Teachers’ Instrumental Genesis and Their Geometrical Understanding in a Dynamic Geometry Environment

Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. International Reviews on Mathematical Education (ZDM), 34(3), 66–72.

Arzarello, F., Bairral, M. A., & Danè, C. (2014). Moving from dragging to touchscreen: geometrical learning with geometric dynamic software. Teaching Mathematics and Its Applications, 33(1), 39–51. doi: 10.1093/teamat/hru002 .

Baccaglini-Frank, A., & Mariotti, M. A. (2010). Generating conjectures in dynamic geometry: the maintaining dragging model. International Journal for Computers in Mathematical Learning, 15, 225–253.

Balacheff, N., & Kaput, J. J. (1996). Computer-based learning environments in mathematics. International handbook of mathematics education (pp. 469–501): Springer.

Bruner, J. S. (1968). Toward a theory of instruction. New York: W. W. Norton.

Common Core State Standards Initiative. (2010). Common core state standards for mathematics Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf .

Davis, R. B. (1992). Understanding “understanding”. The Journal of Mathematical Behavior, 11, 225–241.

Davis, R. B., & Maher, C. A. (1997). How students think: The role of representations. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 93–115). Hillsdale: Lawrence Erlbaum Associates.

Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.

Gattegno, C. (1987). The science of education: Part 1: Theoretical considerations. New York: Educational Solutions.

Goldenberg, E. P. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representation of functions. The Journal of Mathematical Behavior, 7(2), 135–173.

Guin, D., & Trouche, L. (1998). The complex process of converting tools into mathematical instruments: the case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.

Hegedus, S. J., & Moreno-Armella, L. (2010). Accommodating the instrumental genesis framework within dynamic technological environments. For the Learning of Mathematics, 30(1), 26–31.

Hewitt, D. (1999). Arbitrary and necessary part 1: a way of viewing the mathematics curriculum. For the Learning of Mathematics, 19(3), 2–9.

Hohenwarter, J., Hohenwarter, M., & Lavicza, Z. (2009). Introducing dynamic mathematics software to secondary school teachers: the case of GeoGebra. Journal of Computers in Mathematics and Science Teaching, 28(2), 135–146.

Hollebrands, K. F. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38(2), 164–192.

Hsieh, H.-F., & Shannon, S. F. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277–1288.

Lonchamp, J. (2012). An instrumental perspective on CSCL systems. International Journal of Computer-Supported Collaborative Learning, 7(2), 211–237.

Maher, C. A. (2005). How students structure their investigations and learn mathematics: insights from a long-term study. The Journal of Mathematical Behavior, 24(1), 1–14.

Maher, C. A., Powell, A. B., & Uptegrove, E. B. (Eds.). (2011). Combinatorics and reasoning: Representing, justifying and building isomorphisms. New York: Springer.

Mariotti, M. A. (2000). Introduction to proof: the mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1), 25–53.

Mariotti, M. A. (2001). Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning, 6(3), 257–281.

Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 173–204). Sense Publishers: Rotterdam, The Netherlands.

McGraw, R., & Grant, M. (2005). Investigating mathematics with technology: Lesson structures that encourage a range of methods and solutions. In W. J. Masalski & P. C. Elliott (Eds.), Technology-supported mathematics learning environments (Vol. Sixty-Seventh Yearbook, pp. 303–317). Reston, VA: National Council of Teachers of Mathematics.

Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507–528.

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: a framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.

Monaghan, J., Trouche, L., & Borwein, J. M. (2016). Tools and mathematics: Instruments for learning. New York: Springer.

Olivero, F., & Robutti, O. (2007). Measuring in dynamic geometry environments as a tool for conjecturing and proving. International Journal of Computers for Mathematical Learning, 12(2), 135–156.

Pereira, T.d.L.M. (2012). O uso do software GeoGebra em uma escola pública: Interações entre alunos e professor em atividades e tarefas de geometria para o ensino fundamental e médio. Instituto de Ciências Exatas Programa de Pós-graduação em Educação Matemática, Programa de Mestrado Profissional em Educação Matemática. Masters Degree. Universidade Federal de Juiz de Fora.

Piez, C.M., & Voxman, M.H. (1997). Multiple representations—Using different perspectives to form a clearer picture. The Mathematics Teacher, 164–166.

Pirie, S., & Schwarzenberger, R. (1988). Mathematical discussion and mathematical understanding. Educational Studies in Mathematics, 19(4), 459–470.

Powell, A.B., & Alqahtani, M.M. (2015). Tasks and meta-tasks to promote productive mathematical discourse in collaborative digital environments. In I. Sahin, S. A. Kiray, & S. Alan (Eds.), Proceedings of the International Conference on Education in Mathematics, Science & Technology (pp. 84–94). Antalya, Turkey.

Rabardel, P., & Beguin, P. (2005). Instrument mediated activity: from subject development to anthropocentric design. Theoretical Issues in Ergonomics Science, 6(5), 429–461.

Resnick, L.B., Michaels, S., & O’Connor, C. (2010). How (well-structured) talk builds the mind. Innovations in educational psychology: Perspectives on learning, teaching and human development, 163–194.

Robutti, O., Cusi, A., Clark-Wilson, A., Jaworski, B., Chapman, O., Esteley, C., . . . Joubert, M. (2016). ICME international survey on teachers working and learning through collaboration. ZDM, 48(5), 651–690. doi: 10.1007/s11858-016-0797-5 .

Rowe, K., & Bicknell, B. (2004). Structured peer interactions to enhance learning in mathematics. Paper presented at the Proceedings of 27th Annual Conference of the Mathematics Education Research Group of Australasia-Mathematics Education for the Third Millennium, Towards 2010., Townsville, Australia.

Sinclair, N., & Yurita, V. (2008). To be or to become: how dynamic geometry changes discourse. Research in Mathematics Education, 10(2), 135–150.

Stahl, G. (2015). Constructing dynamic triangles together: the development of mathematical group cognition. UK: Cambridge University Press.

Straesser, R. (2002). Cabri-Geometre: Does dynamic geometry software (DGS) change geometry and its teaching and learning? International Journal of Computers for Mathematical Learning, 6(3), 319–333.

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(1), 31–47.

Trouche, L., & Drijvers, P. (2014). Webbing and orchestration. Two interrelated views on digital tools in mathematics education. Teaching Mathematics and its Applications, hru014.