Rina Oktaviyanthi, Tatang Herman, Jarnawi Afgani Dahlan


The purpose of this study was to investigate the flow of thoughts of pre-service mathematics teacher through the answers of limit of a function evaluation by formal definition. This study used qualitative approach with descriptive method. The research subjects were students of mathematics education study program, Universitas Serang Raya. After analyzing the students’ written answers, interview was conducted to get further explanation on their strategies and common mistakes. This study found that based on the students’ results in the limit of a function evaluation by formal definition, there were common strategies, i.e. (1) preparation of proof which consisted of (a) determining delta value by the final statement of formal definition, (b) substitution process, (c) simplifying value in absolute sign, (d) solving inequality, (e) finding delta value; and (2) proving which consisted of (f) positive epsilon statement, (g) defining delta, (h) positive delta statement, (i) substitution of constants and delta values in the initial statement of formal definition, (j) solving inequality to create inequality in the final statement of formal definition.


Formal Definition of Limit; Pre-Service Mathematics Teacher; Proving Limit of Function; Proving Limit Strategy


Astawa, I. W. P., Budayasa, I. K., & Juniati, D. (2018). The Process of Student Cognition in Constructing Mathematical Conjecture. Journal on Mathematics Education (IndoMS-JME), (9) 1, 15-26. Palembang: IndoMS.

Bennet, E. & Maniar, N. (2007). Are Videoded Lectures an Effective Teaching Tool?, (Online), ( &rep=rep1&type=pdf), diakses 12 Januari 2018

Beynon, K. A. & Zollman, A. (2015). Lacking A Formal Concept of Limit: Advanced Non-Mathematics Students’ Personal Concept Definitions. Investigations in Mathematics Learning, 8 (1), 47-62.

Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, CA: SAGE Publications.

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches, 4th ed. Thousand Oaks, CA: SAGE Publications.

Cruse, E. (2007). Using Educational Video in the Classroom: Theory, Research and Practice, (Online), ( training/usingeducationalvideointheclassroom.pdf), diakses 12 Januari 2018

Davis, R., & Vinner, S. (1986). The notion of limit: Some seemingly unavoidable misconception stages. Journal of Mathematics Behavior, 5, 281-303.

Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication & Technology, 30 (4), 233-252. doi: 10.1007/BF02765185.

Ibrahim, M. (2012). Implications of Designing Instructional Video Using Cognitive Theory of Multimedia Learning. Critical Questions in Education, 3 (2), 83-104.

Ilhan, K., Bulent, G. & Erdem, C. (2010). A Cross-Age Study of Students’ Understanding of Limit and Continuity Concepts. Bolema, Rio Claro (SP), 24 (38), 245-264.

Kinnari-Korpela, H. (2015). Using Short Video Lectures to Enhance Mathematics Learning – Experiences on Differential and Integral Calculus Course for Engineering Stduents. Informatics in Education, 14 (1), 67-81. doi: 10.15388/infedu.2015.05.

Kim, D. J., Kang, H. & Lee, H. J. (2015). Two Different Epistemologies about Limit Concepts. International Education Studies, 8 (3), 138-145.

Maher, C. A. & Sigley, D. (2014). Task-based Interviews in Mathematics Education. In Lerman, S. (Ed.), Encyclopedia of Mathematics Education, 579-582. London: Springer.

Mokhtar, M. Z., Tarmizi, M. A. A., Tarmizi, R. A., & Ayub, A. F. M. (2010). Problem-based learning in calculus course: Perception, engagement and performance. Paper presented at the Latest Trends on Engineering Education-7th WSEAS International Conference on Engineering Education, EDUCATION'10, International Conference on Education and Educational Technologies, (Online), (, diakses 29 April 2017

Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27 (3), 249-266.

Oktaviyanthi, R. & Supriani, Y. (2015). Utilizing Microsoft Mathematics in Teaching and Learning Calculus. Journal on Mathematics Education (IndoMS-JME), (6) 1, 63-76. Palembang: IndoMS.

Oktaviyanthi, R. & Herman, T. (2016). A Delivery Mode Study: The Effect of Self-Paced Video Learning on First-Year College Students’ Achievement in Calculus. Paper presented at the 4th International Conference on Quantitative Sciences and Its Applications, Malaysia. Retrieved from:

Oktaviyanthi, R. & Dahlan, J. A. (2017). Developing Guided Worksheet for Cognitive Apprenticeship Approach in Teaching Formal Definition of The Limit of A Function. Paper presented at the 2nd International Conference on Mathematics, Science, Education and Technology, Indonesia. Retrieved from:

Oktaviyanthi, R., Herman, T., & Dahlan, J. A. (2018). Guided Worksheet Formal Definition of Limit. Manuscript submitted for publication.

Petersen, W. L. (2009). A Few Examples of Limit Proofs, (Online), (, diakses 15 Januari 2018

Roh, K. H. (2007). An activity for development of the understanding of the concept of limit. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31th Conference of the International Group for the Psychology of Mathematics Education Volume 4, 105-112. Seoul: PME.

Schwarz, B., & Kaiser, G. (2009). Professional competence of future mathematics teachers on argumentation and proof and how evaluate it. In F-L. Lin, F-J. Hsieh, G. Hanna, & M. de Villiers (Eds.), Proceeding of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education Volume 1, 190-195. Taiwan: The Department of Mathematics, National Taiwan Normal University Taipe.

Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?. Journal for Research in Mathematics Education, 34, 4–36.

Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, 495-511. New York: National Council of Teachers of Mathematics, Macmillan.

Tall, D. (1998). The cognitive development of proof: Is mathematical proof for all or for some?. Paper presented at the Conference of the University of Chicago School Mathematics Project, Chicago, 1998. Chicago: University of Chicago.

Weber, K. (2010). Mathematics majors’ perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12, 306–336. doi: 10.1080/10986065.2010.495468



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Journal on Mathematics Education
Program S3 Pendidikan Matematika FKIP Universitas Sriwijaya
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