Understanding a graph in pairs, in a productive way, improves the comprehension of a concept. In this research, we had 2 objectives: 1) to delve deep into the behavior of 15 pairs of remedial physics students when solving a problem with a graph of velocity, 2) to understand the interchange of personal meanings during their interactions. We posed the problem through an interview about velocity given a graph of position. We analyzed the participants’ behavior based on the mathematical problem-solving theory of Schoenfeld. This analysis brought on the examination of interactions through grounded theory. We found that communication in the interchange of meanings and the quality of interactions is linked to productivity in problem-solving. We worked with a few emergent propositions based on behavior and interactions of pairs, then we identified specific alternative conceptions that students utilized to discuss the problem, how they managed their time and the richness of their contributions. Finally, we concluded that the mapping is a powerful tool that offers a view of students’ mental paths while solving problems that allow to assess the nature of the conceptual models originated by the interaction.

• Barron, B. (2000). Achieving coordination in collaborative problem-solving groups. Journal of the Learning Sciences, 9(4), 403-436. https://doi.org/10.1207/S15327809JLS0904_2
• Beichner, R. (1994). Testing student interpretation of kinematics graphs. American Journal of Physics, 62, 750–762. https://doi.org/10.1119/1.17449
• Bossche, P., Gijselaers, W., Segers, M., Woltjer, G., & Kirschner, P. (2010). Team learning: building shared mental models. Instructional Sciences, 39, 283–301. https://doi.org/10.1007/s11251-010-9128-3
• DeChurch, L. A., & Mesmer-Magnus, J. R. (2010). The cognitive underpinnings of effective teamwork: a meta-analysis. The Journal of applied psychology, 95(1), 32–53. https://doi.org/10.1037/a0017328
• De Cock, M. (2012). Representation use and strategy choice in physics problem solving. Physical Review Special Topics-Physics Education Research, 8(2), 020117. https://doi.org/10.1103/PhysRevSTPER.8.020117
• Dominguez, A., Barniol, P., & Zavala, G. (2017). Test of understanding graphs in calculus: Test of students’ interpretation of calculus graphs. EURASIA Journal of Mathematics, Science and Technology Education, 13(10), 6507-6531. https://doi.org/10.12973/ejmste/78085
• Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1/2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
• Evagorou, M., Erduran, S., & Mäntylä, T. (2015). The role of visual representations in scientific practices: from conceptual understanding and knowledge generation to ‘seeing’ how science works. International Journal of STEM Education, 2(1), 11. https://doi.org/10.1186/s40594-015-0024-x
• Greeno, J. G. (2006). Theoretical and practical advances through research on learning. In: J. L. Green et al., (Eds.), Handbook of complementary methods in education research (pp. 795–806). Mahwah, N.J.: Routledge.
• Hull, D. M., & Saxon, T. F. (2009). Negotiation of meaning and co-construction of knowledge: An experimental analysis of asynchronous online instruction. Computers & Education, 52(3), 624–639. https://doi.org/10.1016/j.compedu.2008.11.005
• Kohl, P., & Finkelstein, N. (2006). Effects of representation on students solving physics problems: A fine-grained characterization. Physical Review Special Topics - Physics Education Research, 2(1), 010106. https://doi.org/10.1103/PhysRevSTPER.2.010106
• Kozlowski, S. W.J., & Ilgen, D. R. (2006). Enhancing the effectiveness of work groups and teams. Psychological Science in the Public Interest, 7(3), 77–124. https://doi.org/10.1111/j.1529-1006.2006.00030.x
• McDermott, L. C., Rosenquist, M. L., & Van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics, 55(6), 503–513. https://doi.org/10.1119/1.15104
• Pérez-Goytia, N. F., Domínguez, A., & Zavala, G. (2010). Understanding and interpreting calculus graphs: refining an instrument. In: S. Mel, C. Singh, y N. S. Rebello (Eds.), Physics Education Research Conference Proceedings (Vol. 1289, pp. 249-252). Portland, Oregon: American Institute of Physics. https://doi.org/10.1063/1.3515213
• Planinic, M., Ivanjek, L., Susac, A., & Milin-Sipus, Z. (2013). Comparison of university students’ understanding of graphs in different contexts. Physical Review Special Topics-Physics Education Research, 9(2), 020103. https://doi.org/10.1103/PhysRevSTPER.9.020103
• Redish, E. F. (2003). Teaching physics with the physics suite. USA: John Wiley and Sons.
• Salett Biembengut, M., & Hein, N. (2004). Modelación matemática y los desafíos para enseñar matemática. Educación Matemática, 16(2), 105-125.
• Schoenfeld, A. H. (1985). A framework for the analysis of mathematical behavior. In: Mathematical problem solving (pp. 14-15). Londres: Academic Press. https://doi.org/10.1016/B978-0-12-628870-4.50007-4
• Schoenfeld, A. H. (2007). What is mathematical proficiency and how can it be assessed? In: A. H. Schoenfeld, (Ed). Assessing mathematical proficiency (pp. 59–73). Mathematical Science Research Institute Publications. https://doi.org/10.1017/CBO9780511755378.008
• Spaapen, J., & van Drooge, L. (2011). Introducing “productive interactions” in social impact assessment. Research Evaluation, 20(3), 211–218. https://doi.org/10.3152/095820211X12941371876742
• Strauss, A., & Corbin, J. M. (1994). Grounded theory methodology. In: N. K. Denzin y Y. S. Lincoln, (Eds.), Handbook of qualitative research (pp. 273–285). Thousand Oaks: Sage Publications.
• Taylor, S. J., & Bogdan, R. (1994). Introducción a los métodos cualitativos de investigación (2^nd Ed.), Barcelona, España: Ediciones Paidos.
• Tejeda, S., & Gallardo, K. E. (2017). Performance Assessment on High School Advanced Algebra. International Electronic Journal of Mathematics Education, 12(9), 777-798.
• Testa, I., Monroy, G., & Sassi, E. (2002). Students´ reading images in kinematics: the case of real-time graphs. International Journal of Science Education, 24(3), 235–256. https://doi.org/10.1080/09500690110078897
• Tuminaro, J., & Redish, E. F. (2003). Understanding Students’ Poor Performance on Mathematical Problem Solving In Physics. In J. Marx, S. Franklin, & K. Cummings, (Eds.), Physics Education Research Conference (Vol. 720, pp. 113–116). Madison, WI: American Institute of Physics.
• Zavala, G., Tejeda, S., Barniol, P., & Beichner, R. J. (2017). Modifying the test of understanding graphs in kinematics. Physical Review Physics Education Research, 13(2), 020111. https://doi.org/10.1103/PhysRevPhysEducRes.13.020111

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.