**A)**

**SUMMARY OF THE PROJECT FINDINGS**

**B) REFERENCES**

Adoniou, M. & Qing, Y. (2014). Language, mathematics and English language learners. *The* *Australian Mathematics Teacher, 70*(3), 3-13.

Arbaugh, F., & Brown, C. A. (2006). Analyzing mathematical tasks: A catalyst for change? *Journal of Mathematics Teacher Education, *8(6), 499-536

Arbaugh, F., & Brown, C. A. (2004). What makes a mathematical task worthwhile? Designing a learning tool for high school mathematics teachers. In R. N. Rubenstein & G. W. Bright (Eds.), *Perspectives on the teaching of mathematics: Sixty–sixth yearbook* (pp. 27-41). Reston, VA: NCTM.

Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: increasing the cognitive demands of instructional tasks used in teachers’ classrooms. *Journal of Research in Mathematics Education, 40*(2), 119-156.

Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach’ to professional development: enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. *ZDM*, *43*(6-7), 965-977.

Cathcart, W., Pothier, Y., Vance, J. & Bezuk, N. (2000). *Learning Mathematics in Elementary and Middle Schools*. United States: Merrill Prentice Hall.

Cengiz, N., Kline, K. & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. *Journal of Mathematics Teacher Education*, *14*(5), 355-374.

Chapin, S. H., O’Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn (2nd ed.). Sausalito, CA: Math Solutions.

Chi, M. T. (2009). Active‐constructive‐interactive: A conceptual framework for differentiating learning activities. *Topics in Cognitive Science*, *1*(1), 73-105.

Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. *American Educational Research Journal*, 29, 573-604.

Dekker, R. (1987). Roos and José, two children in a mixed ability group. *Educational Studies in Mathematics, 18*, 317-324.

Delaney, S. 2017, *Become the Primary Teacher Everyone Wants to Have, *Routledge, Milton Park, Oxon.

Diezmann, C. M., & Watters, J. J. (2000). Catering for mathematically gifted elementary students: Learning from challenging tasks. *Gifted Child Today*, *23*(4), 14-52.

Dooley, T. (2009). A teacher's role in whole-class mathematical discussion: Facilitator of performance etiquette? In V. Durand-Guerrier, S. Souryn Lavergne and F. Arzarello (Eds.), *6 ^{th} Congress of the European Society for Research in Mathematics Education (CERME)* (pp. 894 - 903). Lyon, France: INRP.

Doyle, W. (1988). Work in Mathematics Classes: The Context of Students’ Thinking During Instruction. *Educational Psychologist, 23*(2), 167 – 180.

González, G. & Eli, J. A. (2017). Prospective and in-service teachers’ perspectives about launching a problem. *Journal of Mathematics Teacher Education*, *20*(2), 159–201.

Güven, N. D., & Dede, Y. (2017). Examining social and sociomathematical norms in different classroom microcultures: Mathematics teacher education perspective. *Educational Sciences: Theory & Practice*, *17*, 265–292.

Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. *Journal for research in mathematics education*, 524-549.

Herbst, P. G. (2003). Using novel tasks in teaching mathematics: Three tensions affecting the work of the teacher. *American Educational Research Journal*, *40*(1), 197-238.

Homans, G. (1951). *The Human Group*. London, UK: Routledge.

Kersaint, G. L. A. D. I. S. (2015). Orchestrating mathematical discourse to enhance student learning. Curriculum Associates, LLC.

Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6(3), 283-317.

Lampert, M (2001). *Teaching problems and the problems of teaching. *New Haven: Yale University Press.

Lozano, M. (2017). Investigating task design, classroom culture and mathematics learning: an enactivist approach, *ZDM: Mathematics Education*, 49 (6), 895-907.

Mariotti, M. A. (2012). Proof and proving in the classroom: Dynamic Geometry Systems as tools of semiotic mediation. *Research in Mathematics Education*, *14*(2), 163-185.

Mason, J. 2002, Minding Your Qs and Rs: effective questioning and responding in the mathematics classroom, in L. Haggerty (Ed.) Aspects of Teaching Secondary Mathematics: perspectives on practice, RoutledgeFalmer, London, p248-258. ISBN 0-415-26081-7

O'Brien, T., & Guiney, D. (2001). *Differentiation in teaching and learning*. A&C Black.

Pasquale, M. (2016). Productive Struggle in Mathematics. Interactive STEM Research+ Practice Brief. *Education Development Center, Inc.* Retrieved from http://interactivestem.org/wp-content/uploads/2015/08/EDC-RPC-Brief-Productive-Struggle.pdf

Ponte, J. P., & Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. *Educational Studies in Mathematics, 93*(1), 51-66.

Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi, *Journal of Mathematics Teacher Education* 8(3), 225-281.

Sherin, M. G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. *Journal of Mathematics Teacher Education*, *5*, 205–233.

Smith, M. S., Hughes, E. K., Engle, R. A., & Stein, M. K. (2009). Orchestrating discussions of challenging tasks: Keeping your eye on the mathematics to be learned. *Mathematics Teaching in the Middle School*, *14*(9), 548-556.

Smith, M. S., Stein, M. K., Arbaugh, F., Brown, C. A., & Mossgrove, J. (2004). Characterizing the cognitive demands of mathematical tasks: A task-sorting activity. In G. W. Bright & R. N. Rubenstein (Eds.), *Professional development guidebook for perspectives on the teaching of mathematics: Companion to the sixty–sixth yearbook* (pp. 45-72). Reston, VA: NCTM.

Star, J. R. (2015, April). When not to persevere – Nuances related to perseverance in mathematical problem solving (White paper). Chicago, IL: Spencer Foundation. Retrieved from http://hub.mspnet.org/index.cfm/28127/

Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice.* Mathematics Teaching in the Middle School, 3*(4), 268-275.

Stein, M. K., Engle, R. A., Smith, M. S.& Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. *Mathematical Thinking and Learning*, *10*(4), 313-340.

Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. *American educational research journal*, *33*(2), 455-488.

Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), *Second handbook of research on mathematics teaching and learning* (pp. 319-369). Charlotte, NC: Information Age Publishing.

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2016). *Implementing Standards-Based Math Instruction: A Casebook for Professional Development*. Τόπος: Teachers College Press.

Stein, M., Carnine, D. & Silbert, G. 1997, *Designing Effective Mathematics Instruction: A Direct *

Stigler, J.W., & Hiebert, J. (1999). *The teaching gap: Best ideas from the world’s teachers for improving education in the classroom*. New York: The Free Press.

Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. *Journal of Mathematics Teacher Education*, *18*(2), 123-140.

Sullivan, P., Mousley, J., & Zevenbergen, R. (2006). Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms. *International Journal of Science and Mathematics Education*, 4, 117-143.

Tomlinson, C. A. (2014). *The differentiated classroom: Responding to the needs of all learners *(2^{nd} ed.). VA: Association for Supervision and Curriculum Development.

Tomlinson, C. A. (2017). *How to differentiate instruction in mixed-ability classrooms *(3^{rd} ed.)* Alexandria*, VA: Association for Supervision and Curriculum Development.

Van den Heuvel-Panhuizen, M. (2000). *Mathematics education in the Netherlands: A guided tour*. Freudenthal Institute Cd-rom for ICME9. Utrecht: Utrecht University.

Wallace, A., White, M. & Stone, R. 2010, “Sand and Water Table Play”, *Teaching Children Mathematics*, vol. 16, no. 7, pp. 394 – 400.

Way, J. (2008). Using questioning to stimulate mathematical thinking. *Australian primary mathematics classroom, 13*(3), 22-27.

Williams, E. & Shuard, H. ((1994). *Primary Mathematics Today*. United Kingdom: Longman.

Yackel, E. & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. *Journal for Research in Mathematics Education*, 27 (4), 458- 477.