CHI TIẾT NGHIÊN CỨU …
Tiêu đề
Limits of Infinite Processes for Liberal Arts Majors: Two Classic Examples
Tác giả
Jorgensen T.A.; Shipman B.A.
Năm xuất bản
2012
Source title
PRIMUS
Số trích dẫn
0
DOI
10.1080/10511970.2011.629641
Liên kết
Tóm tắt
This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking. Through exploration of the monotonic convergence of a sequence to a finite limit and oscillatory convergence of a sequence to a finite limit, the two examples recast the essential mathematics in a way that allows liberal arts students to develop a mathematically correct appreciation for convergence to the limit. © 2012 Copyright Taylor and Francis Group, LLC.
Từ khóa
instructional materials; liberal arts; Limit
Tài liệu tham khảo
Cory B., Garofalo J., Using dynamic sketches to enhance preservice secondary mathematics teachers' understanding of limits of sequences, Journal for Research in Mathematics Education, 42, 1, pp. 65-96, (2011); Dudley U., The Trisectors, (1994); Fernandez E., The students' take on the epsilon-delta definition of a limit, PRIMUS, 14, 1, pp. 43-54, (2004); Newton I., Newton's Principia: The Mathematical Principles of Natural Philosophy, (1845); Ringenberg L., Informal Geometry, (1967); Shipman B.A., Active learning materials for critical thinking in a first course in real analysis, (2009); Shipman B.A., Convergence and the Cauchy property of sequences in the setting of actual infinity, Under first revision, to appear in PRIMUS; van Looy H., A chronology and historical analysis of the mathematical manuscripts of Gregorius a Sancto Vincentio (1584-1667), Historia Mathematica, 11, pp. 57-75, (1984); Wantzel P., Recherches sur les moyens de reconnaitre si un probleme de geometrie peut se resoudre a la regle et au compas, Journal de Mathematiques Pures et Appliquees, 2, pp. 366-372, (1837)
Nơi xuất bản
Taylor and Francis Inc.
Hình thức xuất bản
Article
Open Access
Nguồn
Scopus