bob perry peter howard danielle tracey university ...€¦ · pajares, 1992; van zoest, jones, &...

Danielle TraceyUniversity of Western Sydney Macarthur

Head Mathematics Teachers' Beliefs About theLearning and Teaching of Mathematics

,This ,paper reports on an investigation,.of.J.eaclrerhelie£s £OIlcerningthe nature ofmathematics and the learning and teaching of mathematics. The focus is on theespoused beliefs of 40 Head Mathematics Teachers in Australian secondary schools.These beliefs are compared with the espoused beliefs of classroom mathematicsteachers in the same schools and with recent mathematics education reformdocuments from Australia and USA. A confirmatory factor analysis of responsesfrom a specifically constructed survey identified two factors (child-centredness andtransmission) which form the basis for the comparative analysis. Interviews witheight of the Head Mathematics Teachers who responded to the survey providefurther detail for these comparisons. The ramifications of the similarities anddifferences in espoused beliefs of the different groups of teachers and the reformdocuments are discussed.

1999, Vol. 11, No. 1,39-53

Peter HowardAustralian Catholic University

Bob PerryUniversity of Western Sydney Macarthur

Mathematics Education Research Journal

Though the investigation of teachers' beliefs is a relative recent area ofresearch (McLeod, 1992; Thompson, 1992), it is generally agreed that such beliefsplaya critical role in determining how teachers teach (Barnett & Sather, 1992;Pajares, 1992; van Zoest, Jones, & Thornton, 1994)-even if the precise linkbetween what teachers say (espoused beliefs) and what they do (enacted beliefs) isnot nearly so clear (Bishop & Clarkson, 1998; Sosniak, Ethington, & Varelas, 1991;Thompson, 1992). Even further, teachers' espoused beliefs can often seem to be ininternal conflict. Sosniak et a1. (1991), in their study of teachers' beliefs arisingfrom the Second International Mathematics Study, found that teachers can "holdpositions about the aims of instruction in mathematics, the role of the teacher, the Inature of learning, and the nature of the subject matter itself which would seem tobe logically incompatible" (p. 127). In spite of these apparent difficulties, it is clearthat the espoused beliefs about mathematics, mathematics learning, andmathematics teaching are important and studies should be continued. This papercontinues the authors' research agenda commenced in 1994 (Perry & Howard,1994) which has investigated primary and secondary teachers' espoused beliefsabout the learning and teaching of mathematics (Howard, Perry, & Lindsay, 1997;Perry, Howard, & Conroy, 1996; Perry, Tracey, & Howard, 1998), and comparisonbetween the beliefs of these two groups of teachers (Tracey, Perry, & Howard,1998), by considering the espoused beliefs of the curriculum leaders in secondaryschool mathematics and those teachers whom they lead.

Beliefs' about the nature of mathematics and how mathematics is done "areimportant not only because they influence how one thinks about, approaches, andfollows through on mathematical tasks but also because they influence how one

studies mathematics and how and when one attends to mathematics instruction"(Garofalo 1989, p. 502). It is recognised that a student's prime, but by no meansonly, source of mathematical experiences is the classroom (Franke, 1988; NationalCouncil of Teachers of Mathematics, 1998) and that what occurs in themathematics classroom influences student beliefs (Relich, 1995). Critical to theclassroom implementation of the learning and teaching of mathematics is theteacher and, in particular, the beliefs of the teacher. All teachers hold beliefstowards the learning and teaching of mathematics. These beliefs influence andguide teachers in their decision making and in their implementation of teachingstrategies (Baroody, 1987). Indeed, it has been suggested that the investigation ofbeliefs about learning and teaching may well be the most critical factor ineducational research (Pajares, 1992).

One model for categorising beliefs about the teaching of mathematics (Kuhs &Ball, 1986) suggested that teachers hold views falling into four broad categories:learner focused; content focused with an emphasis on conceptual knowledge;content focused with an emphasis on performance; and classroom focused.Another perspective is offered by Thompson (1992) who reported that teachers'conceptions of mathematics appear to be related to their views about teachingmathematics. In particular, their beliefs seem to evolve from their teachingexperience rather than formal study and there appears to be a strong relationshipbetween teachers' conceptions of teaching and their conceptions of students'mathematical knowledge (Sosniak et al., 1991).

We have derived a further model of teacher beliefs from our current researchand from various mathematics education reform statements· (AustralianEducation Council, 1991, 1994; Cobb & Bauersfeld, 1995; National Council ofTeachers of Mathematics, 1989, 1995). This model is based on two factors whichdescribe what teachers believe about mathematics, mathematics teaching, andmathematics learning (Perry et al., 1996; Howard et al., 1997). These two factors,which we call transmission and child-centredness, are defined in the following ways:

• Transmission: the traditional view of mathematics as a static disciplinewhich is taught and learned through the transmission of mathematicalskills and knowledge from the teacher to the learner and where"mathematics [is seen] as a rigid system of externally dictated rulesgoverned by standards of accuracy, speed and memory" (NationalResearch Council, 1989, p. 44);

• Child-centredness: students are actively involved with mathematicsthrough "constructing their own meaning as they are confronted withlearning experiences which build on and challenge existing knowledge"(Anderson, 1996, p. 31).

This duality of factors is not new and has been described by many authors invarious ways. Sosniak et al. (1991) comment as follows:

Jackson (1986) labels these orientations "the mimetic and the transformative,"terms which he says encompass the differences expressed in long-standingdebates between "traditional" and "progressive" educators, over "subject-centred" and "child-centred" practices .... One of the traditions is concerned

40 Perry, Howard, & Tracey

Head Mathematics Teachers

primarily with the transmission of factual and procedural knowledge while theother emphasises qualitative transformations in the character and outlook of thelearner. (p. 121)

Stipek & Byler (1997), in their study of early childhood teachers' ''beliefs aboutappropriate education for young children" (p. 312), designated two similar factorsas "child-centred beliefs" and "basic skills beliefs," while Lubinski, Thornton,Heyl, & Klass' (1994) described factors which can be compared with thoseintroduced above as the ends of a continuum of teachers' beliefs. The analysisreported in this paper considers the two factors as being separate rather than twoextremes of one beliefs factor.

Head Mathematics Teachers1 (HMTs) are the leaders of school mathematicsfaculties, both in terms of curriculum and personnel. The HMT is responsible forthe implementation of the mandatory mathematics syllabuses and for thestandards of teaching and professional development of all the mathematicsteachers in the school. The HMT is also a member of the school executive,responsible for the running of the school, but usually has no role in the selection ofteachers to work in the school.

The role of curriculum leaders such as HMTs in influencing their faculty'sapproaches to teaching or their beliefs about that teaching does not seem to haveexcited a great deal of research activity. However, Weissglass (1991) and Milford(1998) have noted that HMTs do play significant roles in facilitating change intheir teachers, particularly in terms of their classroom behaviours. Milford (1998)suggests that these roles involve modelling, affirmation and support of the facultymembers.

41Head Mathematics Teachers' Beliefs

Research questions

This paper considers the following research questions dealing with the beliefsof HMTs and their faculty about mathematics, mathematics learning, andmathematics teaching.

1. Can the beliefs of secondary mathematics teachers be characterised interms of the belief factors transmission and child-centredness?

2. How do the beliefs of Head Mathematics Teachers (HMTs) and otherclassroom mathematics teachers (OMTs) compare on these two factors?

3. What consequences for mathematics learning and teaching arise from thiscomparison?

Method

The study reported in this paper forms a subset of a larger study"in which a

1 This is the term used in New South Wales public secondary schools. In some systems,they are known as Mathematics Coordinators.

total of 939 primary and secondary mathematics teachers responded to a surveydealing with their use of manipulatives in mathematics learning and teaching andtheir beliefs about mathematics, mathematics learning, and mathematics teaching.The subset of this sample on whose responses this paper is based consists of 233mathematics teachers in secondary schools in the South Western suburbs ofSydney. Only data concerning the espoused beliefs of these teachers are reportedhere.

The region in which the study was conducted is recognised as one of lowsocioeconomic status, in which there are pockets of high unemployment and alarge number of students of non-English speaking background. Employingauthorities describe. it as a relatively 'hard-to-staff' region for teachers and as aconsequence it has a disproportionately high number of young, inexperiencedteachers in its schools.

Two data collection methods were used in the study reported in this paper.The first was a researcher-designed questionnaire containing 20 items dealingwith the teachers' beliefs about mathematics, mathematics learning, andmathematics teaching. Responses were given to each item on a three pOint Likertscale: disagree, undecided, agree. Data gathered from these items relied on theself-reporting of teachers, parallelling the approach of Hatfield (1994). The itemswere constructed from sources including Australian Education Council (1991),Barnett & Sather (1992), Mumme & Weissglass (1991), and Wood, Cobb, & Yackel(1992) and were trialed extensively with both primary teachers and secondarymathematics teachers, as well as being further moderated by experiencedmathematics educators from Sydney universities. Each item was constructed toreflect either the transmission and or the child-centredness factors defined above.The items and their predicted factors are given below in Table 3.

In September 1996, the questionnaires were posted, with reply-paidenvelopes, to 52 secondary schools (15 Catholic and 37 government schools) in theSouth Western suburbs of Sydney. This was all the secondary schools from thesetwo groups in this region of Sydney. Schools were contacted by telephone to gainthe Principals' initial approval to undertake the survey in the schools and toascertain the number of mathematics teachers in each school. Sufficient numbersof the questionnaire were posted to cover all mathematics teachers at each school.

A total of 249 survey responses was received. However, 16 have beenexcluded from the analysis in this paper because the respondents did notdesignate themselves as either an HMT or an OMT. The remaining responsescame from 40 HMTs and 193 OMTs. The maximum number of HMTs who couldhave responded to the survey was 52-the number of schools surveyed-so the 40completed HMT surveys represents a response rate of 77%. The total number ofOMTs in the 52 schools was 323, so the 193 completed OMT surveys represents aresponse rate of 51% for this group of teachers.

The second data collection method involved interviews with eight HMTsselected randomly from the 40 who responded to the survey. These teachers wereinterviewed by the first author for approximately 30 minutes each. Questionswere posed, inter alia, on their beliefs about mathematics, mathematics learning,and mathematics teaching. Each interview was audiotaped and transcribed.


Table 1Percentage Distribution of Teaching Experience ofHMTs and OMTs

Demographic dataThe sample of 233 teachers consisted of the 40 HMTs and 193 OMTs. The

teaching experience of each of the groups is shown in Table 1, while theireducational qualifications are described in Table 2.

Head Mathematics Teachers' Beliefs

Years of teaching

Less than 1

1 to 5

6 to 10

11 to 20

More than 20

Results

HMTs (n = 40)

oo1

33

65

OMTs (n = 193)

4

22

25

34

16

43

Table 2Percentage Distribution of Educational Qualifications ofHMTs and OMTs

Highest teacher education qualification

Two year trained

Three year trained with Diploma

Four year trained with BEd

Four year trained with degree/DipEd/DipTeach

Postgraduate qualification

HMTs (n = 40)

5

o18

63

15

OMTs (n =193)1

5

24

62

7

BeliefsTable 3 shows how the HMTs and OMTs responded to the 20 beliefs

statements on the survey questionnaire. The table also shows the factors(transmission or child-centredness) which the various statements were intendedto measure. All the items are positive with respect to the intended factor, so thatagreement with each item should indicate belief in the corresponding factor.


Table 3Percentage Distribution ofHMT and GMT Responsesa to Survey BeliefStatements

Belief statementb HMTs OMTs

D U A D U A

Mathematics

T 1. Mathematics is computation 61 8 32 31 18 51

T 2. Mathematics problems given to students 70 18 13 60 21 19should be quickly solvable in a few steps

C 3. Mathematics isthedynamicsearclUngfQI 10 13 77 8 18 73order and pattern in the learner's environment

C 4. Mathematics is no more sequential a subject 77 15 8 69 15 17than any oth~r

C S. Mathematics is a beautiful, creative and 5 13 82 5 13 83useful human endeavour that is both a way ofknowing and a way of thinking

T 6. Right answers are much more important in 90 0 10 87 8 5mathematics than the ways in which you getthem

Mathematics learning

C 7. Mathematics knowledge is the result of the 3 15 83 5 13 82learner interpreting and organising theinformation gained from experiences

C 8. Students are rational decision makers capable 28 45 28 40 37 23of determining for themselves what is right andwrong

T 9. Mathematics learning is being able to get the 73 20 8 84 10 7right answers quickly

C 10. Periods of uncertainty, conflict, confusion, 5 8 88 7 10 83surprise are a significant part of themathematics learning process

C 11. Young students are capable of much higher 20 43 38 22 43 35levels of mathematical thought than has beensuggested traditionally

T 12. Being able to memorise facts is critical in 30 20 50 27 15 58mathematics learning

C 13. Mathematics learning is enhanced by 3 5 92 1 15 84activities which build upon and respectstudents' experiences

C 14. Mathematics learning is enhanced by 0 0 100 1 6 93challenge within a supportive environment

Beliefs about mathematics. Very few of the respondents agreed that "rightanswers are much more important in mathematics than the ways in which you getthem." As well, nearly three-quarters of all the teachers believed that"mathematics is the dynamic searching for order and pattern in the leamer'senvironment," while 80% or more of HMT and OMT groups believed that"mathematics is a beautiful, creative and useful human endeavour," perhapsreflecting the fact that most of the respondents were university-trainedmathematicians who should know the value of mathematics. This belief wasreflected in comments made by some of the interviewed Head MathematicsTeachers:

Mathematics teaching

C 15. Teachers should provide instructional 3 5 93 3 17 81activities which result in problematic situationsfor learners

T 16. Teachers or the textbook - not the student - 58 29 13 63 18 20are the authorities for what is right or wrong

T 17. The role of the mathematics teacher is to 33 20 48 21 18 61transmit mathematical knowledge and toverify that learners have received thisknowledge

C 18. Teachers should recognise that what seem 3 15 83 5 23 72like errors and confusions from an adult pointof view are students' expressions of theircurrent understanding

C 19. Teachers should negotiate social norms 8 23 69 13 24 63with the students in order to develop acooperative learning environment in whichstudents can construct their knowledge

C 20. It is unnecessary, even damaging, for 75 20 5 85 14 2teachers to tell students if their answers arecorrect or incorrect

aResponses: D (disagree), U (undecided), A (agree).

bpredicted factors: T (transmission), C (child-centredness).


Table 3 (continued)

Belief statement HMTs

D U A

45

OMTs

D U A

I see mathematics as creative but the kids haven't got this idea at all.

I suppose I sit close to the process line - the fact that maths is creative and looks atpatterns and is a problem solving tool. I think maths is a process. It's a way ofthinking.

An interesting difference between the groups of teachers occurred with thestatement "mathematics is computation." Half of the OMTs agreed with the

Maths should be at least a challenge and enjoyable.

statement compared to onl)'! 32% of HMTs, while 61% of HMTs disagreedcompared with only 31% of OMTs. When a chi-squared analysis was completedon the separate beliefs statements across the two groups of teachers, this item wasthe only one of the 20 statements which yielded any statistically significantdifference (X2 =12.17, P < 0.01). Backing for the HMT position is evident from thefollowing comments by interviewees:

They [the students] are not interested. They just want to know how to dosomething. It's very frustrating. They don't think beyond that. It's disappointing.

I'm very much against just rote learning and memory. I'm no big deal about justgetting answers right.

Beliefs about mathematics learning. There were high levels of agreement fromboth groups of teachers on the statements "mathematics knowledge is the resultof the learner interpreting and organising the information gained fromexperiences," "periods of uncertainty, conflict, confusion, surprise are a significantpart of the mathematics learning process," "mathematics learning is enhanced byactivities which build upon and respect students' experiences," and "mathematicslearning is enhanced by challenge within a supportive environment." Thissuggests that these teachers were, at least, in sympathy with much of the currentreform agenda in mathematics education (Australian Education Council, 1991,1994; National Council of Teachers of Mathematics, 1989, 1995). Comments frominterviewed Head Mathematics Teachers support this position:

Maths learning is helped if you can provide some sort of challenge ... That isbasically my approach - try to challenge the kids.

Perry, Howard, & Tracey46

I love to get them messing about with numbers.

Further support is provided by the large proportions of both groups ofteachers who disagreed that "mathematics learning is being able to get the rightanswers quickly." However, memorisation was still seen to be important with50% of HMTs and 58% of OMTs agreeing with the statement that "being able tomemorise facts is critical in mathematics learning."

Beliefs about mathematics teaching. There were high levels of agreement fromboth groups of teachers on the statements "teachers should provide instructionalactivities which result in problematic situations for learners," "teachers shouldrecognise that what seem like errors and confusions from an adult point of vieware students' expressions of their current understanding," "teachers shouldnegotiate social norms with the students in order to develop a cooperativelearning environment in which students can construct their knowledge," while themajority of both groups disagreed with "teachers or the textbook - not the student- are the authorities for what is right or wrong." Again, there is a suggestion thatthe reform agenda, or, at least its rhetoric, may have gained some strength in thefield.

On the other hand, 48% of HMTs and 61% of OMTs agreed with thestatement "'the role of the mathematics teacher is to transmit mathematicalknowledge and to verify that learners have received this knowledge" and three-quarters or more of both groups disagreed with· "it is unnecessary, evendamaging, for teachers to tell students if their answers are correct or incorrect." Itwould seem that, at least with some teachers, there may be a continuation of thecommon (but stereotypical) view that secondary mathematics teachers are contentoriented, transmission teachers who reluctantly accept that there are ways toteach mathematics beyond those which they may have experienced as students insecondary school and university. Certainly some of the comments from theinterviewed Head Mathematics Teachers would support this position:

I believe that I have some knowledge and I have got to transmit it to the kids.

Mathematics is a perfect science. It is right and right for all time. It is absolute. Itis a means of describing the world.... Persistence is important.

Enjoyment is not a critical aspect.


Table 4Factor Loadings of Beliefs Statements

Statement number Intended factora Factor I Factor II

1 T 0.26 -0.052 T 0.30 0.013 C 0.10 0.434 C -0.14 -0.155 C 0.01 0.41

6 T 0.20 -0.057 C 0.10 0.388 C -0.13 0.309 T 0.36 0.00

10 C -0.05 0.21

11 C -0.23 0.1512 T 0.37 0.0413 C -0.17 0.4114 C 0.13 0.5615 C 0.02 0.44

16 T 0.23 -0.3217 T 0.51 -0.1028 C -0.16 0.3219 C -0.12 0.5320 C -0.29 -0.05

aT: transmission, C: child-centredness.

47

The survey used in this study has been shown, through confirmatory factoranalysis, to be suitable for the categorisation of practising teachers' espousedbeliefs about mathematics, mathematics learning, and mathematics teaching.Further, it has provided evidence for the existence of two factors-transmissionand child-centredness-which can be used in the analysis of these beliefs. Whilethere is no doubt that individual teachers responded to the belief statements inways which would seem to be contradictory, reinforcing the findings of Bishopand Clarkson (1998) and Sosniak et al. (1991), the factor structure appears to allowthe meaningful analysis of these beliefs. The survey results show that manysecondary mathematics teachers espouse sets of beliefs which can be described astransmission beliefs, and many espouse sets of beliefs which could be described aschild-centred.

Confirmation and Comparison ofBeliefs FactorsA confirmatory factor analysis, using principal axis factoring and oblique

rotation, was conducted on the combined responses of the 233 HMTs and OMTsto the questionnaire survey. The two-factor solution led to the loadings shown inTable 4. The solution accounted for 15% of the variance.

Except for Items 4, 11, and 16, all items showed a substantial loading on onefactor and a much smaller loading on the other. Also, with the exception of Items4, 11, 16, and 20, all the items written to measure transmission loaded morestrongly positive on Factor I and all the items written to measure child-centredness loaded more strongly positive on Factor TI. The factor analysis thusgenerally supports the authors' model of teachers' beliefs and provides constructvalidation for the measurement of the two factors using the survey questionnaire.

The factor analysis was used to calculate z-scores (Le., scores with a mean of 0and a standard deviqtion of 1) for transmission (Factor I) and child-centredness(Factor TI), using all the items on the questionnaire. The two scores wereessentially independent (r = -0.12). Table 5 shows that the Head MathematicsTeachers were less transmission-focussed and more child-centred than the othermathematics teachers. The differences between the two groups were not onlystatistically significant, but the effect sizes of about 0.4 show that the differenceswere also substantial.

Table 5Mean factor scores ofHMTs and OMTs

p < 0.05

P < 0.05

Significance

Perry, Howard, & Tracey

2.35

-2.05

t valueMean z-score

Discussion

-0.36 0.07

0.32 -0.06

HMTs OMTsFactor

Transmission

Child-centredness

48

The finding that HMTs scored significantly higher than the OMTs on thechild-centredness factor and significantly lower on the transmission factorrequires some explanation. Firstly, we note that the HMTs in the present samplewere significantly more experienced (X2 = 51.60, P < 0.0001) than the OMTs (seeTable 1). In a system where, until recently, promotion was almost entirely basedon seniority, this was to be expected. On the other hand, there was no significantdifference found between HMTs and OMTs in terms of their educationalqualifications (see Table 2). Hence, the differences in HMTs' and OMTs' beliefswould seem to be the result of HMTs' greater teaching experience. This inferenceis supported by Thompson's (1992) finding that teachers' beliefs aboutmathematics and mathematics teaching seem to evolve from their teachingexperience rather than from their formal study in teacher preparation.

Specifically, the HMTs may feel more comfortable than their less experiencedstaff with the task of teaching mathematics in the sometimes difficult classes thattypify the South Western suburbs of Sydney. Haberman (1994, p. 17) suggests thatin many urban schools in low socioeconomic areas, there exists a "pedagogy ofpoverty" which has been described as "a highly directive style of teaching basedon rote learning of the basics, formulated without reference to adequatepedagogic or social theory" (see also Hatton, 1994, p. 15). Haberman (1994, p. 19)continues by suggesting that "the pedagogy of poverty requires that teachers whobegin their careers intending to be helpers, models, guides, stimulators, andcaring sources of encouragement transform themselves into directiveauthoritarians in order to function in urban schools". Could it be that many of the

Jless experienced OMTs are still working through the "survival" stage of theirbeginning teaching and are reflecting the realities of their difficult classes whereauthority is seen to be paramount-while the HMTs have sufficient experienceand position power to enable them to look beyond basic survival in the classroomand at least contemplate that there might be other ways of learning and teachingmathematics?

Comments in the interviews with HMTs weighed much more heavily onchild-centredness than on transmission, suggesting that they had begun tosynthesise the reform agenda in mathematics into their own thinking, or, at least;'linto their rhetoric. They seemed to be well aware of the need for professionaldevelopment within their mathematics faculties, but they also expressed otherfrustrations:

Head Mathematics Teachers' Beliefs 49

I don't know whether we are churning out any better mathematicians [among ourstudents] but I think the potential is there. However, a lot of the teachers shyaway from it.

We try to make the work relevant but we are constrained by the syllabus.

Sometimes, I feel, the pressure of the syllabus tends to force us to cut corners withthe kids.... If I sound cheesed off, it's just that I may be a disillusioned mathsteacher.

That teachers with such a wide variety of espoused beliefs as has beenreported here can come to grips successfully with the current mandatorysyllabuses and examination systems in New South Wales secondary schools is

Conclusion

amazing. Many of the HMTs interviewed suggested that one way of doing this isto disregard as much of the change as possible:

In our school, the Year 7 and 8 syllabus has not made much difference at all totell you the truth.

From my experience, algebra is still taught in the same sort of way as it alwayshas been.

Like most adults, almost all current teachers were educated at the elementary,secondary and university levels in curricula that promoted the conception ofmathematics as procedures rather than sense-making. Moreover, the schoolenvironments in which teachers now teach demand this rule-based view ofmathematics. Their mathematics textbooks support it. State ... testing programsassess adherence to it. (p.466)

The results of the survey on which this report is based suggest that regularclassroom mathematics teachers feel this pressure to conform to tradition evenmore than their curriculum leaders in the school.

Perry, Howard, & Tracey50

I think people are still doing what they used to do in the old days.

These comments suggest that, for many Head Mathematics Teachers, the road tosurvival for their teachers (and, perhaps, themselves) is to resist much of whatthey see as fashion in mathematics pedagogy. They seem to be saying that if theyadhere to the "tried and true" they will not go far wrong.

In this respect, Australian mathematics teachers seem to be no different fromothers elsewhere in the world. Sosniak et al. (1991) argue that the very structure ofthe settings in which secondary mathematics learning and teaching is undertakendemands a traditional approach by teachers. "Structurally and functionally ...schools and classrooms are designed to support and promote the continuedtransmission of traditional views and practices" (p. 129). Reinforcing this view,Battista (1994) notes, with reference to US schools:

This study has shown that espoused beliefs about mathematics, mathematicslearning, and mathematics teaching can be measured and compared across groupsof teachers. Moreover, it has shown that there can be some differences in thesebeliefs between classroom mathematics teachers and their curriculum leaders insecondary schools. In the context of reform currently occurring in mathematicseducation, the impact of these differences in beliefs might be critical. However, itmay also be that traditional approaches to mathematics education are soentrenched among many of the teachers that the impact of a reform agenda willbe minimal.

The results of this study cannot be generalised to other states of Australia orbeyond because of the differences in the structure of the education systemsinvolved. However, it would be surprising if similar results were not found. Thisbroadening of the sample is one way in which this study will be extended in thefuture. Another is to pursue the challenge to compare espoused and enacted

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Acknowledgements

The research reported in this paper was made possible through an InternalResearch Grant from the University of Western Sydney Macarthur and anotherfrom the Australian Catholic University. The authors also gratefullyacknowledge the assistance of Dr Sue Dockett.


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AuthorsBob Perry, Faculty of Education and Languages, University of Western Sydney Macarthur,PO Box 555, Campbelltown NSW 2560. E-mail: .

Peter Howard, Faculty of Education, Australian Catholic University, Mount St MaryCampus, 179 Albert Road, Strathfield NSW 2135. E-mail: .


Mathematics Education Research Journal, 6,37-55.Weissglass, J. (1991). Teachers have feelings: What can we do about it? Journal of Staff

Development, 12(1), 28-33.Wood, T., Cobb, P. & Yackel, E. (1992). Change in learning mathematics: Change in

teaching mathematics. In H. Marshal (Ed.), Redefining student learning: Roots ofeducational change (pp. 177-205). Norwood, NJ: Ablex.

Danielle Tracey, Faculty of Education and Languages, University of Western SydneyMacarthur, PO Box 555, Campbelltown NSW 2560. E-mail: .

bob perry peter howard danielle tracey university ...€¦ · pajares, 1992; van zoest, jones, &...

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