Session Information
24 SES 01, Mathematics in Transition.
Paper Session
Contribution
This paper explores issues in relation to transition from pre-university study of mathematics to study of mathematics at university, by students on courses of mathematics or in mathematically demanding subjects such as engineering. The study aimed to understand educational practices in Higher Education (HE) from a socio-cultural perspective and how these impact on students’ learning outcomes and developing identities as learners of mathematics.
Our analysis of case study data from five institutions together with a longitudinal series of interviews pointed to three important and interacting themes emerging across cases: (i) provision and use of resources, (ii) meeting individual learners needs, and (iii) issues of transfer of mathematics. This paper extends our initial analysis of the first of these themes drawing on Cultural Historical Activity Theory (CHAT) to consider how students in transition meet not only ruptures (Gueudet, 2008) in the way mathematics is epistemologically formulated but also how this results in dissonances in expectations in relation to the very way in which they are expected to learn. In CHAT terms we identify contradictions both in the activity system in which students find themselves learning mathematics at university and between this and their previous experience of learning mathematics in school/college. Consequently we are led to consider students making two consequential transitions (Beach, 1998): lateral transition as they ‘progress’ from school/college in the conventional sense and collateral transition as their simultaneous participation in other activity systems provides new mediating tools allowing them to reformulate their actions in relation to learning. Our previous analysis suggests that consequently there is potential for a cycle of expansive learning (Engestrom, 2001) as the learning community reflects on its activity and the actions of the individuals involved. In this paper we take our theoretical reflections further focussing on the implications for students as they need to re-learn what it means to learn. In doing so we illustrate this analysis by drawing on a number of students’ experiences in learning mathematics and contrast these with those of another case study in which medicine students are introduced to Problem Based Learning which offers a pedagogic strategy and structure for supporting students in developing skills in self-directed learning to support the learning of core content knowledge and skills (Gallagher, 1997).
Our intention in this paper therefore is to develop a reflective critique of students’ current experiences that is consistent with the way we have framed transition to university -- in terms of lateral and collateral consequential transitions. We rely on activity theory (Dimova & Loughran, 2009) and socio-cultural understandings of identity and learning (Black et al., 2010) to unpack the ways university students learn to learn at university. Thus, we maintain an activity system perspective on transition but focus on the individual student as the unit of analysis. We aim to better understand the ways resources mediate their learning and the ways identities (e.g. as learners, mathematicians or medical doctors) mediate their active engagement with those resources in their learning.
Method
Expected Outcomes
References
Beach K. D. (1999). Consequential transitions: A sociocultural expedition beyond transfer in education. Review of Research in Education, 24, 124-149. Black, L. Williams, J., Hernandez-Martinez, P., Davis, P., Pampaka, M. & Wake, G. (2010). Developing a ‘leading identity’: the relationship between students’ mathematical identities and their career and higher education aspirations. Educational Studies in Mathematics 73, 55–72. Dimova, Y. & Loughran, J. (2009). Developing a big picture understanding of reflection in pedagogic practice. Reflective Practice, 10(2), 205-217. Engestrom, Y. (2001). Expansive Learning at Work: toward an activity theoretical reconceptualisation, Journal of education and work, 14 (1): 133 – 156. European Council. (2006). Recommendations of the European Parliament and the Council of 18 December 2006 on key competencies for lifelong learning. Brussels: Official Journal of the European Union, 30.12.2006. Gallagher, S. A. (1997). Problem-Based Learning: Where did it come from, what does it do, and where is it going? Journal for the Education of the Gifted, 20 (4), 332-62. Gamache, P. (2002). University Students as Creators of Personal Knowledge: an alternative epistemological view. Teaching in Higher Education, 7 (3), 277-294. Gueudet, G. 2008 Investigating the secondary – tertiary transition. Educational Studies in Mathematics 67: 237 – 254. Harvey, L, Drew, S. & Smith, M. (2006). The first-year experience: a review of literature for the Higher Education Academy. Higher Education Academy. Rawson, M. (2000). Learning to learn: more than a skills set. Studies in Higher Education, 25(2), 226-238. Wingate, U. (2007). A framework for transition: Supporting ‘learning to learn’ in higher education. Higher Education Quarterly, 61(3), 391-405.
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