Chapter 2. Performance and Approaches
2.8 Self-Efficacy
The last aspect that is looked at which may influence performance is self-
efficacy. Bandura (1986) defined perceived self-efficacy as “people’s judgement of
their capabilities to organise and execute courses of actions required to attain designated
types of performance” (p.391). The term ‘perceived self-efficacy’ is how students may
view how well they can perform tasks. Whilst students who self-reflect through
metacognitive activities about their ability to perform on tasks can increase their
performance on tasks, Bandura suggested that this may also be a pit-fall for those
students who produce “faulty thought patterns”(p.21). Depending on a student’s self-
efficacy perception, they may consider the following when approaching a task:
• what to do
• how much effort to invest in activities
• how long to persevere in the face of disappointing results and • how to tackle the task i.e. anxiously or self-assuredly (p.21).
Thus, students with a high self-efficacy when solving tasks will have more
success since they will persevere until the task is solved. Often these students during the
solving of the tasks will generate and test alternative forms of strategies (Bandura,
1986: p.391). Alternatively the self-doubters (those with low self-efficacy) will be more
likely to abort their initial efforts if it proved to be deficient. As students with high self-
efficacy have a higher tendency to test alternative strategies this suggests with respect to
exploration, that students with high self-efficacy may explore more with the software by
testing different numbers. However, this should be due to high perceived self-efficacy in
the use of mathematics rather than in the use of computer software as Coupland (2004)
According to Schunk (1991), self-confidence is usually operationalised as the
measurement of self-efficacy (see for example Gist and Mitchell, 1992; Pajares and
Miller, 1994). Bandura (1986) suggested that high confidence students are students who
are more likely to have high success and those with low confidence are more likely to
be self-doubters. In fact, Collins (as cited in Bandura, 1986) carried out a study where
students having high and low mathematical self-efficacy were given difficult problems
to solve. He found that
while mathematical ability contributed to performance, at each ability level, children who regarded themselves as efficacious were quicker to discard faulty strategies, solved more problems, chose to rework more of those they failed, did so more accurately, and displayed more positive attitudes towards mathematics. (Bandura (1986), p.391) Pajares and Miller (1994) in their study of self-efficacy and mathematics
performance using path analysis found that “students' judgments about their capability
to solve math problems were more predictive of their ability to solve those problems”
(p.200) than other variables they investigated such as gender, mathematics self-concept
and students’ prior ability. Their study was conducted with 350 undergraduate students
at an educational college where they were given a series of questionnaires which
measured mathematics confidence, perceived usefulness of mathematics, mathematics
anxiety, mathematics self-concept, prior experience and mathematics performance. Both
the questionnaires for mathematics confidence and mathematics performance consisted
of the same arithmetic, algebra and geometry mathematics tasks and two problem types
(real and abstract). In the mathematics confidence questionnaire, students were asked to
assess how confident they were in solving the task and in the mathematics performance
questionnaire they solved the tasks. The mathematics performance questionnaire was
2.8.1 Self-Efficacy and the Approaches
Thus far this chapter has suggested that processing levels, self-explanations and
explorations affect performance. With the study by Pajares and Miller, students’
academic self-efficacy or confidence is also seen as having a positive impact on
performance. This suggests that there might be a relationship between the processing
levels, academic self-confidence and self-explanations.
Duff (2004) conducted a study using the Revised Approaches to Study Inventory
(RASI) that he administered to 244 business school students. The RASI is a revised
version of the ASI but also includes items for measuring academic self-confidence.
Through a correlation matrix, he was able to determine a relationship between high
academic self-confidence and the deep processing level.
Whilst there are few studies using the RASI for mathematics, it is possible that
students with higher mathematics confidence, similarly to the business students in
Duff’s study, would be more likely than students with lower mathematics confidence to
engage in their work and try to make meaning out of their learning, that is, have a deep
processing level. Students with low mathematics confidence on the other hand would be
less engaged with the mathematical topic and thus adopt a surface processing level.
Therefore, if students with high mathematics confidence should have a deep
processing level, this would probably mean that these students will then appropriate the
software boxes for their mathematics engagement as was noted in Section 2.7.1 (p.40).
Further, as high mathematics confidence students may probably be more au fait with
mathematical concepts and terms, then there is a possibility that their self-explanations
should be within the mathematical domain, whilst those of the low mathematics
2.8.2 Self-Efficacy and Attitudes to Technology
It might be worthwhile to investigate whether attitudes to technology might also
influence performance.
In a bid to find out how technology influenced mathematics learning when these
two are combined, Galbraith and Haines (2000b) developed a Mathematics-Computing
Attitudinal Scale (MCAS) to find out. Their original questionnaire had six scales which
looked at student’s mathematics confidence, computer confidence, mathematics
motivation, computer motivation, computer-mathematics interaction and mathematics
engagement. Mathematics engagement was found to be highly correlated with
mathematics motivation and the former was eventually dropped (Cretchley and
Galbraith, 2002). A similar inventory was developed by Cretchley, Harman, Ellerton
and Fogarty (2000) called the University of South Queensland Mathematics Technology
(MathTech) questionnaire, which had three scales: mathematics confidence, computer
confidence and attitudes to technology in the learning of mathematics.
Both of these inventories were administered to university students in differing
technology programmes. Their results were quite similar (Cretchley and Galbraith,
2002), in that both of the questionnaires had low correlations between attitudes to
mathematics and attitudes to computers. Further, Cretchley and Galbraith noted that
from these two inventories the attitudes of learning mathematics with technology were
more closely associated with the student’s attitude towards technology rather than
mathematics.
Pierce, Stacey and Barkatsas (2005) also sought to research attitudes towards
mathematics and technology; however, unlike the previous two inventories mentioned,
they applied their questionnaire in secondary schools and with a shorter number of
items. Their questionnaire called the Mathematics and Technology Attitude Scales
on similar scales. In addition, the MTAS made use of items of another secondary school
inventory which had items on mathematics and technology by Vale and Leder (2004)
but whose focus was to find gender differences. The MTAS questionnaire had five
scales which assessed student’s mathematics confidence, their confidence with
technology, their attitude of using technology for learning mathematics, affective
engagement with mathematics and behavioural engagement with mathematics.
They found that students’ attitudes to using technology for learning mathematics
were dependent on gender and found for the males that this was positively related to
their confidence with technology. However, for females, their attitudes to technology
for learning mathematics were negatively related to their mathematics self-confidence.
This phenomenon exhibited here by the secondary school students was not found in the
studies at the tertiary level, where perhaps the gender attitudes towards mathematics or
technology even out and are more equal across the genders.
Therefore, university students with a high technology background should not
have an advantage in their performance over those students with a low technology
background when it comes to using the software boxes and solving the tasks. However,
the students with a high mathematics confidence will definitely have an advantage over
those students with low mathematics confidence.