Abstract
The reported research attempts to trace possible reasons for third grade learners’ limited progress in numeracy in a low socioeconomic status (SES) South African context. This is done through two lenses, both stemming from Sfard’s commognitive (The term “commognition” has been offered by Sfard (2008) as an amalgam of “cognition” and “communication,” thus expressing the unity of these concepts. Since its original appearance, some authors (including Sfard herself) have preferred using the word “communicational” to describe Sfard’s framework. We chose to stick with “commognitive” because we believe it clearly points to the specific theoretical stance presented in Sfard (2008), whereas “communicational” might point to many other theories or frameworks that have something to do with human communication.) framework. One lens aims to analyze two learners’ (Mina and Ronaldo (all names are pseudonyms)) mathematical and identity discourse both in one-on-one interviews and in a small group “math club” lesson led by the second author. The other examines the mathematical milieu in which these learners have participated through the analysis of a school mathematics lesson which exemplifies prevalent instructional practices in this milieu. Relying on the distinction between ritual and explorative participation, we show that while Mina was acting in an extremely ritualized manner, Ronaldo was more explorative in his actions. However, the milieu, as seen in the school lesson, encouraged almost exclusively ritual participation. Thus, while Mina was identified as a good student, Ronaldo was identified as an outcast or “troublemaker.” We conclude by drawing implications to the tenacious nature of rituals in the mathematics classroom and the effects that these rituals may have on students’ identities.
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Notes
In South Africa, racial classifications such as "Coloured" continue to be used to analyze the extent to which redress is occurring across previously disadvantaged racial groups in various sectors of society such as education and economic participation.
The Eastern Cape is one of nine South African provinces and is situated in the South Eastern part along the coast. It is one of the poorest provinces with among the lowest education results across the Annual National Assessments (DBE, 2012).
South Africa is a multilingual society and many learners speak more than three languages. Thus, for many learners, the medium of instruction at their school is their third or fourth language rather than a second language.
We are using here the term “ritual” in a very specific sense, as will be defined in the next few paragraphs. Though this use has some resemblance to the colloquial use of the term (as in religious rituals), it also differs from it in many ways. For more on the definition of ritual, see Heyd-Metzuyanim (2015) and Sfard and Lavie (2005).
All teacher names, except that of Mellony, are pseudonyms.
Numbers in square brackets [] refer to the line number in the transcript.
Flard cards are sets of cards with the following numbers on them: 1; 2; 3; …9 and 10; 20; 30; …90, and 100; 200; 300 …. 900, and 1000; 2000; 3000; … 9000. See line 26 of the excerpt for a photograph. They are also called number builder cards and arrow cards. Combining cards allows children to build up numbers and they are a recommended teaching resource in the South African curriculum for the Foundation Phase (grades 1–3).
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Heyd-Metzuyanim, E., Graven, M. Between people-pleasing and mathematizing: South African learners’ struggle for numeracy. Educ Stud Math 91, 349–373 (2016). https://doi.org/10.1007/s10649-015-9637-8
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DOI: https://doi.org/10.1007/s10649-015-9637-8