Mathematical practices in a technological workplace: the role of tools

This paper investigates the role of tools in the formation of mathematical practices and the construction of mathematical meanings in the setting of a telecommunication organization through the actions undertaken by a group of technicians in their working activity. The theoretical and analytical framework is guided by the first-generation activity theory model and Leont’ev’s work on the three-tiered explanation of activity. Having conducted a 1-year ethnographic research study, we identified, classified, and correlated the tools that mediated the technicians’ activity, and we studied the mathematical meanings that emerged. A systemic network was generated, presenting the categories of tools such as mathematical (communicative, processes, and concepts) and non-mathematical (physical and written texts). This classification was grounded on data from three central actions of the technicians’ activity, while the constant interrelation and association of these tools during the working process addressed the mathematical practices and supported the construction of mathematical meanings that this group developed from the researchers’ perspective. Technicians’ emerging mathematical meanings referred to place value, spatial, and algebraic relations and were expressed through personal algorithms and metaphorical and metonymic reasoning. Finally, the educational implications of the findings are discussed.     

The Nature of Argumentation in School Mathematics and Physics Texts: The Case of Periodicity

The present study explores reasoning and argumentation in Greek mathematics and physics texts in specific topics related to the notion of periodicity. In our study, argumentation is taken as the sequence of the modes of reasoning (MsoR) that an author develops in a text when organizing and presenting new knowledge. Inductive content analysis was applied on 71 thematic units taken from 4 mathematics and 4 physics textbooks, and a coding system of categories and subcategories of MsoR was produced. Our analysis discerned 4 main categories of MsoR: empirical, logical-empirical, nomological, and mathematical; we argue that each mode of reasoning (MoR) plays a different role in conceptualizing aspects of periodicity. Analysis of the sequence of MsoR in two thematic units raised pragmatic considerations on the text understanding in relation to the scientific argumentation discourse and highlights ontological differences in the two subjects when ascending from observations to generalizations. Educational implications of the findings are discussed.     

Teacher Educators’ Activity Aiming to Support Inquiry Through Mathematics and Science Teacher Collaboration

This study explores teacher educators’ (TEs’) activity as they support mathematics and science teacher collaboration in co-designing and jointly implementing tasks. We view TEs’ activity through the lens of Activity Theory and expansive learning and draw evidence from data generated within the mascil project that linked mathematics and science teaching with workplace situations through inquiry-based teaching. We focus on five TEs’ actions and goals, use data from their professional development sessions with teachers and from the TEs’ interactions during their own meetings, and highlight the illuminating case of one teacher educator. We trace evidence indicating paths of actions followed by each Teacher Educator and look for indications of their professional learning. Our analysis reveals generic and content-focused actions. All TEs faced different kinds of contradictions and had difficulties handling them. In terms of professional learning, all TEs adapted their prior teacher education practices and appreciated the critical role of epistemological differences between the two disciplines.

     

Evaluation parameters for computer-adaptive testing

With the proliferation of computers in test delivery today, adaptive testing has become quite popular, especially when examinees must be classified into two categories (pass/fail, master/nonmaster). Several well‐established organisations have provided standards and guidelines for the design and evaluation of educational and psychological testing. The purpose of this paper was not to repeat the guidelines and standards that exist in the literature but to identify and discuss the main evaluation parameters for a computer‐adaptive test (CAT). A number of parameters should be taken into account when evaluating CAT. Key parameters include utility, validity, reliability, satisfaction, usability, reporting, administration, security, and thoseassociated with adaptivity, item pool, and psychometric theory. These parameters are presented and discussed below and form a proposed evaluation model, Evaluation Model of Computer‐Adaptive Testing.     

The value of adaptivity based on cognitive style: an empirical study

Adaptive Hypermedia Systems can be developed to accommodate a variety of individual differences, including learning style and cognitive style. This study investigates the hypothesis that adaptive hypermedia accommodating cognitive styles can be beneficial for the observed learning outcomes. A prototype system, designed to be adapted to individual cognitive styles, was developed as a case study. In order to evaluate the effectiveness of the prototype system, an empirical study was conducted. This paper presents the results of the summative evaluation of the system. Statistical analyses indicated that students in the experimental group performed significantly better than students in a control group. These findings indicate that student performance is mainly affected by adaptivity based on individual cognitive styles.     

Revisiting the place value concept in the workplace context: the issue of transfer development

In this paper, we studied the transferring process of five apprentice engineering students concerning the place value concept in a telecommunication workplace setting. In this setting, a physical material, a telecommunication closet (TC), appearing as a concrete representation of the ten-numeration system, supported the process of generating composite units in a sequential way. The data were generated by conducting an interview with each student based on two tasks. In the first task, students were asked to locate the place of a particular wire pair on the telecommunication closet representation (TC representation). In the second task, students were asked to determine the range of values that generate this composite unit. Our theoretical and analytical framework is guided by the three levels of students’ generalization activity by Radford (2003) and the work on developmental transfer by Engeström (2001). By identifying shifts in the students’ activity (from factual to contextual and from contextual to symbolic), we recognized three transferring cases: the immediate transfer case, the developmental transfer case, and the nondevelopmental transfer case. By comparing and contrasting the different cases, we identified four factors that seem to facilitate or constrain the transfer development. These are the use of metaphors, the development of problem solving strategies, the context dependency, and the students’ motivation. In conclusion, we discuss the educational implications of our findings.