Mathematics anxiety in children : a closer look at mathematics avoidance and parental effects

Mathematics Anxiety in Children: A Closer

Look at Mathematics Avoidance and Parental

Effects

Master thesis Developmental Psychology Faculty of Social and Behavioural sciences University of Amsterdam

Abstract

Mathematics anxiety is a fear related to mathematics that influences performance in mathematics negatively. One of the core symptoms of mathematics anxiety that is also related to mathematical performance is the avoidance of mathematics. Mathematics avoidance can be measured in different manners: with an explicit measure (self-reported avoidance on a questionnaire), an implicit measure (an approach avoidance task), and a behavioural measure (a task in which participants could choose the level of difficulty of the mathematics exercises they completed). The first aim of the study was to investigate how the tendency to approach or avoid mathematical stimuli was related to self-reported mathematics anxiety. The second aim was to investigate how the three measures of mathematics avoidance relate to each other and to performance in mathematics. Since it is known that parental factors have a central role in the aetiology of childhood anxiety, it was studied how parental factors like parental mathematics anxiety, parental involvement, and parental expectations were related to childhood mathematics avoidance. Participants were 98 children between 12 and 16 years old and 73 parents. All children completed the mathematics avoidance tasks and questionnaires in a classroom setting and the parents received a link by email to the questionnaires. It was found that there was no approach-avoidance bias for

mathematical stimuli and that there was no significant relation between the three measures of mathematical avoidance. Only the explicit measure of mathematical avoidance was related to the average grade for mathematics. Finally, it was found that the parental factors were not related to the avoidance of mathematics in the children. This study found that using different measures of mathematics avoidance was not related to a more accurate prediction of the actual avoidance of mathematics or mathematical performance. Additionally, the role of parental factors seemed to be of

less importance for mathematical avoidance than for other types of childhood anxiety. Implications for future research and limitations of the study will be discussed.

Mathematics Anxiety in Children: A Closer Look at Mathematics Avoidance and Parental Effects

Mathematics anxiety can be defined as a feeling of tension, apprehension, or fear related to mathematics (Ashcraft, 2002). This anxiety is often related to an

adverse emotional reaction towards doing mathematics or the thought of doing so, and can in turn interfere with working with numbers or solving mathematical problems (Hembree, 1990). Mathematics anxiety can both occur inside and outside the school setting (Wood, 1988). Many consequences of mathematics anxiety have been identified, including the inability to perform in mathematics, the avoidance of mathematics classes, lower achievements in mathematics, lower perceptions of

mathematical abilities and not seeing the values of mathematics in daily life (Ashcraft, Krause, & Hopko, 2007; Ashcraft & Moore, 2009; Ma, 1999; Ma & Xu, 2004;

Vukovic, Kieffer, Bailey, & Harari, 2013). The interference with math performance stresses the importance of understanding mathematics anxiety for the development of effective interventions, since mathematical ability become increasingly important for participation in society (Peterson, Woessman, Hanushek, & Lastra-Anadón, 2011). Therefore, the aim of the current study was to get a better understanding of

mathematics anxiety.

Previous studies suggested that the avoidance of mathematics is a core

symptom of mathematics anxiety (for a review see Suárez-Pellicioni, Núñez-Peña, & Colomé, 2015). Avoidance of mathematics can develop as a result of mathematics anxiety and negative attitudes toward mathematics (Ashcraft, Krause, & Hopko, 2007). Examples of the avoidance of mathematics are taking fewer elective math courses, choosing lower levels of mathematical classes and avoiding career paths that rely on mathematical skills. These types of avoidance behaviour can be described as

global avoidance behaviour. Avoidance of mathematics can also occur at a local level when children are speeding through math exercises or trying to spend less time in mathematics classes (Ashcraft, 2002; Hembree, 1990). As a result, mathematics avoidance can lead to worse performance in mathematics (Ashcraft & Krause, 2007; Dew, Galassi, & Galassi, 1984; Hembree, 1990). Nevertheless, relatively few (recent) studies are available on the avoidance of mathematics in children.

Avoidance is more elaborately studied in other types of childhood anxiety (e.g. Olatunji & Wolitzky-Taylor, 2009). It is known that avoidance of feared stimuli plays a central role in both the aetiology and maintenance of childhood anxiety problems; anxious children tend to avoid the feared stimuli to protect themselves, this confirms the negative views about the stimuli, which in turn leads to avoidance (Beidel & Alfano, 2007; Beidel & Turner, 2007). Research indicated that avoidance is an anxiety related behaviour resulting from a combination of implicit and explicit

processes. These implicit processes are automatic, impulsive and subconscious, while the explicit processes are controlled and conscious. Even when an anxious individual does not want to avoid a feared stimulus, it can still be that they have an automatic reaction of avoiding the feared stimulus. This can be the result of a subconscious and implicit process (McLeod, Wood, & Weisz, 2007; Strack & Deutsch, 2004). Since it is known that implicit avoidance behaviour is hard to access through introspection, measuring avoidance by only asking individuals about their avoidance at an explicit level might not be sufficient (Foa & Kozak, 1986; Heuer, Rinck, & Becker, 2007). Consequently, avoidance can be measured at different levels.

First of all, avoidance can be studied at an explicit level by using questionnaires. In these questionnaires children are asked to reflect on their level of avoidance by answering multiple questions on different situations. Secondly, avoidance can be

measured with behavioural measures. With these measures it is determined with observations or tasks how much children avoid feared stimuli (Bernstein & Nietzel, 1974). Finally, implicit or automatic measures of anxiety related avoidance can be determined with computer tasks, such as an approach-avoidance task (AAT). In an AAT participants are presented with anxiety provoking (test) stimuli and control stimuli. These test or control stimuli are presented in squares that are either tilted to the left or to the right. Depending on this direction participants have to press either the upward or downward arrow on a computer keyboard. When participants press the downward arrow, the picture enlarges and simulates an approach like effect. When participants press the upward arrow, the picture size decreases and simulates an avoid like effect. Half of the test and control stimuli has to be responded with an approach reaction and the other half with an avoid reaction. When participants are faster in giving an avoidance response to the test stimuli than an approach response it can be concluded that participants have a stronger implicit tendency to avoid the test stimuli than to approach them. The AAT has mostly been used to measure approach

behaviour (for instance in addiction research) but was recently also used for

measuring avoidance behaviour (e.g. Field & Lawson, 2003: Hadwin & Field, 2010; Wiers, Gladwin, Hofmann, Salemink, & Ridderinkhof, 2013). Research with adults focusing on implicit avoidance in relation to anxiety found that individuals with a spider phobia had a stronger automatic tendency to avoid pictures of spiders than to approach them on a AAT (Rinck & Becker, 2007). The study of Heuer, Rinck, and Becker (2007) found no differences in the tendency to avoid faces for individuals with high levels of social anxiety compared to individuals with low levels of social anxiety. A study that focused on spider anxiety in children found that children were in general faster in pushing pictures of spiders away than approaching them. In girls, the implicit

avoidance of spiders was related to self-reports of spider anxiety and anxious behaviour during a behavioural assessment task. These relations were not found for boys (Klein, Becker, & Rinck, 2011).

The studies described above on mathematics avoidance only used explicit measures (i.e. Ashcraft & Krause, 2007; Dew, Galassi, & Galassi, 1984; Hembree, 1990). There are no studies yet available measuring mathematics avoidance at an implicit level. However, a former study did investigate mathematics anxiety at an implicit level. This study found preliminary evidence of an attentional bias towards mathematics related stimuli, meaning that individuals with high levels of mathematics anxiety had higher attention towards threatening/mathematics stimuli compared to neutral stimuli (Pellicioni, Nuñez-Peña, & Colomé, as cited in

Suárez-Pellicioni, Núñez-Peña, & Colomé, 2015). Additionally, in another study it was found that individuals can be trained to identify themselves more with mathematics at an implicit level with an Implicit Association Task (IAT) (Kawakami, Steele, Cifa, Phills, & Dovidio, 2008). This suggests the possibility of studying implicit concepts about mathematics. Therefore, the first two goals of this study were to investigate the existence of an avoidance bias related to mathematics stimuli and to study how this is related to explicit and behavioural measures of mathematics avoidance.

It is already discussed that avoidance is a core symptom of childhood anxiety problems. In addition, it is also known that parental factors play a central role in the development and maintenance of childhood anxiety disorders (Rapee, 2012). There is evidence for transmission of anxiety from parents to their children through various processes. In these processes children learn both at a conscious and an unconscious level that they have to fear and avoid the situations that their parents fear and/or avoid (Beidel & Turner, 1997; Wood, Mcleod, Sigman, Hwang, & Chu, 2003). For instance,

parents can transmit anxiety to their children by their parenting style, like being overprotective toward their children when they encounter (threatening) situations (for a review see Bögels & Brechman-Toussaint, 2006). Additionally, when children see that their parents are afraid or tend to avoid certain stimuli they can copy this

behaviour. This is called modelling (Muris, Merckelbach, Jong, & Ollendick, 2002; Muris, Steerneman, Merckelbach, & Meesters, 1996).

Since research indicated that parental factors can play an important role in childhood anxiety, it might also be useful to include parental factors in studies investigating mathematics anxiety. So far, only a few studies did include a form of parental factors. Vukovic, Roberts, & Green Wright (2013) studied the role of

parental involvement, such as helping with homework and studying, and expectations, such as aspirations and to what extent parents expect good results, in children’s’ math anxiety and performance in an ethnic minority group. They found that parental school involvement was not related to children’s mathematics anxiety. Parental expectations and home support was related to children’s mathematics anxiety. The relations between parental expectations and home support to children’s mathematical performance was mediated by children’s mathematics anxiety was only present for word problems and algebraic reasoning, but not for whole number arithmetic. Additionally, research indicated that parents’ mathematics anxiety is related to children’s mathematics achievements. However, this relation is less strong when parents are more involved in helping with their child’s homework. Children’s achievements were related to their mathematics anxiety (Maloney, Ramirez,

Gunderson, Levine, & Beilock, 2015). This study suggests that mathematics anxiety in parents, parental involvement and parental expectations can have (indirect) effects on mathematics anxiety and performance and children. However, it is not clear how

these parental factors relate to mathematics avoidance in children. The third aim of the study was therefore to explore how parental factors, like parental mathematics anxiety, parental involvement, and parental expectations, relate to the different measures of childhood mathematics avoidance.

All in all, the current study aimed to get more insight in underlying and

parental component of mathematics anxiety with and explorative design by answering three research questions. The first goal of the study was to find out if there is an implicit avoidance bias related to mathematics anxiety. Based on studies that found an avoidance bias related to other types of childhood anxiety, it was hypothesized that an avoidance bias for mathematics stimuli exists in children with higher levels of

mathematics anxiety. The second goal of the study was to find out how the three measures of mathematics avoidance relate to each other and to performance in mathematics. It was expected that all measures of mathematics avoidance related positively to each other and to the mathematics grade, similarly to findings in other fields of research on childhood anxiety. The final goal of the study was to investigate how parental mathematics anxiety is related to mathematics avoidance in children and to investigate if this relation is mediated by parental expectations and involvement. A positive relation between parental mathematics anxiety and mathematics avoidance in their children was expected, since there is convincing evidence for positive relations between childhood and parental anxiety problems in general (e.g. Wood et al., 2003). Moreover, it was hypothesized that parental involvement and expectations has a partly mediating effect on the relation between parental mathematics anxiety and childhood mathematics avoidance.

2. Methods 2.1. Participants

Participants of the study were 98 children (Nboys = 44, 44.9% boys) aged between 12 and 16 years old (M = 14.43, SD = .86). All children were attending a Dutch regular secondary school. The participant attended different levels of the Dutch education system; 55.1% (N = 54) of the children attended VWO, 29.6% (N = 29) HAVO and 15.3% (N = 15) VMBO. This distribution of the children in our sample over the different school levels differed from the population distribution in the Netherlands, since most children attend VMBO and the smallest groups of children attend VWO (Rijksoverheid, 2017). In the current sample, 15.3% (N = 15) of the children were in the first year of secondary school, 29.6% (N = 29) in the second year and 55.1% (N = 54) in the third year. Additionally, 73 parents participated in the study. In total, 26 fathers (age: M = 47.54 years, SD = 4.46) and 47 mothers (age: M = 49.22 years, SD = 5.46) completed the questionnaires.

The study was approved by the ethical committee of the Department of Psychology of the University of Amsterdam. The first in recruiting participants was asking permission from secondary schools to participate in the study. When a school was willing to participate in the study, all children received an information letter about the study for themselves and their parents. Also, parents received an email with the same information letter and consent form. Parents gave written consent for

participation of both the child and themselves. Children signed a consent form before participating in the study.

2.2 Materials

2.2.1. Childhood mathematics anxiety and avoidance, explicit measure Mathematics anxiety and avoidance in children was measured with the Component Of Math Anxiety Questionnaire (COMAQ). The COMAQ consists 31 items divided over five subscales (general math anxiety, cognition and test, avoidance, effort, asking questions). Participants had to indicate for each item how much the statement fitted their opinion about themselves on a five point Likert-scale (1 = not true at all for me, 5 = is completely true for me). An example item of the COMAQ is “When I have to do a difficult math exercise, I feel nervous”. The questionnaire has an excellent internal consistency, α = .94 (Schmitz, Salemink, Wiers, & Jansen, 2017). In the current sample, the questionnaire also had an excellent internal consistency (α = .93).

Mathematics avoidance in the children was measured with the avoidance subscale of the COMAQ. This subscale measures mathematics avoidance in different situations, like avoidance of mathematics tests, homework, classes and mathematical content. An example item of the avoidance scale of the COMAQ is “During a math test I try to peek to make sure I don’t have to solve the math problem myself”. The subscale consists of seven items and has a good internal consistency, α = .80 (Schmitz, Salemink, Wiers, & Jansen, 2017). In the current sample the avoidance subscale had a low internal consistency, α = .66.

Mathematics anxiety in children was determined with the general math anxiety subscale of the COMAQ. An example item of this subscale is “I feel nervous when I have to do a difficult math exercise”. This subscale had an excellent internal

2.2.3. Childhood mathematics avoidance, implicit measure

An AAT was used to measure the implicit tendency to avoid mathematics stimuli. In the AAT seven pictures of mathematics were used. The pictures were selected based on a previous validation study of the mathematics pictures (Schmitz, Jansen, Wiers, & Salemink, 2017). In this study students indicated whether the stimuli related to mathematics and how threatening the stimulus was for them. Stimuli for the AAT were selected when they were indicated as having strong relations with

mathematics, with mathematics anxiety, and when they were indicated as threatening stimuli. Furthermore, the stimuli were only selected if there was at least a medium correlation between the threat-score of a stimulus and the mathematics anxiety score on a questionnaire. The stimuli had to cover the different aspects of mathematics like graphs, spatial figures, fractions, and calculations. Next, seven schematic control stimuli were selected. These stimuli were matched with the mathematics stimuli based on the shape and size. Examples of the control stimuli were a cake, flower, and a boat. The AAT started some short instructions followed by ten practice trials. Half of the children were instructed to push the downward arrow when the picture was tilted to the left and the upward arrow when the picture was tilted to the right. When the participants pressed the upward arrow, the picture size decreased and simulated an avoid like effect. When the participants pressed the downward arrow, the picture size increased and simulated an approach like effect. The other half of the children

received the reversed instructions. In these practice trials participants were presented with grey squares in a similar size as the stimuli that were tilted to the left or right. After the practice trials all participants completed to blocks with the mathematics and control stimuli. Each block consisted of 56 trials and consisted of the same number mathematics and control stimuli, and half of the stimuli had to be approached and the

other half had to be avoided. The stimuli were presented in random order. D-scores for the mathematics and control condition of the AAT were computed (see data preparation). A positive approach-avoid bias score corresponds with a stronger tendency to avoid the mathematics or control stimuli than to approach these stimuli. 2.2.4. Childhood mathematics avoidance, behavioural measure

Mathematics avoidance in the children at a behavioural level was measured with a Behavioural Assessment Task (BAT). Our BAT was an achievement task which consisted of twelve mathematics equations presented in a grid of four times three. Participants were asked to select and solve four out of the twelve equations. The three columns in the grid represented three levels of difficulty. The easiest level consisted of equations with numbers below 10 and without carry effects (e.g. ‘x + 4 = 8’), meaning that all computations can be completed without carrying numbers over the dozens. The second level consisted of equations with numbers between 10 and 100 with carry effects (e.g. ‘x + 48 = 79’). The hardest level consisted of linear equations with numbers up to 100 with carry effects and a number before the x (e.g. ‘3x + 18 = 36). All linear equations had solutions without any decimal places (e.g. Ashcraft & Faust, 1994; Faust, 1996; Trezise & Reeve, 2014). Participants were presented with six times a screen of twelve mathematical equations. Before analysing the data an average level score of the achievement task was computed. The average scores on the achievement task were computed by determining what the average level (ranging from 1 to 3) was of the exercises the children choose to complete, regardless of whether their answers were right or wrong. Higher scores correspond with higher chosen levels of exercises in the achievement task.

2.2.5. Mathematics grade

Students’ grade for mathematics was measured with the following question: “What was your average grade for mathematics on your latest report card?”.

2.2.6. State anxiety in the children between the mathematics avoidance measures State anxiety during the mathematics avoidance tasks was measured with the faces anxiety scale. The task was designed to measure the level of anxiety children experience when they are working on the achievement task. The state anxiety measure was included to test whether children do experience anxiety when they are working on the mathematics exercises and to test if their level of anxiety changes over time. The state anxiety scale consisted of five faces in a graded sequence from non-anxious to very anxious. The faces anxiety scale had a good test-retest reliability (Bieri, Reeve, Champion, Addicoat, & Ziegler, 1990; Trezise & Reeve, 2014).

2.2.7. Parental mathematics anxiety

The level of mathematics anxiety in the parents was measured with the Abbreviated Math Anxiety Scale (AMAS; Hopko, Mahadevan, Bare, & Hunt, 2003). The questionnaire consisted of 9 items measuring self-reported mathematics anxiety in adults by asking them how anxious they would feel during mathematics related events. An example-item was “Listening to another student explain a math formula”. The AMAS yields a strong internal consistency and test-retest reliability (Hopko et al., 2003). In the current sample the AMAS had an excellent internal consistency, α = .93. 2.2.8. Parental involvement and expectations

Parental involvement and expectations were measured with a short adjusted questionnaire based on the study of Cakiroglu (2004). The original questions were designed to measure parental involvement and expectations to their children’s school work in general. The items were adjusted by changing the focus to mathematics

achievements and homework instead of overall achievements and homework. The questionnaire consisted of three items for measuring involvement and six items for measuring expectations. An example-item of the adjusted questionnaire for the involvement scale was “I feel the need to help my child with his/her mathematics homework”. An example-statement for the expectations scale was “Getting good grades for mathematics”. Parent’s had to indicate on a five point scale to what extent they agree with the statement or find the content of the statement important for their child. The internal consistency of this questionnaire in the current sample was low for the involvement scale, α = .62, and was also low for the expectations scale, α = .69. 2.3. Procedure

The children completed the tasks in a classroom setting on computers. The groups of children varied between 15 and 29 students. First of all, the children read the informed consent and had to indicate whether or not they were willing to participate in the study. All children who read the informed consent were willing to participate and started the tasks. The first task was the AAT. After the AAT children completed the COMAQ and the achievement task in random order. Children could complete all tasks by themselves. Children received a debriefing presentation after the whole class completed the tasks.

The parents received a link by email referring to an online questionnaire with the AMAS and the 8 questions about parental expectations and involvement. The link was sent after the children participated in the study. When the parents did not

complete the questionnaire after a week, they received a reminder by email. When the parents did still not complete the questionnaire a week after the reminder, they were called and asked whether or not they were willing to fill in the questionnaire.

3. Results

3.1. Data preparation

Before analysing, data of the achievement task, AAT, and parental factors were prepared. Due to incomplete data on the achievement task, data of the first screen and data of nine participants were excluded from the analyses. On the first screen 13 participants completed more or less than four than equations. The data of the nine participants were removed since they completed on one or more of the other screens less or more than four equations.

For the AAT data of two participants were not saved during the data collection process. The AAT-scores were computed with a D-score algorithm (see Wiers, Eberl, Rinck, Becker, & Lindenmeyer, 2011). Before computing the D-scores the error response-rate of all trials, except for the practice trials, was computed (8.5%). All responses with latencies faster than 300 ms were removed. Next, means and standard deviations of the response times in each type of trials (mathematics-approach,

mathematics-avoid, control-approach, control-avoid) were computed. For the trials with the incorrect responses the response time was replaced by the average response time of the correct responses for the same trial-type within participant plus a penalty of two standard deviations. Finally, two separate approach-avoid bias scores were computed for the mathematics and control stimuli by subtracting the average approach response time from the average avoid response time and dividing this score by the standard deviation for the mathematics or control stimuli. The more positive an approach-avoid bias score is, the stronger the tendency to avoid the mathematics or control stimuli than to approach them. Negative approach-avoid bias score correspond with a stronger tendency to approach the stimuli than to avoid them.

Data of the parental factors (parent’s mathematics anxiety, parental

involvement, and parental expectations) was prepared by computing the average score on each questionnaire of two parents for each child. When only one parent completed the questionnaire those scores were used in the analyses.

3.2. Implicit avoidance bias

The first goal of the study was to investigate whether there was an avoidance bias for the mathematics stimuli and control stimuli by performing two one-sample t-test. All AAT-data had approximately a normal distribution (mathematics stimuli:

Shapiro Wilk test = .989, p = .620; art stimuli: Shapiro Wilk test = .978 p =.112; see

Figure 1). The first one-sample t-test indicated that the math-approach/avoid D-score (M = .02, SD = .36) did not significantly deviate from zero, t(95) = .53, p = .595, meaning that there was on average no significant bias for approaching or avoiding mathematics stimuli on the AAT. The other one-sample t-test indicated that the control-approach/avoid D-score (M = -.03, SD = .34) did not deviate from zero, t(95) = -.73, p = .468, meaning that there was neither a significant bias for approaching or avoiding the control stimuli. Next, it was checked whether there was a significant difference in bias score between the mathematics and control stimuli with a paired-sample t-test. The bias score for the mathematics and control stimuli did not

significantly deviate from each other, t(95) = .98, p = .329, meaning that there was no difference in bias score between the mathematics and control stimuli.

Figure 1. Distribution of the AAT-data.

3.3. Predicting behavioural avoidance and mathematics achievements The second goal of the study was to investigate whether the implicit and explicit measure of mathematics avoidance did predict the behavioural measure of mathematics avoidance. Additionally, we wanted to study if the three measures of avoidance did significantly predict the achievements in mathematics. The scores on the COMAQ avoidance subscale was in our sample not normally distributed (see Figure 2, Shapiro Wilk test = .901, p < .001; M = 1.48, SD = .44). Almost all of the participants reported very little avoidance of mathematics on the questionnaire. The scores on the general math anxiety subscale of the COMAQ were neither normally distributed (see Figure 2, Shapiro Wilk test = .824, p < .001; M = 1.62, SD = .68). Also the scores on the achievement task were not normally distributed (see Figure 3,

Shapiro Wilk test = .846, p < .001; M = 2.37, SD = .67). Most of the participating

children choose to complete the mathematics exercises with the highest level of difficulty.

Figure 2. Distribution of the COMAQ-data

Figure 3. Distribution of the achievement task data.

An explorative analysis was performed with the state anxiety during the achievement task to test how anxious the participants felt when they had to choose and solve mathematical equations. All participants reported very low levels of anxiety on all time points (state anxiety 1: M = 1.37, SD = .06, state anxiety 2: M = 1.24, SD = .05, state anxiety 3: M = 1.22, SD = .06, state anxiety 4: M = 1.18, SD = .04). A repeated measures ANOVA with the four state measures of state anxiety as within subject factors revealed that the children reported a significant decrease in anxiety during the achievement task on the state anxiety measure, F(3,95) = 6.00, p = .001. A

test of Within-Subject Contrasts revealed that there only was significant decrease of state anxiety between the first and second measurement point of state anxiety (level 1 vs level 2: F(1, 97) = 10.650, p = .002; level 2 vs level 3: F(1, 97) = .190, p = .664; level 3 vs level 4: F(1, 97) = 1.327, p = .252; see Figure 4). There was a medium correlation between the level of state anxiety at the first measurement point and the level of general math anxiety as reported on the COMAQ, r = .49, p < .001.

Figure 4. Decrease of the average level of state anxiety during the achievement task.

Before performing the regression analyses the correlations between the COMAQ avoidance score, the AAT-score, the achievement task score and average grade were computed (Table 1). A hierarchical regression analysis was performed to determine to what extent the AAT mathematics D-score and the avoidance subscale of the COMAQ did predict the achievement task score. In the first step only the

avoidance subscale of the COMAQ was included as a predictor and the mean

achievement task-score as an outcome measure. The model did not significantly fit the data, F(1, 85) = .25, p = .620, R2 = .00. In the next step the mathematics D-score of the AAT was added as a predictor. This analyses indicated that the avoidance subscale

of the COMAQ and the mathematics D-score of the AAT did not significantly predict the mean achievement task score, F(2, 84) = .13, p = .879, R2 = .00, R2-change = .00.

A second hierarchical regression analysis was performed to predict the average self-reported mathematics grade as an outcome measure and the avoidance subscale of the COMAQ, the mathematics D-score of the AAT, and the mean achievement task score as predictors. In the first step of the regression analysis only the avoidance subscale of the COMAQ was included in the analysis, since these variables had the strongest relation. This model did significantly fit the data, F(1, 96) = 7.04, p = .009,

R2 = .06. The avoidance subscale of the COMAQ was a significant predictor of the

self-reported mathematics grade (Table 2). In the next step the mathematics AAT-score was included as a predictor. This model was also a significant fit to the data, F(2, 84) = 3.31, p = .041, R2 = .07, R2-change = .01. However, only the avoidance

subscale of the COMAQ was a significant predictor in this model (Table 2). In the final step of the model the achievement task score was added as a predictor. This model was a significant fit to the data, F(3, 83) = 2.73, p = .049, R2 = .09, R2-change = .02, but only the COMAQ avoidance score was a significant predictor (Table 2).

Table 1

Pearson correlations between the avoidance subscale of the COMAQ, the

mathematics D-score on the AAT, the achievement task score, and the average grade in mathematics. COMAQ AAT Achievement task AAT 0.13 Achievement task -0.03 0.01 Grade -0.26* -0.15 0.12 Note. * p ≤ .01

Table 2

Bèta values of the regression analyses for predicting the average grade of mathematics.

Model Predictor Bèta

1 COMAQ -.25* 2 COMAQ -.24* AAT -.10 3 COMAQ -.23* AAT -.10 Achievement task -.13 Note. * p < .05

3.4. The relation between parental factors and child mathematics anxiety, avoidance, and achievement

The final goal of the study was to investigate the relation between parental factors and childhood mathematics anxiety, avoidance, and achievement. More specifically, the goal was to study if there was a relation between parental

mathematics anxiety and childhood mathematics anxiety and avoidance, and to find out whether this hypothesized relation was mediated by parental involvement and expectations. On the AMAS, almost all parents reported on low levels of mathematics anxiety (see Figure 5; Shapiro Wilk test = .851, p < .001; M = 1.68, SD = .73). The expectations scale was not normally distributed since most parents reported on average and some parents reported high expectations (see Figure 6; Shapiro Wilk test

= .942, p = .007, M = 3.36, SD = .58). Also the involvement scale was not normally

mathematics (see Figure 6; Shapiro Wilk test = .875, p < .001, M = 1.75, SD = .66). Correlations were computed to test whether there was a relation between parental mathematics anxiety, parental involvement, parental expectations, and children’s mathematics anxiety, avoidance, and achievements (see Table 3). It was found that parental involvement was negatively related to the average self-reported mathematics grade of the children, meaning that more parental involvement was related to worse performance in mathematics. Since there was no significant relation between any of the parental factors and childhood mathematics anxiety or avoidance, mediation analyses could not be performed.

Figure 5. Distribution of the AMAS-data.

Table 3

Pearson correlations between all parental factors (parent’s anxiety, involvement, and expectations) and child mathematics anxiety (general math anxiety subscale of the COMAQ), avoidance (avoidance subscale of the COMAQ, mathematics D-score of the AAT, mean achievement-score), and self-reported mathematics achievement.

Parent math anxiety Parent involvement Parent expectations COMAQ - anxiety COMAQ - avoidance AAT Achievement task Parent involvement 0.15 Parent expectations -0.05 0.13 COMAQ - anxiety 0.04 0.17 0.05 COMAQ - avoidance 0.02 0.10 0.00 0.72* AAT 0.06 0.19 -0.08 0.00 0.13 Achievement task 0.12 0.05 0.09 -0.17 -0.03 0.01 Grade -0.16 -0.41* -0.09 -0.26* -0.26* -0.15 0.12 Note. * p ≤ .010

4. Conclusions and discussion

The aim of this study was to get more insight in mathematics avoidance and parental components of mathematics anxiety with an explorative design. First, it was studied whether there was an avoidance bias related to mathematics anxiety. The results showed that the children were not faster or slower with avoiding or approaching the mathematics stimuli, meaning that there was no approach or

avoidance bias related to mathematics. Neither was there a bias for the control stimuli. Second, it was investigated if explicit and implicit mathematics avoidance could

predict mathematics avoidance at a behavioural level or if the three avoidance measures could predict achievements in mathematics. The implicit and explicit measure of mathematics avoidance did not predict mathematics avoidance on the behavioural assessment task. However, it was found that when the children reported higher levels of avoidance of mathematics on the explicit measure they had lower grades for mathematics. Third, it was studied if parental mathematics anxiety could predict children’s mathematics anxiety or avoidance, and if parental involvement and expectations mediated this relationship. There was no relation between the parental mathematics anxiety and children’s mathematics anxiety or avoidance. Neither were parental expectations or parental involvement related to the amount of mathematics anxiety parents reported or to children’s mathematics anxiety or avoidance. It was found that when parents were more involved in their child’s mathematics that children had worse achievements in mathematics.

The finding that there was no implicit avoidance bias of mathematics was not in line with our hypothesis. We expected to find a bias since other studies that used an AAT to study implicit avoidance related to anxiety did find an avoidance bias (Rinck & Becker, 2007; Klein, Becker, & Rinck, 2011). These other studies found an

avoidance tendency for pictures of spiders instead of mathematics stimuli. Therefore, it could be that the mathematics stimuli were not evaluated as threatening by the children, which could explain why we did not find an avoidance bias for mathematics. The stimuli were selected based on a previous study in which the stimuli were rated on how threatening they were and on how much they related to mathematics (Schmitz et al., 2017). The mathematics pictures that covered a variety of mathematics topics, with the highest levels of anxiety and the strongest relation to mathematics were selected. Nevertheless, the descriptive statistics confirmed that the children in the

current sample reported very low levels of mathematics anxiety and state anxiety during the achievement task. As a result it could be that the stimuli we used were not threatening for them at all. Therefore it would be interesting for future research to study if there is an avoidance bias related to mathematics in a selected sample with children that report high levels of mathematics anxiety. For future studies it could also be interesting to let children complete the tasks after a mathematics test in their

regular classroom setting to activate the potential mathematics anxiety related schemas (e.g. Constans, Penn, Ihen, & Hope, 1999). Since the definitions of

mathematics anxiety indicate that the anxiety for mathematics is mostly about doing mathematics, it could be helpful for future research to use pictures of individuals doing mathematics or mathematics classrooms as stimuli (Hembree, 1990).

The hypothesized relations between the three measures of avoidance were not found in this study. Previous studies that investigated the relation between explicit and implicit measures neither found a clear relation on a group level between self-report measures of anxiety and AAT-scores (Heuer et al., 2007; Klein et al., 2011). The lack of a result in the current study could partly be explained by the non-existent avoidance bias of mathematics and the low reported avoidance on the explicit measure.

Additionally, descriptive statistics revealed that there was a floor effect in the current sample; almost all children showed very low levels of avoidance on the behavioural measure of avoidance. The very skewed distribution of these data makes it difficult to study a relation between the variables. For future research it could be useful to make the behavioural measure of avoidance more difficult or add a stress condition to see if children show an avoidance tendency of mathematics under these circumstances. We think that using an achievement task to elicit mathematics anxiety might be useful, since participants reported the highest levels of state anxiety before they received the

information about the achievement task. Yet, the anxiety decreased significantly during the achievement task. This suggests that the achievement task might not have been difficult enough to elicit anxiety and corresponds with the idea to increase the level of difficulty of the equations.

Another factor that could have influenced these results is that data were collected in a classroom setting, which made it possible for children to influence each other in some groups by commenting on the tasks out loud. Peer pressure could for example have led to choosing more difficult exercises in the achievement task (Lashbrook, 2000). In future research it would be good to use smaller groups in the data collection process to prevent children from influencing each other. A final alternative explanation for our results could be that all included child measures were relatively new, which could have affected the reliability of the study.

Contrary to studies on other types of childhood anxiety (e.g. Rapee, 2012), we did not find a relation between parent’s and children’s mathematics anxiety. A

possible explanation for this result could be that both parents and children almost reported no mathematics anxiety. However, the only study that we found in which both parent’s and children’s mathematics anxiety was included did not report a direct relation between parent’s mathematics anxiety and their children’s mathematics anxiety (Maloney et al., 2015). Therefore, it could be that parent’s mathematics anxiety is indeed of less importance in relation to childhood mathematics anxiety. An alternative explanation is that the measure of mathematics anxiety for the parents was not comparable to the measure for the children, because most of the parents are not confronted with mathematics in a similar way as the children. Subsequently, the mathematics anxiety measure for the parents could have measured a different construct than the mathematics anxiety that is measures in the children, which could

explain the lack of a relation between the two measures. In forthcoming studies it could be helpful to study mathematics anxiety in parents in a situation in which they are presented with mathematics to prime possible underlying mathematics anxiety and use a similar approach in the children to prevent measuring different constructs in parents and the children. Moreover, for future research it could be interesting to include measures of teacher’s mathematics anxiety, since the study of Beilock, Gunderson, Ramirez, and Levine (2009) revealed that teachers’ mathematics anxiety is related to children’s mathematics achievements. Finally, it would possibly be interesting to include a general measure of anxiety in the parents and study its relation to (general and) mathematics anxiety in the children. Research has shown that

intergenerational relations of anxiety are often not disorder specific (Eley, 2001; Rapee, 2002). Including the general measures of anxiety could give information about if a general anxious parental attitude is related to mathematics anxiety in children.

We did find a negative relation between mathematics parental involvement and achievement of mathematics in the children. This finding is not completely in line with the finding of Vukovic, Roberts, and Green Wright (2013), who found that there was a positive relation between parental involvement and mathematical performance in the children for whole number arithmetic. The difference might be explained by the difference in sample of the studies; our study mainly used a high to middle class sample, while the other study focussed on a low-income, ethnic minority sample. Children in the ethnic minority possibly receive worse mathematics education and could therefore profit from the help of the involvement of their parents, while children in our sample do not necessarily need their parent’s involvement in addition to the school’s involvement in mathematics.

All in all, the current study found that children’s’ reports about avoiding mathematics relates to achievements in mathematics. This suggest that children who report the tendency to avoid mathematics might need help to decrease their avoidance of mathematics, since it is related to lower grades. However, we also found that parental involvement was negatively related to grades in mathematics. Therefore increasing parental involvement would probably not be an appropriate intervention. Interventions for children who report avoidance of mathematics should therefore be studied more elaborately and possibly more focussed on the mathematics avoidance and anxiety instead of the studying. Future research could focus on studying

mathematics avoidance in a selected, high risk sample or stress evoking situation to obtain a better understanding of the role of avoidance in mathematics anxiety. More research is needed to understand what the role of the environment in children’s mathematics anxiety is and if it is needed to include the environment in treatment for mathematics anxiety.

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