A new instrument to measure pre-service primary teachers’ attitudes to teaching mathematics

Mathematics Education Research Journal, Vol.3, No.2, 1991.

A NEW INSTRUMENT TO MEASURE PRE-SERVICEPRIMARY TEACHERS° ATTITUDES TO TEACHING

MATHEMATICS

Steven Nisbet, Griffith University

This article outlines the development of an instrument to measurepre-service primary teachers' attitudes to teaching mathematics. Atrial questionnaire was devised using the set of Fennema-Sherman scales on students' attitudes to the subject mathematicsas a model. Analysis of the responses to the questionnaire by 155student teachers was carried out to develop meaningful attitudescales and to refine the instrument. The end product is a newinstrument which can be used to monitor the attitudes of studentteachers. The attitude scales identified in the analysis and builtinto the final form of the questionnaire are (i) anxiety, (ii)confidence and enjoyment, (iii) desire for recognition and (iv)pressure to conform.

It was consistently reported to the Panel that students enteringprimary programs do so with feelings of fear and anxiety, andwith negative attitudes to mathematics. Teacher educationprograms will need to give special attention in courses to turnthese negatives to positives. (Department of Employment,Education and Training, 1989, p.66)

It is not surprising that some students start their training withfears about the teaching of mathematics and that traininginstitutions should have difficulty in giving to some of theirstudents the positive attitude to the subject and the confidencewhich are necessary if these students are to be able to teachmathematics well. It must therefore be a major task of those whotrain these students to establish positive attitudes to mathematics... (Cockcroft, 1982, para. 679)

The above quotes from the "Discipline Review of Teacher Education inMathematics and Science" and "Mathematics Counts" highlight a complexproblem in the area of attitudes in the teaching and learning of mathematics

Attitudes to Teaehing Mathematics 35

and in particular the attitudes associated with mathematics held by pre-serviceprimary teacher education students.

Evidence gathered by Cockcroft (1982) points to the fact that althoughchildren commence school eager to learn and find school in general interestingand enjoyable, by the time they leave school they hold a wide range ofmathematical attitudes and levels of confidence, from positive to negative andhigh to low respectively. Cohorts of students commencing pre-service teachereducation courses display such a range of attitudes and levels of confidenceincluding a proportion (sometimes alarming) which have negative attitudes tomathematics.

Australian studies reveal a similar problem of negative attitudes. Priorto the reporting of the problem in the Discipline Review (Department ofEmployment Education and Training, 1989), Sullivan (1987) reported thatabout half of a sample of beginning teachers had negative attitudes tomathematics on entering college. In a comparison of Education and Sciencestudents at a university, Watson (1987) found that about a quarter of theEducation students feit uneasy, confused, uncomfortable, and nervous aboutmathematics. About 40% of the Education students appeared to be less thanconfident with mathematics.

Implied in the quotes above are a number of assumptions concerningmathematical attitudes. The first is that to teach mathematics well one needs tohave a positive attitude to the subject. The second is that the importantattitudinal matters are bound up with attitudes to mathematics exclusively.

This article suggests that to study attitudes of student teachers, oneneeds to identify a number of different facets of mathematical attitudes whichinfluence the behaviour of student teachers - namely attitudes to the subjectmathematics education, attitudes to their teaching of the subject, as well asattitudes to the subject mathematics itself. The final product of this study is aninstrument (questionnaire) to measure student teachers' attitudes towards theirteaching of mathematics.

Becoming a Teacher of Mathematics

Student teachers are on a journey. The journey takes them from theschool situation where they have been pupils, along various paths to a teachereducation institution, and then back to the school situation, the second time asteachers. In the past the overwhelming majority of pre-service primary teachereducation students came to the training institution directly from secondaryschool. In more recent times there has been an increase in the number ofstudents entering teacher education at a later stage after a period ofemployment in the workforce, or raising a family, or after some time in adifferent tertiary course. These students bring with them varying abilities inand attitudes towards mathematics. These attitudes have been influenced notonly by experiences and achievements in school mathematics, but also byteachers, parents, employers and their peers.

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At their respective teacher education institutions student teachers meetwhat is for them a new discipline -mathematics education, and a new activity -teaching mathematics. The teaching of mathematics occurs usually in a schoolsetting during practice teaching sessions. Consequently student teachersdevelop attitudes to the new subject and the new activity, and experiencevarying degrees of success and failure in both areas during the program.Simultaneously, they hold or revise their attitudes to the subject mathematicsitself.

Graduating students who are successful in obtaining a teachingposition, move on to the school sector to take up their teaching roles inclassrooms. They take with them into this role experiences, achievements andattitudes in the three distinct fields - subject knowledge, pedagogicalknowledge, and mathematics teaching. It is interenting and significant to notethe views of recently trained teachers reported in the Cockcroft Report (1982,para. 671). ("Recently trained" meaning teachers in their first, second or thirdyear of teaching, and including both primary and secondary teachers.) Inrelation to the items;

I enjoy teaching mathematics very muchI am happy teaching mathematics in my present schoolI am very satisfied with the duties of my present job

over 90% of teachers responded "moderately" or above, and 50% responded"strongly". Sullivan (1987) reported that 87% of one particular sample ofbeginning teachers viewed the prospect of teaching mathematics positively and70% of the sample felt confident about teaching mathematics.

Components of Mathematical Attitudes

The positive and encouraging results relating to attitudes to teachingmathematics above may seem surprising in the light of data, quotedpreviously, indicating that many student teachers have negative attitudestowards mathematics when they commence their training. It is generally heldthat mathematics attitudes are formed primarily during grades 4 to 8 (Kulm,1980), and that by age 15, these attitudes have gelled and are strong enough toinfluence students' choices of school subjects and career paths (AssessmentPerformance Unit, 1983).

How can it be that so many recently trained teachers feel so positiveabout teaching mathematics when significant proportions of commencingstudent teachers report negative biases to mathematics? Do miracles happenduring training or during the initial period of employment? Are the responsesto questionnaire items reliable? Are the respective sets of questions testing thesame characteristics? Is Kulm (1980, p.371) correct to suggest that studentteachers who have a positive motivation to becoming teachers can change theirattitude toward aspects of it?

In order to answer these questions and explain such anomalies, thewriter suggests that a more analytical approach to the issue of measuring

Attitudes to Teaching Mathematics 37

mathematical attitudes of student teachers is called for. A distinction betweenthe various facets of mathematical attitudes, namely between attitudes to thesubject mathematics and attitudes to teaching mathematics is required to clarifythe situation and provide a more realistic base for the measurement of suchattitudes and for monitoring them over a period of time.

Watson (1987) has stated that there is a need for a scale developedspecifically for use with pre-service teachers: "A proposed new scale mightvery well reflect the factors present in previous scales but it would includestatements written in the context of future classroom situations" (p.54). Thisauthor hopes that the results of this study is a step toward fulfilling the aboveneed.

Measuring Attitudes to the Subject Mathematics

The role of attitudes occupies a deservedly important place in the studyof teaching and learning because of the posed link between behaviour andattitude. The theory of personal action of Fishbein and Ajzen (1975) assumesthat the best predictor of behaviour is intention. Behavioural intentions, intum, are said to be a function of one's attitude toward the behaviour and one'ssubjective norms (Tesser & Shaffer, 1990). Further, attitudes can be seen asflowing from experiences as well as being predictors of behaviour. Positiveattitudes of students to various subject areas and indeed their general attitudesto leaming, are important outcomes which some curriculum programs arespecifically aiming to foster (Dungan & Thurlow, 1989).

There are many research reports which have focussed on the attitudesof students to the subject mathematics. Early studies were concemed primarilywith the enjoyment factor (Shumway, 1980, p.380) Subsequently additionalfactors such as usefulness and the nature of mathematics were suggested.Specific factors proposed include value of mathematics (Aiken, 1974), natureof mathematics (Bowling, 1976), liking and disliking of mathematics(Kiryluk, 1980; Helfers, 1986; Corbitt, 1984), anxiety (Ilunt, 1985; llolden,1987), motivation (Aiken, 1976), and gender (Leder & Sampson, 1989;Willis, 1989).

Fennema and Sherman (1976) proposed the following scales for themeasurement of attitudes to mathematics in their study of attitudes insecondary school students:

AS Attitude toward Success in MathematicsN1D Mathematics as a Male DomainM Perception of Mother's Attitude toward one as a Learner of

MathematicsF Perception of Father's Attitude toward one as a Learner of

MathematicsT Perception of Teacher's Attitude toward one as a Learner of

MathematicsC Confidence in Learning MathematicsA Mathematics AnxietyE Effectance Motivation (degree of active enjoyment)U Usefulness of Mathematics

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Principal Components Factor Analysis of the scales produced 4 main factors.The first factor was made up of C (Confidence), T (Perception of Teacher'sAttitude) and E (Effectance Motivation).The second was made up of M(Perception of Mother's Attitude), F (Perception of Father's Attitude) and U(Usefulness of Mathematics). The third and fourth factors were sex rolefactors, which include AS (Attitude toward Success) and MD (Mathematics asa Male Domain).

The APU surveys (1982) identified four predominant factors inattitudes towards mathematics: Reported Enjoyment of Mathematics;Perceived Utility of Mathematics; Perceived Difficulty of Mathematics; andPerceived Usefulness of Mathematics in the Future.

Measuring Attitudes to Teaching Mathematics

A number of studies of student teachers' attitudes have been conductedsince the 1960s and the thrust of these studies has been firstly on the negativeattitudes held generally in relation to mathematics as a subject and secondly onchanges of attitudes which have occurred during courses on mathematicseducation. However, studies of student teachers' attitudes seem to have lessemphasis on teaching mathematics. In relation to the studies addressing theissue, Shumway (1980) reports on some work which relates grade levelpreference to attitude toward teaching mathematics. Sullivan (1987) in a studyof mathematical attitudes of beginning teachers proposed four dimensions ofattitudes to teaching mathematics: Confidence, Liking, Interest, and Ease.Watson (1987) suggested various questionnaire items relating to fears aboutpractice teaching and reasons for disliking mathematics.

The writer suggests that in order to analyse the attitudes of studentteachers to teaching mathematics, scales parallel to those identified in thedomain of mathematics could be developed. The Fennema-Sherman Scales(1976) are most suitable as a base and hence have been selected for this taskbecause they acknowledge factors arising out of previous research, namelygender, enjoyment, confidence, anxiety, motivation, usefulness, and theperception of "significant others".

Table 1 gives details of proposed scales developed in parallel with thosein the Fennema-Sherman instrument. One scale which requires clarification is"Usefulness of Mathematics Teaching". The term "Usefulness" applies toteachers feeling that they are doing something useful by teaching mathematicsto their pupils.

Items for Scales in Attitudes to Teaching MathematicsThe items for the scales in attitudes to teaching mathematics were

produced by taking statements from the Fennema-Sherman scales and alteringthem to suit the notion of teaching mathematics rather than mathematics per se.Also, in writing the items, half were expressed positively, the other halfnegatively. For example, in the confidence scale Item 1 read "Generally I feelsecure about the idea of teaching mathematics", and Item 66 read "I won't be a


Bood teacher of mathematics". In the Effectance Motivation scale, a positivelyexpressed item was "Teaching mathematics at practice teaching is enjoyableand stimulating to me" and a negatively expressed item was "I do not enjoyhaving to teach mathematics at practice teaching".

Table 1Scales Parallel to the Fennema-Sherman Scales

Scales in Mathematics Attitudes Scales in Attitudes to TeachingMathematics

Confidence in Learning Mathematics Confidence in Teaching Mathematics

Mathematics Anxiety Scale

Attitude toward Success inMathematics

Mathematics as a Male Domain

Effectance Motivation inMathematics

Usefulness of Mathematics

Perception of Mother's, Father'sor Teacher's Attitude towardone as a Leamer ofMathematics (3 Scales)

Mathematics Teaching Anxiety Scale

Attitude toward Success in TeachingMathematics

Mathematics Teaching as a MaleDomain

Effectance Motivation in MathematicsTeaching

Usefulness of Mathematics Teaching

Perception of Mother's, Father's orTeacher's Attitude toward oneas a Teacher of Mathematics(3 Scales)

The new items were referred to another mathematics educator to checkthe face validity of the items in relation to the essence of the scales. The facevalidity was confirmed, and it was noted that there would probably be arelationship between confidence and anxiety. Evidence for a relationshipappears in the writing of negative items from the anxiety scale and positiveitems from the confidence. (See anxiety item 4 and confidence item 1, inAppendix 1.) The issue was flagged for attention in the analysis stage.

The scales are presented in full in Appendix 1.

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Administering the Draft QuestionnaireThe draft survey instrument was assembled by taking the items from

the various scales, with positively expressed items randomly ordered withthose negatively expressed. Additional information was sought at thebeginning section of the questionnaire, general information such as semesterof study, level of mathematics studied, sex, age, and strand of program. Thesurvey was administered to 155 students in a pre-service teacher educationprogram in September 1989.

Results from the Draft Questionnaire

General Information About the StudentsSex. The sample was predominantly female: 135 out of 155 (87%). (This isa similar figure to the national percentage (85.2%) published by the DisciplineReview of Teacher Education in Mathematics and Science (Department ofEmployment Education and Training, 1989)Age. Table 2 gives details of the age distribution of the students. Students'ages ranged from 17 to 49, with a mean of 22 and a median of 20.Secondary mathematics background. Tables 3 and 4 give breakdownsof the student group by age and level of mathematics studied. Seventy sevenpercent of students had studied mathematics to year 12 level at secondaryschool. Just over half of these had completed a traditional (pure) mathematicscourse with the remainder completing a social mathematics course at that level.Almost all of the students (94%) who had entered the teacher educationprogram as school leavers had completed year 12 mathematics, whereas thestudents who had not studied year 12 mathematics were the mature age entrystudents. The recommendation from the Speedy Report concerning the Year11/12 mathematics criterion for entry into primary teacher education programswould have serious implications for this group of mature age students.

Table 2Age Distribution

Age % of sample

17-21 7022-25 1026-30 1031+ 10


Table 3Analysis of Students With - Year 12 Mathematics by Age Group(Calculations rounded to nearest %)

Age % of sample % who studied year 12 mathematics

% of sample % of age group

17-21 70 66 9422-25 10 7 7326-30 10 3 2531+ 10 1 13

Table 4Analysis of Students Without Year 12 Mathematics by Age

Age % of sample % who studied < year 12 mathematics

% of sample % of age group

17-21 70 4 622-25 10 3 2726-30 10 7 7531+ 10 9 88

Tertiary mathematics background. Four percent of the students hadcompleted tertiary mathematics discipline studies apart from units included inthe teacher education program. Three per cent had completed 1 year of tertiarymathematics, and 1% had completed 2 years.Strand. The sample included students from the regelar primary program(45%), early childhood strand (10%), special education strand (28%), musiceducation (2%) and the "P to 10" strand (15%). (Students in the P - 10 strandspend part of their program studying the school curriculum in the context ofthe continuum from year 1 primary to year 10 in the secondary, thecompulsory years. They graduate as primary teachers but are expected to havea significant knowledge of the transition period from primary to secondaryschool.)

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Responses on Individual Survey ItemsThe results for the separate survey items are available from the author.

Thé responses quoted in percentage terras are tabled (from 1 to 7 i.e. DisagreeStrongly to Agree Strongly), followed by the percentage of no responses, andthe mean score for the item. The median score is circled for each item.

Responses for Items Within Original Attitude ScalesUsefulness of teaching mathematics scale. Analysis of the items Ulto U8 (Questions 5, 14, 23, 32, 41, 47, 52, and 57) reveals an overwhelmingconsensus of opinion that teaching mathematics to children is worthwhile andthat mathematics will be of great use to the children in their lives.Crosstabulations and correlations indicated no relationships between theresponses to these items and variables such as semester of program, sex,years of school mathematics and age. Items in this scale all had extreme meanvalues (1.5, 1.6 or 6.3, 6.4) and low percentages of "undecided" responses(1% to 5%).

This indicates a noticeable difference between the range of views ofsecondary school students on the usefulness of mathematics and the range ofviews of teacher education students on the usefulness of teachingmathematics. Fennema and Sherman (1976) established usefulness ofmathematics as a significant scale and factor component associated with theirinstrument to measure students attitudes to mathematics.

With this consensus and independence established with respect toattitudes to teaching mathematics, there is sufficient justification in omittingthe items of this scale from the attitudes instrument in future.Teaching mathematica as a male domain scale. Analysis of the itemsMD1 to MD8 (Questions 4, 23, 22, 31, 40, 46, 51, and 56) reveals anotherconsensus of opinion; this time that it is just as appropriate for females toteach mathematics as males, and that females can be just as good at it too.

Crosstabulations and correlations indicated no relationships between theresponses on these items and variables such as age, sex, semester of program,and previous mathematical study. Once again, there is a noticeable differencebetween the range of views of secondary school students on mathematics as amale domain, and the range of views of teacher education students on teachingmathematics as a male domain. Although this scale, established by Fennemaand Sherman (1976), was shown to be a key component for school pupils'attitudes, there is no useful purpose served by including it in the survey ofattitudes to teaching mathematics.Teaching mathematics anxiety scale. Items in the teaching mathematicsanxiety scale were numbers 2, 11, 20, 29, 38, 44, 50, 55, 60, and 63. Theoverall impression from reading the statistics on these items is that there is nota high level of anxiety amongst the students. Some of the items showed thatthe level of anxiety decreased during the course of the students' study. Acomposite score for teaching mathematics anxiety was computed and it wasfound to correlate negatively with current year of study (level of significance


.04). Students in 3rd year were less anxious about teaching mathematics than2nd year students, who were in turn less anxious than 1 st year students.Confidence in teaching mathematics scale. Items in this scale werenumbers 1, 10, 19, 28, 37, 43, 49, 54, 59, and 62. Most of the studentsexpressed confidence in their own ability to teach mathematics. Taking all theconfidence items into a composite score, it was found that there was a positivesignificant correlation (at the .03 level) with year of study. Studentsapparently gain in confidence as they progress through the 3 years of theprogram. Males express greater levels of confidence than females.Effectance motivation in teaching mathematics scale.This scale(comprising items 6, 15, 24, 33, 42, 48, 53, 58 and 64) is concemed withenjoyment and interest in teaching mathematics, along with accepting thechallenges in various facets of teaching mathematics. In general students doenjoy teaching mathematics, and although 22% are undecided, 66% didrespond positively to item 64 dealing with enjoyment. A composite score ofthis scale produced a positive correlation with year of study (significant at the.03 level). By 3rd year, the number of "undecided" and "disagree" responsesvirtually disappear.Attitude to success in teaching mathematics scale. The 6 items ofthis scale (items 3, 12, 21, 30, 39 and 45) are associated with pride in beingrecognised as a good teacher of mathematics. For instance, 67% respondedpositively to item 12 (being proud to be an outstanding teacher ofmathematics). Only 12% responded negatively and 17% were undecided.Correlations of computed composite scores for this scale with other variableswere significant only for the students' current year of study (at the .006 level).Perhaps this demonstrates a manifestation of the saying that nothing succeedslike success.Perception of mother's, father's, lecturer's and teacher'sattitudes towards one as a teacher of mathematics scales (3scales). The items in these scales produced some extraordinary results interms of percentages of "undecided", "no response", and the spread ofresponses (see Table 5).

Table 5Results on Perception. Items

For perception items For other items

Undecided

32%, 37%, 42%, 5%, 8%, 13%, etc.

No responses

8%, 10%, 12%, 1%, 3%, 4%, etc.

Stand. Dev. approx. 2 approx. 1 to 1.5

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Interestingly, these items prompted also a number of unsolicited verbalresponses such as:

Who cares about our parents for this survey.My mother hates maths.My mum and dad support me in everything I do, including maths.My mum thinks I can do anything (when she was alive).

A composite score of the items of the scale, perception of mother'sattitude, was found to correlate only with the level of tertiary mathematicsstudied. A similar correlation was noted for the scale, perception of father'sattitude, and the level of school mathematics and level of tertiary mathematics.

For the scale, perception of lecturer's and teacher's attitude, asignificant positive correlation with current year of study was noted (at the.0002 level). By third year, all students perceived positive attitudes about theirteaching in their supervising teachers and lecturers at practice teaching.

Relationships Between General Variables and Composite Scoreson the Original ScalesAge. The results of this study show that age has no bearing on the attitudesof primary teacher education students in all the indicated areas - anxiety,confidence, effectance motivation, attitude towards success, and perception ofothers towards one as a teacher of mathematics. Mature age students are nodifferent from their younger counterparts in terms of attitudes to teachingmathematics.Current year of study. This study shows that students in latter part oftheir program of study are more confident, less anxious, more motivated andinterested, and want to achieve more highly in teaching mathematics. Thesestudents' perceptions of the attitudes of their supervising lecturers andteachers are more positive than those of the students in earlier stages of theprogram.Sex. The only composite scale score that showed a significant differencebetween males and females was the confidence in teaching mathematics scale.Males registered a higher confidence level than females (at the .03 level).Level of secondary mathematics. There was found to be a significantpositive correlation between perception of fathers' attitudes and level ofsecondary mathematics attained (significant at the .02 level). The only othervariable which correlated with level of secondary mathematics was Item 12(I'd be proud to be an outstanding teacher ... ).

Factor Ananlysis of ItemsAs described earlier, it was noticed that mant' questionnaire items did

not serve any useful purpose in analysing attitudes to teaching mathematicsand explaining the variance in the responses. There was an overwhelmingconsensus of opinion on the items in the "Usefulness" scale, the "Male


Domain" scale, two items on the "Effectance Motivation" scale and one of theitems of the "Perception of Lecturer's/Teacher's Attitude" scale. These itemswere therefore deleted from the instrument.

Other items deleted from the questionnaire were those from the"Perception of Mother's/Father's Attitude" scales because of the highproportion of responses in the "Undecided" and "No response" categories.Many of the unsolicited comments written on the questionnaire were to theeffect that such questions were completely irrelevant (to put it mildly).

Having reduced the number of items from 64 to 39, a series of factoranalytic procedures (principal axis factoring) were carried out to determine theunderlying factors. The initial exploratory run indicated that at least 4 factorswould be required in the solution (scree test). After a number of runs itbecame clear that the best solution was in fact that with 4 factors. Extractingmore than 4 factors produced factors with insignificant variable loadings. Thesolution produced by varimax rotation (simplifying columns of the factormatrix) was almost identical to that produced by quartimax rotation(simplifying rows of the factor matrix), the only variations being in slightdifferences in loadings on the factors.

The best factor solution is shown in Table 6. There are a number ofsignificant features about the results of the factor analysis:* The issue of anxiety in teaching mathematics is of utmost importance in

attitudes to teaching mathematics. Because anxiety is a majorcomponent of such attitudes it should be addressed directly in teachereducation programs.

* Anxiety and confidence in teaching mathematics are independentfactors. They are not opposite extremes of the one continuum. Themost confident students are not necessarily the least anxious.

* The nature of the second factor illustrates the close relationship betweenconfidence and enjoyment in teaching mathematics. There is noindication of a cause/effect situation with the two characteristics, merelythat the two are closely related.

* The third factor reveals a fundamental human need, that of recognition,along with a motivation to be successful at one's chosen career.

* Notwithstanding the existence of factor 3, there appears to be a strongAustralian cultural influence on the students' attitudes to teachingmathematics. Factor number 4 can be denoted as a pressure to conformor a reluctance to be seen as a "tall poppy" to use the commonAustralian term.

* Where factor 3 could be called attitude toward success (in Fennema-Sherman language), factor 4 could be labelled attitude towardmediocrity.After defining the components of these factors, scale reliabilities were

calculated for each of the four factors. The Spearman-Brown coefficients wereas follows:

Anxiety scale: .80 Desire for recognition scale: .71Confidence and enjoyment scale: .89 Pressure to conform scale: .74

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TABLE 6Factor Solution

FACTOR ASSOCIATED ITEMS

1. ANXIETY 1. Generally I feel secure about the idea of teachingmathematics.2. Of all the subjects, mathematics is the one I worry aboutmost in teaching.11. I would get a sinking feeling if I came across a hardproblem while teaching mathematics at practice teaching.20. The thought of teaching mathematics makes me feelrestless, irritable and impatient.29. Teaching mathematics at practice teaching makes me feelnervous.38. The thought of teaching mathematics makes me feelnervous.54. I'm not the type of person who could teach mathematicsvery well.62. Mathematics is the subject I'm least confident aboutteaching.

2. CONFIDENCE 28.1 am confident about the methods of teaching& ENJOYMENT mathematics.

37. I have a lot of self confidence when it comes to teachingmathematics.44. I feel at ease when I'm teaching mathematics at practiceteaching.48. I enjoy the challenge of teaching a new and difficultconcept in mathematics.58. Time passes quickly when I'm teaching mathematics atpractice teaching.61. Teaching mathematics at practice is enjoyable andstimulating to me.63. Teaching mathematics doesn't scare me at all.64.1 like teaching mathematics at practice teaching.

3. DESIRE FOR 3. It would make me happy to be recognised byRECOGNITION other teachers as an excellent teacher of mathematics.

12. I'd be proud to be the outstanding teacher ofmathematics amongst my peers.21. I would like the school pupils to recognise me as a goodteacher of mathematics.

4. PRESSURE TO 30. Being an outstanding teacher of mathematicsCONFORM would make me feel unpleasantly conspicuous.

39. My peers would think I was strange if I was anoutstanding teacher of mathematics.45. I would not want to let on that I was good at teachingmathematics.


The Revised Instrument

The revised instrument to measure students' attitudes towards teachingmathematics is presented in Appendix 2.

Relationships Between General Variables and Scores on the NewScales

Composite scores on the new attitude stales in teaching mathematics(anxiety, confidence and enjoyment, desire for recognition and pressure toconform) were calculated for Bach respondent and the relationships betweenthese scores and the independent variables were analysed.Anxiety. There was a weak but significant negative correlation between levelof anxiety and year of program. The level of anxiety is significantly lower for3rd year students than for 2nd and 1 st year students. Differences existedamongst the various strands of the program (significant at the 0.02 level). Theorder from lowest to highest anxiety is:

P- 10 StrandSpecial EducationPrimary (P - 7)Early EducationMusic Education

Confidence and Enjoyment. Level of confidence and enjoymentcorrelated significantly (weak, positive) with year of program. Studentsbecome more confident and enjoy teaching mathematics more as they progressthrough the program. There were differences among the various strands of theprogram, and the order of strands was similar to that for anxiety, the orderfrom highest to lowest being:

P- 10 StrandSpecial EducationEarly EducationPrimary (P - 7)Music Education

Desire for recognition. This factor is similar to the attitude towardssuccess scale referred to in the dévelopment of the original instrument. Scoreson the desire for recognition scale correlate weakly but positively with thenumber of years of school mathematics taken by the students.Pressure to conform. There are 3 general variables that correlatesignificantly with the scale scores on pressure to conform. The one positivecorrelation is with type of mathematics (social mathematics to puremathematics). Year of study correlates strongly and negatively, and agecorrelates weakly and negatively. Hence it can be raid that students feel thepressure to conform less later in their course, and more mature students feel itless also.

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Summary. In Table 7 there is a summary of the significant correlations(Pearson's r) or crosstabulations (chi-squared) between the general variablesand the new scales, along with the associated levels of significance (p).

TABLE 7Significant Correlations and Crosstabulations Between GeneralVariables and the New Scales

Recognition ConformityGeneral Anxiety ConfidenceVariable & Enjoyment

Age... ...

Year r=-.15 r=+.15

p= .03 p= .03

Sex... ...

Yearschool ... . .

Typemath ... ...

Strand 2=34.9 2=47.9p= .02 p= .002

... r=-.15p= .03

... r=-.31

Mm

r=+.17 ...p= .02

... r=+.16p= .02

In Conclusion

On the assumption that the results reported here can be generalised toother courses, the elements of the new instrument to measure student teachers'attitudes towards teaching mathematics are indicative of significant issues thatshould be addressed specifically in teacher education programs. Firstly it canbe assumed that many student teachers will be anxious about teachingmathematics as well as the subject mathematics, but efforts should be made toincorporate into mathematics education courses topics and strategies whichcan assist in reducing anxiety levels. It is reassuring to know that students intheir final year of teacher education are less anxious than their counterparts inearlier years.


Similarly, it is reassuring to know also that levels of confidence andenjoyment are higher for final year students. Mathematics education coursedesigners and lecturers should offer opportunities for their students to haveexperiences which can boost their confidence and provide enjoyment in thecontext of teaching mathematics to children.

Factors 3 and 4, "Desire for recognition" and "Pressure to conform",offer food for thought in terms of the personal emotional needs of people (notonly students) and the social pressures which affect human behaviour. Itwould be interesting to investigate the Jatter in terras of the Australian culture,namely the "tall poppy syndrome", which refers to the tendency to cut asuccessful person "down to size" by extremely negative criticism, and whichleads to a tendency for many people not to want to be seen as outstanding intheir respective fields. Further studies could be conducted in other countries toinvestigate the phenomenon in other cultures.

The object of this attitudes instrument is to enable teacher educators togauge the attitudes of student teachers towards the teaching of mathematicsand to monitor such attitudes during a teacher education program (3 years or 1year). Student should indicate their responses on a seven point Likert scalefrom "Agree strongly" to "Disagree strongly". (see Appendix 2). Compositescores should be calculated for each scale - anxiety, confidence andenjoyment, recognition, and conformity. If attitudes are to be monitored overa period of time, a system of identification which stil protects anonymityshould be employed. One such system is given on the General Informationsheet of the instrument (Appendix 2).Work to be carried out subsequent to this study entails administering theinstrument to large numbers of student teachers in a variety of institutions toestablish nórms. This will enable teacher educators to make comparativeassessments across locations and over time. In addition, mathematicseducators may be in a better position to evaluate whether some of the concernsabout attitudes raised in documents such as the Discipline Review (Departmentof Employment, Education and Training, 1989) have been addressedsatisfactorily or not.

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Appendix 1

ITEMS BASED ON THE FENNEMA-SHERMAN SCALES

Items for the Confidence in Teaching Mathematics Scale

No, Weighting Item

1. + Generally I feel secure about the idea of teaching mathematics.2. + I am sure I could teach mathematics in the upper primary grades

as well as the lower grades.3. + I am sure that 1 could be a good teacher of mathematics.4. + .I am confident about the methods of teaching mathematics.5. + I have a lot of self confidence when it comes to teaching

mathematics.6. - I won't be a good teacher of mathematics.7. - I don't think I could teach mathematics in the upper primary

grades.8. - I'm not the type of person who could teach mathematics very

well.9. - I'm not sure about what to do when teaching mathematics.10. - Mathematics is the subject I'm least confident about teaching.

Items for the Mathernatics Teaching Anxiety Scale

1. + Teaching mathematics doesn't scare me at all.2. + It wouldn't bother me to teach a lot of mathematics at school.3. + I haven't usually worried about being able to teach mathematics.4. + 1 feel at ease thinking about teaching mathematics.5. + I feel at ease when I'm teaching mathematics at practice teaching.6. - The thought of teaching mathematics makes me feel nervous.7. - Teaching mathematics at practice teaching makes me feel

nervous.8. - The thought of teaching mathematics makes me feel restless,

irritable and impatient.9. - I would get a sinking feeling if I came across a hard problem

while teaching mathematics at practice teaching.10. - Of all the subjects, mathematics is the one I worry about most in

teaching.

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Items for the Attitude toward Success in Mathematics Teaching Scale

1. + It would make me happy to be recognised by other teachers as anexcellent teacher of mathematics.

2. + I'd be proud to be the outstanding teacher of mathematicsamongst my peers.

3. + I would like the school pupils to recognise me as a good teacherof mathematics.

4. - Being an outstanding teacher of mathematics would make me feelunpleasantly conspicuous.

5. - My peers would think I was strange if I was an outstandingteacher of mathematics.

6. - I wouldn't want to let on to other teachers that I was good atteaching mathematics.

Items for the Mathematics Teaching as a Male Domain Scale

1. + Females are as good as males at teaching mathematics.2. + Teaching mathematics is as appropriate for women as for men.3. + I would trust a woman as much as a man to teach mathematics.4. + Women are certainly logical enough to teach mathematics.5. - It's hard to believe that a female could be an excellent teacher of

mathematics.6. - I would have more faith in a male mathematics teacher than a

female.7. - Women who enjoy teaching mathematics are a bit peculiar.8. - I would expect a competent female mathematics teacher to be a

masculine type of person.

Items for the Usefulness of Teaching Mathematics Scale

1. + Children at school need to be taught mathematics for their futurework.

2. + Mathematics is taught at school because it is so useful.3. + Mathematics is a worthwhile and necessary subject for children.4. + Children will need to be able to do mathematics for everyday

uses when they become adults.5. - School mathematics is of no relevance to children's lives.


6. - Mathematics will not be very important for the future careers ofchildren.

7. - Mathematics is a subject children will use in their daily lives lateras adults.

8. - Teaching mathematics is mostly a waste of time for children.

Items for the Effectance Motivation in Teaching Mathematics Scale

1. + I like teaching mathematics at practice teaching.2. + Teaching mathematics at practice teaching is enjoyable and

stimulating to me.3. + Time passes quickly when I'm teaching mathematics at practice

teaching.4. + If a child is having difficulty with a mathematics problem, I want

to explain it so the child will understand it.5. + I enjoy the challenge of teaching a new and difficult concept in

mathematics.6. - I do not enjoy having to teach mathematics.7. - Teaching mathematics is such a drag at practice teaching.8. - When I am teaching mathematics, I think that I'd rather be

teaching something a lot more interesting.9. - I'd prefer not to have to explain mathematics problems to slow

children in the class.10. - If I taught in a team or with a teaching partner, I'd like to have

another teacher to teach mathematics in the class.

Items for the Perception of Mother's Attitudes towards one as a Teacher ofMathematics

1. + My mother thinks that 1 could be a good mathematics teacher.2. + My mother has been interested in my progress and has

encouraged me in being a good mathematics teacher.3. - My mother could not have been a teacher of rnathematics.4. - My mother does not think it is important whether or not I am a

good teacher of mathematics.

Items for the Perception of Father's Attitudes towards one as a Teacher ofMathematics

1. + My father thinks that I could be a good mathematics teacher.2. + My father has been interested in my progress and has encouraged

me in being a good mathematics teacher.

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3. - My father could not have been a teacher of mathematics.4. - My father does not think it is important whether or not I am a

good teacher of mathematics.

Items for the Perception of Teacher's/Lecturer's Attitudes towards one as aTeacher ofMathematics

1. + My supervising lecturers and teachers at practice teaching thinkthat I teach mathematics well.

2. + My supervising lecturers and teachers at practice teaching havebeen interested in my progress and have encouraged me in beinga good mathematics teacher.

3. - My supervising lecturers and teachers at practice teaching are notvery concemed about my achievements in teaching mathematics.

4. -

My supervising lecturers and teachers at practice teaching thinkthat I am wasting my time when I teach mathematics.


APPENDIX 2

MATHEMATICS TEACHING ATTITUDE QUESTIONNAIRE

AN INSTRUMENT TO MEASURE PRIMARY STUDENT TEACHERS'. ATTITUDES TO TEACHING MATHEMATICS

General Information

A. What program are you enrolled in?

B. Which semester have reached in the program?

C. Age

D. Sex

Dip.Teach.B.Teach.Grad.Dip.T.

1 2 34 5 6

Male Female

E. What was the highest level of mathematics you studieti at school? Year10 Year 12

Year 11Other

F. Your responses to this questionnaire are confidential,but it is necessary to have a unique identification code fora follow up survey. Please print your initials (up to 3) andyour month and year of birth.

e.g. John Wayne Smith, Feb. 1968-> JWS 02 68Mary Smith, October 1970-> MS 10 70

Initials:

Birth Date:Month Year

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Survey items

The following are statements on teaching mathematics, about which youropinion is sought. Please indicate the extent to which you agree or disagreewith the statements by ticking the relevant boxes on the response sheet.AS means Agree Strongly UN means Undecided DS means Disagree StronglyAG means Agree Generally DG means Disagree GenerallyAL means Agree a Liule DL means Disagree a Little

1. Generally I feel secure about the idea of teaching mathematics.2. Of all the subjects, mathematics is the one I worry about most in

teaching.3. It would make me happy to be recognised by other teachers as an

excellent teacher of mathematics.4. I would get a sinking feeling if I came across a hard problem while

teaching mathematics at practice teaching.5. I'd be proud to be the outstanding teacher of mathematics amongst my

peers.6. The thought of teaching mathematics makes me feel restless, irritable

and impatient.7. I would like the school pupils to recognise me as a good teacher of

mathematics.8. I am confident about the methods of teaching mathematics.9. Teaching mathematics at practice teaching makes me feel nervous.10. Being an outstanding teacher of mathematics would make me feel

unpleasantly conspicuous.11. I have a lot of self confidence when it comes to teaching mathematics.12. The thought of teaching mathematics makes me feel nervous.13. My peers would think I was strange if I was an outstanding teacher of

mathematics.14. I feel at ease when I'm teaching mathematics at practice teaching.15. I would not want to let on that I was good at teaching mathematics.16. I enjoy the challenge of teaching a new and difficult concept in

mathematics.17. I'm not the type of person who could teach mathematics very well.18. Time passes quickly when I'm teaching mathematics at practice

teaching.19. Teaching mathematics at practice is enjoyable and stimulating to me.20. Mathematics is the subject I'm least confident about teaching.21. Teaching mathematics doesn't scare me at all.22. I like teaching mathematics at practice teaching.