Students’ Difficulties and Misconceptions in Learning Concepts of Limit, Continuity and Derivative
Keywords:
Conceptual knowledge, Learning calculus, Limit Concept, Misconception, Procedural knowledge
Abstract
This study aimed at examining students’ difficulties and misconceptions in learning concepts of calculus at preparatory secondary schools of Dire Dawa city. Accordingly, students’ conception of concepts in calculus, students’ misconceptions, and factors influencing the teaching-learning of concepts were surveyed. Descriptive survey approach was used as a research method for the study. Achievement test was the prime instrument used for gathering the necessary data. One hundred thirty-five students were involved in the study. The study result indicated gaps between the aspiration of the mathematics syllabi prepared by the Ethiopian Federal Ministry of Education and students’ actual achievement. It also indicated the presence of misconceptions, on the part of students, regarding the basic concepts of calculus.
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References
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Engelbreeht, J. et.al, (2007). Understanding Students’ Performance and Confidence in Procedural and Conceptual Mathematics. Retrieved from http://Science.up.ac.za/muti/conceptualmath.pdf. Ellis, R. and Gulick, D. (1993). Calculus with Analytic Geometry. (5th ed). Gay,L.R. and Airasia,P.(2000). Educational Research: Competencies for Analysis and Application (6th ed). New Jersey: prentice-Hall, inc.
Koul, L. (1996). Methodology of Educational Research. School Revised Edition. New Delhi: Vikas. Larcombe A. (1985). Mathematical Learning Difficulties in the Secondary School. Philadelphia: Open University Press. MoE. (2006a). Mathematics Syllabus for Grade 11 and 12. Ministry of Education, Addis Ababa, Ethiopia MoE.(2006b). Mathematics students’ textbook, Grade 12, Revised Edition. Ministry of Education, Addis Ababa, Ethiopia NTCM. (2002). Curriculum and Evaluation Standard for School Mathematics. Reston,VA: Author. Orton,A.(1980a). A cross-sectional study of the understanding of elementary calculus in adolescents and young adults, unpublished PhD. Leeds University. Orton, A.(1980b). An investigation into understanding of elementary calculus in adolescents and adults, Cognitive Development Research in Science and Mathematics, University of Leeds 201-215. Rittle-Johnson, B. and Siegler, R.S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In Donald, C (ed.). The development of mathematical skills (pp. 75-328). Hove, UK: Psychology Press. Roseman, Louis (1985). The Essential Concepts for Remediation in Mathematics. The Mathematics Teacher, vol. 78, No. 7
Schneider, M. and Stren, E. (2005). Conceptual and Procedural Knowledge of Mathematics Problem: Their Measurement and Their Causal Interrelations. Retrieved from http://www.cogsci.rpi.edu/CSjarchive/procceding/2005/docs/p1955.pdf
Schwarzenberger, R.L.E& Tall, D.O. (1978).Conflicts in the learning of real numbers and limits, Mathematics Teaching 82, 44-49.
Stump, D. (2002). The Limit Concept. Retrieved from http://www.pa.msu.edu/~Stump/Stump Tall, D. (1980). Mathematical Intuition, with Special Reference to Limiting Processes. Proceedings of the Fourth international congress on Mathematics education. Berkeley: 170-181. Tall, D. and Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity. Educational Studies in Mathematics, 12:151-169.
Bosse, M. J. and Bahr, D. L. (2005). The State of Balance between Procedural Knowledge and Conceptual Understanding in Mathematics Teachers Education. Retrieved from http://www.Cimt.plymouth.ac.uk/journal/bossebahr.pdf Cohen, L. and Manion, L. (1994). Research Method in Education (4th ed). Routledge New York. Cornu, B. (1981). Advanced Mathematical Thinking. In Nesher, P. and Kilpatrick, J. (eds), Mathematics and Cognition.(pp 113-134). Cottril, J. et.al. (1996). Understanding the Limit Concept: Beginning with a Coordinated Process Schema. Journal of Mathematical Behavior, 15,167-192.
Engelbreeht, J. et.al, (2007). Understanding Students’ Performance and Confidence in Procedural and Conceptual Mathematics. Retrieved from http://Science.up.ac.za/muti/conceptualmath.pdf. Ellis, R. and Gulick, D. (1993). Calculus with Analytic Geometry. (5th ed). Gay,L.R. and Airasia,P.(2000). Educational Research: Competencies for Analysis and Application (6th ed). New Jersey: prentice-Hall, inc.
Koul, L. (1996). Methodology of Educational Research. School Revised Edition. New Delhi: Vikas. Larcombe A. (1985). Mathematical Learning Difficulties in the Secondary School. Philadelphia: Open University Press. MoE. (2006a). Mathematics Syllabus for Grade 11 and 12. Ministry of Education, Addis Ababa, Ethiopia MoE.(2006b). Mathematics students’ textbook, Grade 12, Revised Edition. Ministry of Education, Addis Ababa, Ethiopia NTCM. (2002). Curriculum and Evaluation Standard for School Mathematics. Reston,VA: Author. Orton,A.(1980a). A cross-sectional study of the understanding of elementary calculus in adolescents and young adults, unpublished PhD. Leeds University. Orton, A.(1980b). An investigation into understanding of elementary calculus in adolescents and adults, Cognitive Development Research in Science and Mathematics, University of Leeds 201-215. Rittle-Johnson, B. and Siegler, R.S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In Donald, C (ed.). The development of mathematical skills (pp. 75-328). Hove, UK: Psychology Press. Roseman, Louis (1985). The Essential Concepts for Remediation in Mathematics. The Mathematics Teacher, vol. 78, No. 7
Schneider, M. and Stren, E. (2005). Conceptual and Procedural Knowledge of Mathematics Problem: Their Measurement and Their Causal Interrelations. Retrieved from http://www.cogsci.rpi.edu/CSjarchive/procceding/2005/docs/p1955.pdf
Schwarzenberger, R.L.E& Tall, D.O. (1978).Conflicts in the learning of real numbers and limits, Mathematics Teaching 82, 44-49.
Stump, D. (2002). The Limit Concept. Retrieved from http://www.pa.msu.edu/~Stump/Stump Tall, D. (1980). Mathematical Intuition, with Special Reference to Limiting Processes. Proceedings of the Fourth international congress on Mathematics education. Berkeley: 170-181. Tall, D. and Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity. Educational Studies in Mathematics, 12:151-169.
Published
2012-12-01
Section
Articles