General Information

This project focuses on investigating the development of students' ability in transformational geometry. Transformational geometry concepts are not explicitly taught in the current Cyprus curriculum of elementary education; they are mainly introduced through the concept of symmetry. However, it is critical in several foreign mathematical curriculums and it will be emphasized in the on-going developing of new curricula in Cyprus. Therefore, investigating how transformational geometry ability is developed in elementary school students is important. Moreover, it is essential to explore ways to enhance its' learning and increase students' ability. There are indications that instruction using an interactive-dynamic instructional environment is more beneficial for students' abilities in the concepts of reflection and rotation, compared to traditional teaching (Dixon, 1995).

However, some doubts have been recently raised in research on whether dynamic learning environments actually improve understanding (Ploetzner & Lowe, 2004). The argument of this position is the possibility of such dynamic environments to place great information processing requirements on learners and overburden their cognitive capacities. Hegarty (2004b) draws attention to the fact that there are many different types of dynamic displays, and that it might be simplistic to generalize results from studies with one dynamic display, therefore the relative effectiveness of different types of dynamic displays, for different types of learning and content should be examined.

Relevant research which lately focuses on the effects of such different multimedia educational resources (e.g. with different level of interactivity or motion effects) on learning and abilities, tends to emphasize on the effect that these resources may have on people with individual differences on characteristics such as prior-knowledge (Park, Lee, & Kim, 2009), and especially spatial abilities (Muzner, Seufert, & Brunken, 2009; Keehner, Hegarty, Cohen, Khooshabeth, & Montello, 2008; Smith, Gerretson, Olkun, Yuan, Dogbey, & Erdem, 2009). According to Hegarty (2004a), people with better internal visualization skills may have an advantage in comprehending visual displays of motion. Especially in the case of transformational geometry, Kirby and Boulter (1999) raise concerns on whether such complex visual environments will have negative impact on students with low spatial abilities. Abilities in transformational geometry have been also been previously connected to spatial abilities (Kirby & Boulter, 1999; Dixon, 1995), although some researchers believe that working with transformational geometry can improve spatial abilities (Clements & Battista, 1992). Hence, it is important to investigate the relative effectiveness of different types of dynamic displays on the learning of people with different characteristics.

References

Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grows (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: McMillan.

Dixon, J. K. (1995). English language proficiency and spatial visualization in middle school students' construction of the concepts of reflection and rotation using the "The Geometer's Sketchpad". Dissertation Abstracts International. 56(11). 4307A.

Hegarty, M. (2004a). Diagrams in the mind and in the world: Relations between internal and external visualizations. In A. Blackwell, K. Mariott and A. Shimojima (Eds.). Diagrammatic Representation and Inference. Lecture Notes in Artificial Intelligence 2980 (pp. 1-13). Berlin: Springer-Verlag.

Hegarty, M. (2004b). Dynamic visualizations and learning: Getting to the difficult questions. Learning and Instruction, 343-351.

Keehner, M. Hegarty, M., Cohen, C. A., Khooshabeh, P., & Montello, D. R. (2008). Spatial reasoning with external visualizations: What matters is what you see, not whether you interact. Cognitive Science, 32, 1099-1132.

Kirby, J. R., & Boulter, D. R. (1999). Spatial ability and transformational geometry. European Journal of Psychology of Education, 14(2), 283-294.

Munzer, S., Seufert, T., & Brunken, R. (2009). Learning from multimedia presentations: Facilitation of animations and spatial abilities. Learning and Individual Differences, 19(4), 481-485. doi:10.1016/j.lindif.2009.05.001.

Park, S. I., Lee, G., & Kim, M. (2009). Do students benefit equally from interactive computer simulations regardless of prior knowledge levels? Computers and Education, 52 (3), 649-655.

Ploetzner, R., & Lowe, R. (2004). Dynamic visualizations and learning. Learning and Instruction, 14, 235-240.

Smith, G. G., Gerretson, H., Olkun, S., Yuan, Y., Dogbey, J., & Erdem, A. (2009). Stills, not full motion, for interactive spatial training: American, Turkish and Taiwanese female pre-service teachers learn spatial visualization. Computers and Education, 52, 201-209.