## Position/Status

- Reader in Mathematics Education
- Fellow, Hughes Hall
- Chair, Mathematics Education Research Group

## E-mail Address

as899@cam.ac.uk

## Phone

(+44) 01223 767550

## Qualifications

- PhD in Mathematics Education, University of Michigan, USA
- MSc in Mathematics, University of Michigan, USA
- MSc in Mathematics Education, University of Michigan, USA
- MA, University of Cambridge, UK
- Postgraduate Diploma in Learning and Teaching in Higher Education, University of Oxford, UK
- BA in Education (major) with Mathematics (minor) and primary school teaching certification, University of Cyprus, Cyprus

## Profile

Andreas Stylianides is a Reader in Mathematics Education at the Faculty of Education and a Fellow 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.

Stylianides is the Chair of the Mathematics Education Research Group. His research is committed to understanding and acting upon problems of classroom practice. A premise underlying this dual commitment is that, by engineering ways to address problems of practice, one develops also a better theoretical understanding of the processes (didactical, cognitive, epistemological, etc.) underpinning the problems. Specifically, a great part of his research has involved the design of theory-based classroom interventions to help address students' difficulties with some mathematical practices that are essential for mathematical sense making, notably: mathematical reasoning, proving, and problem solving. As these mathematical practices span mathematical domains (arithmetic, algebra, geometry, etc.) and educational levels (from the primary school to the university including teacher education), his research projects have involved a diverse group of participants and addressed several other related topics including the following: teachers' mathematical/pedagogical knowledge and beliefs; the teaching and learning of early algebraic ideas; task design, analysis, and implementation. He used different methodologies in his projects, including 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.

Stylianides served as a Guest co-Editor of special issues in Educational Studies in Mathematics (2017, vol. 96, issue 2, pp. 119-274) and in ZDM - The International Journal on Mathematics Education (2013, vol. 45, pp. 333-495), and he completed his term of office as the Deputy Editor of the International Journal of Educational Research. He is currently an Editorial Board member of Research in Mathematics Education, Science & Education, and the International Journal of Science and Mathematics Education, and an Advisory Board member of the International GeoGebra Institute. He was a co-chair of the Proof Topic Study Group of the 13th International Congress on Mathematical Education (Germany, 2016) and a co-leader of the Curricular Resources and Task Design Working Group of the 10th Congress of European Research in Mathematics Education (Ireland, 2017), and he served as a member of the Organising Committees for a number of other conferences including the Proof Topic Study Group of the 12th International Congress on Mathematical Education (Korea, 2012). He has done External Examining (Masters or Doctorate) for the Universities of London (Institute of Education) and East Anglia in England, the Marino Institute of Education (Trinity College Dublin) and Dublin City University in Ireland, and the University of Sydney in Australia. 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, vol. 38, pp. 289-321).

## Academic Area/Links

## Research Topics

- The teaching and learning of mathematical reasoning, proving, and problem solving
- Classroom-based instructional interventions
- Teachers' mathematical knowledge and beliefs
- Teachers' selection and use of instructional resources
- Task design, analysis, and implementation
- Design experiment methodology

## Prospective PhD/EdD Applications

*Stylianides is currently seeking a new student for the 4-year programme (MPhil+PhD) to work on the interdisciplinary project "Designing Interactive Virtual Classroom Environments to Support Teacher Learning of Proof-related Instruction in Mathematics." Full funding is available for the successful applicant. Further information is available *

*here*

*.*

Stylianides would welcome informal contact from prospective PhD/EdD students on any of the research topics mentioned above or other related topics in mathematics education.

Topics of doctoral students who worked with Stylianides (completed theses):

- Hui-Chuan Li (2014):
*A problem-based learning approach to developing fifth grade students' fraction sense in Taiwan: challenges and effects.* - Eleni Demosthenous (2015):
*Algebra-related topics: A multiple case study in Cypriot primary school classrooms.*(co-supervision with Paul Andrews)

Topics of doctoral students currently working with Stylianides:

- Calculation fluency: A mixed methods study in English Y6 primary classrooms
- Towards a problem-solving pedagogy in mathematics classrooms: Multiple case studies of self-efficacious elementary mathematics teachers in Egyptian private schools
- Lessons to be shared: A comparative study of competent mathematics teachers in Qatar and the UK
- Designing and evaluating a virtual English enrichment course for improving Chinese learners' communicative competence
- Students' perceptions of proofs that convince and proofs that explain: the role of proof comprehension and different types of proof

## Research Projects

*Designing Interactive Virtual Classroom Environments to Support Teacher Learning of Proof-related Instruction in Mathematics.*Research project with M. Jamnik (funding opportunity available)*Classroom-based interventions in the areas of proving and problem solving*. Research project with G. J. Stylianides (ongoing)*Exploring the minus sign in the school curriculum: A connected approach to a complex symbol.*Research project with H. Siedel. (ongoing)*Enhancing students' proof competencies in secondary mathematics classrooms.*Research project funded by the UK's Economic and Social Research Council. Role: Principal Investigator. (Numbered List of Outputs referenced in the End of Award Report; Numbered List of Outputs referenced in the Impact Report) (completed)*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. (completed)*Content knowledge for teaching elementary school mathematics*. Research project funded by the Spencer Foundation. Role: Co-principal Investigator with G. J. Stylianides and A. H. Schoenfeld. (completed)

## Course Involvement

- Deputy Director of Learning & Teaching
- Doctoral and Masters student supervision
- Teaching contributions primarily to the MPhil Research Methods Strand and the Masters in Mathematics Education

## Principal Publications

### Books

**Stylianides, A. J.**, & Harel, G. (Eds.). (2018). *Advances in mathematics education research on proof and proving: An international perspective*. Springer. [Research Monograph]

**Stylianides, A. J.** (2016). *Proving in the elementary mathematics classroom.* Oxford, UK: Oxford University Press. [Research Monograph]

Related blog: Is elementary school mathematics "real" mathematics? OUPblog, 9 October 2016.

### Journal Special Issues Edited

Stylianides, G. J., & **Stylianides, A. J.** (Eds.). (2017). Research-based interventions in the area of proof. *Educational Studies in Mathematics, 96*(2), 119-274.

**Stylianides, A. J.**, & Stylianides, G. J. (Eds.). (2013). Classroom-based interventions in mathematics education. *ZDM – The International Journal on Mathematics Education, 45*(3), 333-495.

### Chapters in Research Handbooks

Stylianides, G. J., **Stylianides, A. J.**, & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (Ed.), *Compendium for research in mathematics education* (pp. 237-266). Reston, VA: National Council of Teachers of Mathematics.

**Stylianides, A. J.**, Bieda, K. N., & Morselli, F. (2016). Proof and argumentation in mathematics education research. In A. Gutiérrez, G. C. Leder, & P. Boero (Eds.), *The s**econd handbook of research on the Psychology of Mathematics Education* (pp. 315-351). Rotterdam, The Netherlands: Sense Publishers.

### Articles in Refereed Journals

**Stylianides, A. J.** (2018). Secondary students' proof constructions in mathematics: the role of written vs. oral mode of argument representation. *Review of Education*.

Li, H.C., & **Stylianides, A. J.** (2018). An examination of the role of the teacher and students during a problem-based learning intervention: lessons learned from a study in a Taiwanese primary mathematics classroom. *Interactive Learning Environments, 26*(1), 106-117.

Demosthenous, E., & **Stylianides, A. J.** (2018). Algebra-related tasks: Teachers’ guidance in curriculum materials. *La matematica e la sua didattica*, 26(1), 7-27.

Diamond, A. H., & **Stylianides, A. J.** (2017). Personal epistemologies of statisticians in academia: An exploratory study. *Statistics Education Research Journal, 16*(2), 335-361.

Stylianides, G. J., & **Stylianides, A. J.** (2017). Research-based interventions in the area of proof: The past, the present, and the future. *Educational Studies in Mathematics, 96(2)*, 119-127*.*

Stylianides, G. J., & **Stylianides, A. J.** (2014). The role of instructional engineering in reducing the uncertainties of ambitious teaching. *Cognition and Instruction*, *32*(4), 374-415.

**Stylianides, A. J.**, & Stylianides, G. J. (2014). Impacting positively on students’ mathematical problem solving beliefs: An instructional intervention of short duration. *The Journal of Mathematical Behavior, 33, *8-29.

McCrory, R., & **Stylianides, A. J.** (2014). Reasoning-and-proving in mathematics textbooks for prospective elementary teachers. *International Journal of Educational Research, 64, *119-131.

**Stylianides, A. J.**, & Stylianides, G. J. (2014). Viewing “mathematics for teaching” as a form of applied mathematics: Implications for the mathematical preparation of teachers. *Notices of the American Mathematical Society, 61*(3), 266-276.

Note: This article was translated into Chinese and was published in Mathematical Advances in Translation (2015, vol. 34, no. 4, pp. 346-357), which is supported by the Chinese Academy of Sciences.

Stylianides, G. J., **Stylianides, A. J.**, & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. *International Journal of Science and Mathematics Education, 11*(6), 1463-1490.

**Stylianides, A. J.**, & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: Classroom-based interventions in mathematics education. *ZDM – The International Journal on Mathematics Education, 45*(3), 333-341.

Roberts, N., & **Stylianides, A. J.** (2013). Telling and illustrating stories of parity: A classroom-based design experiment on young children’s use of narrative in mathematics. *ZDM – The International Journal on Mathematics Education, 45*(3), 453-467.

** 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.** (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.**, & 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.**, & 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, 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 Mathematics Enthusiast, 4*(1), 103-114.

Stylianides, G. J., & **Stylianides, A. J.** (2005). Validation of solutions of construction problems in Dynamic Geometry Environments. *Technology, Knowledge and 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.

### Chapters in Edited Volumes

Siedel, H., & **Stylianides, A. J.** (2018). Teachers’ selection of resources in an era of plenty: An interview study with secondary mathematics teachers in England. In L. Fan, L. Trouche, C. Qi, S. Rezat, & J. Visnovska (Eds.), *Research on mathematics textbooks and teachers’ resources: Advances and issues *(pp. 119-144). Springer.

**Stylianides, A. J.**, & Delaney, S. (2018). Pre-service mathematics teachers’ knowledge and beliefs. In G. J. Stylianides & K. Hino (Eds.), *Research advances in the mathematical education of pre-service elementary teachers: An international perspective* (pp. 219-228). Springer.

**Stylianides, A. J.**, & Stylianides, G. J. (2018). Addressing key and persistent problems of students’ learning in the area of proof. In. A. J. Stylianides & G. Harel (Eds.), *Advances in mathematics education research on proof and proving: An international perspective** *(pp. 99-113). Springer.

**Stylianides, A. J.** (2015). Proof in school mathematics as early as the elementary grades. In E. A. Silver & P. A. Kenney (Eds.), *More lessons learned from research* (Vol. 1, pp. 59-70). Reston, VA: National Council of Teachers of Mathematics.

Stylianides, G. J., & **Stylianides, A. J.** (2015). Creating a need for proof. In E. A. Silver & P. A. Kenney (Eds.), *More lessons learned from research *(Vol. 1, pp. 9-22). Reston, VA: National Council of Teachers of Mathematics.

**Stylianides, A. J.** (2014). Proof. In P. Andrews & T. Rowland (Eds.), *MasterClass in Mathematics Education: International Perspectives on Teaching and Learning* (pp. 101-112). London: Bloomsbury Publishers.

Zaslavsky, O., Nickerson, S. D., **Stylianides, A. J.**, Kidron, I., & Winicki, G. (2012). 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 Study Series, Vol. 15, pp. 215-229). 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 collection 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 Professional Journals

Stylianides, A. J., & Stylianides, G. J. (2015). The Blond Hair problem. *Mathematics Teaching, 247*, 20-24.

**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.

### Book Review

**Stylianides, A. J.**, & Rogers, L. (2013). The Cult of Pythagoras: Math and Myths, by A. Martinez [Book Review]. *Science & Education, 22, *2351-2355. (Published also in the June 2013 Newsletter of the “International History, Philosophy and Science Teaching Group”: http://ihpst.net/newsletters/jun2013.pdf)

### Article Based on an Invited Plenary Talk

**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 Conferences

Harel, G., **Stylianides, A. J.**, Boero, P., Miyazaki, M., & Reid, D. (2017). Topic Study Group No. 18: Reasoning and proof in mathematics education. In G. Kaiser (Ed.), *Proceedings of the 13th International Congress on Mathematical Education *(pp. 459-461). ICME-13 Monographs.

**Stylianides, A. J.**, & Stylianides, G. J. (2017). Promoting prospective elementary teachers’ knowledge about the role of assumptions in mathematical activity. In T. Dooley & G. Guedet (Eds.), *Proceedings of the 10th Congress of the European Society for Research in Mathematics Education* (pp. 3748-3755). Dublin, Ireland: DCU Institute of Education and ERME.

**Stylianides, A. J**., & Stylianides, G. J. (2016). Classroom-based interventions in the area of proof: Some design considerations. *Article to be available at the website of the 13th International Congress on Mathematical Education, under Topic Study Group 18*. Hamburg, Germany.

Li, H-C., & **Stylianides, A. J.** (2016). The roles of teacher and students during a problem-based learning intervention. *Article to be available at the website of the 13th International Congress on Mathematical Education, under Topic Study Group 26*. Hamburg, Germany.

Siedel, H., & **Stylianides, A. J.** (2016). Teachers’ selection of resources in an era of plenty. *Article to be available at the website of the 13th International Congress on Mathematical Education, under Topic Study Group 38*. Hamburg, Germany.

**Stylianides, A. J.** (2015). The role of mode of representation in students’ argument constructions. In K. Krainer & N. Vondrová (Eds.), *Proceedings of the 9th Congress of the European Society for Research in Mathematics Education *(pp. 213-220). Czech Republic, Prague. (Published at HAL archives website: https://hal.archives-ouvertes.fr/)

Demosthenous, E., & **Stylianides, A. J.** (2014). Algebra-related tasks in primary school textbooks. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), *Proceedings of the Joint Meeting of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(Vol. 2, pp. 369-376). Vancouver, Canada.

Siedel, H., & **Stylianides, A. J.** (2014). If not textbooks, then what? English mathematics teachers’ use of alternative resources. In K. Jones, C. Bokhove, G. Howson, & L. Fan (Eds.), *Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014) *(pp. 543-544). Southampton, UK: University of Southampton.

**Stylianides, A. J.**, Stylianides, G. J., & Shilling-Traina, L. N. (2012). “The big hurdle to overcome is getting students out of the mode of thinking that math is just plug-in and move on kind of thing”: Challenges in beginning to teach reasoning-and-proving. *Article available at the website of the 12th International Congress on Mathematical Education, under Topic Study Group 14* (http://www.icme12.org/upload/UpFile2/TSG/0965.pdf). Seoul, Korea.

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 European Research in Mathematics Education *(pp. 1209-1218). Rzeszów, Poland.

**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 European Research in Mathematics Education* (pp. 311-321). France, Lyon.

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

**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, 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/Stylianides&Stylianides_LONG(21).pdf). San Diego, California.

**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 European Research in Mathematics Education* (pp. 665-674). Cyprus, Larnaca.

**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, 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.

**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.

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 arguments 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)