Metacognitive failure in constructing proof and how to scaffold it

This research aims to describe the students’ metacognitive failure in constructing proof and the scaffolding support. The participants of this qualitative case study were eight preservice mathematics teachers of six-semester, State University of Malang. We carried out a test about proof construction problems in Abstract Algebra. Then we verified the data using triangulation of constant comparative method from a test and a task-based interview with the stimulated recall. The results indicated two groups of students in proving strategy. Group I performed “appropriate” syntactic strategy and Group II vice versa. Blindness was experienced by the subject that does not recognize errors detection or the ambiguity of the proof. Mirage occurred when the subject recognizes an error detection on the proper strategy or application of a theorem, then is unable to verify the truth of his work. Misdirection appeared when the subject recognizes a lack of progress, then uses an incomplete or irrelevant concept. Vandalism emerged with no progress or detection of errors of the strategy then the subject performs some irrelevant steps to the issue or uses a misconception. Practically, the teachers can use these results for learning innovations in scaffolding-based proof courses. The scaffolding might need some development and application in supporting students to overcome difficulty in proving mathematical sentences.

“Desire Is Like a Dreadful Monster”: Analysis of Extended Metaphors in L2 Argumentative Essays by Chinese Learners of English

This article explores the use, function, and understanding of extended metaphors in L2 argumentative essays by Chinese learners of English. The analysis starts with the identification of linguistic metaphors and extended metaphors in 72 argumentative texts produced by 37 intermediate Chinese English majors. The function of extended metaphors is then analyzed by adopting the bottom-up approach of establishing systematic metaphors from those identified extended metaphors, to draw learners’ communicative intentions in producing extended metaphors. To understand learners’ thinking processes behind using extended metaphors while writing, four of nine writers were interviewed about the process of writing extended metaphors in their texts in the stimulated recall interviews. It is found that extended metaphors, expressed through similes or direct metaphors at strategic stages in L2 argumentative essays, are often the result of learners’ conscious manipulation of L1 in producing L2 for various communicative purposes, such as the desire for vividness, coherence, comprehensibility, when there is a knowledge gap between L1 and L2, and for evaluative and persuasive power. These communicative functions are consistent with the ideational, interpersonal, and textual functions of language, which also coincide and interact with the rhetorical goals of moves and stages in L2 argumentative essays. Metaphoric thinking, L1 influence, and struggling to express meaning and persuade, cited in learners’ thought reports, are major factors triggering extended metaphors. The findings of this article can contribute to the knowledge of learners’ metaphoric competence in L2, which can, in turn, enrich teachers’ metaphor knowledge and draw teachers’ attention to learners’ creative ways of using metaphors and then raise metaphor awareness in L2 writing, teaching, and learning.

Willing, Silent or Forced Participation? Insights from English for Academic Purposes Classrooms

This study explores students’ participation in English for Academic Purposes classrooms from both teachers’ and students’ perspectives. Data were collected from videotaping of 11 English for academic purposes classes, semi-structured interviews with 12 teachers and stimulated-recall interviews with 33 students. The results indicate that three types of participation were identified, including willing, silent and forced participation. The results also show that a range of contextual and individual factors affect students’ participation in class activities and discussions. The contextual factors include class atmosphere, teacher support, peer participation, task, topic and interactional pattern. The individual factors include students’ confidence, personality and their perceived and actual communicative competence. Pedagogical implications and directions for future research are also discussed.

Care as technology for exclusion

In this article, we explore and problematise admission tests to specialist music teacher education in Sweden from a governing perspective, where higher music education is considered a discursive practice. It illustrates how power operates in legitimating the tests. The study uses stimulated recall in jury members’ talk about assessing applicants for music teacher education programmes, and uses Foucault’s concept of governmentality to reveal entrance tests as something regarded as generally good for all. This operating discourse is built on governmental rationality and processes that make it possible to reach conclusions about the applicants’ personalities and prospects for learning and developing in the future. Through care as technology of power, failing applicants are excluded from becoming music teachers and at the same time they are rescued from struggling in the future. The results are discussed in relation to issues of democratic music education, ethics and requirements for widened access to higher music education.

Exploring task-based cognitive processes

This paper argues that TBLT researchers should dedicate more effort to investigating the cognitive processes in which L2 learners engage during task work to facilitate theory-construction and to inform pedagogical practices. To help achieve this, a review follows of various subjective (questionnaires, interviews, think-aloud/stimulated recall protocols) and objective (dual-task methodology, keystroke-logging, eye-tracking) methods that are available to TBLT researchers to examine cognitive processes underlying task-based performance. The paper concludes that, to obtain a more valid understanding of task-generated cognitive processes, it is best to combine various methods to overcome the limitations of each. Finally, some methodological recommendations are provided for future cognitively-oriented TBLT research.

Novice and expert Grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra

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.

Peer interactions among under three years old children in Malaysian childcare centres: A case study approach

<p>Research on infants’ and toddlers’ peer interactions in childcare centres shows many benefits for children’s social competence. With increasing participation of under-three year olds in group-based early childhood services worldwide, there is also growing interest in the role played by childcare adults in supporting children’s social competence. In the Malaysian context, where the number of childcare settings is growing rapidly, early childhood research remains limited and is non-existent within the field of understanding the complexity of infants’ and toddlers’ peer interactions. At the same time there has been a mounting discourse by Malaysian economists promoting the benefits of non-cognitive skills to a country, thus focussing attention on social skills, of which peer interactions are a form. This study opens up this under-researched field in Malaysia through three qualitative case studies – one in each of three childcare centres in the state of Selangor. Each case study involved individual semi-structured interviews with the childcare practitioners, video-recorded observations of the children’s peer interactions, and video-stimulated recall interviews. A focus group discussion was conducted too with all of the practitioners after that. The aim of the study was to examine how practitioners perceived peer interactions among children under three years old in their childcare centres, and the kinds of peer interactions that occurred among the children. Drawing on constructs from a range of social constructivist theoretical perspectives, the findings revealed that at the start of the study, the practitioners saw themselves as promoting peer interactions by facilitating group activities and managing interactions between children by responding to their conflicts. The observations of children’s peer interactions revealed complex negotiations by the children who were actively creating a sense of belonging and togetherness at their childcare centres like embracing the centre’s routines, and responding to the needs of others including through humour and laughter. In the process of these interactions, children exercised their agency and learned the skills of becoming socially competent participants in their centre. Through video-stimulated recall interviews and focus group discussion, the practitioners deepened their thoughts on children’s peer interactions and saw peer interactions to be linked with learning around three main themes: learning through play; learning through gaining familiarity with others; and learning about having friends. My findings provide a picture of how the children’s peer interactions were understood by largely untrained practitioners, and how the complexity of children’s lived experiences remained hidden to the practitioners until they took part in the video-stimulated recall interviews; the latter opened up and deepened the practitioners thoughts about children’s peer interactions. This study differs from earlier studies in that it is based in Malaysia where the provision of group-based early childhood care and education services is still a relatively new social and educational endeavour staffed by largely unqualified practitioners. This has implications for future childcare training initiatives in Malaysia.</p>

The implementation of task-based language teaching in EFL primary school classrooms: A case study in Vietnam

<p>Research into the introduction of task-based language teaching (TBLT) in Asian primary school classrooms is rare, despite curriculum initiatives in many Asian countries promoting communicative and task-based teaching and learning. This study addresses this gap by investigating the implementation of TBLT in EFL classrooms in primary schools in Vietnam, a context hitherto under-research from a TBLT perspective. The research was conducted in two phases. Phase 1 was a multiple case study which used classroom observations, stimulated recall and in-depth interviews to investigate how seven Vietnamese EFL primary school teachers implemented speaking lessons and how they viewed the lessons. The results showed that all teachers followed the presentation-practice-production (PPP) sequence specified in the textbooks, but that they independently incorporated communicative activities into the lessons. The teachers’ view of the PPP lessons varied but they shared a concern about the mechanical nature of the PPP lessons. Phase 2 investigated the implementation of two task-based lessons redesigned from PPP speaking lessons in a textbook by three teachers who participated in Phase 1 of the study. The data were collected from classroom observations, stimulated recall and in-depth interviews with the teachers, interviews with pupils, and recordings of task performances by nine pairs of learners. The results showed that all three teachers successfully carried out the two task-based lessons and reported a higher level of learner engagement and communication in their classes. Analysis of pupil interview data reveals evidence to support the teachers’ views. All pupils expressed interest in the task-based lessons with stronger pupils affirming the scaffolding role of the pre-tasks and communicative value of the main tasks. Weaker pupils reported challenges of completing the main tasks due to lack of pre-teaching of the target structural patterns. Analysis of task interaction data showed that all dyads worked consistently towards completing the main tasks in the task-based lessons, although the achieved outcomes varied slightly. They were able to assist each other to co-construct their utterances, correct their own errors and help correct each other’s errors, negotiate for meaning to overcome comprehension difficulties and use L1 to foster task completion. All of these strategies were found to facilitate task completion and provided a fruitful context for language development. In sum, the results point to the viability of TBLT in the Vietnamese EFL primary school context. They contribute to an understanding of the implementation of TBLT in authentic classrooms and the nature of task interaction among EFL primary school pupils.</p>

The implementation of task-based language teaching in EFL primary school classrooms: A case study in Vietnam

<p>Research into the introduction of task-based language teaching (TBLT) in Asian primary school classrooms is rare, despite curriculum initiatives in many Asian countries promoting communicative and task-based teaching and learning. This study addresses this gap by investigating the implementation of TBLT in EFL classrooms in primary schools in Vietnam, a context hitherto under-research from a TBLT perspective. The research was conducted in two phases. Phase 1 was a multiple case study which used classroom observations, stimulated recall and in-depth interviews to investigate how seven Vietnamese EFL primary school teachers implemented speaking lessons and how they viewed the lessons. The results showed that all teachers followed the presentation-practice-production (PPP) sequence specified in the textbooks, but that they independently incorporated communicative activities into the lessons. The teachers’ view of the PPP lessons varied but they shared a concern about the mechanical nature of the PPP lessons. Phase 2 investigated the implementation of two task-based lessons redesigned from PPP speaking lessons in a textbook by three teachers who participated in Phase 1 of the study. The data were collected from classroom observations, stimulated recall and in-depth interviews with the teachers, interviews with pupils, and recordings of task performances by nine pairs of learners. The results showed that all three teachers successfully carried out the two task-based lessons and reported a higher level of learner engagement and communication in their classes. Analysis of pupil interview data reveals evidence to support the teachers’ views. All pupils expressed interest in the task-based lessons with stronger pupils affirming the scaffolding role of the pre-tasks and communicative value of the main tasks. Weaker pupils reported challenges of completing the main tasks due to lack of pre-teaching of the target structural patterns. Analysis of task interaction data showed that all dyads worked consistently towards completing the main tasks in the task-based lessons, although the achieved outcomes varied slightly. They were able to assist each other to co-construct their utterances, correct their own errors and help correct each other’s errors, negotiate for meaning to overcome comprehension difficulties and use L1 to foster task completion. All of these strategies were found to facilitate task completion and provided a fruitful context for language development. In sum, the results point to the viability of TBLT in the Vietnamese EFL primary school context. They contribute to an understanding of the implementation of TBLT in authentic classrooms and the nature of task interaction among EFL primary school pupils.</p>