Educational performances differ because of a number of considerations, such as individual characteristics, emotion, behaviour, as well as environmental factors (Anable, 2005). Such factors obstruct the learning process in the HES. Experience is one of the characteristics that enhance learning statistics.
One of the issues affecting the learning process in middle school is, the students cannot fully conceive probability, until they understand the different concepts of it, with its approaches and relationships (Jones, 2006). Exploring these approaches, results in various conceptions of probability. In addition, the notion of distribution and the law of large numbers are central constructs in the learning of probability at this level. However, these key ideas are often avoided in order to make probability more accessible. Supervisors are supposed to design tasks that focus on the use of distribution and the law of large numbers. This enhances the students‟ ability to make valid probability predictions, in the context of random events, which is important for students to appreciate that understanding probability is about understanding randomness (Garfield & Ben-Zvi, 2008).
Another issue is age related. Postgraduate students find statistics learning difficult and acknowledge the ineffectiveness of traditional ways of lecturing (Garfield & Ben-Zvi, 2007;
Biggs, 2011). The reason for this is that traditional ways of lecturing rely solely on the curriculum, instead of the real life problems. Postgraduate students do not seem to be comfortable with seminars/tutorials as opportunities for learning (Brockbank & McGill, 2007;
Nightingale & O‟Neil, 2012). Students also do not interact well with their colleagues;
therefore, they fail to benefit from the advice offered by fellow peer students (Brophy, 2013).
Riding & Rayner (2013) reveal that students learn better when observing challenging tasks (application work in statistics). This can be done through practicing their communication skills, and integrating, as well as applying their statistical knowledge to write-up their report
(Burbules & Berk, 1999; Kolb & Kolb, 2005). Students are more likely to develop the capacity for critical thought, when they are challenged by activities, as well as by reflective supervisors, who help them to explore these experiences about their world (Kolb & Kolb, 2005; Prince & Felder, 2006).
The third issue relates to facilitators and researchers. For statistics learning to be more effective and less fearful, facilitators and researchers need to focus on the beliefs and attitudes, developed during their educational experiences (Gal & Ginsburg, 1994). Often, facilitators do not know how to penetrate the belief systems of students, and, therefore, fail to influence the students to appreciate the course. The assessment of the attitudes and beliefs of students, enable educators to understand the presumptions, and identify specific areas of the students‟ frustration. The focus of new vision is to improve the assessment of learning statistics that cope with effective strategies to overcome challenges (Bryson, 2011). Garfield et al. (2007) also assert that students compute probability, chance and random events correctly, but the persistence of misconception, appears in the application of these main concepts, in the concrete context that reveal the students‟ misunderstanding.
Related to the above issue, is the expectation of students that the application and usefulness of statistics are often not met, leading to anxiety. Gal and Ginsburg (1994) argue that students disempower themselves, instead of following examples with commentary, which highlight guidance to improve their learning. This initiates a tendency to return to traditional ways of learning, and, therefore, obstructs creativity. The complexity of many statistical ideas, assumptions and rules, constitute major challenges for students. With poor mathematical skills (proportions, decimals and arithmetical formulas), students encounter difficulty in learning statistics content and often confuse the With poor mathematical skills (proportions, decimals and arithmetical formulas), students encounter difficulty in learning statistics content and often confuse the dual role that the average plays as both a number and a random variable (Martin, 2003; Garfield et al., 2007). The completion of average is done randomly.
Many students are not aware of that. However, an average is the consequence of a formula which lies in sampling variability. Students are not familiar to this concept. Perhaps it is the way students think about data that causes them to fail in confusion. Most students accept easily that large samples lead to better inferences; therefore, the availability of more information exists in a larger sample. It is not sufficient; there should be less variability (in the average) from larger samples (Lin, Lucas & Shmueli, 2013). Students do not certainly
compare “more information” with “less variability”. They simply do not think about how the average might behave, if the sampling were repeated frequently (Martin, 2003; Garfield et al., 2007). They are able to study statistics as a particular subject, rather than some of the courses on offer, which explore the deeper recesses of probability theory.
According to Ben-Zvi and Garfield (2004), an increase in learning statistics does not affect the perception that many students have of the statistics course, namely, a difficult, frustrating and unpleasant course to learn. These problems mislead the students; therefore, their experiences are based on wrong perceptions, errors and misconceptions that do not provide an appropriate answer, or allow them to choose a correct statistical method. When confronted with uncomfortable and tainted data, students do not want to think beyond the content, given that potential elucidations are founded on different expectations (Ben-Zvi & Garfield, 2004).
The manipulation of data requires randomness, to avoid bias in the application (Demšar, 2006). This concept of randomness remains a challenge for many students. However, it is important to notice that probability is likely about events that are just as unplanned. The prediction of an event does not mean that the occurrence is assured; therefore, it is reasoning under uncertainty (Savard, 2010). The use of prediction, as a way of revealing the outcome with certainty, is wrong; given that it depends on randomness. Similarly, everyday events occur randomly, which makes the study of possibility a little more concrete. Informally, a random event is a member, or subset of the sample space (Shapiro, 2009).
The increased student diversity in academic settings affects achievement outcomes (Schunk
& Pajares, 2010). Postgraduate students originate from different cultural backgrounds and have different understandings of writing and presentations. In the area of learning, they should approach new ideas, or concepts, critically and analytically. Some interpret these approaches as different from their previous academic environment. Bandura (1986) also acknowledges that student‟s self-efficacy can be affected by his/her behaviour and contextual factors. It is essential to know how students combine the influence of new contextual factors and their prior experiences from previous academic settings, to achieve relevant self-efficacy judgments (predictions). These new social factors include a low perceived value of the learning setting, as well as the perception of autonomy. Facilitators, parents, peers and supervisors contribute to students‟ self-assurance. It is noteworthy that, students with great levels of self-efficacy for learning, but who feel separated from the university environment,
may score little in inspiration and accomplishment (Brophy, 2013). A clear challenge is to determine how self-efficacy with social factors influence on academic completions.
Learning involves the construction of knowledge (Novak, 2010). Garfield et al. (2007) assert that facilitators are aware of the procedures and methods. Students are not able to practice on their own. They often need impelling, as well as the monitoring of their ability to do, and to discern. They need to be encouraged and reassured. According to Ben-Zvi and Garfield (2004), the ability of students to think and reason statistically has not been achieved yet.
Students have to apply their minds to think critically by reading articles, or books, for example, given that during their undergraduate studies, learning approaches were more passive, as receivers of knowledge. They rarely argued about anything that should be implemented in their lives. Students should continue to apply their minds to think critically, until they are confident enough. The self-confident judgment in reflections appears like an original sense of the individual‟s early experience. The challenge of different attitudes to learning could offer the postgraduate a possible approach to the issues of critical thinking.
Therefore, the integrity of international education is preserved.
In addition, the practical challenges involve a new academic research difficulty to conceptualise, for instance, how to organize the presentation of an academic writing;
specifically, the order, the steps between tasks, paragraphs, sub-topics. A good order in a specific work enables a reader to follow and understand easily. In addition, the feedback with fewer questions could be expected, as well. A lack of understanding, regarding the framework and structure of different kinds of tasks, should be avoided (Laurillard, 2013).
Students learn with processors, but are tested without computers, as it is in many other courses. However, the introduction of technology in statistics education increases the need for thoughtfulness to the individual student‟s concerns and reaching (Ertmer, 1999; Tam, 2000).
But the challenges arise regarding when and how to use computers in meaningful ways. The way in which computers are used introduces the failure that obliges monitors and students to rethink their approach of teaching and learning. If supervisors need technology to complete student outcomes, they also require abilities for designing, choosing and adjusting software, determining plans that make use of its technology.
Finally, the issue of calibration complicates the role of self-efficacy in learning settings.
There are factors that can affect student‟s self-efficacy differently, than the ways in which they affect their learning and performance on the corresponding tasks (Pajares & Kranzler, 1995). When students assess that they are proficient of performing a task, and perform it, or when they judge that they are capable of accomplishment it, and cannot do it, they are well calibrated, because self-efficacy accurately predicts achievement. Conversely, when students judge that they are capable of executing a task, but do not perform it, they are poorly regulated, because of the deficiency of correspondence between self-efficacy and performance. In fact, calibration is necessary, but complicated, in academic settings. Students, who overestimate their ability, may sometimes fail, which could reduce motivation. Those who underestimate what they can do may be unwilling to try the task, and thereby delay their skill acquisition. Self-efficacy judgment that slightly exceeds what a student can do is desirable, because such overestimation can increase determination and perseverance, but recurring overestimation could lead to constant failure, with resulting decrements in the students‟ motivation to learn (Bandura, 1997).
3.7. Synthesis and Partial Conclusion
The literature review revealed that most of the research, conducted on the topic, were based more often on assumptions and documentary reviews, than data analysis of the determinants of statistics learning (Johnson & Christensen, 2010; Ary, Jacobs, Razavieh, Sorensen &
Walker, 2013). However, a few existent researches examined the problem with very simple and limited analysis methods, and only very rare papers, or articles, concentrated on multivariate analysis of the phenomenon (Meyers, Gamst & Guarino. 2006; Izenman, 2008).
Two principal approaches emerged from the literature. Some authors believe that prevention measures of statistics-learning-related difficulties are not robust enough to curb the trend of the level of knowledge, understanding and skills; therefore, emphasis should be given to adequately solve difficulties. The idea is that mis-understanding, or mis-perception related frustrations can never be avoided totally, whatever the dispositions taken (Kolb, 2014). It is very difficult to detect, or suspect some distortions, even with participation in workshops, seminars and conferences.
Conversely, other authors are of the opinion that, for a long time, privilege has been given to postgraduate students to reduce direct statistics anxiety, for instance, as the result of
confusions, lack of knowledge and skills. Therefore, these authors are in favour of giving priority to postgraduate students to participate in workshops, seminars and conferences on statistics ability [prevention approach] (Bisgaard et al., 2008; Wood, 2010). Researchers, who support the prevention approach, believe that implementing actions, to avoid failure in SELS beliefs among students with difficulties, is realistic in the short and mean term (Johnson &
Christensen, 2010). In universities, such as UWC (with a high concentration of black students from disadvantaged areas), adopting a policy based on providing well organised assistance in statistics services, freely accessible to students (along with well-trained statistics monitors, and developing consultations with peers), could be helpful to achieve the desired outcomes, with special regard for the financial constraints of these students.
The main difference between the two approaches is the period of effectiveness. Some recommendations could have immediate effects, but need unrealistic financial means to implement in short or mean terms (Pattillo, 2013). Others are slow to action, but could be implemented with relatively modest financial investment. In general, there is consensus about the importance of using both prevention and direct intervention approaches to statistics difficulties (McCardle, Scarborough & Catts, 2001; Dunlap et al., 2006).
From the writings review, it is perfect that most analyses only focus on identifying the explanatory factors of SELS beliefs failure, without considering the path through which the influence occurred (McCarthy & Rogerson, 1992). In fact, very few studies explored the complex mechanisms of the actions of SELS beliefs predictors. In addition, almost no study, currently has attempted an analysis of SELS beliefs failure at universities in South Africa, or provided specific recommendations for a regional scale (Coetzee & Van der Merwe, 2010;
Mji, 2009). This study aims to provide scientific recommendations for actions against SELS beliefs failure, adapted to particularities of the UWC, UCT and its regions.