### Using APOS Theory Framework: Why Did Students Unable To Construct a Formal Proof?

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Andrew, L. (2009). Creating a Proof Error Evaluation Tool for Use in the Grading of Student-Generated Proofs. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 2009. 19 (5), 447-462.

Arnon, I., Cottrill, J., Dubinsky, E., OktacÂ¸ A., Fuentes, S.R., Trigueros, M., Weller, K. (2013). APOS Theory A Framework for Research and Curriculum Development in Mathematics Education. New York : Springer.

Baker, D. & Campbell, C. (2004). Fostering the development of mathematical thinking: Observations from a proofs course. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 14 (4), 345- 353.

Bruce M. McLaren, B.M., van Gog, T. Ganoe, C. & Karabinos, M. (2016). The efficiency of worked examples compared to erroneous examples, tutored problem solving, and problem solving in computer-based learning environments. Computers in Human Behaviour , 55, 87-99

Cai, J. (2000). Mathematical thinking involved in US and Chinese students' solving of process-constrained and process-open problems. Mathematical Thinking and Learning, 2(4), 309-340.

Creswell, W.J. (2012). Educational Research : planning, conducting, and evaluating quantitative and qualitative research - 4th Edition. Boston : Pearson Education.

Dreyfus, T. (1991). Advanced Mathematical Thinking Processes. In David Tall (Eds.), Advanced Mathematical Thinking (pp. 25-41). New York : Springer Netherlands.

Dreyfus, T. (2002). Advanced mathematical thinking processes. In David Tall (Eds.), Advanced Mathematical Thinking (pp. 25-41). New York : Kluwer Academic Publishers.

Dubinsky, E. (2002). Reflective abstraction in advanced mathematical thinking. In David Tall (Eds.), Advanced Mathematical Thinking (pp. 95-126). New York : Kluwer Academic Publishers.

Dubinsky, E., & Tall, D. (2002). Advanced mathematical thinking and the computer. In David Tall (Eds.), Advanced Mathematical Thinking (pp. 231-248). New York : Kluwer Academic Publishers.

Gibson, D. (1998). Students' use of diagrams to develop proofs in an introductory analysis course. Students' proof schemes. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in Collegiate Mathematics Education, III, 284-307. Washington : AMS.

JAppinen, A. K. (2005). Thinking and content learning of mathematics and science as cognitional development in content and language integrated learning (CLIL): Teaching through a foreign language in Finland. Language and Education, 19(2), 147-168.

Kilpatrick, J., Swafford, J. & Findell. (2002). Adding it-up : Helping Children Learn Mathematics. National Research Council. National Academy Press. Washington DC

Margulieux, L.E & Catrambone, R. (2016). Improving problem solving with sub-goal labels in expository text and worked examples. Learning and Instruction , 42, 58-71.

Mason, J., Burton, L. & Stacey, K. (2010). Thinking Mathematically. Second Edition. London : Pearson.

McLaren, B.M.,van Gog, T., Ganoe, C., Karabinos, M. & Yaron, D. (2016). The efficiency of worked examples compared to erroneous examples, tutored problem solving, and problem solving in computer-based learning environments. Computers in Human Behavior , 55 (1), 87-99

Mejia-Ramos, J.P., Fuller, E., Weber, K., Rhoads K. & Samkoff, A. (2012). An assessment model for proof comprehensionin undergraduate mathematics. Educational Studies in Mathematics 79, 3-18.

Moore, R.C. (1994). Making the transition to Formal Proof. Educational Studies in Mathematics. 249-266.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: The Council.

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 (1), 4-36.

Sowder, L. & Harel, G. (2003). Case studies of mathematics majors' proof understanding, production, and appreciation. Canadian Journal of Science, Mathematics and Technology Education, 3 (2), 251-267.

Syamsuri, Purwanto, Subanji & Irawati, S. (2016). Characterization of Students Formal-Proof Construction in Mathematics Learning. Communications in Science and Technology, 1(2), 42-50.

Tall, D. (1992). The psychology of advanced mathematical thinking : functions, limits, infinity and proof. In Douglas A. Grouws (Eds.), Handbook of Research on Mathematics Teaching and Learning (pp. 495-514). New York : Macmilan Publishing Company.

Tall, D. (2002). The transition to advanced mathematical thinking. In David Tall (Eds.), Advanced Mathematical Thinking (pp. 3-21). New York : Kluwer Academic Publishers.

Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20(2), 5-24.

Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor's lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior, 23, 115-133.

Weber, K. (2006). Investigating and teaching the processes used to construct proofs. In F.Hitt, G. Harel& A. Selden (Eds), Research in Collegiate Mathematics Education, VI, 197-232. AMS.

Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003). Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), Research in Collegiate Mathematics Education V (pp. 97-131). Providence, Rhode Island: American Mathematical Society.

DOI: http://dx.doi.org/10.12928/ijeme.v1i2.5659

### Refbacks

- There are currently no refbacks.

Copyright (c) 2017 Syamsuri Syamsuri, Purwanto Purwanto, Subanji Subanji, Santi Irawati

This work is licensed under a Creative Commons Attribution 4.0 International License.

**International Journal on Emerging Mathematics Education**

Kampus 2 Universitas Ahmad Dahlan

Jalan Pramuka No. 42, Pandeyan, Umbulharjo, Yogyakarta - 55161

Telp. (0274) 563515, ext. 4902; Fax. (0274) 564604

Email: ijeme@uad.ac.id

p-ISSN: 2549-4996 | e-ISSN: 2548-5806

This work is licensed under a Creative Commons Attribution 4.0 International License