ERIC Number: EJ681883
Record Type: Journal
Publication Date: 2004
What Is First-Year Mathematics Students' Actual Knowledge about Improper Integrals?
Gonzalez-Martin, Alejandro S.; Camacho, Matias
International Journal of Mathematical Education in Science and Technology, v35 n1 p73-89 2004
This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of given improper integrals, but also intuitive questions and some paradoxical results too (for example, a figure with an infinite longitude which closes the same area as the unit circumference, or an infinite figure with a finite volume). In particular, the students were asked to interpret most of the results they had obtained. Answers given by the students to each of the questions were categorized, which allowed some initial conclusions to be reached regarding this research. From analyses carried out, one can conclude that there are students who have difficulties in articulating the different systems of representation, and have problems in connecting and relating this knowledge as a generalization of previous concepts, such as definite integrals, series and sequences.
Descriptors: College Mathematics, Higher Education, Calculus, Mathematics Education, Algebra, College Freshmen, Graphs
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: Higher Education
Authoring Institution: N/A