Search results for " Mathematics Education"

A Teaching proposal for the study of eigenvectors and eigenvalues

2017

[EN] In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students¿ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

TAKING A LOOK AT CHINESE PEDAGOGY IN SHUXUE [MATHEMATICS]: A DIALOGUE BETWEEN CULTURES TO APPROACH ARITHMETIC AT FIRST AND SECOND ITALIAN PRIMARY CLA…

2013

The purpose of this paper is to analyze two cases of task design about straws and word problems in different cultural traditions (the Eastern and Western one). By means of two paradigmatic examples developed in Italy, we aim at showing, on the one hand, the effects and advantages of intercultural dialogue and, on the other hand, the need to take into account and to respect culturally rooted pedagogies, avoiding uncritical transfer from one culture to another. This perspective implies a reciprocal respect of the different approach modalities and hence a continuous back and forth between the practical and the deeply related theoretical dimension

Topic Study Group No. 54: Semiotics in Mathematics Education

2017

Il ruolo di Luigi Cremona nella prima formazione scientifica di Eugenio Beltrami attraverso la loro corrispondenza

In October 1862 Beltrami was appointed, before graduating, as a professor at the University of Bologna, and here he met again his friend and colleague Cremona. The correspondence between the two mathematicians clearly shows not only the intimate friendship between them, but also Cremona’s role as Beltrami’s mentor in those years. The former is indeed generous with advice, encouragement and recommendations to his friend.

Factors constraining students' establishment of algebraic generality in shape patterns: A case study of didactical situations in mathematics at a uni…

2011

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Non-Hierarchical Clustering as a method to analyse an open-ended questionnaire on algebraic thinking

2016

The problem of taking a data set and separating it into subgroups, where the members of each subgroup are more similar to each other than they are to members outside the subgroup, has been extensively studied in science and mathematics education research. Student responses to written questions and multiple-choice tests have been characterised and studied using several qualitative and/or quantitative analysis methods. However, there are inherent difficulties in the categorisation of student responses in the case of open-ended questionnaires. Very often, researcher bias means that the categories picked out tend to find the groups of students that the researcher is seeking out. In this paper, …

Commentary 1 on Reflections on Theories of Learning by Paul Ernest

2009

Paul Ernest is an internationally recognised authority on the philosophy of social-constructivism particularly in the context of mathematics education. He has published widely on the issue, perhaps his two best known and widely cited works are ‘The Philosophy of Mathematics Education’ (Ernest 1991), and ‘Social Constructivism as a Philosophy of Mathematics’ (Ernest 1998). As one engages with this short paper it is evident that one is in the company of a ‘master’ of the topic. It is quite remarkable how within the space of about 4000 words he manages to produce an erudite and informative account of 4 related theories of learning, and outline some of their implications for teaching.

Learning to Teach Mathematics: Expanding the Role of Practicum as an Integrated Part of a Teacher Education Programme

2009

The premise of the 15th ICMI Study is that teachers are key to students' opportunities to learn mathematics. What teachers of mathematics know, care about, and do is a product of their experiences and socialization, together with the impact of their professional education. The Professional Education and Development of Teachers of Mathematics assembles important new international work- development, research, theory and practice - concerning the professional education of teachers of mathematics. As it examines critical areas to reveal what is known and what significant questions and problems warrant collective attention, the volume also contributes to the strengthening of the international co…

“How Real People Really Need Mathematics in the Real World”—Authenticity in Mathematics Education

2018

This paper discusses authenticity from the perspective of mathematics education. Often, school mathematics offers students inauthentic word problems, which don’t show the authentic usefulness of mathematics in real life. In some tasks, authentic aspects are combined with inauthentic ones (e.g., an authentic context, but the question is artificial and different from what people within that context would ask). Several studies show that students are more motivated by authentic questions than by authentic contexts. Embedding these findings, I discuss issues associated with defining authenticity in education. A first issue is that philosophers use the term to characterize a person’s existential …

Analysing tasks for the Flipped Classroom from the perspective of Realistic Mathematical Education

2018

International audience; The advent of Flipped Classroom as a framework for organizing the teaching and learning of mathematics has the potential to revitalize the attention to tasks as a vehicle for meaningful learning in tertiary education. Flipped Classroom is based on the idea of student active learning under close guidance of the university teacher. Due to the possibility to engage the students in meaningful discovery of how mathematics can relate to real-life situations during in-class sessions, the tasks are seen to have a central role in a successful implementation of Flipped Classrooms. This paper explores the realistic mathematics education (RME) as a theoretical framework for task…