1,720,986 research outputs found
Approaching Early Algebra: Teachers’educational processes and classroom experiences
No full textAfter a short survey of the main steps which lead to the birth of “Early Algebra” as a specific field of studies, we sketch the main features of our theoretical frame and our work to promote algebraic thinking in the students and to educate the teacher at putting into practice constructive paths of teaching of early algebra. We then present an excerpt of a didactical process, realized in a third-grade class, which is meaningful from the point of view of pupils’ productions and of the classroom culture induced by the teacher. We conclude with some considerations about the effectiveness of our methodology of work for the pupils’ learning and for the teachers’ professional development
Futuri Insegnanti di fronte a problemi dimostrativi: giochi di interpretazione, pensieri anticipatori e coordinamento tra linguaggio verbale ed algebrico
No full textQuesto contributo è parte di un lavoro più ampio, che coinvolge insegnanti in formazione, mirato a favorire in loro una presa di consapevolezza circa l’importanza di sviluppare negli studenti un effettivo ‘symbol sense’. In questa ottica, una parte essenziale del nostro lavoro con i futuri insegnanti consiste in attività dimostrative in ambito aritmetico. Contemporaneamente, siamo interessati ad analizzare l’uso ed il ruolo del linguaggio algebrico nello sviluppo di tali dimostrazioni. In questo articolo presentiamo una iniziale analisi e successiva classificazione dei comportamenti di futuri insegnanti nell’affrontare la dimostrazione di una congettura da loro prodotta a partire dall’esplorazione di una situazione numerica loro proposta. L’analisi dei protocolli è stata condotta in riferimento a particolari chiavi interpretative che riflettono la nostra idea circa le abilità richieste per sviluppare dimostrazioni attraverso l’uso del linguaggio algebrico: l’applicazione di frames concettuali specifici, i giochi di interpretazione tra diversi frames, i pensieri anticipatori, l’uso di conversioni e trattamenti ed il coordinamento tra diversi registri di rappresentazione. Da un punto di vista educativo, questa analisi può rappresentare uno strumento metodologico sia per aiutare i futuri insegnanti ad identificare le loro difficoltà in algebra, sia per promuovere una effettiva comunicazione con e tra essi
Improving awareness about the meaning of mathematical induction
No full textThis work is part of a wider project of didactical innovation aimed at fostering students’ conscious use of algebraic language through teaching experiments on proof in elementary number theory (ENT). In this paper we will analyze the role played by the teacher as a guide to the enactment of fundamental skills for the construction of reasoning by means of algebraic language, pointing out the specific characteristics of the teacher’s effective action in serving as a role model to his/her students
Proof of statements in elementary number theory: analysis of trainee teachers productions
No full textThe study involves a group of pre-service middle-school teachers attending educational and training courses at our university. The aim is to classify their behaviour in solving a problem that requires the proof of a statement in elementary number theory not easy to be formalized. This study highlights mental blocks in those who are not able to create an algebraic model for the problem and widespread difficulties related to the impact of abilities both in translating algebraic expressions into the algebraic code and in interpreting algebraic expressions built during the construction of the proof in order to get to the thesis
Future teachers facing proof problems: games of interpretation, anticipating thought and coordination between verbal and algebraic register
No full textAchieving the meaning of algebraic representations and being able to differently interpret them in relations to the context are central aspects in the teaching and learning of algebra. According to Arcavi’s (1994) idea about development of an effective symbol sense in students, we are working with groups of Secondary school pre and in-service teachers with the main aim of making them aware of the importance of developing in students a conception of algebra as a tool for thinking (Arzarello et Al., 1994, 2001). In this perspective, a fundamental part of our work with them are activities on proofs in arithmetic. In this paper we face the question of the use and the role of algebraic language in the development of such proofs, presenting an initial analysis and classification of trainees’ behaviours in facing a proof problem in arithmetic. The classification is realized according to interpretative keys based on the following theoretical aspects: a) The activation of conceptual frames through which interpreting the expressions produced during the proving activity (Arzarello et Al. 1994, 2001); b) The role of anticipatory thoughts (Boero, 2001); c) The use of conversions and treatments in the coordination between different registers of representation (Duval, 2006)
ANALYSIS OF THE TEACHER’S ROLE IN AN APPROACH TO ALGEBRA AS A TOOL FOR THINKING: PROBLEMS POINTED OUT DURING LABORATORIAL ACTIVITIES WITH PERSPECTIVE TEACHERS
No full textIn this work we present an activity we carried out with perspective teachers (PTs) during a brief training course aimed at providing them with theoretical and methodological tools useful for the analysis of class processes concerning the development of reasoning through algebraic language. After an outline of the theoretical framework we introduced during the course, we will deal with the problem of the use of theory in the analysis of class processes, highlighting the difficulties faced by PTs
THE ROLE OF THE TEACHER IN DEVELOPING PROOF ACTIVITIES BY MEANS OF ALGEBRAIC LANGUAGE
No full textThis work is part of a wider project of didactical innovation aimed at fostering students’ conscious use of algebraic language through teaching experiments on proof in elementary number theory (ENT). In this paper we will analyze the role played by the teacher as a guide to the enactment of fundamental skills for the construction of reasoning by means of algebraic language, pointing out the specific characteristics of the teacher’s effective action in serving as a role model to his/her students
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Design of digital environments aimed at fostering asynchronous working group activities: emerging categories of students' collaborative processes
No full textIn this study we focus on the collaborative processes developed within an asynchronous small group activity carried out through an instant messaging platform. To investigate the ways students communicate and collaborate during the asynchronous activity, we refer to the theoretical lenses provided by the dimensions introduced by Weinberger and Fischer (2006) to study the processes realised within computer-supported collaborative learning environments. In particular, we develop a combined analysis that takes into account both the quantity of students’ interventions and their social modes of co-construction. This analysis has revealed two main macro-categories of collaborative processes activated by the groups of students who participated in the study, which mainly differ in the level of sharing and comparison within the groups and in the aim that guided their work
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