This paper investigates the effects of different instructional approaches (problem-based vs. direct instructional) on student teachers‘ analysis of practice when using authentic representations of ...practice in teacher education. We assigned 638 student teachers from 21 equivalent teacher education courses to one of the two conditions. Students’ analyses of practice were evaluated on selective attention, reflective thought, and theory-practice integrations in a pre-post-design. In line with inconsistent findings from prior research, we were able to produce evidence for equivalent effects of the instructional approaches on all dependent variables using Bayesian data analyses. As called for in a review on the topic, we additionally explored the role of the instructors administering the field study interventions. Findings revealed that a positive attitude toward the instructional approach the instructors administered was related to more theory-practice integrations in the students’ analyses.
Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among ...the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and higher order thinking through the same mathematical activities-an aim which requires empirical examination. For empirically valid hybrid task design, evidence is required about the nature of the interrelatedness of content-related and higher order thinking. In this article, we choose the example of statistical thinking and critical thinking for exploring the interrelatedness of these different modes of thinking when solving hybrid tasks. Even if theories about statistical thinking and critical thinking have so far followed almost separate strands, there are commonalities at the theoretical level, which facilitate hybrid task design. We report an empirical study, in which a bottom-up analysis of thinking-aloud interviews with adult learners around solution processes of hybrid tasks affords insight into how these modes of thinking may interact when solving such tasks. The results show that the tasks did evoke both statistical thinking and critical thinking: Both modes of thinking entered in an interplay in which we observed instances of mutual support of both modes of thinking, but also cases in which a strong focus on statistical thinking or critical thinking appeared to impede the other mode of thinking, respectively. The findings can inform the further development of hybrid tasks: Based on the observations, the task format can be enriched with specific reflective stimuli intended to support a fruitful interplay of statistical thinking and critical thinking. Author abstract
This study explores how students deal with material resources in their peer interaction when working in pairs in an open-ended problem-solving task. The productive use of material resources can be ...expected to support successful peer work. However, research into social phenomena in peer interaction is needed in order to identify and describe productive and less productive forms of dealing with material resources as students participate in open-ended problem-solving tasks. Consequently, this explorative study responds to this research need. Based on multimodal data, including video recordings, transcribed talk and the written contributions from four pairs of Year 7 students aged 12-13 years, the analysis focuses on different ways in which students deal with material resources while negotiating their participation as they respond to the task. The findings indicate that aspects of participation are a key factor for describing productive and less productive ways of dealing with material resources by the student pairs. Foregrounding aspects of participation for an increased awareness of potential obstacles to student-centred work is among this study’s contributions for classroom practice and theory development.
Teachers notice through the lens of their professional knowledge and views. This study hence focuses not solely on teachers' noticing, but also on their knowledge and views, which allows insight into ...how noticing is informed and shaped by professional knowledge. As a discipline-specific perspective for noticing we chose dealing with multiple representations, since they play a double role for learning mathematics: On the one hand they are essential for mathematical understanding, but on the other hand they can also be an obstruction for learning. This comparative study takes into account pre-service as well as in-service teachers in order to explore the role of teaching experience for such professional knowledge, views and noticing. The participants answered a questionnaire addressing different components of specific knowledge and views. For eliciting the teachers' theme-specific noticing, vignette-based questions were used. The data analysis was done mainly by quantitative methods, but was complemented by a qualitative in-depth analysis focusing on how the teachers' themespecific noticing was informed by different components of their professional knowledge. The results suggest that pre-service as well as in-service teachers do not fully understand the key role of multiple representations for learning mathematics in the sense of their disciplinespecific significance. The participating in-service teachers distinguished themselves however from the pre-service teachers especially regarding their theme-specific noticing. Moreover, the evidence indicates that teachers' noticing of critical instances of dealing with multiple representations draws on situated as well as on global knowledge and views.
With the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate ...empirical results, and make progress
as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so that researchers from multiple disciplines with different theoretical perspectives could work together to examine the
complexity of the mathematics classroom. In this paper, we reflect on the multiple analytical accounts generated from the project, drawing from the notions of complementarity and commensurability. Two parallel analyses, applying the
commognitive framework and the theory of representations respectively, are used as illustrative examples for discussion regarding complementarity and commensurability. The paper addresses two focal questions, as follows: in what ways do
divergence or contradiction in incommensurable analytical accounts reflect methodological discrepancies or fundamental differences in the underpinning theories? Furthermore, in what ways do the accounts generated by the parallel analyses
predicated on different theories lead to differences in instructional advocacy? The answers to these questions provide empirically-grounded insights into the consideration of incommensurability in educational research, and suggest ways
in which researchers and practitioners might apply the notion of complementarity to reconcile or exploit incommensurable analytical accounts that have resulted in different instructional advocacies. Author abstract
Although teachers' professional knowledge and instructional beliefs are known to have a variety of subcomponents, research on the structure and interrelations of these subcomponents is relatively ...scarce. This article presents some findings of a preliminary, quantitative empirical study examining the relationships between mathematics teachers' views concerning specific classroom situations, their content domain-specific pedagogical content beliefs and their more global instruction-related beliefs. The findings suggest that global beliefs—in terms of cognitive constructivist or direct transmission views of teaching and learning, on the one hand, and beliefs about the stability of individual mathematical abilities, on the other—can impact teachers' content domain-specific beliefs and their views related to videotaped classroom situations from introductory lessons on geometrical proof.
Although raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a ...specific aspect of noticing, namely teachers’ analysis of how representations are dealt with in mathematics classroom situations. For the purpose of such analysis, we examined the role of context on the levels of
mathematical content area
and
classroom situation
. Using a vignette-based test instrument with 12 classroom situations from the content areas of fractions and functions, we investigated how teachers’ analyses regarding the use of representations are related concerning these two mathematical content areas. Beyond content areas, we were interested in the question of whether an overarching unidimensional competence construct can be inferred from the participants’ analyses of the different individual classroom situations. The 12 vignettes were analysed by
N
= 175 secondary mathematics teachers with different degrees of teaching experience and their written answers provided the data for this study. Our findings show that the data fit the Rasch model and that all classroom situations contributed in a meaningful way to the competence under investigation. There was no significant effect of the mathematical content area on the participants’ analyses regarding the use of multiple representations. The results of the study indicate that explicitly considering questions of context can strengthen research into teacher noticing.
Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students' learning. In order to support ...students' learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we described as teachers' analysing of classroom situations in prior research. Although teachers' professional knowledge plays a critical role in such competence, empirical evidence regarding different facets of such knowledge and their interplay is still scarce. This study investigates different facets of teachers' knowledge of using multiple representations in the context of learning fractions and their role for teachers' corresponding competence of analysing. We asked N = 298 teachers at different levels of expertise to analyse six classroom situations presented as text, comic or video. Our findings indicate that knowledge facets related to mathematical content are significant predictors for teachers' competence of analysing.
Summary
Objectives Visible skin condition of women is argued to influence human physical attraction. Recent research has shown that people are sensitive to variation in skin color distribution, and ...such variation affects visual perception of female facial attractiveness, healthiness, and age.
Methods The eye gaze of 39 males and females, aged 13 to 45 years, was tracked while they viewed images of shape‐ and topography‐standardized stimulus faces that varied only in terms of skin color distribution.
Results The number of fixations and dwell time were significantly higher when viewing stimulus faces with the homogeneous skin color distribution of young people, compared with those of more elderly people. In accordance with recent research, facial stimuli with even skin tones were also judged to be younger and received higher attractiveness ratings. Finally, visual attention measures were negatively correlated with perceived age, but positively associated with attractiveness judgments.
Conclusions Variation in visible skin color distribution (independent of facial form and skin surface topography) is able to selectively attract people's attention toward female faces, and this higher attention results in more positive statements about a woman's face.
Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these ...aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should be possible to stimulate both forms of thinking through the one task. This paper explores the implications of an exploratory qualitative study into processes when working on tasks encompassing both these areas for the design of tasks that simultaneously stimulate critical thinking and domain-specific thinking.Tareas híbridas: promover el pensamiento estadístico y el pensamiento crítico por medio de las mismas actividades matemáticasAunque desde un punto de vista teórico, el pensamiento estadístico y el pensamiento crítico parecen tener fuertes conexiones, la investigación empírica sobre la intersección y la potencial interrelación entre estos aspectos de competencia es escasa. Nuestra investigación sugiere que las habilidades de pensamiento en ambas áreas pueden ser interdependientes. Dada esta interconexión, debería ser posible estimular ambas formas de pensamiento mediante una tarea. Este artículo explora las implicaciones de un estudio cualitativo exploratorio sobre los procesos de pensamiento en tareas que abordan ambas áreas para el diseño de tareas que simultáneamente estimulan el pensamiento crítico y pensamiento específico de un dominio.Handle: http://hdl.handle.net/10481/30509
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