Juxtaposing Secondary Mathematics Procedural Routines and their Meta-narratives—Exploring the Vocabulary of Student Teachers

Abstract

This paper analyses student teachers’ meta-narratives associated with ‘doing’ mathematics. The quality of the vocabulary associated with the doing of the mathematical objects of a sample of 56 multilingual third-year mathematics methodology students preparing to be secondary teachers was explored and assessed. Sfard’s theoretical concept of ‘pronounced foci’ and her ‘critical categories’ for determining if a narrative was mathematical were used to analyse the data. Meta-narratives refer to the written mathematical metacognitive monologues that manifested students’ thinking while they were doing the mathematical objects. Students were required to write, in language suitable for teaching, a description of the procedure which led to a solution. The procedures and their associated meta-narratives provided data for a mixed-method analysis in this case study. The absence of a mathematical vocabulary presented difficulties when students engaged in meta-narratives. The data also show that inexact mathematical vocabularies are not culturally specific since the 11 English mother tongue students demonstrated a similar lack of command of mathematical language as their peers. Meta-narratives revealed mathematical misconceptions that may not have been detected without them. For two of the three mathematical objects there is a significant but moderate positive correlation between correct vocabulary and correct procedure. The findings support the need for mathematical vocabulary (and language) to be a teaching focus when preparing teachers for their careers and that the assessment of tasks is not completely achieved by evaluating only the procedural ‘doing’ of mathematics.

Keywords:

• Initial teacher education
• mathematical vocabulary
• meta-narratives
• misconceptions
• routine procedures

ORCID

Pieter Paul van Jaarsveld http://orcid.org/0000-0002-6131-3348

Notes

1 ‘Commognitive conflict, in contrast, is defined as the phenomenon that occurs when seemingly conflicting narratives are originating from different discourses—from discourses that differ in their use of words, in the rules of substantiation, and so forth. Such discourses are incommensurable rather than incompatible; that is, they do not share criteria for deciding whether a given narrative should be endorsed’ (Sfard, 2008, p. 257).

2 for example is sovereign since it produces one and only one root because the sign of the radical is positive which means that what it is equal to, , can only be positive or zero. Its equivalent form , after squaring both sides, produces two roots one of which is not valid in terms of sovereignty of the original equation .