Search results for " Overview"
showing 10 items of 155 documents
Reading data from graphs: a study on the role of language.
2015
International audience; The work described in this paper is framed in a larger study focused on written argumentations produced by university students in tasks regarding graphs, conversions between graphs and their analytic properties and relations among different graphs. Using the functional linguistics framework, we analyse difficulties related to an examination task on functions and their derivatives. The use of colloquial and literate registers in mathematics problem solving is the lens through which we analyse and discuss the errors. We draw attention to the difficulties concerning the use of literate registers and how these difficulties influence the errors in the interpretations of t…
Tool use in mathematics: A framework
2015
International audience; In the course of research into the interpretation of tools in the didactics of mathematics I found both voids and conflicts. This paper presents the results of my research and a resultant statement on tool use in mathematics education. The statement incorporates constructs from several theoretical frameworks and I consider the consistency of my statement on tool use with regard to activity theory.
Tasks and Digital Tools
2016
International audience; This chapter considers scholastic tasks with digital tools. The first two sections consider tasks in ‘ordinary’ classrooms (tasks for learning) and issues relating to tasks using mathematical software. The first section presents examples of tasks with digital tools to highlight potential problems and opportunities for learning. The second section considers issues arising from the literature on tasks design with and without digital tools. The final section looks at task-tool issues in larger-than-the-individual classroom research and in assessment; it also comments of avenues for further development
Mathematics teachers and digital tools
2016
International audience; This chapter considers mathematics teachers’ appropriation and classroom use of digital tools. The first section considers teachers—who are they, how are they conceived in the literature and what aspects of teachers have been studied? The second section examines twenty-first century research on mathematics teachers using digital tools. This sheds light on the complexity of mathematics teachers’ appropriation and classroom use of digital tools but what we find is that our focus is too narrow and we need to consider digital tools within the range of resources use in planning and realising their lessons, which leads us to the third section, mathematics teachers using re…
From art to geometry: Aesthetic and beauty in the learning process
2015
Starting from the concept that knowledge comes as element of mediation between the convergent thinking, founded on experience, and the divergent thinking, placed in the perceptive, intuitive, creative dimension, in this paper we want to present an idea for developing an educational path combining the concept of “beauty” and some historical notes. It is possible to use this dissertation as a starting point to conceive a geometric laboratory that drawing inspiration from artistic works, get to create geometric shapes provided with fascinating symmetries
An empirical study of the understanding of formal propositions about sequences, with a focus on infinite limits
2018
International audience; In this paper, we analyze the answers of one group of high-school students and two groups of first-year University students to a questionnaire designed to test their level of recognition and understanding of the formal definition of the concept of infinite limit. Although this empirical study is ancillary to a larger project centred on didactic engineering, its analysis sheds light on the key issue of the logical prerequisites for the learning of the fundamental concepts of analysis. It also provides a new tool to investigate students' concept-image of limits, and assess the impact of teaching contexts and teaching paths.
Are all denumerable sets of numbers order-isomorphic?
2018
International audience; In this paper we study cognitive conflicts on the issue of number sets being dense, ordered and denumerable. We first provide historical-epistemological background related to these notions. Then we consider the cognitive conflicts under the lenses of concept image and concept definition, which we use to analyse empirical data collected in order to understand better the didactical and cognitive issues at stake.
Defining as discursive practice in transition – Upper secondary students reinvent the formal definition of convergent sequences
2018
International audience; The investigation of limits is at the heart of analysis at university. Accordingly, it is a worthwhile topic for transition courses. The present study engages upper secondary students in reinventing the definition of convergent sequences. Using a commognitive framework, the central development stages of the definition from experiential to abstract are empirically investigated in terms of activated secondary school discourses. The students' familiarity with secondary school discourses is critical, as it allows them to transition from grasping processes with metaphors towards grasping them as formal and abstract objects. For this, school objects act as intermediate s…
Non-standard Problems in an Ordinary Differential Equations Course
2018
International audience; We report first results from a teaching intervention in an ordinary differential equations (ODEs) course for engineering students. Our aim is to challenge traditional approaches to teaching of Existence and Uniqueness Theorems (EUTs) through the design of problems that students cannot solve by applying well-rehearsed techniques or familiar methods. We analyse how the use of nonstandard problems contributes to the development of students' conceptual understanding of EUTs and ODEs.
Teachers' procedures when introducing algebraic expression in two Norwegian grade 8 classrooms
2015
International audience; We investigate similarities and differences in two teachers’ way of introducing algebraic expressions by designed examples. One teacher moves from the specific to the general, and the other moves from the general to the specific. They both mediate the passage from the students’ real world and the school mathematics they know, to algebra.