Search results for "Teaching and learning of analysis and calculus"
showing 9 items of 9 documents
A study of transitions in an undergraduate mathematics program
2018
International audience; In this paper, we introduce an in-progress study of the transitions students face as they advance in their mathematics courses. Previous work has discussed the changes that occur in the transition from high school to university. With regards to the knowledge students are expected to learn, however, significant similarities have been noted: to do well in introductory university courses, students can learn to solve a particular subset of tasks through routinized techniques, with limited awareness of the supporting mathematical theory. In contrast, students in advanced courses are required to work with and on that theory. The first stage of our project aims to better un…
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…
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 …
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.
Weekly homework quizzes as formative assessment for Engineering students are a fair and effective strategy to increase learning?
2018
International audience; A strategy to apply online weekly homework quizzes as formative assessment for Engineering students was designed and tested in order to study if it increases student's learning. The strategy was to make optional weekly online quizzes not randomly generated that students may retry over and over again until to reach the correct answer, they contribute to 10% of grade but only if students get 45% or more in traditional assessment.The quizzes were applied to two different mathematics courses (Single and Multivariable Calculus) of two different Engineering degrees, each one to around 100 students and during a semester. Student's adherence was very high, nearly all student…
First-year university students making sense of symbols in integration
2020
International audience; This paper focuses on first year university engineering students and their sensemaking of integration and its symbolism. Through a semiotic approach, attention is given to two students and their attempt to verbally express their reflections on integration and the related meaning of symbols. Findings suggest that students tend to interpret the symbols mainly as operations, in terms of calculations to be carried out. They express uncertainty concerning what the symbols stand for, and the mathematical objects they represent. For example, the symbols ∫ and are respectively conceived of as “finding the integral with respect to x” and students are unclear on how Riemann su…
From single to multi-variable Calculus: a transition?
2018
International audience; We recently used the notion of praxeology from the Anthropological Theory of the Didactic to model the knowledge that is necessary for students to learn in order to succeed in an undergraduate multivariable Calculus course. We considered the presence and absence of elements of the knowledge to be taught, as proposed by curricular documents, in the knowledge to be learned, as indicated by final exams. Our results indicate that the mathematical activities expected of students at this level align with the activities observed in differential and integral Calculus, where exercise-driven assessments set students' work mainly in the recognition of types of tasks and recolle…
Bridging probability and calculus: the case of continuous distributions and integrals at the secondary-tertiary transition
2018
International audience; This paper focuses on two mathematical topics, namely continuous probability distributions (CPD) and integral calculus (IC). These two sectors that are linked by the formula P(a<=X<=b)=int_a^b f(x)dx are quite compartmented in teaching classes in France. The main objective is to study whether French students can mobilize the sector of IC to solve tasks in CPD and vice versa at the transition from high school to higher education. Applying the theoretical framework of the Anthropological Theory of the Didactic (ATD), we describe a reference epistemological model (REM) and use it to elaborate a questionnaire in order to test the capacity of students to bridge CPD and IC…
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.