Transcript

AustralianEducationalResearcher Vol. 20, No. 3 1993

MATHEMATICS ANXIETY OF SOME PRE- SERVICE PRIMARY SCHOOL TEACHERS

John M c C o r m i c k and Deborah Scot t

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.

Introduct ion

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).

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:

30 McCormick & Scott

'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'.

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.

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.

Background

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.

Mathematics Anxiety 31

Methods

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.

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'.

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

32 McCormick & Scott Table 1

A sample of questions in the Progressive Achievement Test in Mathematics 3A.

2. Which row has its numbers in order of size?

14.

A 164, 641, 614, 461 B 641, 461, 614, 416 C 461, 416, 164, 146 D 641, 164, 614, 146

Which of these numerals can replace n in 3762< n <3817?

3641 3713 3799 3817 3946

36. P Q

R If a mirror were placed edge-on along QR, then the triangle and its image together would look like a

A square B parallelogram C rectangle D hexagon E triangle

49.

oo l.oo t40 o t6oo Q 00 320 640 960

FREEZING POINT BOILING POINT

800 1280

This table shows the freezing point and the boiling point of a liquid on two linear temperature scales P and Q. What does a P scale temperature of 750 equal on the Q scale?

470 850

1000 1150 1200

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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.

The third measure was a score on the PATMATHS3A previously discussed.

Results and Discuss ion

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)

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points out: " reachers are most knowledgeable and perform best in those areas which they enjoy".

Table 2 Pearson Correlations of Biographical and Single Measures

Math Everyday General General General Age Education abbility anxiety - anciety anxiety

to use need to use teaching teaching math math math other

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* * *

.65***

.25**

11 - .32**

.37***

05 -.07 - .29** -.11 -.24**

significant at .05 level significant at .01 level significant at .0001 level

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.

Mathematics Anxiety 35

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

categories of "much" and 'very much'.

FACTOR 1: DOING MATHEMATICS ANXIETY

Loading Percentage

Listening to a person explain how she figured out your expenses on a trip, including meals,

transportation, housing etc. .82 5

Adding up 596 + 777 on paper .80 3

Reading and interpreting graphs and tables .70 4

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

Estimating how much liquid a container can hold .60 8

Explaining how you got an answer to a maths problem .56 7

Solving a maths problem without any help .56 2

FACTOR 2: MATHEMA TICS EV ALUATION ANXIETY

Sitting for a maths exam .84 14

Doing a maths assignment .80 5

Solving a square root problem .76 5

Thinking about taking a basic maths competency test .67 6

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.

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

36 McCormick & Scott

ANXIETY, accounting for 25% of the variance is the better predictor. The higher contribution by tiffs factor is, on the surface, somewhat surprising. One explanation is that these students perceive situations where mathematics needs to be used as being associated with evaluation. If this is indeed the case, it is a matter of concern, and at odds with the belief that mathematics should be seen as relevant to the context in which it is used. Another explanation is that these students self-evaluate when in situations where they need to use mathematics and a lack of success could be related to a lowering of self-esteem. Evidence of this is not provided by this study, but a direction for future enquiry is certainly indicated.

Table 4 Multiple (forward selection) linear regression of nanxiety felt when in a situation

where mathematics needs to be used" with mathematics anxiety factor scores.

step Factor R 2 R 2 change F

1 Mathematics Evaluation Anxiety 2 Doing Mathematics Anxiety

.25 31.5"**

.46 .21 39.8***

*** significant at 0.001 level

For the second regression, the self-rating of 'ability to use mathematics in everyday life' was used as the dependent variable; statistics are shown in Table 4. In this regression, only the MATHEMATICS EVALUATION ANXIETY factor, accounting for 30% of the variance, was entered in the equation. This is of interest as, yet again, this factor appears as the better predictor. This suggests that these students associate their ability to use mathematics in everyday life with evaluation. This may be so because their self-rating is a reflection of evaluation. A slightly different explanation is that they generally associate their use of mathematics with evaluation.

Ttable 5 Multiple (forward selection) linear regression of "ability to use mathematics in

everyday life" with mathematics anxiety factor scores.

step Factor R 2 F

1 Mathematics Evaluation Anxiety .30 42.546***

*** significant at 0.001 level

The third regression uses the general anxiety felt 'about the prospect of teaching mathematics lessons to children' as a dependent variable; statistics are shown in Table 5. Together, both factors account for 54% of the variance with DOING MATHEMATICS ANXIETY being the better predictor, accounting for 35% of the variance. This is interesting for two reasons. First, it indicates what we might

Mathematics Anxiety 37

expect. Namely, that for these students, anxiety about mathematics and anxiety about teaching mathematics are associated. Second, we can interpret these results in light of the earlier regressions. The distinction between the two factors is reinforced. The future teaching role involves performing and doing mathematics, hence DOING MATHEMATICS ANXIETY is the better predictor. EVALUATION MATHEMATICS ANXIETY, in this regression model, may be more an indication of anxiety associated with an individual's self-concept. Of course, this is purely speculative, but is worth following up in the future.

Table 6 Multiple (forward selection) linear regression of "anxiety felt about the prospect of teaching mathematics lessons to children" with mathematics anxiety factor scores.

step Factor R 2 R 2 change F

1 Doing Mathematics Anxiety .35 2 Mathematics Evaluation Anxiety .54

50.3*** .19 55.1"**

*** significant at 0.001 level

C o n c l u s i o n s

This study has looked at the 'mathematics anxiety' of a group of beginning Australian university students intending to graduate as primary school teachers. The design of the study is such that results are not generalisable. The study, however, is reported not because it provides firm conclusions, but rather directions for future research. The measures used have, apart from those related to teaching, been at a level consistent with the year levels these students will eventually teach. Anxiety experienced in the actual 'doing' of mathematics and anxiety related to evaluation in mathematics, appear to be distinct factors of the construct 'mathematics anxiety'. For these students, MATHEMATICS EVALUATION ANXIETY was the better predictor of their self-rating of 'ability to use mathematics in everyday life' and 'anxiety felt when in a situation where mathematics needs to be used'. This suggests the possibility that these students are more likely to relate mathematics to an evaluation context rather than that in which it is used. This may be a product of these students' own mathematics education. At any rate, it suggests that a future longitudinal study might be valuable in investigating associations, if any, between dimensions of 'mathematics anxiety' and classroom practice. Further, it is likely to be more valuable to investigate 'mathematics anxiety' in terms of its composite factors than as a single phenomenon. Whilst there is no evidence to claim that EVALUATION MATHEMATICS ANXIETY is associated with self-concept, the authors believe that a future study should investigate the possible existence and nature of such an association.

38 McCormick & Scott

References

Aiken, L.R. (1976), "Update On Attitudes and Other Affective Variables in l_e, aming Mathematics", Review of Educational Research, 46, pp.293-311.

Australian Council For Educational Research (1984), PATMATHS: Progressive Achievement Tests in Mathematics, Teachers Handbook, Hawthorne, Victoria, ACER.

Bulmahn, B.J. and Young, D.M. (1982), "On the Transmission of Mathematics Anxiety", Arithmetic Teacher, 30(3), pp.55-56.

Bush, W.S. (1989), "Mathematics Anxiety in Upper Elementary School Teachers", School Science and Mathematics, 89(6), pp.499-509.

Dew, K.M., Galassi, J.P. and Galassi, M.D. (1984), "Math Anxiety: Relation With Situational Test Anxiety, Performance, Physiological Arousal, and Math Avoidance Behavior", Journal of Counseling Psychology, 31(4), pp.580-583.

Ferguson, R.D. (1986), "Abstraction Anxiety: A Factor of Mathematics Anxiety", Journal For Research In Mathematics Education, 17(2), pp. 145-150.

Genshaft, J.L. (1982), 'q'he Use Of Cognitive Behaviour Therapy For Reducing Math Anxiety", School Psychology Review, 11 (1), pp.32-34.

Kelly, W.P. and Tomhave, W.K. (1985), "A Study of Math Anxiety/Math Avoidance in Preservice Elementary Teachers", Arithmetic Teacher, 32(5), pp.51-53.

Olson, A. and Gillingham, D. (1980), "Systematic Desensitisation of Mathematics Anxiety Among Pre-Service Elementary Teachers", The Alberta Journal of Educational Research, 26(2), pp.32-34.

Richardson, F. and Suinn, R. (1972), "/'he Mathematics Anxiety Rating Scale: Psychometric Data.", Journal Of Counseling Psychology, 19, pp.551-554.

Rounds, J. and Hendel, D. (1980), "Measurement and Dimensionality Of Mathematics Anxiety", Journal Of Counseling Psychology, 27, pp. 138-149.

Hake, B.S. and Parker, C.S. (1982), "/'he Development and Validation of a Revised Version of the Mathematics Anxiety Rating Scale", Educational~ Psychological Measurement, 42, pp.551-557.

Sovchik, R., Meconi, L.J. and Steiner, E. (1981), "Mathematics Anxiety of Preservice Elementary Mathematics Methods Students", School Science and Mathematics, 81(8), pp.643-648.

Tishler, A.G. (1982), "Attitude-Achievement Interaction in Mathematics with Preservice Elementary Teachers", Capstone Journal of Education, 2(2), pp.40- 45.

Wood, E.F. (1988), Math Anxiety and Elementary Teachers: What Does Research Tell Us?", For the Learning of Mathematics, 8(8), pp.8-13.


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