Exploring the effect of Professional Noticing in the Context of Algebraic Fractions: A Case Study of National Certificate Vocational L3 Lecturers in a TVET College

Abstract

Expertise in professional noticing of students mathematical reasoning is an integral component of effective mathematics discourse. What a teacher notices or fails to notice impacts students’ performance significantly. Professional noticing of students mathematical thinking, in the mathematics classroom, involves attending to, interpreting, and deciding how to respond to students reasoning (Jacobs et al., 2010). Based on the significance of the construct of noticing, this study explored the effect of professional noticing on the pedagogical practices of NCV Level 3 (L3) lecturers in relation to the simplification of algebraic fractions. Specifically, this study sought to answer the following questions: how do NCV L3 lecturers attend to students mathematical reasoning in relation to simplifying algebraic fractions; how do NCV L3 lecturers interpret students mathematical reasoning in relation to simplifying algebraic fractions; and what course of action do NCV L3 lecturers take based on students mathematical reasoning in relation to algebraic fractions. To answer these research questions, a qualitative research design, particularly a case study approach was used. Data were collected in the form of student written responses to a pre-test, field notes, and audio recorded lessons, in the topic of algebraic fractions. Participants were purposively and conveniently recruited. A total of two NCV L3 lecturers and their respective classes, from TVET College B, consented to participate in the study. Before the data collection process, a professional noticing development program (workshop), facilitated by the researcher was conducted. Lecturer participants were requested to analyse the written responses of students by providing a detailed explanation on what they noticed about students reasoning in relation to the simplification of algebraic fractions. Furthermore, the audio recorded lessons were transcribed by the researcher, and transcripts were read several times to accurately determine the degree of noticing displayed by the participants. The three strands of professional noticing and the levels of sophistication framework served as analytical tools to determine the extent to which lecturers attended to, interpreted, and responded to students mathematical reasoning. Verbatim quotations were used to highlight the noticing skills of the participants. The findings of the study suggest that the lecturers displayed predominantly low (0) and medium (1) levels of noticing when analysing the written responses of students. In terms of noticing in action, participant lecturers were observed demonstrating primarily low (0) levels 6 of noticing. The study also revealed that participants found it challenging to notice students reasoning during the teaching of algebraic fractions. In conclusion, since noticing can be learned (Jacobs et al., 2010), to support lecturers in noticing students mathematical reasoning, it is recommended that TVET colleges provide training programs and workshops that explicitly focus on the learning and implementation of professional noticing. Furthermore, the study suggests that there is a need for the conceptualisation of noticing from a perspective that appreciates and integrates the socio- cultural realities of the students as well as the realistic setting of the classroom, since factors such as students background knowledge, classroom culture, and resources may affect the efficiency of noticing. Therefore, it is advisable that adaptations be made to acknowledge and accommodate the diversity and contextual circumstances of our South African classrooms to cultivate a more inclusive approach to noticing.