### HOW DOES PRE-SERVICE MATHEMATICS TEACHER PROVE THE LIMIT OF A FUNCTION BY FORMAL DEFINITION?

#### Abstract

*f(x)*and

*L*process, (3) simplifying value in the absolute sign, (4) solving the inequality, and (5) finding the delta value. The stage of proving consisted of (1) stating positive epsilon, (2) defining delta, (3) stating positive delta, (4) substituting the constants and delta values in the initial statement of formal definition, and (5) solving the inequality to create the final inequality statement of the formal definition.

#### Keywords

#### Full Text:

PDF#### References

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

Bennet, E. & Maniar, N. (2007). Are Videoded Lectures an Effective Teaching Tool?. Retrieved from http://podcastingforpp.pbworks.com/f/Bennett%20plymouth.pdf.

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. Retrieved from https://www.safarimontage.com/pdfs/training/UsingEducationalVideoInTheClassroom.pdf.

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.

Hendroanto, A., Istiandaru, A., Syakrina, N., Setyawan, F., Prahmana, R. C. I., & Hidayat, A. S. E. (2018). How Students Solves PISA Tasks: An Overview of Students’ Mathematical Literacy. International Journal on Emerging Mathematics Education, 2(2), 129-138.

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

Karatas, I., Guven, B., & Cekmez, E. (2011). A Cross-age Study of Students' Understanding of Limit and Continuity Concepts. Boletim de Educação Matemática, 24(38), 245-264.

Kim, D. J., Kang, H., & Lee, H. J. (2015). Two different epistemologies about limit concepts. International Education Studies, 8(3), 138-145.

Kinnari-Korpela, H. (2015). Using Short Video Lectures to Enhance Mathematics Learning--Experiences on Differential and Integral Calculus Course for Engineering Students. Informatics in Education, 14(1), 67-81.

Maher, C. A., & Sigley, R. (2014). Task-based interviews in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 579-582). Dordrecht: 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. Proceedings of the 7th WSEAS international conference on engineering education, 21-25. Wisconsin, USA: World Scientific and Engineering Academy and Society.

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

Oktaviyanthi, R., & Dahlan, J. A. (2018). Developing Guided Worksheet for Cognitive Apprenticeship Approach in Teaching Formal Definition of The Limit of A Function. IOP Conference Series: Materials Science and Engineering, 335(1), 012120.

Oktaviyanthi, R., & Herman, T. (2016). A delivery mode study: The effect of self-paced video learning on first-year college students’ achievement in calculus. AIP Conference Proceedings, 1782(1), 050012.

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

Petersen, W. L. (2009). A Few Examples of Limit Proofs. Retrieved from http://www.math.utah.edu/~petersen/1210/LimitProofs.pdf.

Row, 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, 4, 105-112. Seoul: PME.

Schwarz, B., & Kaiser, G. (2009). Professional competence of future mathematics teachers on argumentation and proof and how to evaluate it. Proof and Proving in Mathematics Education, 19, 190-195.

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.

Shahrill, M., Putri, R. I. I., Zulkardi, & Prahmana, R. C. I. (2018). Processes involved in solving mathematical problems. AIP Conference Proceedings, 1952(1), 020019.

Tall, D. (1992). The Transition to Advanced Mathematical Thinking: Functions, Limits, Infinity and Proof. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 495-514). New York: National Council of Teachers of Mathematics.

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: University of Chicago.

Weber, K. (2010). Mathematics majors' perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12(4), 306-336.

DOI: https://doi.org/10.22342/jme.9.2.5684.195-212

### Refbacks

- There are currently no refbacks.

**Journal on Mathematics Education**

Kampus FKIP Bukit Besar

Jl. Srijaya Negara, Bukit Besar

Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Journal on Mathematics Education is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

View My Stats