Mathematics teachers beliefs and curriculum reform

University of Wollongong Research Online Faculty of Social Sciences - Papers Faculty of Arts, Social Sciences & Humanities 2003 Mathematics teachers' beliefs and curriculum reform B Handal Cumberland High School Anthony Herrington University of Wollongong, tonyh@uow.edu.au Follow this and additional works at: https://ro.uow.edu.au/sspapers Part of the Education Commons, and the Social and Behavioral Sciences Commons Recommended Citation Handal, B and Herrington, Anthony, "Mathematics teachers' beliefs and curriculum reform" (2003) Faculty of Social Sciences - Papers 1028 https://ro.uow.edu.au/sspapers/1028 Research Online is the open access institutional repository for the University of Wollongong For further information contact the UOW Library: research-pubs@uow.edu.au Mathematics teachers' beliefs and curriculum reform Abstract This paper discusses the role of mathematics teachers’ beliefs and their impact on curriculum reform It is argued that teachers’ beliefs about the teaching and learning mathematics are critical in determining the pace of curriculum reform Educational change is a complex process in which teachers hold strong beliefs about the quality and the process of innovation Curriculum implementation may only occur through sufferance as many teachers are suspicious of reform in mathematics education given its equivocal success over the past decades It is not surprising then that many teachers, when they come to enact the curriculum in their classes, rely more on their own beliefs than on current trends in pedagogy These beliefs, conservative as they might be, have their own rationality in the practical and daily nature of the teaching profession, and in the compelling influence of educational systems from which these teachers are paradoxically the social product The literature indicates that many of these teachers hold behaviourist beliefs, a fact that has strong implications for the success of constructivist-oriented curriculum reform In general, studies of teachers’ pedagogical beliefs reveal the extreme complexity of bringing about educational change, and largely explains the failure of many past reform endeavours Keywords reform, beliefs, mathematics, curriculum, teachers Disciplines Education | Social and Behavioral Sciences Publication Details Handal, B & Herrington, A (2003) Mathematics teachers' beliefs and curriculum reform Mathematics Education Research Journal, 15 (1), 59-69 This journal article is available at Research Online: https://ro.uow.edu.au/sspapers/1028 Mathematics Education Research Journal 2003, Vol 15, No 1, 59 69 Mathematics Teachers' Beliefs and Curriculum Reform Boris Handal Cumberland High School, Sydney Anthony Herrington Edith Cowan University This paper discusses the role of mathematics teachers' beliefs and their impact on curriculum reform It is argued that teachers' beliefs about the teaching and learning mathematics are critical in determining the pace of curriculum reform Educational change is a complex process in which teachers hold strong beliefs about the quality and the process of innovation Curriculum implementation may only occur through sufferance as many teachers are suspicious of reform in mathematics education given its equivocal success over the past decades It is not surprising then that many teachers, when they come to enact the curriculum in their classes, rely more on their own beliefs than on current trends in pedagogy These beliefs, conservative as they might be, have their own rationality in the practical and daily nature of the teaching profession, and in the compelling influence of educational systems from which these teachers are paradoxically the social product The literature indicates that many of these teachers hold behaviourist beliefs, a fact that has strong implications for the success of constructivistoriented curriculum reform In general, studies of teachers' pedagogical beliefs reveal the extreme complexity of bringing about educational change, and largely explains the failure of many past reform endeavours Mathematics Teachers' Beliefs and Practices Teachers' belief systems reflect personal theories about the nature of k n o w l e d g e a n d k n o w i n g t h a t , in turn, i n f l u e n c e t e a c h e r s ' c u r r i c u l u m d e c i s i o n m a k i n g a n d t e a c h i n g a p p r o a c h e s ( H o f e r & P i n t r i c h , 1997; L o v a t & S m i t h , 1995; P a j a r e s , 1992) A c c o r d i n g to T h o m p s o n (1984) t e a c h e r s ' b e l i e f s " s e e m e d to be m a n i f e s t a t i o n s o f unconsciously h e l d v i e w s o f e x p r e s s i o n s o f v e r b a l c o m m i t m e n t s to a b s t r a c t i d e a s t h a t m a y be t h o u g h t o f as p a r t o f a g e n e r a l i d e o l o g y o f t e a c h i n g " (p 112) T h e y r e p r e s e n t i m p l i c i t a s s u m p t i o n s a b o u t c u r r i c u l u m , s c h o o l i n g , s t u d e n t s , t e a c h i n g a n d l e a r n i n g , a n d k n o w l e d g e a n d act as c o g n i t i v e a n d a f f e c t i v e f i l t e r s t h r o u g h w h i c h n e w k n o w l e d g e a n d e x p e r i e n c e is i n t e r p r e t e d a n d e n a c t e d ( A r t z t & A r m o u r T h o m a s , 1996; L o v a t & S m i t h , 1995) Mathematics t e a c h e r s ' b e l i e f s can be t h o u g h t o f as a n i n d i v i d u a l ' s p e r s p e c t i v e on h o w one e n g a g e s in m a t h e m a t i c a l t a s k s ( S c h o e n f e l d , 1985) a n d pedagogical practices A growing body of literature shows that mathematics teachers' beliefs affect their classroom practices although tile nature of the r e l a t i o n s h i p is h i g h l y c o m p l e x a n d d i a l e c t i c a l ( P a j a r e s , 1992; T h o m p s o n , 1985) A l t h o u g h m a n y s t u d i e s on t e a c h e r s ' b e l i e f s s u g g e s t t h a t t h e r e is a r e l a t i o n s h i p , c a u s a l i t y is d i f f i c u l t to e x p l a i n S o m e s t u d i e s s t r o n g l y s u g g e s t t e a c h e r s ' b e l i e f s influence instructional behaviour, while in o t h e r cases i t a p p e a r s t h a t i n s t r u c t i o n a l p r a c t i c e i n f l u e n c e s t e a c h e r s ' b e l i e f s ( B u z e i k a , 1996; M c G a l l i a r d , 1983) T h e r e s e a r c h also i n d i c a t e s t h a t m a n y o t h e r factors m e d i a t e a n d i n f l u e n c e the direction and magnitude of the relationship between beliefs and practices such as t e a c h e r s ' own s c h o o l e x p e r i e n c e s ( B r o w n & Rose, 1995; Foss & K l e i n s a s s e r , 1996; R a y m o n d , 1993, 1997; T h o m p s o n , 1984, 1985) It is a p p a r e n t t h a t t h e r e is a 60 Handal & He~rington range of obstacles t h a t teachers face w h e n trying to implement e i t h e r t h e i r own beliefs or t h e m a t h e m a t i c a l ideas underpinning a p a r t i c u l a r curriculum innovation Curriculum Change in Mathematics Education In education, t h e r e is frequently a m i s m a t c h between t h e intended, t h e i m p l e m e n t e d and t h e a t t a i n e d curriculum (Cuban, 1993) The intended curriculum is t h e one prescribed by policy makers, t h e implemented curriculum is t h e one t h a t is a c t u a l l y carried out by teachers in t h e i r classrooms, and the a t t a i n e d curriculum is t h e one learnt by students (Howson & Wilson, 1986) Part of t h e m i s m a t c h is due to t h e fact t h a t teachers and students w o r k on more l i m i t e d goals t h a n those proposed by curriculum developers, t e a c h e r educators, writers of syllabuses, and textbook authors ( H a n d a l , 2001) M a t h e m a t i c s teachers, for example, are concerned only w i t h students acquiring facts and performing s k i l l s prescribed by t h e syllabus r a t h e r t h a n being concerned about broader e d u c a t i o n a l goals O t h e r factors affecting curriculum alignment and change in m a t h e m a t i c s education h a v e been e x t e n s i v e l y discussed by Anderson and P i a z z a (1996), C l a r k e (1997), Memon (1997), and Mumme and Weissglass (1991) In the context of a school based curriculum d e v e l o p m e n t project, C l a r k e (1997) i d e n t i f i e d 12 factors t h a t a p p e a r e d to influence the change process: (a) t h e reform movement in general; (b) t h e p r i n c i p a l and school community: (c) internal support personnel; (d) the spirit of c o l l e g i a l i t y , collaboration, and experimentation; (e) the g r a d e l e v e l team of teachers; (0 i n n o v a t i v e curriculum m a t e r i a l s ; (g) t h e in service program; (h) external support personnel; (i) t h e r e s e a r c h e r acting as a p a r t i c i p a n t observant and critical friend; (j) outcomes v a l u e d by t h e teacher; (k) d a y to d a y conditions under w h i c h teachers work; and (1) t e a c h e r knowledge Memon (1997) suggested a more comprehensive list of factors affecting curriculum change t h a t are grouped as curricular, instructional, and o r g a n i s a t i o n a l factors and reproduced in Table It is clear t h a t curriculum change is a complex process and w h i l e t h e r e are m a n y resource and s u p p o r t factors t h a t a p p e a r to influence change, it is a p p a r e n t t h a t any successful reform w i l l need to t a k e into account m a t h e m a t i c s t e a c h e r s ' beliefs about t h e intended, t h e implemented, and t h e a t t a i n e d curriculum Curriculum Change and Mathematics Teachers' Beliefs If an i m p l e m e n t e d curriculum is a set of beliefs put into action, as S h o r t and Burke (1996) h a v e argued, then curriculum p o l i c y makers m a y w e l l to look in d e p t h at m a t h e m a t i c s t e a c h e r s ' beliefs If tile m a t h e m a t i c s teachers' beliefs are not congruent w i t h the beliefs underpinning an educational reform, then t h e a f t e r m a t h of such a m i s m a t c h can affect the degree of success of t h e innovation as w e l l as t h e t e a c h e r s ' morale and willingness to implement f u r t h e r innovation 61 Mathematics Teachers'Beliefs and Curriculum Reform Table Factors A f f e c t i n g E d u c a t i o n a l R e f o r m i,~ M a t h e m a t i c s E d u c a t i o n Curriculum factors Instructional factors Organisational factors Externally imposed innovation Importance attached by teachers to old practice Lack of supportive mechanism Lack of curriculum users' participation N o n clarity of curriculum changes Inadequate knowledge of subject matter, method and student assessment Examination dominated teaching Lack of coordination Mismatch between official curriculum and actual curriculum Change is not responsive to curriculum users' needs Imported innovation Unplanned change Mismatch between teachers, belief system and curriculum goals Lack of detailed planning Lack of motivation, incentives and rewards Lack of professional development Lack of communication Lack of classroom materials Lack of physical facilities Lack of resources Lack of INSET Lack of community participation Influences of political leaders Influence of bureaucracy Lack of classroom interaction Lack of students' interest Mathematics teachers' beliefs can p l a y either a facilitating or an inhibiting role in translating curriculum guidelines into the complex and d a i l y r e a l i t y of classroom teaching (Haynes, 1996; Jackson, 1968, 1986; Koehler & Grouws, 1992; Sosniak, Ethington, & Varelas, 1991) If teachers hold beliefs compatible w i t h the innovation then acceptance will be more likely to occur However, if teachers hold opposing beliefs or perceive barriers in enacting the curriculum, then low take up, dilution and corruption of the reform will l i k e l y follow (Burkhardt, Fraser, & Ridgway, 1990) Prawat (1990) has affirmed t h a t teachers can be either conveyances of, or obstacles to, change No matter how much is expected of them to support reform, it is always possible t h a t their views not coincide w i t h those underpinning the reform and therefore become a major impediment in t h a t effort H a r t (1992) adds t h a t when teachers consider new tasks to be t r i v i a l and superficial t h e y tend to mistrust other innovations Unfortunately, innovations can create disunity because groups of 'resisters' are formed (Fullan, 1993) H a l l (1997) explained t h a t any innovation represents an encounter of two cultures in which conflict of values and goals needs to be minimised and hopefully blended Aborted reforms affect teachers' morale causing stress, cynicism, burnout syndromes, anxiety and scepticism (Fullan, 1993; Sinclair & McKinnon, 1987) The h i g h rate of failure of educational innovations (Fullan, 1993) has drawn 62 Handal & He~rington researchers to look more closely at teachers' beliefs as a significant m e d i a t o r in curriculum i m p l e m e n t a t i o n Fullan and Stegelbauer (1991) h a v e s t a t e d t h a t it is very u n l i k e l y t h a t teachers can m o d i f y t h e i r t e a c h i n g practices w i t h o u t changing t h e i r values and beliefs Change can also be cosmetic, t h a t is, a t e a c h e r can be using new resources, or m o d i f y t e a c h i n g practices, w i t h o u t accepting intern a l l y the beliefs and principles underlying t h e reform (Fullan, 1983) B u r k h a r d t , Fraser, and R i d g w a y (1990) w a r n t h a t even i n n o v a t i v e programs t h a t boast of h a v i n g a t t a i n e d changes on a large scale, h a v e a c c o m p l i s h e d these changes w i t h a ' t r a v e s t y ' of t h e explicit and original principles underlying t h e innovation This m i s m a t c h between curriculum goals and teachers' b e l i e f systems is a factor t h a t affects current curriculum change in m a t h e m a t i c s education Anderson and P i a z z a (1996, p 54) argued t h a t "teachers, w h o must be t h e agents of change, are products of t h e system t h e y are trying to change" and proposed t h a t t e a c h e r s ' feelings, beliefs, and values t h a t are opposite to constructivism are a barrier to reform in m a t h e m a t i c s education Sosniak, Ethington, and V a r e l a s (1991) h a v e described t h e complexity of this m i s m a t c h in the context of changing beliefs, t e a c h i n g a p p r o a c h e s and resources in t h e United States in the 1950s and 1960s These authors argued t h a t t h e success of i n n o v a t i v e m a t h e m a t i c s programs was constrained by inconsistencies between t h e content of new m a t e r i a l s and t h e working requirements of t h a t content by teachers The degree of change was limited, due to t h e fact t h a t the beliefs about m a t h e m a t i c s underlying t h e innovation did not m a t c h teachers' beliefs In addition, these programs required new roles and teachers' responsibilities t h a t were too demanding Not only did teachers feel u n f a m i l i a r w i t h t h e content change, t h e y h a d to align to a new w a y of teaching According to Martin (1993a, 1993b) curriculum i m p l e m e n t a t i o n a p p r o a c h e s t h a t not consider teachers' beliefs h a v e a t e m p o r a r y life U n f o r t u n a t e l y , m a n y educational reforms in m a t h e m a t i c s h a v e h a d a top down a p p r o a c h ( K y e l e v e & W i l l i a m s , 1996; Martin, 1993a, 1993b; Moon, 1986) t h a t did not t a k e into account m a t h e m a t i c s t e a c h e r s ' beliefs and b e l i t t l e t h e fact t h a t " t h e u l t i m a t e fate of an innovation would seem to depend upon user decisions" (Doyle & Ponder, 1977, p 3) These reforms were often disseminated using a t r a d i t i o n a l a p p r o a c h in w h i c h teachers were presented w i t h a p r e p a r e d product and a rigid set of procedures to follow The major cause of failure of these programs was t h e i r negligence in failing to t a k e into account teachers' pedagogical k n o w l e d g e and beliefs as w e l l as t h e contexts in w h i c h these t e a c h i n g b e h a v i o u [ s occurred (Knapp & Peterson, 1995) In o t h e r words, curriculum change in t h e last s e v e r a l decades r e l i e d on t h e simplistic assumption t h a t teachers will, m a c h i n e like, a l t e r t h e i r b e h a v i o u r s because t h e y were s i m p l y told w h a t was good for t h e m and for t h e i r students (Grant, Hiebert, & Wearne, 1994) Current a p p r o a c h e s to curriculum i m p l e m e n t a t i o n need to r e l y on more r e a l i s t i c assumptions about teachers' beliefs, recognising t h a t it is d i f f i c u l t to change teaching styles because changing practices demands a process of unlearning and learning again (Mousley, 1990) It also needs to be recognised t h a t change w i l l cause feelings of discomfort t h a t can be unpleasant and i n t i m i d a t i n g (Martin, 1993b) Mathematics Teachers' Beliefs and Curriculum Reform 63 Ball (1997) argues t h a t oftentimes teachers are afraid of w h a t parents and administrators will t h i n k in regard to a curriculum innovation and therefore must defend things t h e y are trying even before t h e y themselves feel convinced or selfi confident It is therefore risky and burdensome to be a reformer because the system itself does not encourage innovation and change but rather a "stable and harmonious classroom" (Sullivan, 1989, p 15) In the r e a l i t y of today's school climate, students resist unfamiliar approaches, administrators not provide adequate support either in professional training or in resource materials and t h e y dislike less orderly classrooms As well, curriculum guidelines suggest content coverage and pacing rather than teaching for understanding (Ball, 1997) In the past several decades, mathematics was the subject w i t h the h i g h e s t number of fleeting innovation attempts It is this reality, hanging on teachers' minds, t h a t causes many teachers to fi'own (Blane, 1990) To add to this scepticism, many reform documents are presented as "panaceas," "chimeras," and "cures" (Dengate, 1999; Fleener, Westbrook, & Rogers, 1995; Wilson, 1990) Clements (1995) and Clements and Ellerton (1996) complain t h a t in the last three decades teachers have been swamped w i t h magical instructional recipes such as Cuisenaire rods, the New Math, mastery learning, problem solving, applicable mathematics, metacognition, and more recently outcomes based education Many of these innovations represent large scale changes t h a t were poorly defined in operational terms and without positive gains in student learning (Hall & Loucks, 1978) Hence, it is important t h a t teachers believe t h a t any new innovation is workable and l i k e l y to enhance student learning (Martin, 1993b) Traditional mathematics teaching is easier than attempting more progressive approaches (Skemp, 1978) as innovations bring additional burdens to teachers, despite the merits and advances t h a t each innovation might potentially bring Teachers' difficulties in adopting innovations in mathematics education have been reported in the use of Cuisenaire rods (Hassall, 1986), t h e New Math(s) (Clements & Ellerton, 1996), mastery learning (Herrington & Wolf, 1985), teaching in themes (Clements, 1987; Henderson & Landesman, 1995), teaching for problem solving (Hembree & Marsh, 1993; Schroeder & Lester, 1989), teaching metacognitive skills (Schoenfeld, 1992) and outcomes based education (Clements & Thomas, 1996) Case Studies of the Mismatch between Beliefs and Curriculum Innovations Besides the N e w M a t h , other major failing reforms in the 1960s included attempts to use "different number bases to help young people understand t h e i r own base ten systems of numeration Instead of using it to develop such understanding, teachers were demanding proficiency in multiplying and dividing w i t h base six" (Price, 1995, p 488) The 1960s also saw curricular emphasis on applied mathematics in order to show students the power and usefulness of mathematics, and as a channel to bring mathematics to the masses (Clements, 1987) As Burkhardt, Fraser, and Ridgway (1990, p 4) noted: "In the outcome, this aspect is barely visible in the classrooms in which tile resultant materials were used, where 'practical situations' were entered, if at all, as another sort of 64 Handal & He~rington m a t h e m a t i c a l content." S e v e r a l recent cases showing a m i s m a t c h between teachers' beliefs and t h e beliefs underlying p a r t i c u l a r curricular innovations h a v e been documented Brew, Rowley, and Leder (1996) i n t e r v i e w e d 40 t e a c h e r s on t h e i r perceptions of t h e i m p l e m e n t a t i o n of the Victorian C e r t i f i c a t e o f Education (VCE), a curriculum t h a t r e l i e d h e a v i l y on i n v e s t i g a t i v e work The authors found t h a t a number of teachers h e l d contradictory beliefs to t h e reform and some t e a c h e r s were finding difficulties w h i l e o t h e r t e a c h e r s were just paying lip service to t h e curriculum goals but not implementing them Among the m i t i g a t i n g factors accounting for these b e h a v i o m s were h e a v y work loads, lack of training, and t h e pressure on content coverage In a r e l a t e d study, Martin (1993a) reported t e a c h e r s ' concerns about t h e i m p l e m e n t a t i o n of the VCE indicating the need for g r e a t e r professional d e v e l o p m e n t on course content and assessment B u z e i k a (1996) i n t e r v i e w e d t h r e e Auckland p r i m a r y teachers in regard to t h e M a t h e m a H c s in the N e w Z e a l a n d Curriculum, w h i c h e m p h a s i s e d constructivist practices, and found t h a t t h e p a r t i c i p a n t s h a d personal concerns about the curriculum being implemented Among these concerns, teachers felt t h a t t h e curriculum was vague and unstructured Teachers h a d difficulties in i d e n t i f y i n g t h e m a t h e m a t i c a l content l e a r n e d by students w i t h i n a p a r t i c u l a r strand At t h e same time teachers l a c k e d k n o w l e d g e about some topics and terminology used in t h e curriculum Furthermore, teachers h a d "difficulties in m a i n t a i n i n g control over w h a t was h a p p e n i n g i f children were left to explore an i d e a for t h e m s e l v e s " (p 97) F r y k h o l m (1995) i n v e s t i g a t e d m a t h e m a t i c s teachers' beliefs of 44 prese[wice m a t h e m a t i c s teachers t h r o u g h o u t a t w o y e a r s t u d y in order to determine teachers' adherence to the reforms p o s t u l a t e d in the CuIriculum and E v a l u a t i o n Standards for School M a t h e m a t i c s ( N a t i o n a l Council of Teachers of M a t h e m a t i c s , 1989) A l t h o u g h most p a r t i c i p a n t s agreed w i t h the principles s t i p u l a t e d in the S t a n d a r d s and s t a t e d t h a t t h e y were a c t u a l l y implementing them, t h e y were unable to implement them due to t h e i r p e r c e i v e d lack of training in the principles underpinning t h e reform P a r t i c i p a n t s felt pressurised w i t h i n t h e i r t e a c h i n g education programs to accomplish those principles Some p a r t i c i p a n t s r e v e a l e d t h a t t h e S t a n d a r d s were "not as p r a c t i c a l as t h e y were m a d e out to be, e s p e c i a l l y in dealing w i t h t h e structure of most schools short periods, no collaboration, no team teaching" ( F c f k h o l m , 1995, p 14) as w e l l as rigid d e p a r t m e n t a l policies, lack of support from cooperating teachers, and textbooks Sowell and Zambo (1997) p r o v i d e d evidence of the lack of alignment between t h e S t a n d a r d s ' reform goals and teachers' strategies The authors found t h a t t h e use of official guidelines, competency based examinations, and school textbooks were insufficient in providing the k n o w l e d g e and incentives for teachers to m o d i f y t h e i r teaching In particular, t h e authors found t h a t teachers w h o h e l d conceptions of t e a c h i n g based on transmission were u n l i k e l y to align to the goals of t h e S t a n d a r d s and t h e r e f o r e continued to t e a c h t r a d i t i o n a l l y Likewise, Konting (1998) reported a substantial m i s m a t c h between t h e principles of good practice prescribed by an i n n o v a t i v e m a t h e m a t i c s curriculum in M a l a y s i a and t h e t e a c h i n g practices of teachers w h o were previously i d e n t i f i e d as e f f e c t i v e Mathematics Teachers' Beliefs and Curriculum Reform 65 practitioners W a t t s (1991, cited in S c h w a r t z & Riedesel, 1994), studied 36 inse~wice teachers' beliefs about t h e S t a n d a r d s The researcher found t h a t only four of t h e respondents h e l d a perspective congruent w i t h t h e principles of problem solving outlined in the S t a n d a r d s According to S c h w a r t z and Riedesel (1994): The respondents' agreement that mathematics education should focus on problem solving evidently reflected their explicit belief However, their underlying meaning for problem solving indicated their implicit beliefs The difference between explicit and implicit beliefs resulted in apparent agreement with reformers about the need for problem solving, but in actual disagreement with reformers about what that meant (p 10) O t h e r recent examples of conflicting views and demands in t h e i m p l e m e n t a t i o n of educational reform in m a t h e m a t i c s h a v e been documented by Anderson and P i a z z a (1996), Desforges and Cockburn (1987), Moreira and Noss (1995) and Wilson (1990) It can be argued t h e r e f o r e t h a t policy m a k e r s and implementers h a v e l a r g e l y neglected m a t h e m a t i c s teachers' beliefs in t h e process of reform and the training process t h a t all i n n o v a t i v e enterprise should t a k e into account in order to prevent confusion and anxiety In this respect, it is n o t e w o r t h y to acknowledge t h e lack of r e l e v a n t training t h a t accompanies m a n y innovations in m a t h e m a t i c s education (Stephen & Varble, 1995) Many t e a c h e r s feel sceptical about innovation as t h e y h a v e not been p r o p e r l y informed of t h e t e c h n i c a l i t i e s i n v o l v e d or given the support t h a t is necessary H a s s a l l (1986), for example, reports cases of confused teachers reluctant to ask questions to curriculum implementers for fear of being l a b e l e d as incompetent Conclusion Successful curriculum change is more l i k e l y to occur w h e n the curricular reform goals relating to teachers' practice t a k e account of teachers' beliefs Argyris (1978, 1993) refers to this as a ' t h e o r y of action' making a distinction between an i n d i v i d u a l ' s espoused t h e o r y and his o r h e r t h e o r y in use ( w h a t t h e y a c t u a l l y do) For Argyris, this b e h a v i o u r can be in conflict not only at t h e personal but also at the o r g a n i s a t i o n a l level This tension can be addressed through honest consultation, looking beyond the symptoms, self reflection and a t i m p r o v e d communication w i t h i n t h e organisalion itself The times of t h e w e l l p o l i s h e d , ' t e a c h e r p r o o f ' curricular documents are gone Policy m a k e r s should no longer assume t h a t curriculum i m p l e m e n t a t i o n is a process t h a t t r a n s l a t e s d i r e c t l y into the classroom r e a l i t y Teachers are t h o s e w h o u l t i m a t e l y decide the fate of any educational enterprise Consequently, teachers' attitudes, feelings, and perceptions must be recognised well before t h e launching of any innovation L i k e l y discrepancies between teachers' opinions and t h e ideas underpinning a curriculum innovation need to be i d e n t i f i e d , a n a l y s e d , and addressed The current trends in m a t h e m a t i c s education towards constructivist learning environments and assessment of learning based on demonstrable outcomes w i l l only succeed i f teachers' beliefs about these reforms are considered and confronted O t h e r w i s e , teachers w i l l m a i n t a i n t h e i r h i d d e n agendas in t h e p r i v a c y of t h e i r classrooms and t h e i m p l 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' beliefs about t h e intended, t h e implemented, and t h e a t t a i n e d curriculum Curriculum Change and Mathematics Teachers' Beliefs If an i m p l e m e n t e d curriculum is a set of beliefs