Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241.
Visualization is the process of seeing the unseen. This process can be developed through graphs, diagrams, experimentations, and mathematical models to make visual and algebraic reasoning.
Hall, J., & Chamblee, G. (2013). Teaching algebra and geometry with GeoGebra: Preparing pre-service teachers for middle grades/secondary mathematics classrooms. Computers in the Schools, 30(1–2), 12–29.
Due to the highly manipulative nature of GeoGebra, constructing many geometric shapes or objects becomes relatively easy. Also, the speed and ease of making constructions can allow students to explore the concepts, rather than manually drawing the figures in traditional ways.
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, 164–192.
Technological tools allow students to understand the distinction between drawing and construction in order to operate and manipulate geometrical objects. Dynamic interactions with geometric objects allowed students to test construction, verify conjectures, observe behaviors, and search for inconsistencies by employing proactive and reactive strategies.
Iranzo, N., & Fortuny, J. M. (2011). Influence of GeoGebra on problem solving strategies. In Model-Centered Learning (pp. 91–103). Springer.
GeoGebra enables students to understand mathematics better and attempt to find alternative solutions. GeoGebra activities influence students’ learning behaviors (autonomous, instrumental, procedural, naive, ) and fosters a more geometrical/visual thinking.
Jacinto, H., & Carreira, S. (2017). Mathematical problem solving with technology: the techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 15(6), 1115–1136.
Mathematical problem solving with digital technology incorporates Schoenfeld’s five stages (read, analysis, exploration, planning and implementation, and verification) of problem solving and Martin & Grudziecki’s (2006) sequential processes (statement, identification, accession, evaluation, interpretation, organization, integration, analysis, synthesis, creation, communication, dissemination, and reflection.) The objective is to produce mathematical thinking by means of digital technologies.
Presmeg, N. C. (2006). Research on visualization in learning and teaching mathematics. Handbook of Research on the Psychology of Mathematics Education, 205–235.
Visualization in mathematics education enhances students to actively interact with objects and ask questions when solving problems. High school students use concrete images (pictures in mind), kinesthetic images (physical movements), dynamic images, and memory images (formulae) to visualize mathematical objects.
Saha, R. A., Ayub, A. F. M., & Tarmizi, R. A. (2010). The effects of GeoGebra on mathematics achievement: enlightening coordinate geometry learning. Procedia-Social and Behavioral Sciences, 8, 686–693.
Findings from this study indicate that certain group of students (low on spatial visualization) perform significantly better when using GeoGebra as opposed to traditional classroom instruction. Use of GeoGebra was found to enhance students learning and understanding.
Schoenfeld, A. (2009). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. Colección Digital Eudoxus, (7).
The roles of problems in problem-solving are to provide justification for teaching mathematics, motivation for leaning mathematics, recreational activities in the classroom, and opportunities to develop new skills and practice and master techniques. Classrooms are recommended to model problem-solving behavior, create an atmosphere where students can try out their ideas, invite students to communicate with each other at various stages, and present contextualized rich and complex problems that students can relate to in their everyday lives.