Relationships of mathematics performance, control and value beliefs with cognitive and affective math anxiety

Highlights

• Construct validity of cognitive (CMA) and affective math anxiety (AMA) was examined.

• Results support the two-dimensional math anxiety model.

• Performance related stronger to CMA, whereas control beliefs related stronger to AMA.

• Girls' higher AMA and CMA disappeared after controlling for motivational variables.

• Control beliefs might mediate performance on AMA differentially stronger than on CMA.

Abstract

The study examines whether mathematics performance, control beliefs (self-concept in mathematics), and value beliefs (regarding domain interest and achievement outcome) differentially relate to cognitive math anxiety (worry about failure) and affective math anxiety (nervousness) and, thus, support the differentiation between these two math anxiety components. A sample of 368 fourth grade students reported cognitive and affective math anxiety and self-perceived beliefs, and completed a mathematics test. Confirmatory factor analyses supported the differentiation between cognitive and affective math anxiety. Multivariate regression analyses on the cross-sectional data revealed that mathematics performance was differentially stronger negatively related to cognitive math anxiety than to affective math anxiety, whereas control beliefs related stronger negatively to affective as compared to cognitive math anxiety. Therefore, longitudinal studies should investigate whether these differential relation patterns also manifest in the long term and occur reciprocally, which may indicate differential developmental mechanisms and effects of cognitive and affective math anxiety.

Introduction

Becoming proficient in mathematics is fundamental for economic and social participation because many professions and situations in everyday life demand the application of math operations (Patton & Cronin, 1997). Like all other school-related performances, achievement in mathematics is associated with cognitive (e.g., working memory; Ashcraft & Kirk, 2001), motivational (e.g., mathematics self-concept and domain interest; Ahmed, Minnaert, Kuyper, & van der Werf, 2012), and affective characteristics of the learner (Pekrun, Goetz, Frenzel, Barchfeld, & Perry, 2011). Affective characteristics include achievement emotions, which are directly linked to ongoing achievement activities (e.g., enjoyment when dealing with mathematics tasks in class) or to outcomes of these activities (e.g., anxiety of failure).

Math anxiety is one of the most studied outcome emotions in mathematics that has received considerable attention in educational and psychological research because of its assumed negative associations with cognitive and motivational variables (e.g., mathematical achievement, self-perceived competences, and values; Ashcraft, 2002, Frenzel et al., 2007, Hembree, 1990, Ma, 1999, Schwarzer et al., 1989, Suárez-Pellicioni et al., 2015, Wigfield and Meece, 1988). Math anxiety can be defined as the feeling of tension, apprehension, or fear in the processing of mathematical problems in daily life and in school settings (Ashcraft, 2002). Long term studies suggest that math anxious individuals exhibit negative attitudes toward activities involving mathematical problems (Ahmed et al., 2012, Hembree, 1990, Ho et al., 2000, Kyttälä and Björn, 2010, Ma, 1999, Schwarzer et al., 1989). Accordingly, they tend to avoid mathematics oriented situations altogether (Hembree, 1990, Maloney and Beilock, 2012) and take, for example, courses in school or choose college majors that are less related to mathematics, which may in turn limit their career choice options (Scarpello, 2005).

Although math anxiety has overlaps with general test anxiety, both constructs can be differentiated from each other (Hembree, 1990, Hunsley, 1987). As shown for general test anxiety (Hembree, 1988, Liebert and Morris, 1967, Schwarzer et al., 1989), math anxiety is assumed to be a multidimensional construct, including two psychological dimensions: emotionality represents the affective component and includes feelings of nervousness, tension, and unpleasant physiological reactions. Conscious worry or concern is the cognitive component and involves self-deprecatory thoughts about one's performance, negative expectations, and preoccupation with anxiety-causing situations (Wigfield & Meece, 1988). Research on general test anxiety indicates a strong association between the affective (emotionality) and the cognitive (worry) component (0.67 ≤ r ≤ 0.78, p < 0.01, cf. Hembree, 1990), whereas there are only a few studies on math anxiety examining this relationship. In contrast to general test anxiety research, low to moderate correlations between cognitive and affective math anxiety (0.25 ≤ r ≤ 0.38) were found (Ho et al., 2000, Kazelskis, 1998, Wigfield and Meece, 1988), thus, providing evidence to differentiate between the two components.

Although there is a vast body of research on the developmental mechanism and the effects of math anxiety, most studies do not differentiate between the affective and the cognitive component but report an overall (sum or mean) score (Ashcraft and Kirk, 2001, Baloğlu and Koçak, 2006, Frenzel et al., 2007, Radišić et al., 2015, Ramirez et al., 2013, Suárez-Pellicioni et al., 2015, Suinn, 1972, Vukovic et al., 2013). Given the moderate correlations and the low proportion of common variance between these two dimensions (Wigfield & Meece, 1988), it is yet unclear whether variables that have been discussed as critical antecedents and consequences (e.g., control and value beliefs, mathematics performance; Pekrun, 2006) are differentially associated with affective and cognitive math anxiety.

Building on the control-value theory of achievement emotions (Pekrun, 2006), which served as the theoretical framework in the present study, we aimed to explore whether mathematics performance and control and value beliefs differentially relate to math anxiety components and thus support their differentiation. The results of this cross-sectional study may provide first indications whether further longitudinal research on differential developmental mechanisms and effects of cognitive and affective math anxiety is needed.

In the last few years, appraisal theories have been proven useful to describe the origins of human emotions with several attributional antecedents (e.g., controllability, situational and motivational state, and valence; Pekrun, 2006, Roseman et al., 1996, Weiner, 1985). The control-value theory of achievement emotions (Pekrun, 2006) integrates core principles from appraisal theories (Weiner, 1985) and considers control and value appraisals as the most critical antecedents of students' emotional experiences. According to this theory, control-related appraisals include self-perceived competence, outcome expectancies, and causal attributions. Value-related appraisals involve the value of an activity in a specific domain (domain value), that is, individuals may enjoy mathematics because they appreciate the activity of dealing with mathematical problems and learning new mathematical procedures. Value-related appraisals may also refer to the importance of an achievement outcome (achievement value), for example, achieving a good grade in order to meet the expectations of significant others such as parents and teachers (cf. Frenzel et al., 2007). Furthermore, valuing an activity or outcome for its own sake refers to the intrinsic value, whereas valuing an activity or outcome because of its usefulness for achieving a specific goal refers to the extrinsic value.

Habitual control beliefs (e.g., self-concept of ability) and value beliefs, (e.g., domain interest and achievement value) are assumed to develop through repeated experiences within different settings (e.g., success or failure in a mathematics test) and to evoke appraisals in specific situations. The result of control and value beliefs is thought to elicit positive or negative emotions related to learning activities (e.g., enjoyment) and to learning outcomes (e.g., pride, anxiety). For example, the theory proposes that enjoyment results from high control beliefs along with high domain values, whereas pride is expected from a combination of high control beliefs and high achievement values. By contrast, low control beliefs along with high achievement values and low domain values should evoke anxiety (Pekrun, 2006). Previous research clearly indicates specific patterns for several emotions that are stable across different domains, cultures, and gender (Frenzel et al., 2007, Goetz et al., 2010, Lichtenfeld et al., 2012).

Furthermore, positive emotions (e.g., enjoyment, pride) are assumed to facilitate the use of flexible learning and self-regulation strategies and to foster intrinsic and extrinsic motivation (Pekrun, 2006). Negative emotions, such as anxiety, may however have different effects on students' learning. Although they could promote extrinsic motivation to avoid failure (cf. Ho et al., 2000), it is likely that the negative effects on academic performance outweigh the advantageous consequences. For example, anxiety was shown to impede intrinsic motivation and to foster the use of less flexible learning strategies, such as rehearsal (Pekrun, 2006, Ramirez et al., 2016).

The control-value theory further assumes reciprocal relationships between emotions and their antecedents, including mathematics performance and control and value beliefs (Pekrun, 2006). By implication, control and value beliefs are thought to mediate the effect of learning experiences (e.g., grades or performances) on emotions and vice versa. In the next two sections, we summarize empirical findings on math anxiety and its relations with mathematics performance and control and value beliefs, which provide evidence for the core assumptions of the control-value theory.

Previous research repeatedly found moderately negative associations between math anxiety and mathematical problem solving and achievement (− 0.27 ≤ r ≤ − 0.34, p < 0. 05; cf. Hembree, 1990, Ma, 1999) across different age groups (Ashcraft, 2002, Ashcraft and Moore, 2009, Hembree, 1990, Ma, 1999, Ma and Xu, 2004, Vukovic et al., 2013). According to the control-value theory, high math anxiety is assumed to be the cause (interference model) as well as the effect (deficits model) of low mathematics performance (Hembree, 1990, Ma and Xu, 2004). For example, the study by Kyttälä and Björn (2010) supports the deficits model. The authors applied path analyses and showed that mathematics performance of Finnish students in 8th grade predicted affective math anxiety in 9th grade indirectly through self-efficacy in mathematics. However, math anxiety did not predict mathematics performance at the end of ninth grade over and above prior performance. Similarly, Ma and Xu (2004) investigated the causal ordering between affective math anxiety and mathematics performance in students between 7th and 12th grades. Low achievement in mathematics consistently predicted higher levels of affective math anxiety (deficits model) but not vice versa. By contrast, Vukovic et al. (2013) found evidence for the interference model. Specifically, the authors showed that higher levels of math anxiety (including cognitive and affective components) of second grade children predicted lower calculation skills and reduced performance in mathematical applications (word problems, algebra, and probability) in third grade when controlling for early numeracy skills.

According to the interference model, worrisome thoughts are assumed to exert the negative effect on performance by co-opting the limited resources of the working memory system, presumably in the central executive (Baddeley, 2001), which are otherwise used for task processing (Ashcraft and Kirk, 2001, Derakshan and Eysenck, 2009). By implication, the cognitive (worry) component of anxiety should be stronger related to performance than the affective (emotionality) component. For general test anxiety, Hembree (1988) and Schwarzer et al. (1989) provided evidence for this assumption in two meta-analyses, indicating that the cognitive component was stronger negatively (− 0.31 ≤ r ≤ − 0.25, p < 0.05) associated with test performance than was the affective component of test anxiety (− 0.19 ≤ r ≤ − 0.15, p < 0.05). By contrast, the few studies on math anxiety that investigated these relationships point into a different direction. Specifically, Wigfield and Meece (1988) showed in a study with 6th through 12th grade students that affective math anxiety correlated negatively with students' mathematics performance, whereas the cognitive scale was not at all related to mathematics performance. Similarly, Ho et al. (2000) reported for 6th graders from China, Taiwan, and the US that affective math anxiety was stronger negatively associated with mathematics performance (− 0.54 ≤ r ≤ − 0.68, p < 0.05) than cognitive math anxiety (0.01 ≤ r ≤ 0.13, n.s. for China and US, and r = 0.25 for Taiwan, p < 0.05) after controlling for the overlap with the other math anxiety dimension.

The research results on general test anxiety and math anxiety may differ because the worry scales captured different cognitive aspects. More precisely, the test anxiety items (Liebert & Morris, 1967) address concerns about negative evaluations and failure, whereas the math anxiety items of the worry scale (Ho et al., 2000, Wigfield and Meece, 1988) address concerns about positive evaluations and success. In the long term, concerns about success may motivate individuals to invest more effort in order to avoid failure (cf. Pekrun, 2006). To the best of our knowledge, there are no other studies that have explored the relationships between mathematics performance and the two dimensions of math anxiety, thereby particularly considering concerns about negative evaluations in the worry scale.

In accordance with the control-value theory, cross-sectional and longitudinal studies indicate that control beliefs are moderately negatively associated with math anxiety (Hembree, 1990, Kesici and Erdogan, 2010, Kyttälä and Björn, 2010, Meece et al., 1990). Furthermore, Ahmed et al. (2012) found reciprocal relationships between control beliefs (math self-concept) and math anxiety in a sample of 7th grade students. However, the effects of anxiety on control beliefs were relatively weak (− 0.06 ≤ β ≤ − 0.07, p < 0.05) and appeared to be considerably lower as compared to the paths of control beliefs on anxiety (−.15 ≤ β ≤ − 0.14, p < 0.01). Also in line with the control-value theory (Pekrun, 2006), outcome related achievement values were shown to be positively associated with math anxiety (Frenzel et al., 2007, Kyttälä and Björn, 2010), whereas activity related domain values have been found negatively or not at all related to math anxiety (Frenzel et al., 2007, Peixoto et al., 2016). Furthermore, control beliefs related stronger to math anxiety than domain or achievement values when these variables were considered simultaneously (Frenzel et al., 2007, Kyttälä and Björn, 2010).

Only a few studies have tested whether control and value beliefs mediate the relationship between mathematics performance and math anxiety as theoretically proposed (Pekrun, 2006). For example, Kyttälä and Björn (2010) found that the effect of mathematics performance in 8th grade on affective math anxiety in 9th grade was completely mediated by control beliefs in 9th grade, whereas achievement value had no mediating function. Similarly, the results of a two year longitudinal study with 7th to 9th graders by Meece et al. (1990) suggested that students' self-concept predominantly mediated the negative effect of prior performance on later math anxiety (involving cognitive and affective components) but not vice versa. Also, Frenzel et al. (2007) investigated the relationships between prior mathematics achievement (grade) of 5th graders and their later control beliefs (self-concept), domain values (interest in mathematics), achievement values, and math anxiety (composite measure of cognitive and affective components). The authors found that control beliefs, domain values, and achievement values in mathematics partially mediated the effect of prior mathematics achievement on later math anxiety.

In line with previous research (Hyde et al., 1990, Meece et al., 1990), Frenzel et al. (2007) also identified higher levels of math anxiety as well as lower levels of control beliefs and domain values in girls compared to boys, whereas boys and girls did not differ in the value they attached to achieving a good grade in mathematics (achievement value). The results of the study indicated that girls' higher math anxiety was in particular attributable to their lower control beliefs, which may result from several social and environmental factors (e.g., socialization, interactions with other, and instructional practices). Recent research suggests that female teachers and parents may transmit their gender stereotypes as well as their own math anxiety in particular to female children (Beilock et al., 2010, Maloney et al., 2015). For example, Beilock et al. (2010) showed that female elementary school teachers' math anxiety related to higher levels of math anxiety in female students. Specifically, throughout the school year teachers transmitted their gender stereotypes (“Mathematics is a male domain.”) to female students, who internalized the teachers' belief (“Boys are better in mathematics than girls.”) and adjusted their behavior to meet the teachers' expectations. As a consequence, girls' competence beliefs decreased, they reported higher math anxiety and performed worse in the mathematics test as opposed to boys. Thus, anxiety seems to be an important factor that transmits stereotype threat effects on performance.

Although math anxiety is thought to be a multidimensional construct, the literature review shows that most studies tend to report a unidimensional overall (sum or mean) score of math anxiety that may reflect cognitive and affective aspects to varying degrees, which are often confounded with mathematical settings (e.g., test, classroom) (Ashcraft and Kirk, 2001, Kazelskis, 1998, Krinzinger et al., 2009, Kyttälä and Björn, 2010, Lichtenfeld et al., 2012, Pekrun et al., 2011, Ramirez et al., 2013). Furthermore, the only studies on math anxiety that examined cognitive and affective components separately addressed concerns about success in the worry scale (Ho et al., 2000, Wigfield and Meece, 1988) but concerns about failure are assumed to be negatively related with math anxiety (Derakshan & Eysenck, 2009). Thus, it remains unclear whether the same relation patterns of performance and control and value beliefs with math anxiety components emerge, as implicitly proposed by the control-value theory and previous research that used a unidimensional math anxiety measure. Considering the relatively small body of research that has investigated cognitive and affective math anxiety separately, the aim of the present cross-sectional study was twofold:

First, we examined whether cognitive and affective math anxieties constitute structurally different components when mathematical settings and content areas (e.g. arithmetic) are systematically captured in both scales. Based on the literature reviewed, we expected that a two-dimensional model of math anxiety provides a better fit to the empirical data than a one-dimensional general factor model of math anxiety. In the present study, the cognitive scale reflected worries about failure (Liebert & Morris, 1967). Therefore, we expected the two components of math anxiety to be stronger correlated as in previous math anxiety studies that addressed worries about success in the cognitive scale (Ho et al., 2000, Wigfield and Meece, 1988).

Second, we explored the construct validity of the two-dimensional model of math anxiety. Based on the theoretical framework of the control-value theory (Pekrun, 2006), we applied multivariate and univariate regression analyses in order to examine whether and to what extent mathematics performance and control and value beliefs differentially account for specific proportions of variance in cognitive and affective math anxiety. Following theoretical considerations, we assumed that mathematics performance should be more closely associated with cognitive math anxiety as opposed to affective math anxiety (Eysenck, Derakshan, Santos, & Calvo, 2007).

Building on previous research results (Frenzel et al., 2007, Kyttälä and Björn, 2010), we also expected control beliefs to be differentially stronger related to cognitive and affective math anxiety than domain and achievement values. Previous research showed that control beliefs fully mediated the effect of prior achievement on later affective math anxiety (Kyttälä & Björn, 2010), which was not the case for a composite math anxiety score involving cognitive and affective components (Frenzel et al., 2007). Therefore, we expected control beliefs to completely account for the variance between mathematics performance and affective math anxiety, whereas we predicted that control beliefs only partially account for the common variance between mathematics performance and cognitive math anxiety. In line with previous findings, we expected achievement value beliefs to be positively and domain value beliefs to be negatively or not at all associated with cognitive and affective math anxiety (Frenzel et al., 2007, Kyttälä and Björn, 2010, Peixoto et al., 2016).

Finally, we included gender as a control variable because previous research indicated that girls reported higher levels of math anxiety, lower control and value beliefs, and they may perform worse than boys in mathematics tests (Beilock et al., 2010, Hyde et al., 1990). By implication, we expected girls' lower control and domain value beliefs to account for the gender differences in both cognitive and affective math anxiety (Frenzel et al., 2007).