Development of math anxiety and its longitudinal relationships with arithmetic achievement among primary school children☆
Introduction
Math anxiety is most commonly defined as feelings of nervousness and tension interfering with manipulating numbers and solving mathematical problems “in a wide variety of ordinary life and academic situations” (Richardson & Suinn, 1972). Even in childhood, math anxiety has been found to be a unique construct, separate from both test anxiety and general anxiety (Carey, Hill, Devine, & Szücs, 2017). Knowledge of the development of math anxiety during school is limited: whether the average level of math anxiety varies in different grade levels, how stable math anxiety is during school years, and whether stability is affected by age. Moreover, there is a lack of research about the causal relations between math anxiety and math achievement—which one influences the other and whether the relation is reciprocal. Among adolescents and adults, math anxiety has been found to be related to achievement (Hembree, 1990; Richardson & Suinn, 1972), but among primary school students, previous findings about the relationships have been contradictory (Sorvo et al., 2017). Longitudinal studies on math anxiety are scarce, and knowledge of the developmental aspects of math anxiety is needed for effective targeting of early interventions.
In our previous, cross-sectional study we investigated the prevalence of math anxiety and its relation with arithmetic skills among primary school children (Sorvo et al., 2017). Literacy review revealed that some studies have operationalized math anxiety as being unable to do something in mathematics (Dowker, Bennett, & Smith, 2012; Haase et al., 2012; Krinzinger, Kaufmann, & Willmes, 2009; Thomas & Dowker, 2000). In our study, this aspect of math anxiety is defined as anxiety about failure in mathematics (Sorvo et al., 2017). On the contrary, other studies have stressed operationalization anxiety in various math-related situations without emphasizing the expected outcomes, successes, or failures (Vukovic, Kieffer, Bailey, & Harari, 2013; Wu, Barth, Amin, Malcarne, & Menon, 2012). This aspect has been defined as anxiety about math-related situations (Sorvo et al., 2017). Interestingly, contradictory findings seem to be related to the aspect of math anxiety measured. The results of our study confirmed the hypotheses raised from previous literature and showed that these two ways of operationalizing shed light on two separable but related (correlation 0.40) aspects of math anxiety, and these aspects were differently related to mathematical achievement (Sorvo et al., 2017). However, because our first study was cross-sectional, we couldn't examine development or longitudinal relationships. The aim of the present study is to shed light on the development of these two aspects of math anxiety among primary school children over the course of a school year as well as the longitudinal relationship between aspects of math anxiety and math achievement.
The limited understanding of the development of math anxiety among primary school students results, at least partly, from the paucity of studies focusing on this age group and from the incoherency of the findings. There are a few studies investigating the development of the level of math anxiety longitudinally (Krinzinger et al., 2009; Ma & Xu, 2004) and some investigating differences between several age groups cross-sectionally (Gierl & Bisanz, 1995; Gunderson, Park, Maloney, Beilock, & Levine, 2018; Sorvo et al., 2017). Use of different methodological approaches might explain some of the incoherency in the earlier findings and hinder the formation of a lucid understanding of the development of math anxiety. The methodological diversity concerns not only the above-mentioned operationalization of math anxiety but also the approach chosen in examining stability and change in anxiety over time. The approaches to investigate stability and change in math anxiety have varied from the stability of, or change in, the average level of math anxiety (i.e., mean level change; Krinzinger et al., 2009) to the stability of, or change in, the relative position of the individuals within a group over time (i.e., rank-order stability; Krinzinger et al., 2009; Ma & Xu, 2004) by analyzing stability coefficients of math anxiety between different time points.
The results of the previous studies concerning the development of math anxiety during primary school years are somewhat contradictory. One reason for this might be that they have measured different aspects of math anxiety. Krinzinger et al. (2009) assessed the mean level of anxiety about failure longitudinally from first to third grade and found that the level increased over time. Thus far, to our knowledge, the development of anxiety about math-related situations has not been studied longitudinally in primary school, but the knowledge about the mean level change is based on cross-sectional studies comparing students in different grade levels. Gierl and Bisanz (1995) found no differences between third and sixth graders in the level of math anxiety in problem-solving situations, but the mean level of math anxiety concerning test situations was higher among older children than younger. Sorvo et al. (2017) compared the prevalence of anxiety about failure and anxiety about math-related situations in grade levels 2 to 5. There were no differences in the prevalence of anxiety about failure between children at different grade levels, but anxiety about math-related situations was more common among younger students compared with older students. The latter result was in line with the results of Gunderson et al. (2018) who found that the level of anxiety about math-related situations was lower among second than among first graders.
Besides the mean-level of math anxiety, Krinzinger et al. (2009) investigated the anxiety about failure in mathematics also from the perspective of rank order stability. They found lower stability for anxiety (one-year stability coefficients from 0.49 to 0.60) than for achievement (one-year stability coefficients from 0.79 to 0.91). To our knowledge, anxiety about math-related situations has not been investigated from the perspective of rank-order stability among primary school children. Ma and Xu (2004) examined the development of anxiety about math-related situations from seventh to twelfth grade using this approach. They found that math anxiety remained relatively stable from grade 8 onward (one-year stability coefficients were slightly below 0.60), although not as stable as achievement in mathematics (one-year stability coefficients were over 0.90). Although the mean-level change approach provides information about the development of math anxiety at the group level, by investigating the rank-order stability we get knowledge of the stability of math anxiety at the individual level within the group—in other words, whether the same students report anxiety over time.
These two approaches are complementary, and both approaches are needed in order to get a clearer picture of the development of anxiety. It is possible to find decreasing or increasing average levels of anxiety over time, but stable rank-order would reveal that individuals maintain their relative position within a group with respect to their anxiety level. Similarly, it is possible to find low stability in rank-order, indicating individual changes in math anxiety while the anxiety at the group level remains constant. However, these two approaches are rarely used in the same study. More research with a repeated-measures design, taking into account both perspectives as well as different ways of operationalizing math anxiety, is needed in order to better understand the development of math anxiety during primary school.
Recent studies on math anxiety suggest that it is related to performance in the primary school years (Carey, Devine, Hill, & Szűcs, 2017; Cargnelutti, Tomasetto, & Passolunghi, 2017; Devine, Fawcett, Szücs, & Dowker, 2012; Ramirez, Chang, Maloney, Levine, & Beilock, 2016; Ramirez, Gunderson, Levine, & Beilock, 2013; Sorvo et al., 2017; Wu et al., 2012). However, there are also studies questioning this relationship (Devine, Hill, Carey, & Szücs, 2018; Dowker et al., 2012; Haase et al., 2012; Hill et al., 2016; Krinzinger et al., 2007, Krinzinger et al., 2009; Thomas & Dowker, 2000; Wood et al., 2012). The inconclusive results of previous studies may be understood considering the varying operationalizations of math anxiety (Sorvo et al., 2017). Most of the studies that did not find a relationship between math anxiety and math performance among primary school children operationalized math anxiety as anxiety about failure in mathematics (Dowker et al., 2012; Haase et al., 2012; Krinzinger et al., 2007, Krinzinger et al., 2009; Thomas & Dowker, 2000; Wood et al., 2012). However, studies that operationalized math anxiety as anxiety in math-related situations in general have usually revealed the relationship (Cargnelutti et al., 2017; Harari, Vukovic, & Bailey, 2013; Jameson, 2013; Vukovic et al., 2013; Wu et al., 2012; Wu, Willcutt, Escovar, & Menon, 2014). When the two operationalizations were examined together, it was found that anxiety about failure in math is more common among primary school children, but anxiety about math-related situations in general is directly and more strongly related to performance in mathematics (Sorvo et al., 2017). However, the existence of the relationship between math anxiety and achievement cannot be fully explained by the operationalization of math anxiety. Hill et al. (2016), who investigated anxiety about math-related situations, did not find the relationship between anxiety and achievement among primary school students, but they found it among secondary students. Also, Devine et al. (2018) assessed anxiety about math-related situations of primary and secondary school students and found that nearly 80% of highly math-anxious students had typical or high performance in math, questioning the link between math anxiety and achievement.
Even if anxiety about math-related situations has been found to be more strongly related to achievement than anxiety about failure among primary school children (Sorvo et al., 2017), the causal relationships between the aspects of math anxiety and math achievement remain unclear. To shed light on the contradictory findings of the relationship between math anxiety and achievement, three competing models have been suggested (Carey, Hill, Devine, & Szücs, 2016). First, the model with the causal direction from high math anxiety to poor math performance is called the debilitating anxiety model (Carey et al., 2016). Based on a meta-analysis, Hembree (1990) claimed that math anxiety would weaken math performance, but he did not find any evidence suggesting that poor performance would increase anxiety. This model is supported by the finding that math anxiety seems to cause an “affective drop” in performance: math-anxious individuals are likely to underperform every time they have to do math in a timed setting (Ashcraft & Moore, 2009). There are also some studies among first and second graders with results supporting the debilitating anxiety model. Cargnelutti et al. (2017) found an indirect effect of math anxiety in grade 2 on achievement in grade 3. In a study by Vukovic et al. (2013), anxiety about math-related situations in second grade was found to predict skill development in math, but because anxiety was not assessed longitudinally, strong conclusions about the causal relations could not be made. Besides, Ramirez et al. (2016) studied math anxiety of first and second graders and found that especially children with high working memory are likely to underperform when they experience high math anxiety.
The second model, deficit theory (i.e. poor math performance elicits math anxiety; Carey et al., 2016), is supported by a study among junior and senior high school students by Ma and Xu (2004) indicating that prior low math performance predicts later high math anxiety, but prior high mathematics anxiety hardly predicts later low achievement. Furthermore, studies have shown that primary school children with math learning disabilities report more anxiety than their typically achieving peers (Passolunghi, 2011; Rubinsten & Tannock, 2010; Wu et al., 2014), giving support to this model.
Carey et al. (2016) as well as Foley et al. (2017), in their reviews based on previous studies, suggest that one reason for the conflicting results of previous research supporting either deficit theory or debilitating anxiety model might be that the studies actually shed light on different aspects of a bidirectional relationship. In this third model, reciprocal theory, math anxiety and achievement influence one another in a vicious circle (Carey et al., 2016). Carey, Devine, et al. (2017) investigated math anxiety with latent profile analysis. Based on their results, it seems that some individuals might develop math anxiety as a result of poor performance and some only because of their predisposition to anxiety generally. However, math anxiety also seemed to lower performance, to some degree, regardless of why it had developed. Therefore the researchers suggest that math anxiety and achievement affect each other reciprocally. Also Gunderson et al. (2018) found reciprocal cross-lagged relations between math anxiety and achievement of first and second graders. Even though the relations were reciprocal, the impact of initial achievement on later anxiety was stronger than the effect of anxiety predicting later achievement. They state that children who achieve lower in math and lack some of the math concepts foundational for later development when they start school are more likely to develop math anxiety but also that a higher level of math anxiety is more likely to lead to poorer achievement over time.
Previous longitudinal studies among primary school children have usually focused on relatively young students from first to third grade and have not taken into account different aspects of math anxiety. Longitudinal research taking into account both anxiety about math-related situations and anxiety about failure in math is needed before conclusions concerning the causal directions of the relationship between math anxiety and achievement can be made. More research about the causal relations is needed, especially in primary school when math anxiety and basic math skills are just developing.
Section snippets
The present study
The aim of the present study is to examine the development of primary school students' math anxiety and its relationship with arithmetic achievement longitudinally during one school year. This study extends our previous work examining the two types of math anxiety: anxiety about failure in math and anxiety about math-related situations in general (Sorvo et al., 2017), by investigating the development of these two aspects of math anxiety and their longitudinal relationship with achievement.
The
Participants and procedure
This research is based on data from a longitudinal study on the development of self-beliefs and academic skills of primary school aged children. The participants were from 20 Finnish schools, situated in urban and semi-urban areas in central Finland. The participating schools were recruited via basic education municipality officials. The participating special education teachers recruited volunteering classroom teachers of grade levels 2 to 5 at their schools. Participation was voluntary, and
Invariance of math anxiety measure over time and across grade levels
The invariance test (p = .32) indicated small differences between the RMSEA values of the freely estimated model (RMSEA = 0.05) and the model with most constraints (the factor loadings and intercepts over time and across the grade levels; RMSEA = 0.06; see Table 1). Thus, the measures of math anxiety and achievement were assumed to be invariant across time. The fit indices for the measurement model with factor loadings and intercepts constrained to be equal over time and across all grade levels
General discussion
This study investigated change in math anxiety among primary school children and examined relations between math anxiety and math fluency measured at the beginning and the end of the school year using a cross-lagged design. The development of math anxiety during one school year was examined from two perspectives of stability or change: the mean level of anxiety and the rank-order of individuals. Two aspects of math anxiety—anxiety about math-related situations in general and anxiety about
References (51)
- et al.
A comparison of predictors of early emerging gender differences in mathematics competency
Learning and Individual Differences
(2008) - et al.
“My questionnaire is too long!” The assessments of motivational-affective constructs with three-item and single-item measures
Contemporary Educational Psychology
(2014) - et al.
Maths anxiety in primary and secondary school students: Gender differences, developmental changes and anxiety specificity
Learning and Individual Differences
(2016) - et al.
The causal ordering of mathematics anxiety and mathematics achievement: A longitudinal panel analysis
Journal of Adolescence
(2004) - et al.
On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies
Journal of Experimental Child Psychology
(2016) - et al.
Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance
Contemporary Educational Psychology
(2013) - et al.
Mathematics anxiety and the affective drop in performance
Journal of Psychoeducational Assessment
(2009) - et al.
The 3-minute basic arithmetic test
(2007) Comparative fit indexes in structural models
Psychological Bulletin
(1990)Prevalence, distribution, and correlates of math anxiety in college students
Journal of Counseling Psychology
(1978)