ABSTRACTHOW ARE THE MATHEMATICAL IDENTITIES OF LOW ACHIEVING SOUTH AFRICAN ELEVENTH GRADERS RELATED TO THEIR ABILITY TO SOLVE MATHEMATICAL TASKS?ByCorvell Cranfield The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Grootenboer and Zevenbergen (2008) define mathematical identity as the students' knowledge, abilities, skills, beliefs, dispositions, attitudes and emotions, that relates to mathematics and mathematics learning. A key part of this relationship that students have with mathematics is the students' evolving sense of self to understand how mathematics fits with this self (Black et al, 2010). Research shows that students' identity has many facets or multiple identities that are formed throughout their life history; engagement with their peers, family, and teachers; as well as engagement with mathematical tasks. Doing mathematics can be viewed as mathematical activity that involves integrating mathematical thinking by using mathematical facts and knowledge, and requires active student learning. Mathematical tasks used in the classroom form the basis for student's learning (Doyle, 1988) and different tasks are used to develop different types of skills and thinking (QCDA report). These tasks often appear in curricular or instructional materials in textbooks and should be within the current experiential space of students (Jurdak, 2008).This study investigated how the mathematical identities of low achieving South African eleventh graders are related to their ability to solve mathematical tasks. I used a variety of methods including mathematical stories, biographical interviews, focus-group interviews, mathematical tasks, and clinical interviews. These methods were used to investigate the salient features of mathematical identity, the performance in mathematical tasks, and the relationship between mathematical identity and mathematical performance. This case study focused on five eleventh graders who were underperforming in mathematics at a low-socioeconomic school located in a working class community in the Western Cape Province in South Africa. The framework for analysis used concepts from Leont'ev's (1981) cultural historical activity theory, but build on the construct of a `leading identity', which formed the basis for the study's theory of identity (Black et al., 2010). This notion of leading identity suggests a hierarchy of motives, with the most significant motive forming the leading identity. My results show that the relationship between math identity and math performance are characterized by "discontinuities and continuities" (Stentoft & Valero, 2009) between these two components. This conceptualization helped in understanding and explaining the fragility of mathematical identity as produced in practice. I discuss the implications of this relationship between math identity and math performance for future research, teachers, and math education.
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