Alan J. Bishop

Monash University (Australia), Melbourne, Victoria, Australia

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Publications (30)0.55 Total impact

  • 01/2010: pages pp. 179 – 194;
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    ABSTRACT: This chapter argues that school mathematics involves more than just the “performance” of students and that “working mathematically” means far more than being good at a specified set of skills, as well as more than being able to show mastery of various conceptual structures. It suggests that experienced teachers understand that the wellbeing of many students can diminish when they are asked to engage with mathematics learning. Underlying such engagement and hence mathematical performance is a command of a specific language that holds the conceptualizing process together. Moreover, of particular importance for this chapter are the values, and their language, that are embedded within mathematics and its pedagogy and how they can be invoked to enable better engagement, improved student wellbeing and consequently better performance.
    12/2009: pages 111-135;
  • Alan J. Bishop
    Journal of Mathematics Teacher Education 01/2009; 12(4):305-310.
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    Alan J. Bishop
    01/2008;
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    Alan J. Bishop
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    ABSTRACT: The paper discusses assisting teachers to nurture mathematical thinking in their students by using findings from research on mathematical values. The author begins by sharing three theoretical perspectives on how mathematical thinking develops in a student from Lancy (1989), Billett (1998), and Bishop (1988). Using White"s (1959) three component analysis of culture, the author presents 6 mathematical values which are important to the development of Mathematics, and thus underpinning the development of mathematical thinking in the classroom. An exploratory Values and Mathematics Project (VAMP) shows that teachers found it difficult to discuss values they held about Mathematics education in relation to Mathematics. The introduction of some of the theoretical terminology helped teachers to discuss their teaching. In conclusion, the author proposes some implications for practice and policy.
    01/2008;
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    Alan J. Bishop
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    ABSTRACT: This paper raises issues concerning the teaching of values in the context of mathematics education. It argues that a focus on education for democracy inevitably involves educating about values. It reviews the major relevant research and theoretical perspectives and argues for more research attention to be paid to this area. Although there has been relevant research done in the affective domain, both in general and in relation to mathematics, and in social and cultural issues, there is little direct research focus on either values or valuing. Teachers are rarely aware of teaching values either explicitly or implicitly, yet values teaching clearly does take place, mostly implicitly. If there are desires to change the directions of mathematics teaching to be more attuned to life in modern democratic societies then this aspect of mathematics education needs to be better understood in order that it can be better taught.
    12/2007: pages 231-238;
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    ABSTRACT: This article arises from a study whose overall purpose was to investigate the relationship between Colombian mathematics teachers’ conceptions of beginning algebra and their conceptions of their own teaching practices. The teachers’ understandings of their teaching practices were explored with a view to unravelling their conceptions of change in their teaching. Focusing on the perspectives of teachers afforded opportunities that exposed the powerful role that the teachers’ conceptions of social/institutional factors of teaching played in their conceptions of their practices. The degree to which the teachers attributed these (external) factors as crucial reasons for what they do in their teaching was the basis of a categorisation of their conceptions of the crucial determinants of their teaching practices into three types. The findings are particularly relevant to our understanding of the stability of mathematics teaching approaches in the Colombian context but have likely implications for a range of international education contexts. Specific implications for the development of the research into teachers’ conceptions of mathematics and its teaching, and for teacher education programmes are presented.
    Journal of Mathematics Teacher Education 01/2007; 10(2):69-93.
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    Zhongjun Cao, Alan Bishop, Helen Forgasz
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    ABSTRACT: This paper explores the perceived parental influence (PPI) on mathematics learning among over 700 students across three year levels (Years 5, 7, 9) in China and Australia. It was found that the PPI of students was less strong as year levels increased in both countries. Students in China had stronger perceived parental encouragement and higher perceived parental educational expectation than students in Australia. The PPI of students from different home language backgrounds was also investigated. Students in China demonstrated stronger perceived parental encouragement and parental expectation than English speaking students and other language speaking students in Australia, and they also demonstrated stronger perceived parental expectation than Chinese speaking students in Australia, and similar perceived parental encouragement. Within the three groups of students in Australia, Chinese speaking students and other language speaking students demonstrated similar levels of perceived parental encouragement and expectation, but they both demonstrated a higher level of perceived parental encouragement and expectation than English speaking students. Possible reasons for the similarities and differences between the different groups of students were discussed.
    Educational Studies in Mathematics 01/2007; 64(1):85-106. · 0.55 Impact Factor
  • Zhongjun Cao, Helen Forgasz, Alan Bishop
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    ABSTRACT: International studies represent one important aspect of the phenomenon of the internationalization and globalization of mathematics education and have attracted the interest of many organizations and researchers. There are challenges and difficulties in conducting surveys in different cultural settings which have not been well documented in the mathematics education literature. This chapter accounts for some of the challenges and difficulties involved in selecting a survey topic, designing the survey, and administering it as occurred in a recently conducted study exploring students’ attitudes towards mathematics in China and Australia. It is suggested that awareness of cultural differences is a key issue that researchers should pay attention to when conducting cross-cultural research in mathematics education
    12/2006: pages 303-320;
  • Wee Tiong Seah, Alan J. Bishop
    12/2005: pages 523-535;
  • Zhongjun Cao, Wee Seah, Alan Bishop
    12/2005: pages 483-493;
  • Alan Bishop, Wee Tiong Seah, Chien Chin
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    ABSTRACT: Values are at the heart of teaching any subject, but are rarely explicitly addressed in the mathematics teaching literature. In particular, research on values in mathematics education is sadly neglected. This chapter addresses these gaps by drawing together the various research and theoretical fields that bear upon the values dimension of mathematics education. It begins with a theoretical reflection on the distinctions between values, beliefs and attitudes, and continues with reviewing the literature relating teachers' values to their decisions and actions in the classroom. Moving to the limited research on values in mathematics education, there is discussion of values in the increasingly researched area of socio-cultural aspects of mathematics education. The second half of the chapter is devoted to issues regarding research approaches to studying values in our field, and presents two projects, one based in Monash University, Australia and the other at the National Taiwan Normal University in Taipei. The first project focused on the relationship between teachers' intended and implemented values, and the second explored teachers' values as constituting their pedagogical identities. Implications of this research for teachers' professional development are drawn, and the chapter finishes by outlining the research difficulties inherent in this area, and offers a set of challenges designed to carry the research agenda forward.
    01/2003;
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    01/2001;
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    ABSTRACT: 1. Teachers' decisions and values Imagine that you are a Grade 4 mathematics teacher. It is the first day back after the Christmas holiday, and you are talking with your class before getting down to work. You ask if anyone had any 'mathematical' presents. One boy says that he had been given a mathematical game from his uncle's country. He says it is very interesting, it has many variations, and he asks if he can show the class how it is played. What would you do? Would you let him show the class and see what develops? Would you say something like: "Well that would be nice, but we don't have time now to do it, maybe later" or maybe: "Excellent, show me after the class, and I'll decide then if we can play it." Are mathematical games a part of your teaching ideas? Would this game fit within your curriculum? Does that matter? In any case, you would probably make your choice in the way that you normally do, and not think much more about it. But the fact remains that you must make a choice, and that choice depends on your values.
    In W. Horng & F Lin (Eds.), History in Mathematics Education: Challenges for a new millennium (pp. 147-154)., Taipei, Taiwan: National Taiwan Normal University.; 08/2000
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    ABSTRACT: Values are taught in every lesson. However in mathematics classes this seems to be implicit rather than explicit. This paper outlines methodological difficulties encountered in researching the values teachers teach. One crucial area that has emerged is finding a common language with which meaningful dialogue can occur. We also reflect on differences, due to the different cultures, that have emerged between this Australian project, and a parallel project in Taiwan, including the influence of personal value systems. Why research values? Values in mathematics education are the deep affective qualities which education aims to foster through the school subject of mathematics (Bishop, FitzSimons, Seah, & Clarkson, 1999). They are a crucial component of the classrooms affective environment. Although values teaching and learning inevitably happen in all mathematics classrooms, the teaching of values appears to be mostly implicit. Thus it is likely that teachers have only a limited understanding of what values are being taught and encouraged. Values are rarely considered in any discussions about mathematics teaching. A casual question to teachers about the values they are teaching in mathematics lessons often produces an answer to the effect that they do not believe they are teaching any values. This widespread belief that mathematics is the most value-free of all school subjects (Bishop, 1988) is not just held by teachers, but is also strong among parents, university mathematicians and employers (Ellerton & Clements, 1989). However mathematics is just as much human and cultural knowledge as is any other field of knowledge, and adults certainly express feelings, beliefs and values about mathematics which clearly relate to the mathematics teaching they experienced at school (Brew, 1999; FitzSimons, 1994). Hence it is clear that values teaching and learning does go on in mathematics classes, as it does in all classrooms. Furthermore we believe that the quality of mathematics teaching would be improved if we understood more about this phenomenon.
    01/2000;
  • Paper presented at the annual conference of Australian Association of Research for Education.; 01/2000
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    ABSTRACT: Values in mathematics education are those deep, affective qualities which education aims to foster through the school subject of mathematics and are a crucial component of the classroom affective environment. As a result of demands that students become more economically oriented and globally conscious, mathematics educators are being challenged as to which values should be developed through mathematics education. The concern is that, although values teaching and learning inevitably happen in all mathematics classrooms, they appear to be mostly implicit. Thus, it is likely that teachers have only limited understanding of what values are being taught and encouraged. The new questions asked include: (a) What are teachers' understandings of their own intended and implemented values? (b) To what extent can mathematics teachers gain control over their own values teaching? and (c) Is it possible to increase the possibilities for more effective mathematics teaching through values education of teachers and teachers in training? In order to begin to answer these questions, the authors theorize values teaching in mathematics. In this paper the authors analyze three interrelated sources of values which permeate mathematics classrooms: general educational, mathematical, and specifically mathematics educational. The authors also analyze the various influences on teachers' values with regard to explicit and implicit values teaching through an adaptation of Billett's (1998) framework for the genesis of social knowledge. (Contains 64 references.) (Author/ASK)
    01/1999;
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    Wee Tiong Seah, Alan J. Bishop
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    ABSTRACT: Provision of general education, including mathematics education, in Southeast Asia over the last thirty to forty years have been instrumental in creating economic wealth and maintaining socio-politico stability in the region. (The mainly cognitive) developments in mathematics education have opened many windows of knowledge, and equipped many with the latest scientific/technological know-how. The region's entry into the new millennium is, however, one accompanied by tremendous economic, technological and social changes and challenges. Mathematics education's response in the region should then also include the realization of system intentions of balancing cognitive and affective developments. Indonesia's 'Panca Sila', Malaysia's 'Rukunegara' and 'Nilai-Nilai Murni', as well as Singapore's 'Shared Values' and 'Desirable Outcomes of Education' are examples of governmental desires to instill values through school subjects. Specific mathematics curricula also promote values education. But values education in mathematics teaching has always been ongoing. Values in the mathematics classrooms - mathematical, mathematics educational, and general educational - are situated in the contexts of institutional, epistemological and societal values. There are implications for certain Western values in the Asian societies. Thus, the nature and pervasiveness of values transmission need to be investigated and made more explicit. This is crucial for the continual optimization of mathematics teaching/learning, and in contributing towards developing the citizen in a pupil.
    01/1999;
  • Alan Bishop
    Mathematics Education Research Journal 01/1999; 10(3):76-83.
  • Bishop A., Clarkson P.C.
    Melbourne: Mathematics Association of Victoria conference; 01/1998