**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32799

##### Didactical and Semiotic Affordance of GeoGebra in a Productive Mathematical Discourse

**Authors:**
I. Benning

**Abstract:**

Using technology to expand the learning space is critical for a productive mathematical discourse. This is a case study of two teachers who developed and enacted GeoGebra-based mathematics lessons following their engagement in a two-year professional development. The didactical and semiotic affordance of GeoGebra in widening the learning space for a productive mathematical discourse was explored. The approach of thematic analysis was used for lesson artefact, lesson observation, and interview data. The results indicated that constructing tools in GeoGebra provided a didactical milieu where students used them to explore mathematical concepts with little or no support from their teacher. The prompt feedback from the GeoGebra motivated students to practice mathematical concepts repeatedly in which they privately rethink their solutions before comparing their answers with that of their colleagues. The constructing tools enhanced self-discovery, team spirit, and dialogue among students. With regards to the semiotic construct, the tools widened the physical and psychological atmosphere of the classroom by providing animations that served as virtual concrete to enhance the recording, manipulation, testing of a mathematical idea, construction, and interpretation of geometric objects. These findings advance the discussion of widening the classroom for a productive mathematical discourse within the context of the mathematics curriculum of Ghana and similar sub-Saharan African countries.

**Keywords:**
GeoGebra,
theory of didactical situation,
semiotic mediation,
mathematics laboratory,
mathematical discussion.

**References:**

[1] C. Giberti, F. Arzarello, G. Bolondi, and H. Demo, “Exploring students’ mathematical discussions in a multi-level hybrid learning environment”. ZDM, vol. 54, pp. 403–418, 2022.

[2] S. M. Calor, R. Dekker, J. P. van Drie, and M. L. Volman, “Scaffolding small groups at the group level: Improving the scaffolding behavior of mathematics teachers during mathematical discussions”. J. of the Learning Sciences, vol. 31, no. 3, pp. 369-407, 2022.

[3] J. Moschkovich, Supporting the participation of English language learners in mathematical discussions. For the learning of mathematics, vol. 19, no. 1, pp. 11-19, 1999.

[4] C. Attard and C. Curry, “Exploring the use of iPads to engage young students with mathematics”, in Mathematics education: Expanding horizons. Proc. of the 35th annu. Conf. of the Mathematics Education Research Group of Australasia, Singapore, 2012.

[5] V. Geiger, H. Forgasz, H. Tan, N. Calder, and J. Hill, “Technology in mathematics education”, in Research in mathematics education in Australasia 2008-2011, B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenless, Eds. Rotterdam, The Netherlands: Sense Publisher, 2012, pp. 111-114.

[6] E. J. Swenson, Teaching Mathematics to Children, New York: Macmillan, 1973.

[7] K. Das, “Significant of mathematics laboratory activities for teaching and learning”, Int. J. on Integrated Education, vol. 2, no. 5, pp. 19-25, 2019.

[8] L. S. Vygotsky, Mind in Society: The Development 7 of Higher Psychological Processes. Cambridge, Massachusetts: Harvard University Press, 1978.

[9] M. Maschietto and L. Trouche, “Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories”. ZDM, vol. 42, no. 1, 33-47, 2010.

[10] G. Brousseau, The Theory of Didactical Situations in mathematics. Dordrecht: Kluwer, 1997.

[11] T. Miyakawa and C. Winsløw, “Didactical designs for students’ proportional reasoning: an open approach lesson and a fundamental situation”. Educ. Studies in Mathematics, vol. 72, no. 2, pp. 199-218, 2009.

[12] F. Ligozat and M. L. Schubauer, “The joint action theory in didactics: why do we need it in the case of teaching and learning mathematics?”, in Proc of the 6th Cong. of the European society of Mathematics Education, INRP/IFE, pp. 1615-1624, 2010.

[13] M. A. Mariotti, “Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS”. ZDM, vol. 45, no. 3, pp. 441-452, 2013.

[14] P. E. T. E. R. Vankúš, “History and present of didactical games as a method of mathematics’ teaching”, Acta Didactica Universitatis Comenianae-Mathematics, vol. 5, pp. 53-68, 2005.

[15] M. Bussi, and M. A. Mariotti, “Semiotic mediation: From history to the mathematics classroom”, For the Learning of Mathematics, vol. 19, no. 2, pp. 27-35, 1999.

[16] A. Leung, and J. Bolite-Frant, “Designing mathematics tasks: the role of tools”, in Task Design in Mathematics Education: The 22nd ICMI Study (New ICMI Study Series), A. Watson and M. Ohtani Eds. New York: Springer, 2015, pp. 191–225.

[17] J. S. Bruner, Toward a theory of Instruction. Massachusetts: Harvard University Press, 1966, vo. 59.

[18] J. M. Furner and C. A. Marinas, “Learning math concepts in your environment using photography and GeoGebra”, in Electronic Proceedings of the Twenty-fifth Annual International Conference on Technology in Collegiate Mathematics, Boston, Massachusetts, Mar. 2013.

[19] M. Hohenwarter, D. Jarvis, and Z Lavicza, “Linking geometry, algebra, and mathematics teachers: GeoGebra Software and the Establishment of the International GeoGebra Institute”. The Int. J. for Technology in Mathematics Education, vol. 16, no. 2, pp. 83-87, 2009.

[20] M. S. Uwurukundo, J. F. Maniraho, and M. Tusiime, “GeoGebra integration and effectiveness in the teaching and learning of mathematics in secondary schools: A review of literature”. African Journal of Educational Studies in Mathematics and Sciences, vol. 16, no. 1, pp. 1-13, 2020.

[21] K. Jones, “The value of learning geometry with ICT: lessons from innovative educational research”. Maths Educ. with Digital Technology, pp. 39-45, 2011.

[22] V. Braun, and V. Clarke, Successful Qualitative Research: A Practical Guide for Beginners. London, United Kingdom: Sage, 2013.