References
- De Villiers MD. Some adventures in Euclidean geometry. Durban: University of Durban-Westville; 1996.
- Hanna G. Proof, explanation and exploration: an overview. Educ Stud Math. 2000;44(1–2):5–23. doi: 10.1023/A:1012737223465
- Presmeg N. Overcoming pedagogical barriers associated with exploratory tasks in a college geometry course. In: Zaslavsky O, Sullivan P, editors. Constructing knowledge for teaching secondary mathematics. New York (NY): Springer; 2011. p. 279–290.
- Edwards L. Exploring the territory before proof: students’ generalizations in a computer microworld for transformation geometry. Int J Comput Math Learn. 1997;2:187–215. doi: 10.1023/A:1009711521492
- Christou C, Mousoulides N, Pittalis M, et al. Proofs through exploration in dynamic geometry environments. Int J Sci Math Edu. 2004;2(3):339–352. doi: 10.1007/s10763-004-6785-1
- Durand-Guerrier V, Boero P, Douek N, et al. Argumentation and proof in the mathematics classroom. In: Hanna G, de Villiers M, editor. Proof and proving in mathematics education. Dordrecht: Springer; 2012. p. 349–367.
- Hemmi K. Three styles characterising mathematicians’ pedagogical perspectives on proof. Edu Stud Math. 2010;75(3):271–291. doi: 10.1007/s10649-010-9256-3
- Jahnke HN, Wambach R. Understanding what a proof is: a classroom-base approach. ZDM. 2013;45(3):469–482. doi: 10.1007/s11858-013-0502-x
- Reid DA, Knipping C. Proof in mathematics education: research, learning, and teaching. Rotterdam: Sense Publishers; 2010.
- Yan X, Mason J, Hanna G. An exploratory teaching style in promoting the learning of proof. In: Dooley T, Gueudet G, editors. Proceedings of the tenth congress of the European society for research in mathematics education (CERME10); 2017 Feb 1–5; Dublin. Dublin: DCU Institute of Education and ERME; 2017. p. 283–290.
- Sinclair N, Bartolini Bussi MG, de Villiers M, et al. Recent research on geometry education: an ICME-13 survey team report. ZDM Math Edu. 2016;48(5):691–719. doi: 10.1007/s11858-016-0796-6
- Kim D, Ju MK. A changing trajectory of proof learning in the geometry inquiry classroom. ZDM. 2012;44(2):149–160. doi: 10.1007/s11858-012-0411-4
- Grenier A. Research situations to learn logic and various types of mathematics reasoning and proofs. Proceedings of the 8th Congress of the European Society for Research in Mathematics Education; Antalya, Turkey. 2013. p. 136–145.
- Lakatos I. Proofs and refutations. Cambridge: Cambridge University Press; 1976.
- De Villiers M. An illustration of the explanatory and discovery functions of proof. Pythagoras. 2012;33(3):1–8. doi: 10.4102/pythagoras.v33i3.193
- Leikin R. Problem posing for and through investigations in a dynamic geometry environment. In: Singer FM, Ellerton N, Cai J, editors. Problem posing: from research to effective practice. Dordrecht: Springer; 2015. p. 373–391.
- Mariotti MA. Justifying and proving in the Cabri environment. Int J Comput Math Learn. 2001;6:257–281. doi: 10.1023/A:1013357611987
- Caglayan G. Math majors’ visual proofs in a dynamic environment: the case of limit of a function and the ϵ-δ approach. Int J Math Educ Sci Technol. 2015;46(6):797–823. doi: 10.1080/0020739X.2015.1015465
- Chan KK, Leung SW. Dynamic geometry software improves mathematical achievement: systematic review and meta-analysis. J Educ Comput Res. 2014;51(3):311–325. doi: 10.2190/EC.51.3.c
- Olivero F, Robutti O. Measuring in dynamic geometry environments as a tool for conjecturing and proving. Int J Comput Math Learn. 2007;12(7):135–156. doi: 10.1007/s10758-007-9115-1
- Wares A. Dynamic geometry as a context for exploring conjectures. Int J Math Educ Sci Technol. 2018;49(1):153–159. doi: 10.1080/0020739X.2017.1366559
- Stupel M, Segal R, Oxman V. Teaching locus with a conserved property by integrating mathematical tools and dynamic geometric software. Aus Senior Math J. 2016;30(1):25–44.
- Mason J. Teaching as disciplined enquiry. Teachers Teaching Theory Pract. 2009;15(2):205–223. doi: 10.1080/13540600902875308
- Mason J. Teachers’ roles. In: Mason J, Johnston-Wilder J, editors. Fundamental constructs in mathematics education. New York, NY: Routledge Falmer; 2004. p. 217–222.
- Mason J. Attention and intention in learning about teaching through teaching. In: Leikin R, Zazkis R, editors. Learning through teaching mathematics: developing teachers’ knowledge and expertise in practice. Dordrecht: Springer; 2010. p. 23–48.
- Bennett J. The dramatic universe (four volumes). London: Hodder & Stoughton; 1956–1966.
- Bennett J. Elementary systematics: a tool for understanding wholes. Santa Fe (NM): Bennett Books; 1993.
- Mason J. Which medium, which message? Visual Education, 1979; Feb: 29–33.
- Burger W, Shaughnessy JM. Characterizing the van Hiele levels of development in geometry. J Res Math Edu. 1986;17:31–48. doi: 10.2307/749317
- Hershkowitz R, Duval R, Bartolini Bussi MG, et al. Reasoning in geometry. In: Mammana C, Villani V, editors. Perspectives on the teaching of geometry for the 21st century. New ICMI Study Series (Vol 5). Dordrecht: Springer; 1998. p. 29–37.
- Van Hiele PM. Structure and insight: a theory of mathematics education. Orlendo (FL): Academic; 1986.
- Usiskin S. Van Hiele levels and achievement in secondary school geometry. Final Report, Cognitive Development and Achievement in Secondary School Geometry Project. Chicago (IL): The University of Chicago. 1982.
- Gardner M. New mathematical diversions from scientific American. Chicago (IL): University of Chicago. 1983.
- Scher DP. Folded paper, dynamic geometry, and proof: a three-tier approach to the conics. Math Teacher. 1996;89(3):188–193.
- Scher DP. Exploring conic sections with the geometer’s sketchpad. Berkeley (CA): Key Curriculum Press; 1995.
- Mason J, Pimm D. Generic examples: seeing the general in the particular. Educ Stud Math. 1984;15(3):277–289. doi: 10.1007/BF00312078
- Marton F. Necessary conditions for learning. Abingdon: Routledge; 2015.
- Tahta D. A Boolean anthology: selected writings of Mary Boole on mathematics education. Derby: Association of Teachers of Mathematics; 1972.