self-beliefs and prior knowledge. In Study II, prior knowledge was more predictive of student achievement than were the other variables included in the study. When self-beliefs were included in the model with prior knowledge, the pre- dictive power of prior knowledge overruled the infl uence of self-beliefs. Contrary to our hypothesis, self-beliefs showed no direct infl uence on student achievement at the course level. This is in line with the fi ndings of Murtonen and Titterton (2004). However, academic self-beliefs strongly and directly affected prior knowl- edge test performance. This suggests that academic self-beliefs may have infl uenced the way in which students responded when they were exposed to the prior knowl- edge test at the beginning of the course. Students who had greater confi dence in their ability to perform well may have persisted longer with the prior knowledge test, which was refl ected in their prior knowledge performance. Similarly, low self- beliefs may also have lessened students’ engagement in the prior knowledge test. Students are more likely to engage in tasks and achieve when they believe they have the potential to do so (Linnenbrink & Pintrich, 2003). Moreover, students tend to confi rm their self-perceptions. Students with positive views of themselves engage in achievement-related behaviours to confi rm their positive self-perceptions (Pajares, Britner & Valiante, 2000). It can also be hypothesised that self-beliefs in the past had an infl uence on achievement behaviour in a similar manner, and that this was refl ected in the students’ prior knowledge level.
Although self-beliefs seemed to have no direct infl uence on student achieve- ment, this does not mean that we should be unconcerned about them. Self-beliefs signifi cantly and indirectly infl uenced student achievement through prior knowl- edge, and also directly infl uenced prior knowledge test performance at the begin- ning of the course. Self-beliefs may infl uence the way in which students make use of their prior knowledge and how they use such prior knowledge as a base for learning, which thus infl uences the entire learning process. Negative self-beliefs may reduce levels of motivation and engagement (Randhawa, Beamer, & Lund- berg, 1993). Furthermore, studies have found that self-beliefs infl uence students’ enjoyment of the subject (Townsend, Moore, Tuck, & Wilton, 1998), which in turn may infl uence subsequent achievement behaviour. The effects of self-beliefs on academic achievement have been found to cumulate over time (Valentine et al., 2004). Moreover, the results of study by Murtonen et al. (2008) suggest that self- beliefs are also related to views of future work and motivational factors. Therefore, negative self-beliefs should be addressed and considered in teaching. Discussions concerning the students’ self-beliefs may help students become aware of the fac- tors that affect their learning. Students’ awareness of their self-beliefs gives them better possibilities to regulate their learning.
Of interest were also the interrelations found between various types of self- belief constructs. Expectation of success and self-effi cacy were strongly correlated, whereas self-perception of ability did not correlate as strongly with the other two self-belief measures. Furthermore, self-perception of ability showed no correla- tion with previous study success or with fi nal grade, and its correlations with the other variables were markedly weak. These results suggest that general self-percep- tions of competence, such as “I’m good at mathematics”, are not valid predictors of student achievement. This result is consistent with the views of Linnenbrick and Pintrich (2003) and Pajares and Miller (1994).