Andreas Stylianides

Position/Status
E-mail Address

as899@cam.ac.uk

Phone

(+44) 01223 767550

Qualifications
Membership of Professional Bodies/Associations

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Profile

Andreas Stylianides is a Lecturer in Mathematics Education at the Faculty of Education and a Senior Member of Hughes Hall. Previously he held an academic fellowship at the University of Oxford and, before that, a postdoctoral appointment at the University of California-Berkeley. A Fulbright scholar, he received MSc degrees in mathematics and mathematics education, and then his PhD in mathematics education, at the University of Michigan.

His research is in the area of mathematics education and is concerned with the teaching and learning of mathematics as a sense-making activity, with particular attention to students' engagement with mathematical reasoning and proving. As these mathematical practices span mathematical domains (arithmetic, algebra, geometry, etc.) and educational levels (from the primary school level to the university level, including teacher education), his research projects have involved a diverse group of participants and addressed several other related topics (students' engagement with early algebraic ideas, teachers' mathematical knowledge for teaching, the design of classroom-based instructional interventions, etc.). He used different methodologies in his projects, notably the design experiment methodology. Part of his research has been carried out with support from the UK's Economic and Social Research Council and the Spencer Foundation.

He is currently a Guest co-Editor of a special issue on classroom-based interventions in mathematics education that will be published in 2013 in ZDM - The International Journal on Mathematics Education, an Editorial Board member of Research in Mathematics Education, an Advisory Board member of the International GeoGebra Institute and the NSF-funded project Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof, and a member of the Organising Committees for the 2012 International Conference on Education Technology and Management (Wuhan, China, November 2012) and for the Proof Topic Study Group of the 12th International Congress on Mathematical Education (Seoul, Korea, July 2012). He has recently completed his term of office as the Deputy Editor of the International Journal of Educational Research. He is the recipient of the 2010 American Educational Research Association SIG/RME Early Career Publication Award for his article "Proof and Proving in School Mathematics" (JRME, 2007, 38, 289-321).

Academic Area/Links

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Research Topics

Prospective PhD Applications

Stylianides would welcome informal contact from prospective PhD students on any of the research topics mentioned above.

Research Projects

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Course Involvement

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Principal Publications

Articles in Refereed International Research Journals

Stylianides, A. J., & Stylianides, G. J. (2011). A type of parental involvement with an isomorphic effect on urban children's mathematics, reading, science, and social studies achievement at kindergarten entry. Urban Education, 46(3), 408-425.

Stylianides, A. J., & Al-Murani, T. (2010). Can a proof and a counterexample coexist? Students' conceptions about the relationship between proof and refutation. Research in Mathematics Education, 12(1), 21-36.

Stylianides, G. J., & Stylianides, A. J. (2010). Mathematics for teaching: A form of applied mathematics. Teaching and Teacher Education, 26, 161-172.

Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72, 237-253.

Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40, 314-352.

Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11, 307-332.

Stylianides, G. J., & Stylianides, A. J. (2008). Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning. Mathematical Thinking and Learning, 10, 103-133.

Stylianides, A. J., & Stylianides, G. J. (2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in "real-life" contexts. Teaching and Teacher Education, 24, 859-875.

Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289-321.

Stylianides, A. J. (2007). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65, 1-20.

Stylianides, A. J. (2007). Introducing young children to the role of assumptions in proving. Mathematical Thinking and Learning, 9, 361-385.

Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers' knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, 145-166.

Stylianides, G. J., & Stylianides, A. J. (2005). Validation of solutions of construction problems in Dynamic Geometry Environments. International Journal of Computers for Mathematical Learning, 10, 31-47.

Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2004). Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55, 133-162.

Articles in Refereed Regional Research Journals

Stylianides, A. J. (2011). Towards a comprehensive knowledge package for teaching proof: A focus on the misconception that empirical arguments are proofs. Pythagoras, 32(1), Art. #14, 10 pages. (doi: 10.4102/pythagoras.v32i1.14)

Stylianides, A. J., & Stylianides, G. J. (2009). Learning about the nature of argument in mathematical and scientific contexts. Mediterranean Journal for Research in Mathematics Education, 8(1), 69-80.

Stylianides, A. J., & Stylianides, G. J. (2007). Learning mathematics with understanding: A critical consideration of the Learning Principle in the Principles and Standards for School Mathematics. The Montana Mathematics Enthusiast, 4(1), 103-114. 

Articles in Edited Volumes

Zaslavsky, O., Nickerson, S. D., Stylianides, A. J., Kidron, I., & Winicki, G. (in press). The need for proof and proving: mathematical and pedagogical perspectives. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education. The 19th ICMI Study, New ICMI studies series (v. 15). Springer, New York.

Stylianides, A. J., & Delaney, S. (2011). The cultural dimension of teachers' mathematical knowledge. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in Teaching (pp. 179-191). Springer.

Stylianides, G. J., & Stylianides, A. J. (2011). Investigation of undergraduate education and mathematics students' conceptions about the use of computer in the proving process: The case of the four color theorem. In A. Gagatsis & C. Charalambous. Research issues in mathematics education: A collocation in honor of Professor George Philippou (pp. 91-100). University of Cyprus, Nicosia, Cyprus. (in Greek) 

Stylianides, A. J., & Stylianides, G. J. (2010). Toward the design of instructional interventions in the area of proof. In A. Gagatsis, T. Rowland, A. Panaoura, & A. Stylianides (Eds.), Mathematics education research at the University of Cyprus and the University of Cambridge: A symposium(pp. 203-218). Nicosia, Cyprus: School of Social Sciences and Sciences of Education, University of Cyprus.

Articles in Teacher Journals

Stylianides, A. J. (2009). Breaking the equation "empirical argument = proof." Mathematics Teaching, 213, 9-14. (Available also at the NRICH website.)

Stylianides, G. J., & Stylianides, A. J. (2004). Dynamic investigation of an optimisation problem: Maximising the volume of rectangular prisms. Micromath, 2(2), 24-29.

Invited Article in Conference Proceedings (plenary lecture)

Stylianides, A. J. (2009). Towards a more comprehensive "knowledge package" for teaching proof. In J. H. Meyer & A. van Biljon (Eds.), Proceedings of the 15th Annual Congress of the Association of South Africa (AMESA) (Vol. 1, pp. 242-263). University of the Free State, Bloemfontein, South Africa.

Articles in Refereed Proceedings or Websites of International Conferences

Stylianides, G. J., & Stylianides, A. J. (2009). Ability to construct proofs and evaluate one's own constructions. In F. Lin, F. Hsieh, G. Hanna, & M. de Villiers (Eds.), Proceedings of the 19th International Commission on Mathematical Instruction: Proof and Proving in Mathematics Education (Vol. 2, pp. 166-171). National Taiwan Normal University, Taipei, Taiwan: ICMI Study Series 19, Springer.

Stylianides, A. J., & Stylianides, G. J. (2008). 'Cognitive conflict' as a mechanism for supporting developmental progressions in students' knowledge about proof. Article available at the website of the 11th International Congress on Mathematical Education, under Topic Study Group 18 (http://tsg.icme11.org/tsg/show/19). Monterrey, Mexico.

Stylianides, A. J., & Stylianides, G. J. (2006). Content knowledge for mathematics teaching: The case of reasoning and proving. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 201-208). Prague, Czech Republic.

Stylianides, G. J., & Stylianides, A. J. (2006). "Making proof central to pre- high school mathematics is an appropriate instructional goal": Provable, refutable, or undecidable proposition? In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 209-216). Prague, Czech Republic.

Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2005). Prospective teachers' understanding of proof: What if the truth set of an open sentence is broader than that covered by the proof? In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 241-248). Melbourne, Australia.

Stylianides, G. J., & Stylianides, A. J. (2004). Reconsidering the drag test as criterion of validation for solutions of construction problems in dynamic geometry environments. Article available at the website of the 10th International Congress on Mathematical Education, under Topic Study Group 15 (http://www.icme10.dk/). Denmark, Copenhagen.

Articles in Proceedings of North American Conferences

Stylianides, G.J., & Stylianides, A. J. (2008). Enhancing undergraduate students' understanding of proof. Electronic proceedings of the 11th Conference on Research in Undergraduate Mathematics Education. San Diego, California.

Stylianides, G. J., & Stylianides, A. J. (2006). Promoting teacher learning of mathematics: The use of "teaching-related mathematics tasks" in teacher education. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 411-417). Mérida, México: Universidad Pedagógica Nacional.

Articles in Refereed Proceedings of European Conferences

Stylianides, G. J., & Stylianides, A. J. (2011). An intervention of students' problem-solving beliefs. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the 7th Congress of the European Society for Research in Mathematics Education (pp. 1209-1218). Poland, Rzeszow.

Stylianides, A. J., & Al-Murani, T. (2009). "Can a proof and a counterexample coexist?" A study of students' conceptions about proof. In, Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (pp. 311-321). France, Lyon.

Stylianides, G. J., & Stylianides, A. J. (2009). The mathematical preparation of teachers: A focus on tasks. In, Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (pp. 1931-1940). France, Lyon.

Stylianides, A. J., & Stylianides, G. J. (2007). The mental models theory of deductive reasoning: Implications for proof instruction. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the 5th Congress of the European Society for Research in Mathematics Education (pp. 665-674). Cyprus, Larnaca.

Articles in Refereed Proceedings of Greek or Cypriot Conferences

Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2003). Undergraduate students' understanding of proof by mathematical induction. In T. Triantafyllides, K. Hadjikyriakou, P. Politis, & A. Chronaki (Eds.), Proceedings of the 6th Panellenian Conference on Didactics of Mathematics and Computers in Education (pp. 150-158). University of Thessaly, Volos, Greece. (in Greek).

Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2002). University students' conceptions of empirical proof and proof by counterexample. In M. Tzekaki (Ed.), Proceedings of the 5th Panellenian Conference on Didactics of Mathematics and Computers in Education (pp. 277-282). Aristotle University of Thessaloniki, Thessaloniki, Greece. (in Greek).

Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2002). University students' conceptions of the contraposition equivalence rule. In Proceedings of the VII Conference of Pedagogical Society of Cyprus on Educational Research in the Era of Globalization (Vol. B, pp. 241-250). The Society, Nicosia, Cyprus. (in Greek).

Stylianides, A. J., Stylianides, G. J., Philippou, G. N., & Christou, K. (2002). University students' conceptions about the use of computer in the proving process. In M. Tzekaki (Ed.), Proceedings of the 5th Panellenian Conference on Didactics of Mathematics and Computers in Education (pp. 283-289). Aristotle University of Thessaloniki, Thessaloniki, Greece. (in Greek).

Stylianides, A. J., Stylianides, G. J., Christou, K., & Georgiou, G. (2001). The transition from informal to formal proof. In A. Gagatsis & G. Makrides (Eds.), Proceedings of the 4th Pancyprian Conference on Mathematics Education (pp. 81-92). Cyprus Mathematical Society, Larnaca, Cyprus. (in Greek).