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In South Africa, limited studies have been conducted investigating responsive teaching and little is known about how teachers respond to unexpected events 'in the moment' that did not form part of their planning. In this article, we report how a Grade 9 novice and expert teacher responded to unexpected learner offers during the teaching of algebra using a qualitative case study approach. Three consecutive lessons for each teacher were video recorded, transcribed and analysed. Our units of analysis for episodes were teachers' responses to unexpected learner offers and we coded the responses as 'appropriate' or 'inappropriate'. Indicators used to highlight the degree of quality of the response were 'minimum', 'middle' and 'maximum' if a response was coded as appropriate to a learner's offer. Once lessons were analysed, the first author conducted video-stimulated recall interviews with each participant to gain insight into the two teachers' thoughts and decision-making when responding to unexpected learner offers. The findings from this study illustrated that the novice teacher failed to press learners when their thinking was unclear, chose to ignore or provided an incorrect answer when faced with an unexpected learner offer. Conversely, the expert teacher continuously interrogated learner offers by pressing if a learner offer was unclear or if she wanted learners to explain their thinking. This suggests that the expert teacher's responses were highly supportive of emergent mathematics learning in the collective classroom space.

This paper contributes to research in responsive teaching in a context of collaborative discussion using video stimulated recall (VSR) techniques. The aim was to gain deeper understanding of the kinds of teachers' reflective awareness that prompts changes (or lack of change) in responsive primary mathematics teaching. Using a case study methodology, I analysed the VSR interviews of two teachers who demonstrated different patterns of changes in responsive teaching. The findings revealed two distinct and complementary forms of evidence of states of awareness and reflections that support change in responsive teaching practices: (a) teachers acknowledging limitations of their practice; and (b) teachers expanding repertoires of tasks and example spaces. These two forms of evidence provide insights into ways of supporting primary mathematics teaching in the context of VSR techniques. The implication of these findings is that for effective use of VSR interviews, attention should be geared towards getting a teacher to acknowledge the limitations of her practice, and through reflection-oriented questions to encourage the teacher to expand task and example space to respond to the limitations noted within the teacher's practice.

Upon return to campus after the pandemic, students were subjected to receiving lectures online, in class, or by the emerging hybrid approaches. This study reports students' preference over the three approaches based on the experience gained during the 2022/23 academic session. The study aimed to understand the post-pandemic considerations/factors likely to influence students' preferences for or against any of the three modes (based on their experiences with each), and implications for developing university sustainability frameworks in the post-pandemic era. One hundred and twenty-seven (127) on-campus Education students in one public university in Malaysia participated in the study. Data were collected through an online forum and interviews with the participants. The data collected were analyzed using content and thematic analysis. Preference for the hybrid approach emerged as a key finding for this study. Additionally, a perceived lack of Faculty engagement and support in the online learning environment, and on-campus learner-environment challenges were identified as factors contributing to the decreased popularity of the online-only class option in the post-pandemic era. Conversely, students' engagement through faculty presence and technology innovation in class and online emerged as factors that made the hybrid approach the most popular. What the students valued the most in the hybrid approach is the face-to-face interaction that is retained, and the in-class faculty's innovative use of technology in content delivery, which they believed made learning more effective and interesting in class than online. These findings imply that institutions should prioritize technology integration into face-to-face instruction, leveraging innovative approaches to enhance student engagement and sustainable learning outcomes. [ABSTRACT FROM AUTHOR]

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and number structure in a primary pre-service teacher education programme at a university in South Africa and reports on an intervention strategy intended to culminate in developing design principles comprising guidelines for the effective teaching of number structure and mathematics equivalence in primary pre-service teacher education programmes. The mixed method study comprises 70 first-year primary pre-service teachers (PSTs) and a teacher educator. The PSTs wrote pre- and post-tests, and were interviewed following the pre-test. Skemp's notion of relational and instrumental understanding guided the design of the intervention and the analysis of the data. The results from the study indicates that PSTs' understanding of the notion of equivalence is similar to what has been reported for students in schools, and that there were some learning gains in the post-test results. Based on the findings from the study in general, some emergent design principles are proposed. [ABSTRACT FROM AUTHOR]