Abstract
Aktuelle Studienergebnisse verdeutlichen, dass sich Kinder bereits im frühen Grundschulalter hinsichtlich ihrer Mathematikangst unterscheiden und dass diese mit deren Mathematikleistung korreliert (Vukovic et al., 2013; Wu et al., 2012). Um eine valide Erfassung der Mathematikangst auch im deutschen Sprachraum zu ermöglichen, zielt diese Studie auf die Entwicklung und psychometrische Überprüfung eines kindgerechten und ökonomischen Verfahrens zur Erfassung der Mathematikangst im frühen Grundschulalter ab. Das Mathematikangstinterview (MAI) erfasst die Angstintensität sowie deren Auswirkung auf verschiedenen Angstebenen. Dazu werden rechenspezifische Situationen sprachlich und bildlich präsentiert und die Kinder u. a. gebeten, ihre Angst mittels Angstthermometer einzuschätzen. Die vorliegende Überprüfung der Gütekriterien erfolgte an einer Stichprobe von 136 Kindern im Alter von sieben bis zehn Jahren. Neben arithmetischen Operationen und Textaufgaben wurde die Selbsteinschätzung hinsichtlich der allgemeinen Ängstlichkeit, der Schul- und Leistungsangst sowie der Selbstbewertung und Einstellung zu Mathematik erfragt. Die Ergebnisse verdeutlichen, dass das Interview eine hohe Reliabilität, ermittelt über die interne Konsistenz, aufweist. Zudem spiegeln die Ergebnisse zur Validität bisherige Untersuchungsergebnisse zur Mathematikangst wider und belegen eine zufriedenstellende Kriteriumsvalidität des MAI. Die moderaten Zusammenhänge zwischen Mathematikangst und Rechenleistung sind weder durch die kognitive Leistung noch durch die erfassten Ängste zu erklären. Durch das MAI fanden sich querschnittlich frühe Unterschiede in der Ausprägung der Mathematikangst sowie moderate Zusammenhänge mit der Rechenleistung. Weiterführend sind Längsschnittstudien zur Entwicklung der Mathematikangst sowie deren Wechselwirkung mit der Rechenleistung nötig, um einen Präventions- und Interventionsbedarf abzuleiten.
Background: Math anxiety can be defined as “… feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (Richardson & Suinn, 1972, p. 551). Furthermore math anxiety meets the criteria for a specific phobia, which is characterised by physiological reactions, negative and dysfunctional cognitions and avoidance behaviour (Hembree, 1990; Lang, 1968). Of particular relevance is the avoidance behaviour, which has a wide influence on individual's math achievement, the engagement in math class and future selection of math related subjects (Ashcraft & Kirk, 2001; Hembree, 1990). As a consequence, this might ultimately contribute to school phobia or psychosomatic distress (Ashcraft, 2002; Dowker, 2005). Devine et al. (2012) specify a vicious circle in which math anxiety leads to negative experiences with math, which results in failure that strengthens in turn math anxiety and causes poor school performance (see also Dowker et al., 2012; Krinzinger & Kaufmann, 2006). Math anxiety is associated with negative attitudes towards mathematics, less enjoyment of mathematics and a lower self-confidence in the subject (Ashcraft & Kirk, 2001; Hembree, 1990; Krinzinger et al., 2007). Especially the relationship between math anxiety and math performance is well reviewed. Numerous studies showed a negative relationship between math anxiety and math performance, most notably for secondary school (Hembree, 1990; Ma, 1999). As a mechanism of action, the influence of math anxiety on working memory has been discussed (e.g. Ashcraft & Kirk, 2001).
The majority of the findings concerning math anxiety are based on studies that refer to young adults (e. g. Ashcraft et al., 2007; Hopko et al., 2003) or children that attend middle school (Meece et al., 1990). Over the past years the focus was expanded on children of early primary school age (Krinzinger et al., 2009; Vukovic et al., 2013; Wu et al., 2012). Studies showed different levels of math anxiety in young children and the relationship between math anxiety and math performance was demonstrated already for children in second and third grade (Ramirez et al., in press; Vukovic et al., 2013).
At this point of time there is one German questionnaire assessing math anxiety available for primary school children (class 1 – 3), that was developed by Krinzinger and colleagues (2007). The “Fragebogen für Rechenangst” (FRA) is based on the “Math Anxiety Questionnaire” (MAQ; Thomas & Dowker, 2000). The authors reported only minor negative correlations between math anxiety scores and math performance (Krinzinger et al., 2007). Furthermore, longitudinal analyses showed no influence of math anxiety on the later math performance or vice versa (Krinzinger et al., 2009). Krinzinger and colleagues (2009) assume that the phrasing of the items in the questionnaire might be too difficult to be understood by young children.
Aims: The aim of the present study was the development of a new economical math anxiety measure suitable for children since there does not exist a valid instrument for the measurement of math anxiety for German-speaking early primary school children at this time (e. g. Krinzinger et al., 2009). Furthermore, psychometric properties of reliability and criterion validity are aimed to be determined. It is expected that a significant negative correlation between math anxiety and math performance can be detected.
Methods: The “Mathematikangstinterview” (MAI) combines two different types of questions while a math related situation is verbally and pictorially presented. The child is initially asked to rate its anxiety intensity concerning the presented situation by an anxiety thermometer. In a second step the different components of anxiety (affective, cognitive, behavioural and physiological; Hembree, 1990; Lang, 1968) are explored. The child is asked to estimate, to what extend specific statements apply to the particular situation, e. g. “I can not get a word out”. Overall four situations are provided (on the eve of a math test, math homework, math class and everyday/shopping). Out of these 20 items a total score is computed with a range from 0 to 60.
136 children at the age of 7 to 10 were included in data analyses, while the mean age was 8.33 years (SD = 0.78). The children attended classes from the second to the fifth grade in Potsdam and Berlin, Germany. Children were excluded if overall intelligence was found to be more than 2 standard deviations below the norm (T-value < 30). The study population involved more girls (n = 89) than boys (n = 47), so the gender ratio deviates significantly from equal distribution (Χ2 (1) = 12.79, p < .001).
The BUEGA was used to assess verbal and nonverbal intelligence as well as their performance in reading, spelling and math word problems (Esser et al., 2007). Moreover, arithmetic performance was measured using the addition and subtraction subtests of the “Heidelberger Rechentest” (HRT, Haffner et al., 2005). A list of 40 addition/subtraction tasks is presented to the children and they are asked to solve as many problems as possible within two minutes. In addition, math anxiety (MAI), school phobia and test anxiety (PHOKI, Döpfner et al., 2006), attitudes towards mathematics and self-evaluation of mathematical competence (FRA) and trait anxiety (KAT-II; Kinder-Angst-Test; Thurner & Tewes, 2000) have been assessed.
Results: As an index of internal consistency a coefficient, Cronbach's α, was computed and found to be .90. The math anxiety scale showed a mean value of 15.22 (SD = 11.54) with a range from 0 – 43.2. No gender differences were detected.
Further analyses showed high correlations between the math anxiety scale with trait anxiety (KAT-II) and with school phobia and test anxiety (PHOKI) (rs > .60, p < .001). High negative correlations were found for the relationship between MAI and FRA, indicating that the higher the levels of math anxiety, the lower the self-evaluation of mathematical performance and the lower the attitudes towards mathematics (rs = –.66, p < .001). Correlation coefficients showed no significant differences between boys and girls. Moreover a minor positive correlation was demonstrated between the math anxiety scale and age (in months) (rs = .14, p = .096).
Further results demonstrated moderate correlations between the math anxiety scale with mathematical performance (addition: rs = .395, p < .001, subtraction: rs = .464, p < .001 as well as math word problems: rs = .419, p < .001). Partial correlations were used to control for the effect of general cognitive performance, trait anxiety, school phobia and test anxiety. These analyses indicated that the math anxiety scale was significantly and negatively correlated with mathematical performance, even after controlling for each of these variables.
Discussion: The aim of the study was to present and psychometrically evaluate a new measure for assessing math anxiety in early primary school children. In summary, the results concerning the validity of the instrument mirror previous research results (Hembree, 1990; Devine et al., 2012; Krinzinger et al., 2007) and demonstrate a satisfying criterion validity of the MAI. The correlations between math anxiety and math performance can be classified as moderate and are therefore higher than the reported findings of other current studies with primary school children (Vukovic et al., 2013; Wu et al., 2012) or existing meta-analyses (Hembree, 1990; Ma, 1999).
It seems important to highlight that the relationship between math anxiety and math performance can be neither explained by general cognitive performance nor by trait anxiety, school phobia or test anxiety. These results are consistent with existing reports concerning math anxiety (Devine et al., 2012; Wu et al., 2012) and support the construct of math anxiety that is assessed with the MAI.
Furthermore the present study revealed no gender differences (see also Ramirez et al., in press). Literature on math anxiety demonstrates inconsistent results concerning gender differences in early primary school children. Probable reasons include the lack of standardised instruments measuring math anxiety in young children. It remains unclear whether girls experience higher levels of math anxiety or are more willing than boys to admit their anxiety (Krinzinger & Kaufmann, 2006). It is assumed that gender differences increase with age (Dowker, 2005), and are therefore in the first grade levels not yet noticeable. Moreover, possible self-selection effects, which were found in clinical diagnostics and treatment of learning disorders, can not be ruled out (Krinzinger & Günther, 2013).
With respect to the sample it has to be considered that the examined children are part of a training program for enhancing numerical cognition. Therefore future studies with the aim to reveal possible sample-specific effects and to evaluate whether the results are transferable to a representative sample are needed. Standard scores should be determined subsequently.
In summary, the results of the present study suggest that a valid and reliable measure to assess math anxiety in primary school children was successfully developed. The MAI is economically to administer and was shown to be suitable for young children. Further investigations of the retest-reliability and the development of the relationship between math anxiety and math performance, as well as potentially later occurring gender differences are planned. For that purpose the existing children's version is aimed to be complemented by a math anxiety questionnaire for parents.
Literatur
(2002). Math Anxiety: Personal, Educational, and Cognitive Consequences. Current Directions in Psychological Science, 11, 181 – 185.
(1994). Mathematics Anxiety and Mental Arithmetic Performance: An Exploratory Investigation. Cognition and Emotion, 8, 97 – 125.
(2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130, 224 – 237.
(2007). Is math anxiety a mathematical learning disability? In D. B. Berch & M. M. M. Mazzocco (Hrsg.), Why is math so hard for some children? (S. 329 – 348). Baltimore, MD: Brookes Publishing.
(2009). Mathematics Anxiety and the Affective Drop in Performance. Journal of Psychoeducational Assessment, 27, 197 – 205.
(2005). Math anxiety and its cognitive consequences: A tutorial review. In J. I. D. Campbell (Hrsg.), Handbook of mathematical cognition (S. 315 – 327). New York: Psychology Press.
(2006). A multivariate investigation of the differences in mathematics anxiety. Personality and Individual Differences, 40, 1325 – 1335.
(1999). Statistik für Sozialwissenschaftler (5. Aufl.). Berlin: Springer.
(2006). Einführung in die Test- und Fragebogenkonstruktion (2. Aufl.). München: Springer.
(2009). Mathematics anxiety in secondary students in England. Dyslexia, 15, 61 – 68.
(1992). Mathematics anxiety and science careers among able college women. Psychological Science, 3, 292 – 295.
(1988). Statistical power analysis for the behavioral sciences. New Jersey: Lawrence Erlbaum Associates.
(2012). Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and Brain Functions, 8, 1 – 9.
(1984). Math Anxiety: Relation With Situational Test Anxiety, Performance, Physiological Arousal, and Math Avoidance Behavior. Journal of Counseling Psychology, 31, 580 – 583.
(2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Hove: Psychology Press.
(2012). Attitudes to mathematics in primary school children. Child Development Research. doi:10.1155/2012/124939
(2006). Phobiefragebogen für Kinder und Jugendliche (PHOKI). Göttingen: Hogrefe.
(1957). The identification of number anxiety in a college population. Journal of Educational Psychology, 48, 344 – 351.
(2008). Basisdiagnostik Umschriebener Entwicklungsstörungen im Grundschulalter (BUEGA). Göttingen: Hogrefe.
(1992). Analysis of physiological reactivity in mathematics anxiety (Unveröffentlichte Doktorarbeit). Bowling Green State University, Bowling Green, Ohio.
(2011). Prüfungsangst. Göttingen: Hogrefe.
(2009). Discovering statistics using SPSS (3. Aufl.). London: Sage.
(2005). Heidelberger Rechentest. Göttingen: Hogrefe.
(1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33 – 46.
(1998). Mathematics anxiety and working memory: Support for the existence of a deficient inhibition mechanism. Journal of Anxiety Disorders, 12, 343 – 355.
(2003). The Abbreviated Math Anxiety Scale (AMAS): Construction, Validity, and Reliability. Assessment, 10, 178 – 183.
(2001). The relation between anxiety and skill in performance-based anxiety disorders: A behavioral formulation of social phobia. Behavior Therapy, 32, 185 – 207.
(1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107, 139 – 155.
(2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96, 284 – 309.
(2009). Mathematics anxiety as a function of multidimensional self-regulation and self-efficacy. Contemporary Educational Psychology, 34, 240 – 249.
(1994). Inducing adaptive coping self-statements in children with learning disabilities through self-instruction training. Journal of Learning Disabilities, 26, 630 – 638.
(2012). Diagnostik und Intervention bei Rechenstörung. Deutsches Ärzteblatt, 45, 767 – 780.
(2013). Lesen, Schreiben, Rechnen – gibt es Unterschiede zwischen den Geschlechtern? Lernen und Lernstörungen, 2, 35 – 49.
(2006). Rechenangst und Rechenleistung. Sprache, Stimme, Gehör, 30, 160 – 164.
et al. (2007). Deutschsprachige Version des Fragebogens für Rechenangst (FRA) für 6- bis 9-jährige Kinder. Zeitschrift für Kinder- und Jugendpsychiatrie und Psychotherapie, 35, 341 – 351.
(2009). Math anxiety and math ability in early primary school years. Journal of Psychoeducational Assessment, 27, 206 – 225.
(2013). Veränderungen psychischer Belastung durch Förderung von rechenschwachen Kindern und Jugendlichen. Zeitschrift für Kinder- und Jugendpsychiatrie und Psychotherapie, 41, 23 – 34.
(1968). Fear reduction and fear behaviour: Problems in treating a construct. In J. M. Schlien (Hrsg.), Research in Psychotherapy (3. Aufl., S. 90 – 102). Washington, DC: American Psychological Association.
(2012). When math hurts: Math anxiety predicts pain network activation in anticipation of doing math. PLoS One, 7, e48076 – e48076.
(1999). A meta-analysis of the relationship between anxiety towards mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30, 520 – 540.
(2004). The causal ordering of mathematics anxiety and mathematics achievement: a longitudinal panel analysis. Journal of Adolescence, 27, 165 – 179.
(2011). The effect of mathematics anxiety on the processing of numerical magnitude. The Quarterly Journal of Experimental Psychology, 64, 10 – 16.
(2012). Math anxiety: who has it, why it develops, and how to guard against it. Trends in Cognitive Sciences, 16, 404 – 406.
(1990). Predictors of math anxiety and its influence on young adolescents' course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82, 60 – 70.
(1998). Aspects of children's mathematics anxiety. Educational Studies in Mathematics, 36, 53 – 71.
(2004). Lernen für die Welt von morgen: Erste Ergebnisse von PISA 2003. Paris: OECD.
(2013). Prüfungsangst, Schulleistung und Lebensqualität bei Schülern. Lernen und Lernstörungen, 2, 111 – 124.
(2012). Relationships between 9-year-olds' math and literacy worries and academic abilities. Child Development Research. doi:10.1155/2012/359089
(in Druck). Math anxiety, working memory and math achievement in early elementary school. Journal of Cognition and Development. doi: 10.1080/15248372.2012.664593
(1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 19, 551 – 554.
(2010). Mathematics anxiety in children with developmental dyscalculia. Behavioral and Brain Functions, 46, 1 – 13.
(2003). Diagnostisches und Statistisches Manual Psychischer Störungen – Textrevision – DSM-IV-TR. Göttingen: Hogrefe.
(1988). Suinn Mathematics Anxiety Rating Scale for Elementary School Students (MARS-E): Psychometric and Normative Data. Educational and Psychological Measurement, 48, 979 – 986.
(2000). Mathematics anxiety and related factors in young children. Paper Presented at British Psychological Society Developmental Section Conference, Bristol.
(2000). Kinder-Angst-Test II (KAT-II). Göttingen: Hogrefe.
(2013). Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance. Contemporary Educational Psychology, 38, 1 – 10.
et al. (2012). Math anxiety questionnaire: Similar latent structure in Brazilian and German school children. Child Development Research. doi: 10.1155/2012/610192
(2012). Math anxiety in second and third graders and its relation to mathematics achievement. Frontiers in Psychology, 3, 1 – 11.
(2012). The neurodevelopmental basis of math anxiety. Psychological Science, 23, 492 – 501.
(2008). Mathematics anxiety among 4th and 5th grade Turkish elementary school students. International Electronic Journal of Mathematics Education, 3, 179 – 192.
