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Abstract
In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses with a specific perspective on learning processes. The study was located in an upper secondary transition course in a teaching unit on elementary number theory in which highly proficient students in their penultimate year of schooling participated. The main finding is that there was not a linear progression towards the intended tertiary mathematical discourse of modular multiplication but a coexistence of two discourses developing in parallel: the intended tertiary discourse and a continuation of school mathematical discourses. Students see these two discourses as the same, connected by the same perceived aim of searching for patterns. Further hindering discursive development are utterances, in which elements of the intended tertiary discourse (words and representations) are used superfluously, so that elementary/secondary utterances appear to be tertiary. These findings illustrate the need to explicate and address metanarratives. Metanarratives can connect two discourses developing in parallel in ways that, in this case, hinder discursive development towards the intended tertiary discourse.
Highlights
The transition from secondary to university mathematics is difficult for many students (De Guzmán et al 1998; Thomas et al 2015)
This study investigates the following research questions in the context of a transition course on elementary number theory: RQ1: What commognitive conflicts occur in such a developmental perspective? RQ2: How do these come into existence when students revisit familiar elementary/
The transition course was communicated to them as a chance to engage with university mathematics
Summary
The transition from secondary to university mathematics is difficult for many students (De Guzmán et al 1998; Thomas et al 2015). The development to a tertiary discourse is here investigated in terms of discursive object level and meta-level developments (Transition as Development of Discourses Section), and from the perspective of how an Beventually-to-be-shared discourse^ emerges out of the individual communicative actions of the discursants In this way, discursive development can be grasped as a dynamic process influenced by both the students’ perceptions of the intended discourse and the actual Bdevelopmental status^ of the classroom discourse. & Communicative actions exert a centripetal force towards establishing the intended tertiary discourse when they use keywords in previously accepted ways and express narratives with new and viable object- and meta-discursive rules. The students presented their solutions and discussed their viability, so that it became visible how secondary and tertiary utterances are picked up and built upon by other students and the teacher
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