scholarly journals Sources of Students’ Difficulties with Proof By Contradiction

Author(s):  
Jeffrey M. Rabin ◽  
David Quarfoot

AbstractThe literature on proof by contradiction (PBC) is nearly unanimous in claiming that this proof technique is “more difficult” for students than direct proof, and offers multiple hypotheses as to why this might be the case. To examine this claim and to evaluate some of the hypotheses, we analyzed student work on proof construction problems from homework and examinations in a university “Introduction to Proof” course taught by one of the authors. We also conducted stimulated-recall interviews with student volunteers probing their thought processes while solving these problems, and their views about PBC in general. Our results suggest that the knowledge resources students bring to bear on proof problems, and how these resources are activated, explain more of their “difficulties” than does the logical structure of the proof technique, at least for this population of students.

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110138
Author(s):  
Yetti Zainil ◽  
Safnil Arsyad

Teachers often code-switch in the EFL classroom, but the question of whether or not they are aware of their code-switching has not been satisfactorily answered. This article presents the study on teachers’ understandings and beliefs about their code-switching practices in EFL classrooms as well as effective language teaching and learning. The participants of this study came from four junior high schools in Padang, West Sumatra, Indonesia: five teachers with their respective classes. This research used the conversation analysis and stimulated recall interviews to analyze the data which came from the video recording of classroom observations and the audio recording of stimulated recall interviews with teachers. The results revealed the pedagogical functions and affective functions of teacher’s code-switching. The data also showed that the use of stimulated recall interviews helped teachers to be consciously aware of their code-switching as well as of their other pedagogical practices in the language classroom. Therefore, stimulated recall interviews can be a useful tool for teacher self-reflection that they were not aware of their code switch. This awareness could be incorporated into language teacher professional development and in-service teacher professional learning.


2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Lisanne S. Welink ◽  
Kaatje Van Roy ◽  
Roger A. M. J. Damoiseaux ◽  
Hilde A. Suijker ◽  
Peter Pype ◽  
...  

Abstract Background Evidence-based medicine (EBM) in general practice involves applying a complex combination of best-available evidence, the patient’s preferences and the general practitioner’s (GP) clinical expertise in decision-making. GPs and GP trainees learn how to apply EBM informally by observing each other’s consultations, as well as through more deliberative forms of workplace-based learning. This study aims to gain insight into workplace-based EBM learning by investigating the extent to which GP supervisors and trainees recognise each other’s EBM behaviour through observation, and by identifying aspects that influence their recognition. Methods We conducted a qualitative multicentre study based on video-stimulated recall interviews (VSI) of paired GP supervisors and GP trainees affiliated with GP training institutes in Belgium and the Netherlands. The GP pairs (n = 22) were shown fragments of their own and their partner’s consultations and were asked to elucidate their own EBM considerations and the ones they recognised in their partner’s actions. The interview recordings were transcribed verbatim and analysed with NVivo. By comparing pairs who recognised each other’s considerations well with those who did not, we developed a model describing the aspects that influence the observer’s recognition of an actor’s EBM behaviour. Results Overall, there was moderate similarity between an actor’s EBM behaviour and the observer’s recognition of it. Aspects that negatively influence recognition are often observer-related. Observers tend to be judgemental, give unsolicited comments on how they would act themselves and are more concerned with the trainee-supervisor relationship than objective observation. There was less recognition when actors used implicit reasoning, such as mindlines (internalised, collectively reinforced tacit guidelines). Pair-related aspects also played a role: previous discussion of a specific topic or EBM decision-making generally enhanced recognition. Consultation-specific aspects played only a marginal role. Conclusions GP trainees and supervisors do not fully recognise EBM behaviour through observing each other’s consultations. To improve recognition of EBM behaviour and thus benefit from informal observational learning, observers need to be aware of automatic judgements that they make. Creating explicit learning moments in which EBM decision-making is discussed, can improve shared knowledge and can also be useful to unveil tacit knowledge derived from mindlines.


KWALON ◽  
2018 ◽  
Vol 23 (2) ◽  
Author(s):  
Krista van Mourik ◽  
Annica Brummel ◽  
Astrid Kemper ◽  
Ilse Menheere ◽  
Mariette Wesselink ◽  
...  

Look at yourself! A reflection on images in research and in practice Social workers play an important role in helping multiproblem families to deal with multiple, interrelated and often intergenerational problems. Social workers indicate that effective collaboration – with clients, their family members and other professionals – is crucial. Defective collaboration can have major consequences for effective support. In this study, six social workers were followed intensively in their collaborative relationships with families, families’ social network and other professionals providing services to these families. Video recordings and stimulated recall interviews were used to explore the behavioral indicators of this collaboration. The value of the method for research and practice is described.


2018 ◽  
Vol 17 (2) ◽  
pp. 333-365 ◽  
Author(s):  
Suzanne Luger

Abstract This article discusses translation processes of proficient students who translate Latin fables into Dutch in secondary school. The participants performed two tasks on a computer. They translated a Latin fable and edited a Dutch translation of another Latin fable while their activities were monitored by eye-tracker, screencast and keystroke logging. Immediately after the tasks the participants were invited to view their eye-tracking film and retrace their thoughts at the time of translating (stimulated recall). The article focuses on the stimulated recall interviews, and more specifically on the role of revision in the translation process. It presents a case study of one participant, as well as the strategies participants described to have used in tackling two specific translation problems. Data suggest that proficient participants rely on text comprehension rather than morphological knowledge to solve translation problems. The research shows three key elements as indicators for successful translation process resulting in a coherent target text: (1) a wide variety of problem-solving strategies and the ability to switch strategies, (2) the availability and use of metalanguage to verbalise the chosen strategy, and (3) revision of the target text.


2021 ◽  
Vol 11 (10) ◽  
pp. 580
Author(s):  
Giuseppe Ritella ◽  
Fedela Feldia Loperfido

Learner-centered blended learning approaches, such as Knowledge Creation, emphasize the self-organizing characteristic of thought and action, and value the students’ autonomy and self-regulation during the engagement in collaborative learning tasks. In blended contexts, the students need to organize their learning paths within a complex environment, including multiple online and offline learning spaces. This process of self-organization during courses based on the Knowledge Creation approach is currently an overlooked topic of research. The present case study is aimed at addressing this research gap by providing an in-depth understanding of the collaborative self-organization of a group of five undergraduate students participating in an interdisciplinary media design course. The course was designed according to the Knowledge Creation approach and was carried out before the start of the COVID-19 pandemic. The dialogical theory of the chronotope and the theory of cultural models constitute the main theoretical tools for the research. We used qualitative methods inspired by ethnography, including participant observation, in addition to the collection and analysis of audio-visual records, stimulated recall interviews, and learning diaries completed by the students. The findings show that the group self-organization changed across different phases of the collaborative task and involved the development of specific practices of self-organization. Cultural models associated with the task contributed to determine the students’ choices related to self-organization.


2021 ◽  
Vol 11 (1) ◽  
pp. 41-70
Author(s):  
Xiaowan Yang ◽  
Mark Wyatt

While it is increasingly recognized that teachers have a crucial role to play in motivating learners, language teacher cognition research that focuses on beliefs about second language (L2) learner motivation and motivational practices is still rare, particularly in English for specific purposes (ESP) settings in Asia. Furthermore, much of what is available does not employ stimulated recall interviews to facilitate a comparison of espoused beliefs elicited beforehand, observed classroom practices and situated cognitions. We have employed such methodology in an under-researched ESP setting in China, to gain insights into the influence of culture and context on teacher beliefs and behavior. Our qualitative case study of three Chinese ESP teachers highlights harmony and tensions between espoused beliefs regarding student motivation and the teacher’s motivational role, and motivational practices, this harmony/disharmony being likely to impact these teachers’ self-determination. It considers possible reasons for identified tensions, including limited professional development opportunities in ESP, apparently dated knowledge of L2 motivation theory, deeply embedded Confucian values and an entrenched assessment culture. Findings suggest the need for awareness-raising and mentoring activities designed to support cognitive harmony regarding motivation and motivational practices amongst ESP teachers.


Author(s):  
Zachary Wahl-Alexander ◽  
Matthew Curtner-Smith

Purpose: To determine the impact of a training program on the ability of preservice teachers (PTs) to negotiate with their students while teaching through the skill themes approach during an early field experience. Method: Participants were 11 PTs who were given specific training on how to negotiate with their students. Data on their ability to negotiate were collected during the early field experience with six qualitative techniques (journaling, document analysis, participant observation, and formal, informal, and stimulated recall interviews) and were analyzed using standard interpretive techniques. Findings: The training program was effective. Patterns of negotiation observed for both PTs and students improved as the PTs’ skill themes units progressed. The volume of positive negotiations increased and the volume of negative negotiations decreased. Key training program components were lecture/discussions, film, journaling, and role playing. Conclusions: Training PTs to negotiate can help them improve their teaching through the skill themes approach. Ability to negotiate may distinguish between effective and ineffective PTs who otherwise have similar pedagogical skills.


2020 ◽  
pp. 1356336X2097133
Author(s):  
Leah K. May ◽  
Matthew D. Curtner-Smith

The purpose of this study was to determine the influence of two effective and expert physical education (PE) teachers’ value orientations on the curricula they delivered and the pedagogies they employed. The specific research questions we attempted to answer were: (a) What were the teachers’ current value orientations? (b) How had these value orientations influenced their curricula and pedagogies? and (c) How had the teachers’ value orientations, curricula, and pedagogies evolved during the course of their careers? Data were collected from PE teachers Hudson and Garrett with the short form of the value orientation inventory and six interpretive techniques (i.e. formal, informal, and stimulated recall interviews; non-participant observations; document analysis; and reflective journaling). Value orientation profiles were graphed. Qualitative data were analyzed by employing analytic induction and constant comparison. Key findings were that the two PE teachers prioritized the disciplinary mastery and social responsibility orientations and they employed curricular models and pedagogies that were congruent with these perspectives. Data also indicated that the self-actualization perspective had a minor influence on Hudson and the learning process orientation had a similar influence on Garrett. Both PE teachers began teaching with a primary focus on disciplinary mastery and expanded their views to include social responsibility later in their careers. The study highlights the importance of exposing preservice and in-service teachers to different value orientations, curricular models, and pedagogies and requiring them to consider the congruence between their goals and objectives and the models and methods they employ.


2009 ◽  
Vol 59 (5) ◽  
pp. 645-661 ◽  
Author(s):  
Marijke De Smet ◽  
Hilde Van Keer ◽  
Bram De Wever ◽  
Martin Valcke

2019 ◽  
Vol 38 (4) ◽  
pp. 377-387 ◽  
Author(s):  
Shrehan Lynch ◽  
Matthew D. Curtner-Smith

The purpose of this study was to determine the influence of one sociocultural foundations class taught by Florence, a teacher educator, on the perspectives and practices of two physical education preservice teachers (PTs), Michael and Bob. Within a narrative inquiry approach, data sources were nonparticipant observation, intraviews, conversations, exit slips, digital interactions, responses to three fictional physical education teaching scenarios, a fictional curriculum outline, three stimulated recall interviews, documents, and various forms of visual data. Theoretical thematic analysis was employed to work with and make sense of the data. Findings indicated that both PTs faced frustration and discomfort during class. Nevertheless, the class resonated and raised the PTs’ critical awareness of sociocultural issues related to physical education. Key reasons for the apparent success of the class were the deinstitutionalizing pedagogical methods employed by Florence and Florence’s “problem-posing” education which prompted the PTs to question their perspectives and assumptions about society and culture.


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