Math anxiety is a relatively frequent phenomenon often related to low mathematics achievement and dyscalculia. In the present study, the German and the Brazilian versions of the Mathematics Anxiety Questionnaire (MAQ) were examined. The twodimensional structure originally reported for the German MAQ, that includes both affective and cognitive components of math anxiety was reproduced in the Brazilian version. Moreover, mathematics anxiety also was found to increase with age in both populations and was particularly associated with basic numeric competencies and more complex arithmetics. The present results suggest that mathematics anxiety as measured by the MAQ presents the same internal structure in culturally very different populations.
Every student knows how unpleasant life can be when the mathematics test is approaching. Although there is no gold standard to measure the levels of math anxiety (MA) that should be considered maladaptive, depending on their intensity and duration, negative physiological reactions, effects, and thoughts regarding mathematics can be considered a form of performancerelated phobia [
Shortterm, online effects of MA on math performance have also been described. Negative emotional and mathrelated primes have been shown to speed up math performance in children with math learning disability [
MA is a multilevel construct keeping similarities with disorders such as social phobia and test and computer anxiety [
Although the latent structure of MA has been investigated in adolescents, to our knowledge, there is no research on the latent structure of MA in elementary school children focused on transcultural similarities and differences. This would be important, as evidence suggests that distinct MA components may differentially correlate to math performance and other factors according to age [
Research on MA has been largely concentrated on highschool and college samples [
Research reported here aimed at comparing MA latent structure, math performance, and sociodemographic correlates in samples of typically developing elementary school children in two countries, Germany and Brazil. While the PISA 2003 math scores of German students are among those with the highest ranks, those of Brazilian students are placed in the lowest ranks [
More specifically, we aimed at examining if the bifactorial structure described by Krinzinger and coworkers [
The Brazilian sample was constituted by children with ages ranging from 7 to 12 years and attending from 1st to 6th grade. The study was approved by the local research ethics committee (COEPUFMG). Children participated only after providing informed consent in written form from their parents, and orally from themselves. Children were recruited from schools of Belo Horizonte and Mariana, Brazil. A wide set of evenly geographically distributed schools was sampled. For this reason, the sample is representative of the Brazilian school population, with 80% of children attending public school, and the 20% attending private schools. In a first phase of testing, children with normal intelligence (i.e., who scored above the 16th percentile in the Raven colored matrices test, [
Descriptive data from Brazilian and German children.
Brazil  Germany  


171  450 
Female (%)  99 (57.9%)  227 (50.4%) 
Male (%)  72 (42.1%)  223 (49.6%) 
Age (mean (sd))^{§}  119.26 (13.2)  96.04 (5.1) 
^{§} expressed in months.
Four hundred fifty children with ages between 6 and 10 years old, attending to grades 1 to 3, who took part in a study aiming to collect norms for the German version of the TEDIMATH [
For the purpose of comparing results between the Brazilian and the German samples, a subsample of those children with ages between 7.6 and 10.1 years was selected, which is the age interval common to both samples (Brazilian
The Math Anxiety Questionnaire (MAQ) was applied both in Brazil as in Germany. Other instruments differed according to country. In Brazil, school achievement was assessed with the TDE and intelligence with the Raven’s Colored Progressive Matrices. Besides, basic computation abilities were assessed with Basic Arithmetic Operations, and shortterm and working memory with the Digitspan and Corsiblocks tests. The TEDIMATH was used in Germany to assess basic math abilities. In the following, these instruments will be described in more detail.
The TDE is the most widely used standardized test of school achievement with norms for the Brazilian population. It comprises three subtests: Arithmetics, singleword Spelling, and singleword Reading. In the screening phase, the Arithmetics and Spelling subtests were used, which can be applied in groups. Norms are provided for schoolaged children between the second and seventh grade. The Arithmetics subtest is composed of three simple verbally presented word problems (i.e., which is the largest, 28 or 42?) and 45 written arithmetic calculations of increasing complexity (i.e., very easy:
General intelligence was assessed with the ageappropriate Brazilian validated version of Raven’s Colored Matrices [
Verbal shortterm memory was assessed with the Brazilian WISCIII Digits subtest [
This test is a measure of the visuospatial component of working memory. It is constituted by a set of nine blocks, which are tapped, in a certain sequence by the examiner. The test starts with sequences of two blocks and can reach a maximum of nine blocks. We used the forward and backward Corsi span tasks according to [
This task consisted of addition (27 items), subtraction (27 items), and multiplication (28 items) operations for individual application, which were printed on separate sheets of paper. Children were instructed to answer as fast and as accurate as they could, time limit per block being 1 minute. Arithmetic operations were organized in two levels of complexity and were presented to children in separate blocks: one consisted of simple arithmetic table facts and the other of more complex ones. Simple additions were defined as those operations with the results below 10 (i.e.,
The TEDIMATH is a battery for the assessment of numerical and arithmetic competencies in 4–9year primary school children. There are norms for the TEDIMATH in three different languages: French, Flemish, and German. The TEDIMATH is a multicomponential dyscalculia test based on cognitive neuropsychological models of number processing and calculation. The German version of the TEDIMATH [
The Math Anxiety Questionnaire is a wellknown scale developed by Thomas and Dowker [
The assessment was performed in an appropriate room in children’s schools. Tests as well as their order of application varied in the two countries. In Brazil, the TDE and Raven were applied during the screening phase, while four different pseudorandomly varying sequences of application were used in the individual testing phase. In Germany, the MAQ was applied immediately after the TEDIMATH. The data from the Brazilian and German samples were obtained originally for very different purposes and at different time points. The aim of the present study to analyze the latent structure of the MAQ emerged after both data sets have been collected. This is the reason why the choice of measurement instruments was so different in Brazilian and German populations.
The internal consistency of all subscales of the MAQ will be calculated for the first time for the Brazilian version of the MAQ. Because of existing findings in the German population [
All children in the Brazilian sample reached a score above the 25th percentile in the subtests of the TDE and can be considered as typically achieving children in both arithmetic and spelling abilities. All children in the German sample can be considered as typically achieving children in arithmetics according to their scores in the TEDIMATH. In the following, results regarding the internal consistency of the MAQ will be presented first. Thereafter, the raw scores of the Brazilian and the German sample will be compared and the predictive validity of the MAQ regarding numeric and arithmetic abilities will be reported. Finally, investigations on the latent structure of the MAQ that employed automatic item classification and multidimensional scaling will be reported.
Means, standard deviations, minimum and maximum and internal consistency (Cronbach’s
To investigate the predictive validity of the MAQ, regressions analyses entering the four MAQ subscales as predictors of numeric and arithmetic abilities were calculated.
Descriptives of MAQ subscales and composite scales (
Scales  Mean  Sd  Minimum  Maximum  Cronbach’s 

Scale A (6 items)  23.66  3.53  11  30  0.71 
Scale B (6 items)  23.00  4.66  8  30  0.71 
Scale C (6 items)  17.80  6.13  6  30  0.88 
Scale D (6 items)  17.20  5.80  6  30  0.80 
Scale AB (12 items)  46.60  7.03  24  59  0.78 
Scale CD (12 items)  35.06  10.55  12  58  0.88 
 
Total (24 items)  81.70  14.67  46  116  0.87 
The impact of math anxiety on simple and complex addition, subtraction, and multiplication tasks was examined in the Brazilian sample. Hundred sixty four children from the Brazilian sample completed all these tasks. In order to ascertain the specificity of the contribution of MAQ scales to explaining variance in the arithmetic tasks, age, sex, grade, general intelligence, verbal and nonverbal shortterm memory and working memory (digit span and Corsi span, both of them forward and backward) were entered in the model as well. Age, sex, grade, and general intelligence were entered first in the model using the method “enter,” while the measures of shortterm memory and working memory were entered using the method “stepwise.” This regression method was adopted to ascertain that the impact more general sociodemographic and cognitive functions has been removed before analyzing the impact of math anxiety on numeric and arithmetic abilities and competencies was investigated. A summary containing the adjusted
As depicted in Table
Regression models for arithmetic abilities.
Task  Adjusted 
Sample size  Significant predictors in the model 

Simple addition  34.7  164  Sex, grade, raven, Corsi backwards, digitspan forward 
Complex addition  38.4  164  Grade, Corsi backward, digitspan forward, Corsi backward 
Simple subtraction  26.1  164  Sex, grade, Corsi backward, Corsi forward 
Complex subtraction  29.9  164  Grade, Corsi backward, digitspan backward, MAQscale A 
Simple multiplication  53.5  164  Grade, Corsi backward, digitspan forward, MAQscale A, MAQscale D 
Complex multiplication  42.9  164  Corsi forward, digitspan forward, digitspan backward, MAQscale A 
^{§}expressed as the proportion of variance in the dependent variable explained by the model.
The internal consistency of the MAQ in the German population has been reported in detail elsewhere [
To investigate the predictive validity of the MAQ, regressions analyses entering the four MAQ subscales as predictors of seven different subtests of the TEDIMATH, which measure numeric and arithmetic abilities, were calculated.
The impact of math anxiety on seven subtests of the TEDIMATH was examined in the German sample. Between 279 and 284 children from the German sample completed all these tasks. In order to ascertain the specificity of the contribution of MAQ scales to explaining variance in the arithmetic tasks, age, sex, grade, and verbal shortterm memory (digit span forward and backward) were entered in the model as well. Age, sex, and grade were entered first in the model using the method “enter,” while the measures of shortterm memory and were entered using the method “stepwise”. This regression method was adopted to ascertain that the impact more general sociodemographic and cognitive functions has been removed before analyzing the impact of math anxiety on numeric and arithmetic abilities and competencies was investigated. A summary containing the adjusted
As depicted in Table
Regression models for numeric and arithmetic abilities.
Task  Adjusted 
Sample size  Significant predictors in the model 

Addition decomposition  5  284  Age, MAQscale A 
Text problems  8  284  Age, grade, MAQscale A 
Magnitude comparison Arabic  2.6  284  MAQscale A 
Magnitude comparison number words  3.3  284  MAQscale A 
Writing number  6.7  284  Age 
Reading number  6.8  284  Age 
Arithmetic concepts  9.6  279  MAQscale A 
^{§} expressed as the proportion of variance in the dependent variable explained by the model.
To compare data between the Brazilian and the German sample, a subsample of each group was selected (Brazilian sample,
To investigate the latent structure of the MAQ, an automatic item classification analysis was employed [
Results of the automatic classification of items (Mokken analysis).
Scale  Brazilian sample ( 
German sample (  

Items (scale)^{§}  Loevinger’s 
Items (scale)^{§}  Loevinger’s  
Scale 1  MAQ_M(C)  ( 
MAQ_M(D)  ( 
MAQ_D(C)  ( 
MAQ_D(D)  (  
MAQ_G(C)  ( 
MAQ_H(D)  (  
MAQ_H(C)  ( 
MAQ_G(D)  (  
MAQ_E(C)  ( 
MAQ_E(D)  (  
MAQ_W(C)  ( 
MAQ_W(D)  (  
MAQ_H(D)  ( 
MAQ_D(C)  (  
MAQ_W(D)  ( 
MAQ_H(C)  (  
MAQ_E(D)  ( 
MAQ_E(C)  (  
MAQ_M(D)  ( 
MAQ_G(C)  (  
MAQ_D(D)  ( 
MAQ_W(C)  (  
MAQ_G(D)  ( 
MAQ_M(C)  (  
 
Scale 2  MAQ_M(A)  (  
MAQ_H(A)  ( 
MAQ_G(A)  (  
MAQ_G(A)  ( 
MAQ_D(A)  (  
MAQ_D(A)  ( 
MAQ_M(B)  (  
MAQ_D(B)  ( 
MAQ_D(B)  (  
MAQ_M(A)  ( 
MAQ_G(B)  (  
MAQ_M(B)  ( 
MAQ_H(B)  (  
MAQ_G(B)  ( 
MAQ_H(A)  (  
MAQ_E(B)  (  
MAQ_E(A)  (  
 
Scale 3  MAQ_W(B)  ( 

MAQ_W(A)  ( 
MAQ_W(B)  (  
MAQ_E(B)  ( 
MAQ_W(A)  (  
MAQ_H(B)  ( 
^{§}Item description is composed of the content of each item, that is: mathematics in general (MAQ_G); easy calculations (MAQ_E); difficult calculations (MAQ_D); written calculations (MAQ_W); mental calculations (MAQ_M); math homework (MAQ_H) and its scale (A), (B), (C), or (D).
Three items could not be classified in the Brazilian sample, while all items could be assigned to a scale in the German sample. Results were replicated when considering only children with ages between 7.5 and 10.1 years. For this reason, these analyses will not be reported here.
To investigate the construct validity of the Brazilian version of the MAQ, multidimensional scaling was employed. The facets diagram (see Figure
Configuration of MAQ items represented in a twodimensional space using multidimensional scaling. Symbols A, B, C, and D represent the different scale items according to their scale assignment. The scale of axes
In the present study, the psychometric properties of a Brazilian version of the MAQ were investigated for the first time as well as its transcultural validity in German Brazilian samples. The internal consistency of all subscales and composite scales obtained in the Brazilian sample is throughout satisfactory or even high. A direct comparison of the raw scores obtained in the Brazilian sample with those obtained in the German sample reveal no differences in the subscale representing “selfperceived performance”. However, the Brazilian sample showed higher scores in the subscales “attitudes towards mathematics,” “unhappiness related to problems in mathematics,” and “anxiety related to problems in mathematics” when compared to the German sample. The investigation of the predictive validity of the MAQ revealed that “selfperceived performance” is a significant predictor of basic numeric abilities such as magnitude comparison as well of more complex arithmetic abilities and competencies. Importantly, “selfperceived performance” remains a significant predictor even after removing the specific effects of grade, age, sex, verbal, and nonverbal shortterm memory and working memory on these abilities. Finally, automatic item selection as well as multidimensional scaling procedures revealed the similarities in the structure of the MAQ between both Brazilian and German samples. In the following, these results will be discussed in more detail.
In Brazil, a raw sample covering a broad spectrum of ages was investigated. The degree of accuracy to describe MA in children is lower than in the larger German sample, where specific norms for children in first and second halves of each grade were obtained [
The Brazilian sample showed higher scores on “attitudes towards mathematics,” “unhappiness related to problems in mathematics,” and “anxiety related to problems in mathematics” when compared to the German sample. These results reveal higher levels of MA in the Brazilian sample when compared to the German sample. This replicates evidence from the recent literature [
One possible interpretation of these results can be derived from the view that there are at least two different ways for MA to impact math performance [
Investigation on the predictive validity of the MAQ revealed specific effects of selfperceived performance on basic number processing abilities such as magnitude comparison. These results replicate those obtained by Maloney and colleagues [
In general, these results suggest that the selfperceived performance is to some extent objectively associated to the actual level of performance observed in school children. This is indicative that the selfperceived performance may be assessed and used to complement the diagnostics of difficulties not only with the most elementary abilities in magnitude processing but also in those arithmetics tasks more typical of the academic context.
Automatic item classification after Mokken produced similar results in both samples. Scales A and B, on the one side, and scales C and D, on the other side, can be grouped into scales AB and CD. Items from scales A and B as well as items from scales C and D seem to load in the same latent dimensions in a way that item difficulty and individual competency are sufficient to describe the properties of the scale. The most central evidence provided by the Mokken analysis is that the items of the MAQ measure a broad spectrum of difficulty regarding MA. These findings are quite intuitive and can be related in a very transparent fashion to the contents of the MAQ items. In other words, the kind of question asked in the MAQ is related to a broad spectrum of expressions of the different facets of the construct “mathematics anxiety.” While items asking for “easy problems” are easy for everyone and have a high probability of being responded positively even by children with high levels of MA, items representing the more complex categories such as “written calculations,” “mental calculations,” or “difficult calculations” have a decreasing probability of being answered positively by children with increasing levels of MA. Moreover, the good scalability of most items of the MAQ put in evidence the property of monotonicity found within each the MAQ scales. The high monotonicity found the different scales of the MAQ reflects the fact that only children with low levels of MA respond positively to more difficult items, while all children (those with low levels of MA as well as those with high levels of MA) tend to respond positively to easier items.
Finally, data from the multidimensional scaling analysis revealed clear similarities between the German and the Brazilian version of the MAQ. In both samples, a clear separation between subscales A and B, on the one side, and C and D, on the other side was observed. Two latent dimensions have been found in the German version of the MAQ by Krinzinger at al. [
The MAQ is a valid and useful scale for measuring mathematics anxiety in children with diverse cultural backgrounds with useful psychometric properties. The MAQ also specifically predicts basic number processing abilities as well as arithmetics performance and should, for this reason, be included in the assessment protocols used in the diagnostics of mathematics difficulties [
G. Wood was supported by Grant (P22577B18 of the Austrian Wissenschaftsfond FWF). Research by the V. G. Haase during the elaboration of this paper was funded by grants from CAPES/DAAD Probral Program, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, 307006/20085, 401232/20093), and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG, APQ02755SHA, APQ0328910, PPM0028012).