Limits Problem Solving in Engineering Careers: Competences and Errors
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33104
Limits Problem Solving in Engineering Careers: Competences and Errors

Authors: Veronica Diaz Quezada

Abstract:

In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: Engineering education, errors, limits, mathematics competences, problem solving.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3299965

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1322

References:


[1] F. Castrillón. E. Arenas. D. Carmona. and B. Garcés. “Una Propuesta para Fortalecer el Énfasis Profesional del Currículo de Ingeniería Química”. Formación Universitaria. vol. 9. no.1. pp.35-44. 2016.
[2] M. Albert-Gómez. M. García-Pérez. and C. Pérez-Molina. “Competencias. formación y empleo. Análisis de necesidades en un programa de Master en Ingeniería”. Formación Universitaria. vol.10. no.2. pp.43-56. 2017.
[3] D. Denyer. D. Tranfield. and J. E. Van Aken. “Developing design propositions through research synthesis”. Organization Studies. (on line). vol.29. pp.249- 269. 2008.
[4] P. Perrenoud. Diez nuevas competencias para enseñar. Invitación al viaje. Barcelona: Graó. 2001.
[5] S. Blázquez. T. Ortega. S. Gatica. and J. Benegas.” Una conceptualización de límite para el aprendizaje inicial de análisis matemático en la Universidad”. Revista Latinoamericana de Investigación en Matemática Educativa. vol. 9. no. 2. pp. 189-209. 2006.
[6] A. Contreras. and M. García. Investigaciones sobre límites. España: Servicio de publi¬caciones Universidad de La Laguna. 2015.
[7] J. A.. Fernández-Plaza. F. J. Ruiz-Hidalgo. and L. Rico. “Razonamientos basados en el con¬cepto de límite finito de una función en un punto”. Enseñanza de las Ciencias. vol. 33. no. 2. pp. 211-229. 2015.
[8] K. Juter. K. “Students’ perceptions of limits”. in The First Sourcebook on Nordic Research in Mathematics Education. B. Sriraman et al. Ed. Charlotte. NC: IAP. 2010. pp. 419-430.
[9] C- Fernández. G. Sanchez-Matamoros. M.Moreno. and M.L. Callejo. “La coordinación de las aproximaciones en la comprensión del concepto de límite cuando los estudiantes para profesor anticipan respuestas de estudiantes. Enseñanza de las Ciencias. vol.36. no.1. pp.143-162. 2018.
[10] A. Zollman. “University students’ limited knowledge oflLimits – from Calculus through Differential Equations”. in 12th International Conference of Mathematics Education in the Future ProjectAt: Herceg Novi. Montenegro. 2014.
[11] J. E. Szydlik. “Mathematical beliefs and conceptual understanding of the limit of a function”. Journal for Research in Mathematics Education. vol.31. no.3. pp.258-276. 2000.
[12] J. Bezuidenhout. “Limits and continuity: Some conceptions of first-year students”. International Journal of Mathematical Education in Science and Technology. vol.32. no.4. pp. 487-500. 2001.
[13] M. Oehrtman. “Collapsing dimensions. physical limitation. and other student metaphors for limits concepts”. Journal for Research in Mathematics Education. vol.40. no. 4. pp.396-426. 2009.
[14] M. Przenioslo. “Images of the limit of function formed in the course of mathematical studies at the university”. Educational Studies in Mathematics. vol.55. pp.103-132. 2004.
[15] K. H. Roh. “An empirical study of students understanding of a logical structure in the definition of limit via the-strip activity”. Educational Studies in Mathematics. vol. 73. pp. 263-279. 2010.
[16] R. W Cappetta. and A. Zollman. “Agents of change in promoting reflective abstraction: A quasi-experimental. study on limits in college calculus”. Journal of Research in Mathematics Education. vol. 2. no.3. pp.343-357. 2013.
[17] B. L. Cory. and J. Gaofalo. “Using dynamic sketches to enhance preservice secondary mathematics teachers understanding of limits of sequences”. Journal for Research in Mathematics Education. vol.42. no.1. pp.65-97. 2011.
[18] P. Dawkins. “Metaphor as a possible pathway to more formal understanding of the definition of sequence convergence”. Journal of Mathematical Behavior. vol.31. no.3. pp.331-343. 2012.
[19] K. Beynon. and A. Zollman. “Lacking a rigorous concept of limit: Advanced nonmathematics students’ personal concept definitions”. Journal Investigation in Mathematics Learning. vol.8. no.1. pp. 47-62. 2016.
[20] S. Liang. “Teaching the concept of limit by using conceptual conflict strategy and Desmos graphing calculator”. International Journal of Research in Education and Science. vol. 2. no.1. pp.35-48. 2016.
[21] J. Kirkley. Principles for teaching problem solving. Bloomington: PLATO Learning. 2003.
[22] A. H. Schoenfeld. “Reflections on problem solving theory and practice”. The Mathematics Enthusiast. vol.10. no. 1-2. pp. 9–32. 2013.
[23] K. Wang. “Implications from Polya and Krutetskii”. in 12th International Congress on Mathematical Education. S.J. Cho. Ed. Seoul. Korea: COEX. 2012.
[24] J. Díaz. and R. Díaz. “Los métodos de resolución de problemas y el desarrollo del pensamiento matemático”. Bolema. vol. 32. no. 60. pp.57-74. 2018.
[25] V. Díaz. and A. Poblete. “A model of professional competences in mathematics and didactic knowledge of teachers”. International Journal of Mathematical Education in Science and Technology. vol. 48. no. 5. pp.702-714. 2017.
[26] V. Díaz. “The competence of solving mathematical problems in the formation of ethical values” World Academy of Science, Engineering and Technology International Journal of Educational and Pedagogical Sciences. vol. 12. no.12. pp.1671-1676. 2018.
[27] V. Díaz. and A. Poblete. Evaluación Longitudinal de Aprendizajes Matemáticos. Objetivos Transversales e Indicadores de Contexto (Longitudinal Evaluation of Mathematical Learning. Transversal Objectives and Context Indicators). Santiago: Comisión Nacional de Investigación Científica y Tecnológica. (Project Fondecyt N°1040035). 2004.
[28] S. W. Siyepu. “Analysis of errors in derivatives of trigonometric functions”. International Journal of STEM Education. vol. 2. no.16. 2015.
[29] K. Brodie. Teaching mathematical reasoning in secondary school classrooms. London: Springer. 2010.
[30] D. Drews. “Children’s mathematical errors and misconceptions: perspectives on the teacher’s role”. in Children Errors in Mathematics: Understanding common Misconceptions in Primary Schools. A. Hansen Ed. Britain: Paperback. 2005. pp.14–21.
[31] D. Foster. “Making meaning in algebra examining students’ understandings and misconceptions”. Assessing Mathematical Proficiency. vol.53. pp.163–176. 2007.
[32] K. Luneta. and P. J. Makonye. “Learner errors and misconceptions in elementary analysis: A case study of a grade 12 class in South Africa”. Acta Didactica Napocensia. vol. 3. no.3. pp.35–46. 2010.
[33] J. Ryan. and J. Williams. Mathematical Discussions with Children: Exploring Methods and Misconceptions as a Teaching Strategy. Manchester: Centre for Mathematics Education. University of Manchester. 2000.
[34] J. Muzangwa. and P. Chifamba. “Analysis of errors and misconceptions in the learning of calculus by undergraduate students”. Acta Didactica Napocensia. vol. 5. no.2. pp.1-10. 2012.
[35] N. Movshovitz-Hadar. O. Zaslavski. and S. Inbar. “An empirical classification model for errors in high school mathematics”. Journal for Research in Mathematics Education. vol.18. no.1. pp.3-14. 1987.
[36] R. Sampieri. R. Metodología de la Investigación. México: Mc Graw Hill. 2014.
[37] N. M. Murdiyani. “Developing non-routine problems for assessing students' mathematical literacy”. Journal of Physics: Conference Series. vol. 983. no.1. 2018.
[38] M. Pantziara. A. Gagatsis. and I. Elia “Using diagrams as tools for the solution of non-routine mathematical problems”. Educational Studies in Mathematics. vol.72. no.1. pp.39-60. 2009.
[39] J. Sweller. R. Clark. and P. Kirschner. “Teaching general problem-solving skills is not a substitute for. or a viable addition to. teaching mathematics”. Notices of the American Mathematical Society. vol.57. pp.1303-1304. 2010.
[40] D. Harris. et al. “Mathematics and its value for engineering students: what are the implications for teaching?” International Journal of Mathematical Education in Science and Technology. vol.46. no. 3. pp. 321-336. 2014.