Nyiayu Fahriza Fuadiah, Didi Suryadi, Turmudi Turmudi


This paper presents the analysis of teaching of Math that took place in the classroom to identify the characteristics of didactical contracts that occur as part of a didactical situation. The design experiment was conducted on 31 seventh grade students and a mathematics teacher on negative integer operations lessons. The researchers analyzed the ongoing learning, how the didactical situation stages evolve in the teacher-student interaction that allows the formation of new knowledge or concepts in the student and how the teacher organizes the responsibility for achieving the learning objectives. The Analysis showed that students, at an early stage, can perform negative integers operations by utilizing the basic concepts they get in primary school. This concept can bridge into a new knowledge that identifies the properties of integer count operations and builds power of mind on problem-solving.



Didactical Contract, Didactical Situation, Negative Integers Operations

Full Text:



Arias, F., & Araya, A. (2009). Analysis of the didactical contracts in 10th grade math classes. Quaderni di Ricerca in Didattica (Matematica), 4(19), 155-163.

Artigue, M., Haspekian, M., & Corblin-Lenfant, A. (2014). Introduction to the theory of didactical situations (TDS). In Networking of theories as a research practice in mathematics education (pp. 47-65). Springer International Publishing.

Bellamy, A. (2015). A critical analysis of teaching and learning negative numbers. Philosophy of Mathematics Education Journal, 29.

Bishop, J.P., Lisa, L.L, Philipp, R.A., Whitacre, I., Schappelle, B., and Lewis, M.L. (2014). Obstacles and affordances for integer reasoning: an analysis of children's thinking and the history of mathematics. Journal for Research in Mathematics Education, 45(1), 19-61.

Brousseau, G. (2002). Theory of Didactical Situation in Mathematics. USA: Kluwer Academic Pulishers.

Brousseau, G., Sarrazy, B. & Novotna, J. (2014). Didactic contract in mathematical education. In Lerman (Ed.), Encylopedia of Mathematics Education (pp. 153 – 159). Dordrecht: Springer.

Fuadiah, N. F., Suryadi, D., & Turmudi, T. (2017). Some difficulties in understanding negative numbers faced by students: A qualitative study applied at secondary schools in Indonesia. International Education Studies, 10 (1), 24-38.

Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49(2), 171–192.

Hefendehl-Hebeker, L. (1991). Negative numbers: obstacles in their evolution from intuitive to intellectual contructs. For the Learning of Mathematics,11(1), 26 – 32.

Hersant, M., & Perrin-Glorian, M. J. (2005). Characterization of an ordinary teaching practice with the help of the theory of didactic situations. Educational Studies in Mathematics, 59 (1-3), 113-151.

Hughes, M. (1986). Children and Number, Difficulties in Learning Mathematics. United Kindom: Blackwell Publishing.

Kinslenko, K (2005). Student’s beliefs about mathematics from the perspective of the theory of didactical situations. In C Winslow (ED.), Didactic of mathematics-the French way (pp. 83-96). Center For Naturfagenes Didaktis University of Copenhagen.

Lamb, L.L., Bishop, J.P., Philipp, R.A., Schappelle, B.P., Whitacre, I., & Lewis, M. (2012). Developing symbol sense for the minus sign. Mathematics Teaching in the Middle School, 18(1), 5-9.

Laborde, C. & Perrin-Glorian, M.J. (2005). Introduction teaching situation as object of research: empirical studies within theoretical perspective. Educational Studies in Mathemathics, 59 (1-3),1–12.

Manno, G. (2006). Embodiment and a-didactical situation in the teaching-learning of the perpendicular straight lines concept. Doctoral Thesis. Departement of Didactic Mathematics Comenius University Bratislava

Perrin-Glorian, M. J. (2008). From producing optimal teaching to analysing usual classroom situations development of a fundamental concept in the theory of didactic situations: the notion of milieu. Accepted from

Ruthven, K., Laborde, C., Leach, J., & Tiberghien, A. (2009). Design tools in didactical research: instrumenting the epistemological and cognitive sspects of the design of teaching sequences. Educational Researcher, 38 (5), 329–342.

Sarrazy, B., & Novotna´, J. (2013). Didactical contract and responsiveness to didactical contract: a theoretical framework for enquiry into students’ creativity in mathematics. ZDM Mathematics Education, 45:281–293.

Seng, L. K. (2012). An error analysis of form 2 (grade7) students in simplifying algebraic expression: a descriptive study. Electronic Journal of Research in Education Psy. 8 (1),139-162.

Stephan, M., & Akyuz,, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43 (4), 428-464.

Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in ‘negativity’. Learning and Instruction, 14(5), 469–484.

Vlassis, J. (2008). The role of mathematical simbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555–570.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.