The research findings are based on accounts given by twelve UKZN post graduate (Masters and PhD) students in the School of Social Science. Although this might seem tentative, the accounts suggest important factors in understanding the interrelationship between students’
learning behaviour, the socio-cultural factors that influence such behaviour and their conceptions and perceptions as meanings and mathematics outcomes. The following three issues are therefore salient for this study.
6.2.1 How Post Graduate Social Science Students Conceptualise Mathematics
The study has defined mathematics as an activity that expresses solutions to social problems by using a communicative and instrumental system of symbols as means of articulating the solutions (Godino and Batanero 1993:8; RSA Department of Education 2011:8). The findings of the study indicate that students conceive mathematical meaning in qualitatively three different ways namely:
a) The meanings attached to mathematical symbols b) The meanings attached to the value of mathematics
c) The meanings they attach to their own mathematical competence
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The link between these conceptualisations has been found to begin with an interaction between the student and the mathematics symbols. This has been termed a collision between the human habitus and the mathematics field. The field legitimises those forms of capital which the students possess (Benson, 2006:190) or which are embedded in the students’
habitus. An evaluation of the valued capital by the field results in the valued cultural capital rewarded by the system and unvalued cultural capital punished by the system. The cultural capital a student possesses is a reflection of the dispositions embedded in their habitus and thus a reflection of who the students are, what they are competent in and what their preferences are. Their habitus as expressed in their competencies as evaluated by the education system is the lens through which they come to understand themselves and their capabilities and thus attach meanings to their own competence.
6.2.2 The Relationship between Conceptions and Perceptions and Mathematics Performance
Although the study set out to establish how students’ conceptions and perceptions influence mathematics, a one directional relationship between the concepts, the study concludes that there is a reverse relationship between the concepts. This is where students’ performance in mathematics can in turn influence how students perceive and conceive mathematics. The study however does not explore this reverse relationship or how the concepts reinforce one another in the study as it was a finding and a confirmation of the existence of such a relationship existence which can be explored by future studies.
6.2.3 Cultural Mismatch between Classroom and Out-of-Classroom Practice
The continued differentiated mathematics outcomes, with some students performing poorly while others are competent in mathematics, is a reflection of the cultures that the students are a product of. That is to say that the mathematics learning enterprise is interpenetrated and influenced by a complicated web of social relations, socio-cultural perspectives and epistemologies which underpin classroom practice, trends and approaches to teaching and learning. These include teachers’ perceptions and public narratives about mathematics classroom practice such as teaching methods and corrective measures, among others. These socio-cultural dynamics channel students into certain ways of perception and conception and not others, as well as how students are likely to act and react in various teaching and learning
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social contexts. It also emphasises the role of these social contexts and dynamics in the establishment of students’ subjective identity and the perception of their mathematical capabilities. The study has found perceptions and conceptions to serve a dual responsibility.
Positive perceptions have been found to be a platform to mathematics proficiency and negative perceptions have been found to be a stumbling block and to be associated with poor mathematics performance.
Continuity between school and out-of-school activities includes the need for a home environment that offers support, empowerment and motivation of students’ educational pursuits. For instance, where the teacher is the guide and support at school, the family or parents should be the guide and support at home. The parents are to reinforce what was learnt at school or make a follow up on their children’s academic progress, following Henderson and Belar’s (1994:29) assertion in the literature that not all activities that parents do with their children amount to academic achievement but hands on involvement in their children’s learning in particular. This suggestion is cognisant of the fact that not all families are structured or positioned equally to provide such support and motivation. Where such support is not available therefore, continuity can be ensured by the student taking the initiative to seek knowledge actively by engaging independently with the mathematical applications through practice in class and out of class regardless of the familial standing. This has been confirmed to work for those students who had no familial or parental support.
School therefore serves as a social plane where society’s cultural dispositions are displayed.
The value of students’ know-how, skills and competencies as cultural tools is validated as the students engage with the mathematics habitus as society’s dominant culture. Students are therefore regarded as poor in mathematics because they lack the cultural know-how, skills and competencies required from them by the mathematics habitus in order to succeed in mathematics learning. This confirms Bourdieu’s assertion that not all families are equally positioned to access the mathematics habitus.
6.2.4 Reshaping the Structural Formations that Inform Habitus
This discussion follows the findings that address the question of what the factors are that inform students’ perceptions and conceptions. Having asserted the existence of a gap in the interaction between school and out-of-school fields, there is need for a change in these
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formations. There needs to be a change in the socio-cultural practices and epistemologies that pattern society’s knowledge constructions, habits and view of how the world naturally works.
The argument is that it is these structural formations in society that mark the limits of the human habitus and prefigure people’s sense of place in society. Shifting the boundaries therefore would allow for the ‘dance of agency’ or easier engagement and compatibility of the human and school habitus. This holds true for the structural adjustments that are implemented in the education system: that any curriculum changes that ignore changing the social environment as a key structuring factor on which parents and teachers’ conceptions and perceptions as well as students’ competencies, skills and knowhow are embedded, is a futile endeavour. This is because teachers, parents or family and children have been identified as key players in mathematics learning. Putting mathematics into everyday language would make it accessible to students.
6.2.5 Student’s Active Participation in their Own Learning: Transcending Structural Boundaries in Mathematics Achievement
Reshaping and restructuring the social environment and habitus is easier said than done. The study has demonstrated how some of the students managed to ‘crack the mathematics code’
by creating their own social space to engage actively in their own learning. Although they are few, they are however a force to reckon with. Fields as “arenas of struggle in which individuals and organizations compete, unconsciously and consciously, to legitimise those forms of capital which they possess” (Benson, 2006:190) essentially means that students are to be active players in the field and make some effort to meet the required standards of the game. As noted in the literature, mastery is not the first stage in knowledge development and thus students have to develop some patience and resilience as they learn and to make a conscious decision not to back down. Having noted how perceptions and conceptions can either be a stumbling block or a stepping stone in learning, perceiving mathematics as do-able is the starting point in transcending the cognitive and socio-cultural limitations to mathematics achievement, as all of reality filters through the body of the perceiver.