Institution of Civil Engineers (ICE) y Chile

input and processes of learning, are also considered to have influence on the cognitive outcomes of learning (e.g. mathematics performance). In the following, I will review the PISA results about non-cognitive outcomes in terms of motivation and self-beliefs, which have been widely discussed in the literature.

3.4.3.1 Motivation to learn mathematics

Motivation, as one category of non-cognitive factors, is basically

distinguished as two types, that is, intrinsic motivation (i.e. interest and enjoyment) and extrinsic motivation (i.e. instrumental motivation), according to the reasons and goals that motivate an action (Deci and Ryan, 1985; Ryan and Deci, 2000). Usually, a student’s motivation to learn is a

composition of both (Husman and Lens, 1999). Both of these two types of motivation are employed in PISA framework to investigate to what extent gaining joy from learning activities (i.e. intrinsic) or believing learning activities are good or important for studies or future career (i.e. extrinsic) motivates students (OECD, 2013d). Previous empirical research has shown that intrinsically motivated students tend to learn better, especially on the heuristic tasks or those requiring deep understanding (Ryan and Deci, 2009). Interest and enjoyment could affect the degree of students’ engagement in learning, the depth of understanding (Schiefele, 2009) and even the types of careers students would like to pursue (Reeve, 2012). By contrast, extrinsic motivation is considered to be influential in students’ choices to involve in mathematics courses (Stevens et al., 2004), and is linked to students’

occupational choices (Eccles, 1994). Discussion on the association between students’ learning motivation and their academic performance have been widely documented (e.g. Wigfield and Eccles, 2000; Lepper at al., 2005). The explanatory power of intrinsic and extrinsic motivation varies amongst education systems, as revealed by PISA (Shin et al, 2009).

In PISA 2003 and PISA 2012 in which mathematics were assessed as the focus domain, the intrinsic motivation to learn mathematics had significant correlation with mathematics performance for the average of OECD

countries (r= 0.19, r=0.22 respectively) (OECD, 2013d). The strength of the relationship between intrinsic motivation and mathematics performance varied across education systems that participated (OECD, 2004; 2013d). On OECD average, intrinsic motivation explained 5% of variance in

mathematics performance in PISA 2012, and one-unit increase in this factor was associated with 19 score points improvement in mathematics

performance (OECD, 2013d). However, this positive relationship was not observed in some systems (OECD, 2013d). It is also noteworthy that some East Asian education systems, such as Shanghai-China, Hong Kong-China, Chinese Taipei, and Singapore, were the exceptions to those showing the relationships for highest-achieving students stronger than for lowest- achieving students (OECD, 2013d).

Compared with intrinsic motivation, instrumental motivation has a more ambiguous relationship with academic performance (Gabriel et al., 2018), since some studies identified it as a positive predictor (e.g. Barron and Harackiewicz, 2001) while others (e.g. Lepper et al., 2005) showed its negative effects. Researchers argue that instrumental motivation may be a positive predictor for college students’ performance, but it may be less predictive for students in elementary and secondary schools (Lepper et al., 2005). In PISA, generally, instrumental motivation has a weaker relationship with performance than intrinsic motivation does (Lee and Stankov, 2013). Instrumental motivation of OECD average has a relationship with

mathematical performance with r=0.14 and 0.20 respectively in PISA 2003 and PISA 2012, which is weaker than intrinsic motivation (r=0.19, 0.22) (OECD, 2013d). The relationship varied across education systems as well. On OECD average, difference in students’ instrumental motivation to learn mathematics explained 4% of variance in their mathematics performance (OECD, 2013d).

3.4.3.2 Self-beliefs in learning mathematics

Self-beliefs are also considered as important non-cognitive outcomes factors influencing students’ performance. The extent to which students are

confident in their own ability of solving specific tasks (i.e. self-efficacy) and students’ overall perception of their own ability (i.e. self-concept) “have an impact on learning and performance on several levels: cognitive,

motivational, affective and decision-making” (OECD, 2013d, p.88).

Although self-efficacy is a judgement of what one can do with the skills one has, and may not necessarily reflect the skills one actually possesses, it is considered that self-efficacy is an important factor influencing performance (Bandura, 1992; 1997). Researchers argue that students with high self- efficacy are more likely to endeavour to solve problems or even challenge difficult problems (Bandura, 1977; Marsh et al., 2006; Schunk and Pajares, 2009; Hoffman, 2010). Self-efficacy is also the outcome of this endeavour.

Performance accomplishments, depending on whether they are successes or failures, could in turn increase or reduce self-efficacy (Bandura, 1977). Consistent with a range of literature that shows that students’ self-efficacy is one of the strongest non-cognitive factors predicting students’ academic performance (e.g. Lee and Stankov, 2013; Şahin and Yıldırım, 2016; Lee and Stankov, 2018), self-efficacy is identified as a strong predictor in PISA as well (OECD, 2004; 2013d). In most education systems, it had a moderate or strong positive correlation with mathematics performance (OECD, 2013d). In PISA 2012, for example, self-efficacy could explain 28% of variance of mathematics performance of students across OECD countries (OECD, 2013d). One-unit increase in self-efficacy was associated with 49 score points higher in mathematics performance (OECD, 2013d). For most education systems, the association between self-efficacy and mathematics performance was greater amongst high-achieving students. However, this is not the case for Belgium and some Asian education systems such as

Shanghai-China, Hong Kong-China, Korea, Macao-China, Chinese Taipei, and Singapore, in which one-unit increase in self-efficacy was associated with larger difference in mathematics performance of low-achieving students than that of high-achieving students (OECD, 2013d).

In terms of self-concept, like extrinsic motivation as relative to intrinsic

motivation, it has a weaker effect than self-efficacy on students’ performance in PISA (OECD, 2004; 2013d). It is suggested that compared with self-

efficacy, self-concept could predict better for affective-motivational variables such as interest and anxiety rather than academic performance (Ferla et al., 2009). As reported in PISA 2012, across OECD countries, one-unit increase in mathematics self-concept was positively associated with a difference of 37 score points in mathematics performance (OECD, 2013d). Although in

general self-concept is positively correlated with performance, it does not necessarily mean that education systems with high average mathematics self-concept also achieve high in mathematics (OECD, 2013d). It is

observed that East Asian areas such as Shanghai-China, Hong Kong-China, Macao-China, Chinese Taipei, Japan, and Korea, which were ranked high in PISA performance (including mathematics) had relatively low mathematics self-concept compared with Western countries (OECD, 2004; 2013d). This phenomenon is consistently found in many other international assessments (Ho, 2009).

As indicated in the measures of self-concept, for example, “I have always believed that mathematics is one of my best subjects; in my mathematics class, I understand even the most difficult work.”) (OECD, 2013a), self-

concept has normative nature because it greatly reflects students’ perception of themselves compared to their peers around (Schunk and Pajares, 2005). Students in high-performing schools tend to have lower self- concept than those with equal ability in low-performing schools, which is called “Big-Fish-Little-Pond effect (BFLPE)” (Marsh and Parker, 1984; Marsh et al., 2008). BFLPE is used to explain the paradox in East Asian areas that students have relatively low self-concept but have high performance (Ho, 2009). Besides in East Asia, BFLPE in relation to self-concept has been supported in studies comparing regional performance within countries (e.g. Seaton et al, 2011). Its generalisability across cultures has also been evidenced (Marsh and Hau, 2003). Response style is another possible reason used to explain East Asian students’ relatively low self-concept, considering that students in East Asia tend to choose the middle point in the Likert-scales which are typically used in self-concept measures (Cheung et al, 2018). After adjusting for response styles, high levels of mathematics self-concept are identified in students of Singapore and Shanghai-China (Cheung et al, 2018).

Mathematics anxiety is another category of self-beliefs in learning

mathematics that is investigated in PISA. It refers to “thoughts and feelings about the self in relation to mathematics, such as feelings of helplessness and stress when dealing with mathematics” (OECD, 2013d, p.88). It is suggested that students’ mathematics anxiety is caused by the composite effect of high mathematics anxiety of people around students (e.g. parents, teachers) and students’ own cognitive predisposition (Beilock and Maloney, 2015). Alpert and Haber (1960) distinguish that anxiety could be facilitative or debilitative. Facilitative anxiety could urge students to make efforts to achieve their learning goals, while debilitative anxiety may make students avoid challenges and therefore hinders their learning (Ho, 2009). Previous studies have widely documented the negative effect of anxiety on

performance (Hembree, 1990).

In terms of its negative effect, anxiety would make students avoid engaging in mathematics (Ashcraft and Krause, 2007; Luttenberger et al., 2018). Besides this, anxiety also hinders mathematics performance through

task, for students with high mathematics anxiety, much of their attention is on negative emotion caused by anxiety, while working memory resources for processing mathematics are greatly impaired (Ashcraft and Krause, 2007). Consistent with previous studies, PISA results reports also have

demonstrated that students’ mathematics anxiety is negatively associated with their mathematics performance (OECD, 2004; 2013d). Following mathematics self-efficacy, mathematics anxiety is considered as another strong predictor of mathematics performance (Lee and Stankov, 2018). In PISA 2012, for example, differences in anxiety of OECD students could explain 14% variation in their mathematics performance (OECD, 2013d). Across OECD countries, one-unit increase in anxiety was related to 35 score points decrease in mathematics performance in PISA 2003 and 34 score points decrease in PISA 2012 (OECD, 2004; 2013d).