73 research outputs found
Credit Usage, Hire Purchase Costs, and Consumer Protection in Retail Institutions in Botswana
This paper analyzes credit purchase practices in Gaborone, Botswana. Adopting a survey and a disguised interview technique, data was collected and analyzed on the usage rate of credit purchases. The hire purchase, which was the most popular form of credit, was examined in greater detail with respect to the costs of hire purchase, their comparison with other types of consumer credit, the compliance of hire purchase sellers to the hire purchase laws. It concludes with policy change recommendations on hire purchase and personal loan transactions.
Key words: Consumer Debt; Hire Purchase; Credit Sales; Micro Finance; Personal Loans
Communities in university mathematics
This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of Communities of Practice. From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form their identity through engagement, imagination and alignment. In addition, when inquiry is considered as a fundamental mode of participation, through critical alignment, the community becomes a Community of Inquiry. We discuss these theoretical underpinnings with examples of their application in research in university mathematics education and, in more detail, in two Research Cases which focus on mathematics students' and teachers' perspectives on proof and on engineering students' conceptual understanding of mathematics. The paper concludes with a critical reflection on the theorising of the role of communities in university level teaching and learning and a consideration of ways forward for future research
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal
Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space
In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their
definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the
notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on
students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional
example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function
Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and
cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the
experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal
meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as
spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis
indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also
it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the
instructional example space; the classroom discussion; and, the role of the teacher
Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames
Automatically discovering composable abstractions from raw perceptual data is
a long-standing challenge in machine learning. Recent slot-based neural
networks that learn about objects in a self-supervised manner have made
exciting progress in this direction. However, they typically fall short at
adequately capturing spatial symmetries present in the visual world, which
leads to sample inefficiency, such as when entangling object appearance and
pose. In this paper, we present a simple yet highly effective method for
incorporating spatial symmetries via slot-centric reference frames. We
incorporate equivariance to per-object pose transformations into the attention
and generation mechanism of Slot Attention by translating, scaling, and
rotating position encodings. These changes result in little computational
overhead, are easy to implement, and can result in large gains in terms of data
efficiency and overall improvements to object discovery. We evaluate our method
on a wide range of synthetic object discovery benchmarks namely CLEVR,
Tetrominoes, CLEVRTex, Objects Room and MultiShapeNet, and show promising
improvements on the challenging real-world Waymo Open dataset.Comment: Accepted at ICML 2023. Project page: https://invariantsa.github.io
Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis
The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis
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