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Andreas Stylianides - Mathematics Education, Faculty of Education University of Cambridge

Andreas Stylianides

Position/Status
  • Lecturer in Mathematics Education
E-mail Address

as899@cam.ac.uk

Phone

(+44) 01223 767550

Qualifications
  • PhD in Mathematics Education (2005), University of Michigan, USA
  • MSc in Mathematics (2002), University of Michigan, USA
  • MSc in Mathematics Education (2002), University of Michigan, USA
  • BA in Education (major) with Mathematics (minor) and primary school teaching certification (2001), University of Cyprus, Cyprus
Membership of Professional Bodies/Associations
  • American Educational Research Association
  • British Educational Research Association
  • British Society for Research into Learning Mathematics
  • European Association for Research on Learning and Instruction
  • International Group for the Psychology of Mathematics Education

Profile

Andreas Stylianides is a lecturer in the Faculty of Education. Previously, he was an academic fellow at the University of Oxford and, before that, he was a postdoctoral fellow 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 (teacher) education and focuses on issues related to the teaching and learning of the fundamental mathematical concept of proof in both school and initial teacher education settings. 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 the Assistant Editor of the International Journal of Educational Research.

Academic Area/Links

  • Initial teacher education of mathematics teachers
  • Mathematics education

Research Topics

Stylianides' research focuses on the teaching and learning of the fundamental mathematical concept of proof and, by implication, the activity of proving and the broader activities of mathematical reasoning and problem solving.

Traditionally, students have first - and sometimes only - encountered the concept of proof at the upper school years or at the university. In recent years, however, many researchers have identified this practice as being a serious problem in students' mathematical education. Because proof is at the core of doing and knowing mathematics, students are deprived of experience with an essential aspect of mathematical thinking and sense-making until late in their mathematical education. Furthermore, when they do experience proof, it seems alien rather than being a natural extension of things they have already learned.

Stylianides' research programme aims to address this problem in students' mathematical education, focusing on the following overarching question: How can proof be made central to the mathematical experiences of all students and as early as the primary school years? From this overarching question several issues emerge, which have been part of Stylianides' research work and span the following general research topics:

  • Task design and implementation
  • Instructional design at the school level (both primary and secondary) to support student learning of mathematics
  • Instructional design at the initial teacher education level to support teacher learning of mathematics and pedagogy
  • Mathematical knowledge for teaching.

Research Projects

  • Enhancing students' proof competencies in secondary mathematics classrooms. Research project funded by the UK's Economic and Social Research Council. Role: Principal Investigator. Duration: March 2008 - February 2010.
  • Preservice teachers' challenges in beginning to teach mathematics: The activity of reasoning and proving. Research project funded by the Spencer Foundation. Role: Co-principal Investigator with G. J. Stylianides (University of Pittsburgh). Duration: October 2007 - December 2009.
  • Content knowledge for teaching elementary school mathematics. Research project funded by the Spencer Foundation.Role: Co-principal Investigator with G. J. Stylianides (University of Pittsburgh) and A. H. Schoenfeld (University of California-Berkeley). Duration: October 2006 - September 2007.

Course Involvement

  • Core Research Training course for the thematic MPhil courses
  • Early Years and Primary PGCE
  • MPhil/MEd in International Perspectives on Mathematics Education
  • Student supervision

Principal Publications

Articles in Refereed Research Journals

Stylianides, G. J., & Stylianides, A. J. (in press). Mathematics for teaching: A form of applied mathematics. Teaching and Teacher Education.

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., & 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., & 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 Teacher or Refereed Online Journals

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

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.

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

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 (http://mathed.asu.edu/crume2008/Proceedings/StylianidesandStylianides_LONG(21).pdf). 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, A. J., & Al-Murani, T. (in press). "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. France, Lyon.

Stylianides, G. J., & Stylianides, A. J. (in press). The mathematical preparation of teachers: A focus on tasks. In, Proceedings of the 6th Congress of the European Society for Research in Mathematics Education. 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).