Search results for "Overview"
showing 10 items of 158 documents
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.
Using schematic representation of resource systems to examine how first year engineering students use resources in their studies of mathematics
2018
International audience; Very little research has been done on how students use resources when studying mathematics. My project aim to examine this both quantitatively and qualitatively. The qualitative data collection includes hierarchical focus interviews and schematic representation of resource system, with the intent to impose as little terminology as possible on the students.
The use of integrals in Mechanics of Materials textbooks for engineering students: the case of the first moment of an area
2018
International audience; Research has reported on the difficulties engineering students face in relating the content of their mathematics courses to what is taught in their professional courses. One way to address these difficulties is by better understanding how mathematical notions are used in professional engineering courses. This paper analyses how the notion of first moment of an area – which is defined as an integral – is used in civil engineering courses. Basing our analysis on elements from the anthropological theory of the didactic, we are currently analysing a classic Mechanics of Materials book. Our findings indicate that although first moments are introduced as an integral, the t…
A university lecturer's role and interactions in a flipped classroom
2018
International audience; This poster explores role of the lecturer in a university level mathematics class utilizing the flipped classroom approach to teaching. The role of the lecturer is investigated using the Systematic Classroom Analysis Notation (SCAN) tool and the theoretical framework of instrumental orchestration.
Learning the concept of family of functions through the modelling process using tablets
2015
International audience; In this study, we present a teaching situation to work on the modelling process using real data taken in classroom with tablets. The situation allowed us to work on the concept of the quadratic function with a group of 11th grade students and take into account the hypothesis that the qualitative analysis of the phenomenon, the knowledge of the qualitative properties of the families of functions and the meaning of the parameters are crucial elements for the management and control of the modelling process. We observed they are key elements to choose the function used as a model and to check its adequacy throughout the modelling process. Some student's conceptions on he…
On the History of Differentiable Manifolds
2012
International audience; We discuss central aspects of history of the concept of an affine dif-ferentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.
The complexity of knowledge construction in a classroom setting
2018
International audience; We study a class of mathematics education MA students in an introductory course on Chaos and Fractals, as they grapple with the Sierpinksi triangle, and in particular with the apparent paradox that its area equals 0, while its perimeter is infinitely long. For this purpose, we network an approach for investigating the construction of knowledge in small groups with one for examining how ideas and ways of reasoning function-as-if-shared in a classroom. Our results show complexities: (i) small group work and whole class discussions mutually influence each other; (ii) ideas may function-as-if-shared in the whole class even if the majority of students have not previously …
Helping lecturers address and formulate teaching challenges: an exploratory study
2018
International audience; In this paper we present an exploratory study on the kind of questions or difficulties lecturers point out at the beginning of an educational course – to be addressed in it. These questions happen to be very general and are poorly connected to the knowledge to be taught. We suggest a twofold interpretation of this phenomenon. On the one hand, and in the line of the didactic transposition theory, teachers do not allow themselves to raise questions about the knowledge that is supposed to be their main field of expertise. On the other hand, the prevailing institutional pedagogy does not provide teachers with a fruitful enough conceptual frame to formulate this kind of q…