Problems with variation: an educational experience of cultural transposition with prospective primary teachers

The paper presents some theoretical reflections and some methodological notes about a Professional Development (PD) path worked out during the last two years by Italian researchers for prospective Primary teachers. The theoretical construct of Cultural Transposition defines the framework of the PD path’s activities and the related research. It was used to define an interesting cultural lent to delineate possible new approaches for effective pre-service teacher education programs, in particular for the Primary level. The defined methodology was based on the possibility to reflect about the decentralization of didactic practices based on a specific cultural context through one or more contacts with other “realities” coming out from different selected cultural contexts. In the last section of the paper we argue that the contact with a different didactic perspective coming from the Chinese “problems with variation” (one of the stimuli proposed in the PD’ path), encouraged some reflections by the Italian pre-service teachers on the use of “variation” in Math word-problems for an early approach to Algebra in Primary level

MATHEMATISATION: SOCIAL PROCESS & DIDACTIC PRINCIPLE

The 69th CIEAEM conference was held from 15th to 19th July 2017 at Freie Universität Berlin, Germany. It successfully involved 100 participants from 20 countries all over the world. CIEAEM 69 was dedicated to Professor Christine Keitel, president of CIEAEM from 1997 to 2003, who tragically passed away one year before the conference. The programme of the conference started with a panel that revisited “Mathematics (Education) and Common Sense”, the theme of the 47th CIEAEM conference, which was held in Berlin in July 1995 and which was hosted by Christine. At the conference, researchers, teachers, educators, and students met to discuss, in a collaborative and inspiring environment, the most prominent problems, obstacles and resources in mathematics education; they also presented their latest research findings in the several conference activities: plenary and semi-plenary talks, two round tables, working groups, workshops, and poster presentations (forum of ideas). As in previous CIEAEM meetings, Working Groups constituted the beating heart of the conference, allowing the participants to fruitfully discuss in critical and constructive ways, in the true CIEAEM spirit, research studies and approaches from different perspectives on the conference theme: Mathematisation: social process & didactic principle. There were four Working Groups: (A) Mathematisation as a didactic principle: mathematizing and modelling of everyday contexts; (B) Mathematisation as a didactic principle: representation and generalization within mathematics; (C) Interconnecting mathematisation as a social process and as a didactic principle; and (D) Mathematisation as a didactic principle: looking at teachers of mathematics. Each Working Group discussed nine papers, and addressed the conference theme from complementary viewpoints (see the Discussion Paper), under the guidance of the group animators. The conference schedule allowed time also to deepen the plenary talks in the dedicated “Meet the plenary speaker” sessions, and to engage participants in workshops, where actual dialogue between research and practice could be fostered. This volume contains the final versions of the 53 papers presented during the conference. We thank all the contributors and the participants to the conference, because they made it such a unique experience, in which we had the good fortune to take part. We are grateful to the International Programme Committee and the Local Organizing Committee that made possible the realization of the conference in every detail with great care. Particularly, we want to thank the Working Group animators, who organized each day the sessions in inclusive as well high-quality ways. A special thanks to all the people who contributed to the realization of the conference, and to Daria Fischer, who helped in editing this volume. As a result, the CIEAEM 69 Proceedings offer a wide overview on national and international studies on the conference theme Mathematisation: social process & didactic principle. We hope that it can constitute an inspiring resource for the research community, for teachers, and for stakeholders in mathematics education. From this perspective, the possibility of free downloading offers to CIEAEM 69 participants, and also to interested people who could not take part in the Conference in Berlin, the possibility of developing a fruitful network of contacts that year after year is becoming richer and wider

A quantitative method to analyse an open-ended questionnaire: A case study about the Boltzmann Factor

This paper describes a quantitative method to analyse an openended questionnaire. Student responses to a specially designed written questionnaire are quantitatively analysed by not hierarchical clustering called k-means method. Through this we can characterise behaviour students with respect their expertise to formulate explanations for phenomena or processes and/or use a given model in the different context. The physics topic is about the Boltzmann Factor, which allows the students to have a unifying view of different phenomena in different contexts

Investigating the quality of mental models deployed by undergraduate engineering students in creating explanations: The case of thermally activated phenomena

This paper describes a method aimed at pointing out the quality of the mental models undergraduate engineering students deploy when asked to create explanations for phenomena or processes and/or use a given model in the same context. Student responses to a specially designed written questionnaire are quantitatively analyzed using researcher-generated categories of reasoning, based on the physics education research literature on student understanding of the relevant physics content. The use of statistical implicative analysis tools allows us to successfully identify clusters of students with respect to the similarity to the reasoning categories, defined as "practical or everyday," "descriptive," or "explicative." Through the use of similarity and implication indexes our method also enables us to study the consistency in students' deployment of mental models. A qualitative analysis of interviews conducted with students after they had completed the questionnaire is used to clarify some aspects which emerged from the quantitative analysis and validate the results obtained. Some implications of this joint use of quantitative and qualitative analysis for the design of a learning environment focused on the understanding of some aspects of the world at the level of causation and mechanisms of functioning are discussed

Exploring the Coherence of Student Reasoning when Responding to Questionnaires on Thermally Activated Phenomena

Many research results show that students often highlight \u201cmixed-type\u201d reasoning when tackling problematic situations and problems. This reasoning is based on the simultaneous use of common-sense and mere descriptions of facts, perceived as sufficient to build an \u201cexplanation\u201d of observed or proposed situations and problems. This fact can be interpreted as a lack of coherence. In this paper, we study the coherence of responses that a sample of undergraduate chemical engineering student give when they are asked to face real-life situations, to create explanations, and to use models in different contexts. We administered open-ended questionnaires before and after a twenty-hour Inquiry-Based workshop related to phenomena activated by a thermal overcoming of a potential barrier. Based on the Physics Education Research literature on student understanding of relevant physics contents, the student responses are analysed by using researcher-generated categories of reasoning and their coherence is studied. Finally, we discuss some implications of the results to improve the development of students' explicative skills. \ua9 2021 the authors; licensee Modestum. All Rights Reserved