16 SES 05 JS, ICT and Mathematics Education
Joint Paper Session NW 16 and NW 24
Dynamic visualizations are fascinating for many people. With the rise of computer technology, the cost for generating them has reduced considerably. This development has raised the hope that dynamic visualizations could facilitate learning. During the last two decades, several interactive computer programs were developed in the domain of mathematics (e.g., interactive geometry software, computer algebra systems) that enable the user to create animated or interactive representations of mathematical phenomena and are intended to support mathematics teaching and learning.
According to empirical studies in different domains, dynamic visualizations are rarely more beneficial for learning than static representations (e.g. Hegarty, Kriz, & Cate, 2003; Mayer, Hegarty, Mayer, & Campbell, 2005). The reason for these results is still up for discussion. Gog, Paas, Marcus, Ayres, and Sweller (2009) assume that dynamic visualizations impose more load on the working memory. This additional load could cause a negative learning effect. Mayer et al. (2005) conjecture that the mental simulation of a dynamic process based on a static representation could induce a higher learning outcome than passively observing a dynamic visualization.
Some researchers, however, reason that dynamic visualizations can be beneficial for learning in certain circumstances. Schnotz and Rasch (2008) argue that dynamic visualizations can foster learning if they release cognitive resources: Either by enabling students to perform a mental process that would otherwise not be executable or by substantially facilitating mental processing. This argument is consistent with Hattie’s (2009) finding that computer-aided learning is most effective in demanding situations. In order to avoid a solely passive observation of a visualization, Koning and Tabbers (2011) suggest requesting students to manipulate representations interactively. Thus, students would connect the internal processing of the dynamic representation with an embodied action.
In the domain of mathematics, quantitative studies about the effect of dynamic visualizations are scarce. In order to address this deficiency, we conducted a laboratory study with secondary students that learned aspects of the concept of function with or without dynamic visualizations. The learning setting was constructed corresponding to the mentioned theoretical assumption that dynamic visualizations can be advantageous if they enable or substantially facilitate the learning process.
We used a three-factor posttest-only design. In the learning setting, the exercises were accompanied with two different forms of dynamic visualizations. In the animated representation, the students could only play an animation and observe the movement of a point on the triangle line and its effect on the length of a chord. In the interactive representation, the students had to drag the point with the mouse on the triangle line and could contemplate the effect of this manual manipulation. In the control condition, students had to solve the same exercises with a static representation and had to mentally simulate the point’s movement.
The instructions of the exercises differed only if necessary. The students using an interactive representation were instructed to “drag point G with the mouse on the triangle line.” The participants working with an animated representation were requested to “press the play button in order to move point G on the triangle line”, whereas the control group was prompted to “move point G in your mind on the triangle line”. The students were randomly assigned to one of the three experimental conditions (interactive, animated, or static representation).
Amthauer, R., Brocke, B., Liepmann, D., & Beauducel, A. (2001). I-S-T 2000 R - Intelligenz-Struktur-Test 2000 R [Intelligence Structure Test 2000 (revised)]. Göttingen, Germany: Hogrefe. Ekstrom, R. B., French, J. W., Harman, H. H., & Derman, D. (1976). Manual for kit of factor-referenced cognitive tests. Princton, NJ: ETS. Gog, T., Paas, F., Marcus, N., Ayres, P. & Sweller, J. (2009). The mirror neuron system and observational learning: Implications for the effectiveness of dynamic visualizations. Educational Psychology Review, 21 (1), 21–30. Hattie, J. (2009). Visible learning. A synthesis of over 800 meta-analyses relating to achievement. London, England: Routledge. Heller, K. A., & Perleth, C. (2000). KFT 4-12+R - Kognitiver Fähigkeits-Test für 4. bis 12. Klassen. Revision [Cognitive Abilities Test (CogAT; Thorndike, L. & Hagen, E., 1954-1986) - German adapted version]. Göttingen, Germany: Beltz. Hegarty, M., Kriz, S., & Cate, C. (2003). The roles of mental animations and external animations in understanding mechanical systems. Cognition and Instruction, 21 (4), 325–360. Koning, B. B., & Tabbers, H. K. (2011). Facilitating understanding of movements in dynamic visualizations: an embodied perspective. Educational Psychology Review, 23 (4), 501–521. Mayer, R. E., Hegarty, M., Mayer, S., & Campbell, J. (2005). When static media promote active learning: Annotated illustrations versus narrated animations in multimedia instruction. Journal of Experimental Psychology: Applied, 11 (4), 256–265. Ramm, G., Prenzel, M., Baumert, J., Blum, W., Lehmann, R., Leutner, D., . . . Schiefele, U. (2006). PISA 2003: Dokumentation der Erhebungsinstrumente [PISA 2003: Documentation of survey scales]. Münster, Germany: Waxmann. Schnotz, W., & Rasch, T. (2008). Functions of animation in comprehension and learning. In R. Lowe & W. Schnotz (Eds.), Learning with animation. Research implications for design (pp. 92–113). Cambridge, England: Cambridge University Press.
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