In the past decade counterpoising the individualistic voice of developmental psychology a new voice has been heard in mathematics education. This is the voice of sociology and associated social theories. Although a social strand has long been present in mathematics education in such seminal works as Griffiths and Howson , deep applications of sociological theory are as yet rare.

Sociology concerns not only individuals and groups and their patterns of inter-relationships. Modern sociology also weaves knowledge and social practice into a complex whole. Until the last decade, studies which recognized this complex character were virtually non-existent in mathematics education. Likewise, the multiculturalist and ethnomathematical movements offered valuable social insights for mathematics teaching, and have become widely endorsed vehicles for the reform of mathematics education.

But all too often they have been offered uncritically or as under-theorized perspectives. Up to the present day there remains a dearth of fully worked out sociological approaches to mathematics education able to supply the missing theoretical perspectives and critique. Ernest, P.

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Firstly, because such addition would practically make it impossible to include those fields in the curricula, due to the unbearable extra load they would represent. A second guiding principle of this research program relates to the fact that in it we are not conceiving the philosophy, history, and sociology of mathematics education as simply a mechanical juxtaposition of themes or problems extracted from the fields of philosophy, history, and sociology of education with other themes produced inside the fields of philosophy, history, and sociology of mathematics.

That is because we believe that the objects and problems upon which both the pedagogical investigation and the pedagogical action in the domain of mathematics education focus are not restricted to those customarily belonging to the fields of history of mathematics , philosophy of mathematics , and sociology of mathematics , neither are they of the same nature, or possess the same pedagogical relevance.

That is because it is unlikely that a conception of such nature would produce more than a compartmentalized, disarticulated and little effective composition of philosophical choices extracted from those two fields. Besides, such composition would not be clarifying, and it would be of little use to face the problems that challenge the mathematics teacher. On one hand, the shortcomings we see in taking the problems that have been constituted in the fields of philosophy, history, and sociology of mathematics as the research backbone of the fields of philosophy, history, and sociology of mathematics education are of at least two orders.

First, the movements around the fields of philosophy, history, and sociology of education, in their recent histories, have chosen as their almost exclusive objects of analysis and reflection the mathematical activities and culture of professional mathematicians, thereby ignoring, because of lack of interest, knowledge, or for prejudice, other forms of mathematical activity and culture that have been produced in various social practices carried out in institutional contexts other than the academic-scientific. Second, in the context of that manner of conceiving and doing the history, philosophy, and sociology of mathematics, the knowledges produced and the different conceptions of mathematics that were revealed were not constituted based on the problems and concerns attending the mathematical activity that is carried out in the exercise of different social practices and, above all, in those carried out in the school institution.

On the other hand, the shortcomings we see in taking the problems that were constituted inside the domains of the history, philosophy, and sociology of education as the research backbones of the fields of philosophy, history, and sociology of mathematics education are also of at least two different orders, analogous to the previous ones. The third guiding principle of our program proposes that the object upon which investigations should focus in these fields should be the mathematics education that has been carried out at schools, that is, under the particular conditions of the school institution.

This principle, to be fully understood, as we want it to be, deserves a few clarifications. It suggests, first of all, that the object upon which the investigations in these fields should focus should be neither the generic and abstract concepts of mathematical knowledge or of mathematical culture , nor the more delimited concepts of school mathematics or of school mathematical culture , but that of school mathematics education.

Even if talking about school mathematics education instead of about school mathematics is an option, such option is not, in our view, a mere terminological choice without greater consequences. Would social practices producing mathematical culture be incommensurate with social practices producing an educative culture related to mathematical culture? We already had opportunity to consider the wider issue of the project of disciplinarization of educative practices related to mathematical culture in Miguel et al.

Schubring , p. It is important to avoid such assumption because it takes us ineluctably to the inadmissible establishment of a hierarchy between invention and transmission, and then causes us to see research as a noble, original, and indispensable activity, and teaching as a secondary activity, whose exercise does not require the same degree of talent, imagination, and education.

But, on the other hand, we must admit that the mathematical activity does not take place or manifest itself solely in one social practice, namely, that in which its promoters put consciously before themselves the task of producing mathematical culture. We can then say that, apart from a specific and particular culture intentionally produced and absolutely necessary for a social practice to be conducted and survive, the communities that conduct it also incorporate, in a re-signifying and institutionally conditioned way, cultures produced in the exercise of other social practices, and end up also producing an educational culture of survival , cultures that, although not perceived as just as important as those intentionally produced when carrying out the reference social practice, are also absolutely necessary for the reference social practice to take place, survive, and fulfill its social purposes.

Our viewpoint is endorsed by Belhoste when he says that even if mathematicians, in their vast majority, are teachers nowadays, given that their activities take place within a university or school context, and even if the public opinion sees mathematics essentially as a school discipline, mathematicians do not see themselves that way. For them, the research activity is the defining element of their professional identity, and teaching mathematics is not seen as an activity sufficient to make a mathematician; for that, one would still, and above all, have to produce mathematical results Belhoste, , p.

Yet, proceeds Belhoste, such representation mathematicians make of their own identities is quite recent, harking back to the late 19th century. So, even if today mathematicians and mathematics educators increasingly constitute two practice communities with different aims, both in the research domain, and in pedagogical action, these communities should not be seen as radically distinct, considering that they not only share at least some objectives, but also carry out activities that are mutually influencing.

Still, such influence may not be immediate, and its nature is not of a passive subordination of one of them to the other; besides, both activities are also conditioned by other activities in the same way that they influence other social practices. In this sense, in the controversy he established with Chevallard , Chervel defended, rightly in our opinion, the epistemological and methodological viewpoint partly contrary to the one that guided the former author that school disciplines are not reflex, vulgarization or pure and simple adaptation of knowledges produced by the sciences of reference.

Alternatively, Chervel then stated that the concept that in his opinion should be put in the center of a reflection about school culture should not be the concept of knowledge , but that of discipline , or even better, that of school discipline or of teaching discipline Chervel, , p.

My studies do not reveal at all the existence of a social group independent from the school, whose function would be that of transforming the scholarly knowledge into knowledge that can be taught. Chervel, , p. On the other hand, this point of view warns us against the danger of identifying the concept of knowledge with that of teaching contents. Indeed, according to Chervel, if the teaching contents, even when understood as cultural contents, cannot be seen as proper knowledges, then school, even if it should be seen as an autonomous locus of cultural production, would not be, strictly speaking, a locus for the production of knowledge.

But the third guiding principle of our research program requires still a second type of clarification. When we propose to replace the concept of school mathematics with that of school mathematics education , the adjective school that qualifies the expression mathematics education is not a simple detail. It not just contextualizes the mathematics education that we wish to consider as object of historical, philosophical, and sociological investigation; more than that, it institutionalizes it. To better understand this point, we must say a few words about the way in which we understand here the sociological concept of institution.

An institution for us is any dynamic and mutable collection of norms socially instituted with the purpose of organizing in a given way the social relations of the members of practice communities which, under the influence of those norms, carry out actions in various places or environments. Thus, for instance, when we refer to IBM, or to science, or still to catholic religion as institutions we are, strictly speaking, referring to the collection, explicit or implicit, of norms that at each given moment organizes, controls, and conditions the interpersonal relations of any nature, as well as the personal modes of thinking and acting of the members of practice communities that have submitted to those norms, independent of the locus or physical space where they are acting or thinking 7.

But it also stops us from imagining a historical moment in which mathematical culture would have existed under a state of institutional emptiness.

According to this viewpoint, mathematical culture is then seen as each and every normative and public system of signals produced through the mathematical activity conducted by different practice communities, and not just by the community of professional mathematicians. However, the mathematical activity producer of mathematical culture is not conceived as a type of activity carried out and conditioned just by a given type or by a unique collection of institutional norms, nor is it seen, alternatively, as an activity that would not be subjected to any kind of institutional conditionings.

Thus, mathematical culture is no longer seen in a uniform manner, that is, as carrying characteristics, properties, and purposes always universal, fixed, good, and noble. This means that the mathematical activity ends up, almost always uncritically, incorporating and retransmitting the guiding interests and values of the political purposes of the social groups that finance the constitution and functioning of the social institutions in which such activity takes place.

Obviously, this sociological point of view on the mathematical activity has immediate repercussions in the sphere of school mathematics education. Cooper, B. Gates Ed. London: Open University Press. Davies, B. Bernstein on classrooms. Atkinson, B. Delamont Eds. Dowling, P. Discursive saturation and school mathematics texts: A strand from a language of description.

### Table of contents

Ernest Ed , Mathematics, education and philosophy: An international perspective pp. Ensor, P. A study of the recontextualising of pedagogic practices from a South African University preservice mathematics teacher education course by seven beginning secondary mathematics teachers. Heath, S. Questioning at home and at school: A comparative study. Spindler Ed. Ways with words: Language, life and work in communities and classrooms.

Cambridge, UK: University of Cambridge. Holland, J. Social class and changes in the orientations to meanings. Sociology , 15 1 , 1— CrossRef Google Scholar.

Lerman, S. Why childrenfail and what mathematics education studies can do about it. Cotton Eds. Lubienski, S. Problem solving as a means towards mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education , 31 4 , — Means, B. Cognitiveapproaches to teachingadvancedskills to educationally disadvantaged students.

Delta Phi Kappan , 73 ,— Elementary teachers' learning to construct high-quality mathematics lesson plans: A use of the IES recommendations. Doganay, A. The measurement of students' achievement in teaching primary school fifth year mathematics classes. Etxeberria, J. Computer-assisted learning in mathematics. Fendrichsalowey, G. Mathematics, quantitative and attitudinal measures for elementary-school boys and girls.

Psychological Reports, 51 1 , — Fernandez, C. Mathematics teacher learning in virtual learning environments. Fischer, U. Interventions supporting children's mathematics school success: A meta-analytic review. European Psychologist, 18 2 , 89— Fisher, C. Freeman, B. Creating a middle school mathematics curriculum for English-language learners. Remedial and Special Education, 29 1 , 9— Garii, B. Integrating social justice with mathematics and science: An analysis of student teacher lessons.

Teaching and Teacher Education, 25 3 , — Geiger, V. Taking advantage of incidental school events to engage with the applications of mathematics: The case of surviving the reconstruction. Stillman, G. Kaiser, W. Brown Eds. Netherlands: Springer. Gerena, L. Gersten, R. Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79 3 , — Giacardi, L.

From Euclid as textbook to the Giovanni gentile reform : Problems, methods and debates in mathematics teaching in Italy. Gibbs, B. Reversing fortunes or content change? Gender gaps in math-related skill throughout childhood. Social Science Research, 39 4 , — Goforth, K. Understanding mathematics achievement: An analysis of the effects of student and family factors.

Educational Studies, 40 2 , — Gottfried, A. Multivariate latent change modeling of developmental decline in academic intrinsic math motivation and achievement: Childhood through adolescence. International Journal of Behavioral Development, 31 4 , — Gregg, J.

Discipline, control, and the school mathematics tradition. Teaching and Teacher Education, 11 6 , — Advancing African-American, urban youth in mathematics: Unpacking the success of one math department. American Journal of Education, 1 , 63— Gutierrez, R. American Educational Research Journal, 39 4 , — Hansen-Thomas, H.

Reform-oriented mathematics in three 6th grade classes: How teachers draw in ELLs to academic discourse. Journal of Language Identity and Education, 8 2—3 , 88— Harcum, P. Case study: Comprehensive teaching of a twelve-year-old mathematics-phobic ed-Mr Boy. Journal of Human Behavior and Learning, 6 1 , 39— Helmane, I. Aspects of thematic choice within the mathematics based on thematic approach in primary school.

Proceedings of the International Scientifical Conference pp. Rezekne: Rezeknes Augstskola. Thematic approach of mathematics textbooks in the primary school. Proceedings fo the International Scientifical Conference Vol. Henderson, R. Effects of thematically integrated mathematics instruction on students of Mexican descent. Journal of Educational Research, 88 5 , — Hess, R. Maternal variables as predictors of childrens' school readiness and later achievement in vocabulary and mathematics in 6th grade.

Child Development, 55 5 , — The nature and effects of middle school mathematics teacher learning experiences.

## Philosophical Dimensions in Mathematics Education. (eBook, ) [jyhoxafi.cf]

Teachers College Record, 1 , — Journal for Research in Mathematics Education, 35 5 , — Teachers' mathematics knowledge for teaching and school context - A study of California teachers. Educational Policy, 21 5 , — Hopkins, M. Infrastructure redesign and instructional reform in mathematics: Formal structure and teacher leadership. Elementary School Journal, 2 , — Howley, A. Standards-based reform of mathematics education in rural high schools. Journal of Research in Rural Education, 22 2 , 1— Hughes, G. Facilitating the development of preservice teachers in a climate of reform: Lessons learned from mathematics and assessment reform.

Journal of Negro Education, 68 3 , — Jackson, K. Supporting African American students' learning of mathematics: A problem of practice. Urban Education, 47 2 , — Jang, S. Exploring the TPACK of Taiwanese elementary mathematics and science teachers with respect to use of interactive whiteboards. Jeschke, S.

Work in progress - Engineering math with early bird. Johnson, W. Teaching with speeches: A black teacher who uses the mathematics classroom to prepare students for life. Teachers College Record, 2 , 1— Kajetanowicz, P. Combining various technologies in effective online math instruction - A nationwide secondary level math project.

Katmada, A. Game based learning in mathematics: Teachers' support by a flexible tool. Ke, F. Computer-game-based tutoring of mathematics. An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing. Kilic, H. The nature of preservice mathematics teachers' knowledge of students. Kiray, S. The effectiveness of an integrated science and mathematics programme: Science-centred mathematics-assisted integration.

Koirala, H. Measuring the effectiveness of a performance-based assessment used in a secondary mathematics teacher preparation program. Kawasaki Eds. Konovalova, K.

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An approach to ordering the subject matter of a college level course of higher mathematics. Koustourakis, G. Changes in school mathematics knowledge in Greece: A Bernsteinian analysis. British Journal of Sociology of Education, 32 3 , — Krainer, K. How can schools put mathematics in their centre? Novotna, H. Moraova, M. Stehlikova Eds. Krause, S. High school teacher change, strategies, and actions in a professional development project connecting mathematics, science, and engineering.

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## Philosophical dimensions in mathematics education /

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