Using APOS Theory Framework: Why Did Students Unable To Construct a Formal Proof?
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., Oktac¸ 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.
Jäppinen, 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.
Article MetricsAbstract view : 629 times
PDF - 326 times
- There are currently no refbacks.
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
This work is licensed under a Creative Commons Attribution 4.0 International License