Computer Use and Visualization in Students' Construction of Reflection and Rotation Concepts

Abstract

The effects of a dynamic instructional environment (based on use qfThe Geometer's Sketchpad, N. Jackiw, 1991, in a computer lab) and visualization on eighth-grade students9 fN = 241) construction of the concepts of reflection and rotation were investigated. Also investigated were the effects of the environment on students' two-and three-dimensional visualisation. After controlling for initial differences, it was concluded that students experiencing the dynamic environment significantly outperformed students experiencing a traditional environment on content measures of the concepts of reflection and rotation, as well as on measures of two-dimensional visualization. The students' environment did not significantly affect their three-dimensional visualization. The Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989) include the following objectives in the standard for middle-level geometry: "In grades 5-8, the mathematics curriculum should include the study ofthe geometry of one, two, and three dimensions in a variety of situations so that students can visualize and represent geometric figures with special attention to developing spatial sense; [and] explore transformations ofgeometric figures" (p. 112). This paper demonstrates that this standard is not being adequately implemented with all students and provides a strategy for its achievement.The Second International Mathematics Study: Report fertile United States (Crosswhite, 1985) identified topics taught in other countries that were not covered by the majority of eighth-grade classes in the United States. "Forexample, topics in transformational geometry, taught in some countries, were reportedly taught by only 12% of United States eighth grade teachers" (p. 20). Furthermore, results ofthe study indicated that teachers primarily taught according to their textbook, with little use of manipulatives or other materials not included with the text. This finding was corroborated by data collected in a comparative study with seventh-and eighth-grade students in the United States and Japan (Iben, 1988).

The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’ Transformational Geometry Success

“…This result shows that the applications performed by the Computer Group were more successful than the applications as performed by the other two groups. When the literature is examined, many studies are seen to show the result that DGS Cabri is very effective in increasing transformational geometry achievement (Dixon, 1997;Hoyles & Healy, 1997;Kurak, 2009;Yavuzsoy-Köse, 2008;Yazlık, 2011). In this context, it can be said that DGS Cabri is an effective tool for increasing the transformational geometry achievement of teacher candidates.…”

“…For all intents and purposes, different software programs such as GeoGebra or Geometry Sketchpad could have been used instead of Cabri II Plus. Hence, the many other studies that have been performed all found an increase in geometry achievement with software no matter which program was used (Dixon, 1997;Harper, 2002). In the scope of this study, the reason for selecting Cabri II Plus was because the researcher has comprehensive experience with the current software and it has a user-friendly Turkish version with easy-to-use menus.…”

“…The important part of these studies is that they used different dynamic software such as Cabri II Plus, Geometry Sketchpad, and GeoGebra; according to the results of these studies, it was seen that the use of software is effective for increasing transformational geometry skills (Akgül, 2014;Dixon, 1997;Egelioğlu, 2008;Gürbüz, 2008;Güven, 2012;Güven & Kaleli-Yılmaz, 2012;Harper, 2002;Karakuş, 2008;Yavuzsoy-Köse, 2008;Yazlık, 2011). These studies also generally preferred to use the experimental method consisting of unique experiments and a control group.…”

“…In the literature, DGS has been determined as an effective tool for overcoming these difficulties (NCTM, 2000;Van De Walle, 2004). It is specified that Cabri DGS has an effective role among the dynamic geometry programs for teaching transformational geometry (Dixon, 1997;Güven, 2012;Güven & Kaleli-Yılmaz, 2012;Hoyles & Healy, 1997;Kurak, 2009;Yavuzsoy-Köse, 2008).…”

Connecting visual and analytic reasoning to improve students' spatial visualization abilities : a constructivist approach

“…Although the literature presents studies in which spatial ability relates to van Hiele levels of geometric thinking, other three-dimensional instruments explicitly integrating mathematical processes should be developed (Del Grande, 1987). Dixon (1997) partly concluded that in her study GSP was not effective in improving students' three-dimensional visualization.…”