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Social inequalities in mathematics from a socialization theoretical point of view – Analysis of problem-solving
processes of students
Belgüzar Kara, Bärbel Barzel
To cite this version:
Belgüzar Kara, Bärbel Barzel. Social inequalities in mathematics from a socialization theoretical point of view – Analysis of problem-solving processes of students. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands.
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Social inequalities in mathematics from a socialization theoretical point of view – Analysis of problem-solving processes of students
Belgüzar Kara1, Bärbel Barzel2
1University of Duisburg-Essen, Germany; [email protected]
2University of Duisburg-Essen, Germany; [email protected] Keywords: Problem-solving, diversity, inequality, habitus
Theoretical background
In the recent German school curriculum, mathematical problem solving is anchored obligatorily as an important competence for mathematics learning. Since 2008, competence expectations for problem solving have explicitly indicated what the pupils are supposed to have acquired at the end of grade 4 (Ministerium für Schule und Weiterbildung des Landes Nordrhein-Westfalen, 2008). But empirical research results indicate that the demands can generate inequalities with regard to social origin (Cooper & Dunne, 2000; Lubienski, 2000). Achievement studies confirm the impact of socio-economic status on mathematic achievement (Stubbe, Schwippert, & Wendt, 2016). Research in mathematics education on social inequalities in the acquisition of mathematical competences observes different achievement in dealing with problem solving tasks specific to social class (Cooper & Dunne, 2000; Piel & Schuchart 2014). The study by Lubienski (2000) shows differences between students with different socioeconomic status (SES) dealing with problem-centered materials. The analyses show, for example, that,
In general, lower-SES students focused more on giving the right answer to a question (...), whereas higher-SES students were more inclined to discuss a method or an idea. (...) lower-SES students were more likely to use language in “common-sense” reasoning that was closely tied to the context of the problems. (...) Higher-SES students were more likely to contribute in relation to abstract, strictly mathematical contexts and to use generalized language and reasoning. (p.
369)
Based on the theories of Bourdieu (1987) and the research work of Lareau (2011), in the study presented here, the problem-solving process is analyzed from a perspective of socialization. The theory of habitus (Bourdieu, 1987) is used as an analytical tool for the mediation between the individual problem-solving process and the structural conditions of the social background. Lareau (2011) identified two milieu-specific child-rearing approaches and characteristic practices associated with the two educational styles: Middle-class families concerted child rearing on cultivation, working-class families concerted child rearing on accomplishment of natural growth. In particular, Lareau (2011) describes the two approaches as differently beneficial learning environments and socialization conditions for school practice. For example, while the discussion and argumentation between child and parents is an essential feature in the child-rearing approach of concerted cultivation of the middle classes, the child-rearing approach of accomplishment of natural growth of the working class is characterized by direct instructions. If the characteristics of child- rearing approaches are considered in competence expectations and the inherent structure of
problem-solving, origin-related differences in competence development can be expected through habitual dispositions. The danger that mathematical competence expectations have undesired impacts for less privileged students, which in turn can have the consequence that accessibility to mathematical contexts and the intended learning processes become more difficult or blocked, is subject of this investigation.
Design and methods of the study
The praxeological approach theory establishes dialectical relationship between objective structures and structured dispositions of the acting actors and serves as the epistemological fundamentals for the investigation. A mathematics performance test and student and parent questionnaires were used to select and classify pupils according to mathematical achievement level and social background.
Data was then collected within the framework of individual clinical interviews during the processing of a total of three mathematical problem-solving tasks to get an insight into possible differences in the process.
Results
The preliminary analysis according to the phases model of Schoenfeld (1985) gives an indication of milieu-specific ways of acting through the phenomenon of the abridged analysis and exploration of mathematical problem-solving tasks of students from families of less privileged origin. The focus on a direct approach like one-word-answers without complete comprehension of the task has so far only been observed in students of less privileged origin. The correct answer seems to be more important than the understanding or discussion of the task which is unfavorably supported by the abridged analysis and exploration.
References
Bourdieu, P. (1987). Distinction: A social critique of the judgement of taste. London: Routledge.
Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: Social class, sex and problem-solving. Buckingham: Open University Press.
Lareau, A. (2011). Unequal childhoods: Class, race, and family life (2nd ed.). Berkeley: University of California Press.
Lubienski, S. T. (2000). A clash of social class cultures? Students’ experiences in a discussion- intensive seventh-grade mathematics classroom. The Elementary School Journal, 100(4), 377–403.
Ministerium für Schule und Weiterbildung des Landes Nordrhein-Westfalen (Ed.) (2008).
Richtlinien und Lehrpläne für die Grundschule in Nordrhein-Westfalen. Frechen: Ritterbach.
Piel, S., & Schuchart, C. (2014). Social origin and success in answering mathematical word problems. The role of everyday knowledge. International Journal of Educational Research, 66, 22–34.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.
Stubbe, T. C., Schwippert, K. & Wendt, H. (2016). Soziale Disparitäten der Schülerleistungen in Mathematik und Naturwissenschaften. H. Wendt, W. Bos, C. Selter, O. Köller, K. Schwippert, &
D. Kasper (Eds.), TIMSS 2015: Mathematische und naturwissenschaftliche Kompetenzen von Grundschulkindern in Deutschland im internationalen Vergleich (S. 299–316). Münster:
Waxmann.
