Fast Kids,Slow Kids,Lazy Kids: Framing the Mismatch Problem in Mathematics Teachers' Conversations

Abstract

This article examines the social nature of teachers' conceptions by showing how teachers frame the “mismatch” of students' perceived abilities and the intended school curriculum through conversational category systems. This study compares the conversations of 2 groups of high school mathematics teachers addressing the Mismatch Problem when implementing equity-geared reforms. Although East High teachers challenged conceptions that were not aligned with a reform, South High teachers reworked a reform mandate to align with their existing conceptions. This research found that the teachers' conversational category systems modeled problems of practice; communicated assumptions about students, subject, and teaching; and were ultimately reflected in the curriculum. Because East High teachers supported greater numbers of students' success in advanced mathematics, this study considers the relation between teachers' understandings of student learning and the success of equity-geared math reforms. In addition, this study contributes to the understanding of how teacher conceptions of students are negotiated and reified in context, specifically through interactions with colleagues and experiences with school reform.     

Teachers’ performances during a practical dynamic open inquiry process

The research goal of this study was to determine whether teachers who participated in an inquiry-based course were able to internalize a dynamic open inquiry process. This study focused on 25 science teachers who participated in an annual inquiry-based academic course. Several teaching tools helped teachers employ an open inquiry process. We concluded that the teaching tools applied by teachers in documenting their inquiry processes enabled them to express dynamic inquiry characteristics. The results indicate consistency between the criteria most frequent in teachers’ inquiries and the criteria running through their reflections. In addition, teachers implemented the dynamic inquiry criteria in their classroom teaching.     

Construct3D: A Virtual Reality Application for Mathematics and Geometry Education

Construct3D is a three dimensional geometric construction tool based on the collaborative augmented reality system Studierstube. Our setup uses a stereoscopic head mounted display (HMD) and the Personal Interaction Panel (PIP) - a two-handed 3D interaction tool that simplifies 3D model interaction. Means of application in mathematics and geometry education at high school as well as university level are being discussed. A pilot study summarizes the strengths and possible extensions of our system. Anecdotal evidence supports our claim that the use of Construct3D is easy to learn and encourages experimentation with geometric constructions.     

Collusion among Accounting Students: Data Visualization and Topic Modeling of Student Interviews

Although classroom cheating violates academic standards of behavior, it occurs frequently. Although the research on cheating is extensive, few researchers have interviewed students directly involved in cheating behaviors. We explore interview responses gathered from a cohort of graduate accounting students, some of whom colluded on an assignment, whereas others did not. We use Latent Dirichlet Allocation (LDA), a powerful text mining algorithm, as our primary tool to explore the underlying topical structure of the interviews and to demarcate subtle differences among students’ reactions to and explanations of their experience. Because LDA does not impose or require a priori theories, we use it to provide ideas for future research rather than to test extant theories about classroom collusion. We identify five primary topics that emerged from the accounting students’ reflections: (1) general course context (including honor code), (2) the rigor of the assignment, (3) student teams as support mechanisms, (4) the perceived repercussions of cheating (colluding), and (5) personality differences between the tax and audit track students. We find subtle language differences between colluders and noncolluders. Colluders considered the nature of the assignment and the difference between tax and audit majors more significant than noncolluders did. Additionally, the role of teams and the general institutional context were somewhat less relevant for colluders than for noncolluders. We conclude by exploring ethical and pedagogical implications of structuring courses as heavily team based for teaching and future research purposes.     

Kinetic contours in infants' visual perception

3-month-old infants' perception of "camouflaged" forms that are only visible when moving was studied. Displays were used in which figure and ground had an identical random dot texture, and no edge indicated the form of the figure. The form was invisible when stationary. Discrimination of 2 different forms was tested (a) when the forms were visible only through motion, and (b) when the forms appeared as stationary white figures on black ground. The babies discriminated the forms in both conditions. Furthermore, when infants were habituated to one of the moving forms and subsequently presented with the same and a new static form, they looked longer at the new form. This indicates that they recognized the static form as either the same or different from the moving form seen before, although the optical sources of information were completely different. At 3 months, infants can therefore effectively use kinetic information to organize the visual input in higher-order structures.     

Evaluation of a numeracy intervention program focusing on basic numerical knowledge and conceptual knowledge: a pilot study

The preliminary results of this study suggested that children with developmental dyscalculia benefit from a numeracy intervention program that focuses on basic numerical knowledge and conceptual knowledge. All children in the experimental group showed considerable and partly significant performance increases on all calculation components. Six children with developmental dyscalculia were trained individually and in small-group settings for a relatively short duration (one school semester). We argue that the positive intervention effects to a large extent are attributable to the explicit teaching of numerical domains that often have been found to be neglected in school mathematics.     

Reading counter-hegemonic practices through a postmodern lens

This paper examines the similarities and differences as well as the limitations and possibilities of critical pedagogy, feminist pedagogy and some of the more radical strands of multicultural education in adult education. As postmodern thought has begun to influence these discourses, a brief look at postmodernism in relation to these three pedagogical theories will be presented. Furthermore, it will be proposed that a synthesis while maintaining difference between these pedagogical strands may have the potential to minimize the limitations and multiply the possibilities of a critical adult pedagogy. It will be suggested that this endeavour may be deepened through the utilization of a strategic postmodern lens of analysis.