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Adult student experiences of a flipped mathematics classroom
Abstract
The flipped classroom is a flexible blended learning model that is growing in popularity due to the emergent accessibility to online content delivery technology. By delivering content outside of class time asynchronously, teachers are able to dedicate their face to face class time for student-centered teaching approaches. The flexibility in implementation of a flipped classroom allows for a diversity in student experiences. The study presented in this paper uses qualitative methods of analytic induction to conduct a case analysis on survey and interview data collected from students participating in a flipped adult mathematics upgrading course at an urban Canadian university near Vancouver, BC. The key phenomenon of interest in the study is how adult students experience a flipped mathematics classroom. Of secondary interest is how factors such as autonomy and goals interrelate with these experiences. It is found that flipped classrooms can bifurcate into two types of student interaction: completely engaged and self-paced. Key interrelated factors in this bifurcation include election of cognitive autonomy, goal orientation, and attendance.
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The flipped classroom is an old concept that has recently been redefined through the emergence of new technologies that allow teachers to deliver content out of class time. As such, various approaches for implementation exist. Most prominently, teachers are able to use class time in a student-centered manner, which allows students to experience the classroom in diverse ways. This study focuses on describing these experiences in a particular flipped adult upgrading mathematics class. Students in the class are surveyed and interviewed about their experiences in relation to autonomy, goals, self-efficacy, and anxiety. It is found that students can bifurcate into engaging in the class completely and engaging in it in a self-paced manner. Key interrelated factors in this bifurcation include election of cognitive autonomy, goal orientation, and attendance. This study also indicates that self-efficacy can be improved within a collaborative learning environment that provides students with autonomy.
This article reports the outcomes of a study, undertaken from a phenomenographic perspective, of academics' conceptions of their own growth and development as a university teacher. A range of ways of understanding teaching development emerged, representing in particular a varying focus on development experienced as an increase in: the teacher's comfort with teaching; the teacher's knowledge and skills; and learning outcomes for students. This work builds on previous studies of university teachers' conceptions of teaching, which has been shown to be related to their approaches to teaching and, thus, to student learning outcomes. Relationships between conceptions of teaching and conceptions of growing and developing as a teacher are also presented and discussed.
Examples, illustrations, occurrences and instances play a central role in the learning of mathematics. Deliberately getting students to generate examples is a particularly powerful tool in teaching, but while some of the possibilities they offer are used by many teachers, the full potential is rarely exploited. The authors came to this notion through reflection on their experience of observing teachers in classrooms, of getting students to take initiatives, and of creating examples while working on their own mathematics. They examine the roles played by examples constructed and generated by students, give illustrations and analyses of the use of this tool, and develop a theory for the act of exemplification as an act of cognition. A framework is developed for researchers and practitioners to further this work.
In addition to classroom activities, teachers provide personal and instructional supports meant to facilitate the developing sense of student autonomy. In this article, we offer a way of thinking about autonomy-supportive practices that suggests that such practices can be distinguished at a featural level and that different practices may in fact have different outcomes in terms of student classroom behavior. Specifically, we propose that autonomy support can be manifested in the classroom in at least 3 distinct ways: organizational autonomy support (e.g., allowing students some decision-making role in terms of classroom management issues), procedural autonomy support (e.g., offering students choices about the use of different media to present ideas), and cognitive autonomy support (e.g., affording opportunities for students to evaluate work from a self-referent standard). We offer vignettes of teachers in their classes to illustrate our proposition that autonomy support may be carried out on several planes and may produce different outcomes. Whereas organizational autonomy support may encourage a sense of well-being and comfort with the way a classroom functions and procedural autonomy support may encourage initial engagement with learning activities, cognitive autonomy support may foster a more enduring psychological investment in deep-level thinking.
Highly math-anxious individuals are characterized by a strong tendency to avoid math, which ultimately undercuts their math competence and forecloses important career paths. But timed, on-line tests reveal math-anxiety effects on whole-number arithmetic problems (e.g., 46 + 27), whereas achievement tests show no competence differences. Math anxiety disrupts cognitive processing by compromising ongoing activity in working memory. Although the causes of math anxiety are undetermined, some teaching styles are implicated as risk factors. We need research on the origins of math anxiety and on its “signature” in brain activity, to examine both its emotional and its cognitive components.
A recurring paradox in the contemporary K-12 classroom is that, although students educationally and developmentally benefit when teachers support their autonomy, teachers are often controlling during instruction. To understand and remedy this paradox, the article pursues three goals. First, the article characterizes the controlling style by defining it, articulating the conditions under which it is most likely to occur, linking it to poor student outcomes, explaining why it undermines these outcomes, identifying its manifest instructional behaviors, and differentiating it from an autonomy-supportive style. Second, the article identifies seven reasons to explain why the controlling style is so prevalent. These reasons show how pressures on teachers from above, from below, and from within can create classroom conditions that make the controlling style both understandable and commonplace. Third, the article offers a remedy to the paradox by articulating how teachers can become more autonomy supportive. Three essential tasks are discussed. Special attention is paid to practical examples of what teachers can do to support students' autonomy.
This study tested whether students who learned with an active orientation would be more intrinsically motivated to learn and would learn more than students who learned with a passive orientation. The active orientation was created by having subjects learn material with the expectation of teaching it to another student; the passive orientation was created by having subjects learn the same material with the expectation of being tested on it. The results indicate that subjects who learned in order to teach were more intrinsically motivated, had higher conceptual learning scores, and perceived themselves to be more actively engaged with the environment than subjects who learned in order to be examined. The two groups were equal, however, in their rote learning scores. The effects of exposure to the material were ruled out as an explanation because the two groups reported spending equal time with the material. The results are discussed in terms of intrinsic motivation theory.
Following interviews with thirty-nine college lecturers, a questionnaire was developed that identifies two orientations to teaching: knowledge transmission and learning facilitation. Departments with high scores on knowledge transmission discouraged students from adopting a deep approach to study. Departments in which learning facilitation predominated seemed less likely to induce surface approaches.