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<ul><li><p>AustralianEducationalResearcher Vol. 20, No. 3 1993 </p><p>MATHEMATICS ANXIETY OF SOME PRE- SERVICE PRIMARY SCHOOL TEACHERS </p><p>John M c C o r m i c k and Deborah Scot t </p><p>Abstract . The construct 'mathematics anxiety' is explored with a sample of first year primary education university students. Self reported measures of anxiety about needing to use mathematics, and anxiety about the prospect of teaching mathematics, are moderately andpositively correlated. The factor structure of a set of 13 items related to 'mathematics anxiety' is consistent with previous studies and the associations of these factors to other, related measures are explored using multiple linear regression of the factor scores. It is argued that it is likely to be more valuable to investigate 'mathematics anxiety' in terms of its composite factors than as a single phenomenon. Directions for future investigations are ind~ated. </p><p>Introduct ion </p><p>The term 'mathematics anxiety' has been widely used in the literature, in spite of quite differing notions of to what it is the term actually refers (Aiken, 1976; Sovchik et al., 1981). Although the meamng of the term may appear obvious, this has not always been the case. Genshaft (1982: 32), for example, gave a definition: "Adolescent girls of average achievement were defined as math anxious if their achievement in mathematics was at least one year lower than their reading achievement", which appears to confound mathematics anxiety with mathematics achievement. We have adopted Richardson and Suinn's (1972: 551) definition: "...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". However, some researchers have come to the conclusion that no such distinct phenomenon exists, and that so-called 'mathematics anxiety' is merely an expression of a more general anxiety (Olson and Gillingham, 1980). </p><p>The relationship of mathematics anxiety (MA) with test anxiety has received considerable attention. The Mathematics Anxiety Rating Scale (MARS) d e v e l ~ by Richardson and Suinn (1972) was shown to have a two factor structure: </p></li><li><p>30 McCormick & Scott </p><p>'numerical anxiety' and 'mathematics test anxiety' (Rounds and Hendel, 1980). Ferguson (1986) isolated these two factors as well as an additional factor which he named 'abstraction anxiety'. Wood (1988) asserted that mathematics anxiety was not caused by actually doing mathematics, but that it was strongly related to 'test anxiety'. However, Dew, Galassi and Galassi (1984), reporting a study involving physiological measures, maintained that whilst there was an association between 'mathematics anxiety' and 'test anxiety', they were indeed different constructs. That is, 'mathematics test anxiety' is not identical to the more general construct 'test anxiety'. </p><p>A population which has attracted the attention of researchers of 'mathematics anxiety', particularly in the US, is that of elementary school teachers, both before and after beginning service (for example: Wood, 1988; Tishler, 1982; Sovchik et a/., 1981). Elementary school teachers broadly correspond to primary teachers in Australia, in the sense that the latter tend to teach younger children and are not subject specialists. Bulmahn and Young (1982) suggested that in general, elementary teachers are not people who appreciate and enjoy mathematics. </p><p>Because early experiences of mathematics are likely to play an important part in the development of attitudes to the subject, the question of whether, or not, 'mathematics anxiety' is contagious has been canvassed (Bush, 1989; Wood, 1988; Kelly and Tomhave, 1985; Bulmahn and Young, 1982). In specifically addressing the question of whether or not maths anxious elementary teachers transmit their problem to their students, Bush (1989) found no significant relationship between 'teacher mathematics anxiety' and 'student mathematics anxiety'. However, Bush did find "...a slight tendency for MA teachers to be more traditional in their teaching" (p.508). If, indeed, mathematics anxious teachers do teach differently to teachers who are not mathematics anxious, the association of this construct with pre-service primary teachers' initial anxiety, if any, about teaching mathematics, should be of value. The main purpose of this study, however, is to investigate whether the construct 'mathematics anxiety' which has been identified in the US context (Richardson and Suinn, 1972; Rounds and Hendel 1980; Hake and Parker 1982)also exists in this particular context, and if it does, to investigate what relationship it might have with teaching mathematics. </p><p>Background </p><p>The students who made up this sample were in their first year of an initial university course preparing them to be primary school teachers. None of them studied mathematics at a level beyond high school. In this course, the students are not required to take any mathematics subjects other than those related to primary teaching. However, some elementary mathematics content is integrated with the method subjects. </p></li><li><p>Mathematics Anxiety 31 </p><p>Methods </p><p>Sample and Procedures The sample consisted of 113 of a possible 138 university students, enrolled in a primary teacher training course. Ninety subjects were female, twenty two male and one did not indicate her or his sex. With the exception of a measure of mathematics achievement, the Progressive Mathematics Achievement Test 3A (PATMATHS3A) (ACER, 1984), all measures were obtained by a self-report questionnaire, administered during the students' orientation to the course and before they began coursework. This test was specifically developed by the Australian Council For Educational Research for use in Australian schools with children in the approximate age range of 11 to 14 years. The PATMATHS3A was not administered at that time as it was a requirement of the course that the students sit for the test during their method subject. Some questions from the PATMATHS3A are provided as examples in Table 1. The test was admimstered in the fourth week of the method subject. However, since the students were formed into two cohorts, one doing the method subject during semester 1 and the other during semester 2, there are doubts about the validity of this measure. Whilst we considered this to be unsatisfactory, we deemed it to be less so than creating or nurturing negative attitudes. Not all items were completed by every subject. </p><p>The Instruments Data were essentially gathered in three sections. In the first sections, the students provided some biographical information, ie sex, age and highest level of mathematics studied. The next item asked students: "IN GENERAL, how do you rate your ability to use mathematics in every day life?". The choices were 'very poor', 'quite poor', 'neutral', 'quite able' and 'very able'. The following three items required students to, in general, rate how anxious each felt: (1) when in a situation where she or he needed to use mathematics; (2) about the prospect of teaching mathematics lessons to children; and (3) about the prospect of teaching non-mathematics lessons to children. The choices for each of these three items were: 'not at all', 'a little', 'a fair amount', 'much' and 'very much'. </p><p>The second section of the survey consisted of 15 items describing situations involving mathematics and asking each student to indicate how anxious he or she would feel in each situation; choices were: 'not at all', 'a little', 'a fair amount', 'much' and 'very much'. Five of these items were taken directly from Plake and Parker's (1982) well-validated, 24 item, revised version of Richardson and Suinn's (1972) Mathematics Anxiety Rating Scale (MARS). Others were essentially from the MARS, but with altered wording, and the remainder were included because of their expected relevance to this particular group. This configuration was chosen principally for four reasons. First, we considered it important to use a scale which </p></li><li><p>32 McCormick & Scott Table 1 </p><p>A sample of questions in the Progressive Achievement Test in Mathematics 3A. </p><p>2. Which row has its numbers in order of size? </p><p>14. </p><p>A 164, 641, 614, 461 B 641, 461, 614, 416 C 461, 416, 164, 146 D 641, 164, 614, 146 </p><p>Which of these numerals can replace n in 3762< n </p></li><li><p>Mathematics Anxiety 33 </p><p>did not overestimate the level of mathematical sophistication of these particular students. Second, because one of the purposes of the study is to investigate the relationship, if any, between these students' mathematics anxiety and their anxiety about the prospect of teaching mathematics, we considered it to be important that the scale reflect the level of mathematics which they were preparing to teach. Thus, the kind of items used by Ferguson (1986) which defined the factor which he isolated and called 'abstraction anxiety', were not considered for inclusion. Third, some MARS items were inappropriate in the Australian context, for example, 'figuring sales tax'. Fourth, given that Rounds and Hendel (1980) and Plake and Parker (1982) were able to reduce the 98 items of the MARS to 30 and 24 items respectively, whilst basically maintaining the same underlying structure, it was our intention to be parsimonious in our selection of items for inclusion, but to also benefit from the aforesaid underlying structure and validity. We intended to adapt the already revised MARS to local conditions, rather than to create a new instrument. For these 15 items, Cronbach's alpha and split half reliabilities are 0.91 and 0.87 respectively. </p><p>The third measure was a score on the PATMATHS3A previously discussed. </p><p>Results and Discuss ion </p><p>Pearson Correlations of the Biographical and Single Measures Intercorrelations were calculated for items in the first section and the PATMATHS3A score. The significance of each correlation was tested using a one-tailed z-test and the direction of the association was as expected in each case. Correlations are shown in Table 2. Although several correlations reached significance, they generally indicate quite mild associations. As might be expected, PATMATHS3A (achievement) has negative correlations with the single measures of anxiety and positive correlations with the measure of ability ('to use mathematics in everyday life') and age. The correlation of general anxiety ('when you are in a situation where you need to use mathematics') with the self-rated general ability ('to use mathematics in everyday life') is negative. One correlation, however, is worthy of more attention. The correlation between self-rated general anxiety 'about the prospect of teaching mathematics lessons to children', and general anxiety 'when you are in a situation where mathematics needs to be used' is 0.65. This is not surprising, but it does add some weight to the importance of improving our understanding of the inter-relationships of the mathematics anxiety of these students, their own learning and preparation to be teachers of mathematics and their eventual teaching of mathematics in the classroom. It should be worthwhile investigating this association more closely, particularly in terms of the degree to which the association is sustained after actual classroom experience. In the context of preparing these students to be teachers, it would be a worthwhile goal to identify problems in this domain as early as possible. Tishler (1982: 40) </p></li><li><p>34 McCormick & Scott </p><p>points out: " reachers are most knowledgeable and perform best in those areas which they enjoy". </p><p>Table 2 Pearson Correlations of Biographical and Single Measures </p><p>Math Everyday General General General Age Education abbility anxiety - anciety anxiety </p><p>to use need to use teaching teaching math math math other </p><p>Everday ability to use math .2 8 * * General anxiety - need -. 1 1 -.3 5"** to use math General anxiety 1 . 1 3 -. 29" * teaching math General anxiety 0 7 -. 1 1 teaching other Age -.32*** -. 1 0 PATMATH3A .3 7 .40* * * </p><p>.65*** </p><p>.25** </p><p>11 - .32** </p><p>.37*** </p><p>05 -.07 - .29** -.11 -.24** </p><p>significant at .05 level significant at .01 level significant at .0001 level </p><p>Principal Components Analysis of the Mathematics Anxiety Items A principal components analysis with var imax rotation was carried out on the fifteen mathematics anxiety items. Two factors, which we have named DOING MATHEMATICS ANXIETY and MATHEMATICS EVALUATION A N X I E q ~ were isolated with eigenvalues 7.3 and 1.8 and accounting for 49 and 12 percent of the variance respectively. The 13 i tems comprising these factors, with factor loadings and the percentage of students who responded in the two most extreme categories of 'much' and 'very much' anxiety, are reported in Table 2. As expected, these two factors are consistent with the two factor solution obtained by Plake and Parker (1982). Although the percentages of students reporting anxiety in the two extreme categories appear, on first inspection, to be quite low, it is a considerable source of concern as the mathematics required is at quite an elementary level. Estimating ~ow much liquid a container can hold' and explaining 'how you got an answer to a maths problem' are precisely the sorts of activities which should be part of primary mathematics experiences. </p></li><li><p>Mathematics Anxiety 35 </p><p>Table 3 Principal components analysis with varimax rotation of "mathematics anxiety' items with factor loadings and (rounded) percentages of responses in the two most extreme </p><p>categories of "much" and 'very much'. </p><p>FACTOR 1: DOING MATHEMATICS ANXIETY </p><p>Loading Percentage </p><p>Listening to a person explain how she figured out your expenses on a trip, including meals, </p><p>transportation, housing etc. .82 5 </p><p>Adding up 596 + 777 on paper .80 3 </p><p>Reading and interpreting graphs and tables .70 4 </p><p>Listening to a salesman show you how you would save money by buying his higher priced product because it reduces long term expenses .69 3 </p><p>Estimating how much liquid a container can hold .60 8 </p><p>Explaining how you got an answer to a maths problem .56 7 </p><p>Solving a maths problem without any help .56 2 </p><p>FACTOR 2: MATHEMA TICS EV ALUATION ANXIETY </p><p>Sitting for a maths exam .84 14 </p><p>Doing a maths assignment .80 5 </p><p>Solving a square root problem .76 5 </p><p>Thinking about taking a basic maths competency test .67 6 </p><p>Multiple Linear Regressions of the Single Measures With Factor Scores Factor scores were generated for the two factors from the principal components analysis. Regression analysis, by forward selection, was carried out with the factor scores as independent variables (predictors)and, separately, each of three of the single measures as a dependent variable. </p><p>The first measure used as a dependent variable was the measure of 'anxiety felt when in a situation where mathematics needs to be used'; statistics are shown in Table 3. Both factors were entered into the equation, and together they account for approximately 46% of the variance. The factor MATHEMATICS EVALUATION </p></li><li><p>36 McCormick & Scott </p><p>ANXIETY, accounting for...</p></li></ul>