The Use of Technology Tools to Study Many Geometric Ideas
Technology tools are essential for effective teaching and learning of mathematics. For instance, in mathematics education computer technology is effective because it usually focuses on higher-order cognitive skills, such as hypothesizing, reasoning, investigating, and making generalizations (Beckmann, 2013). Use of technology tools motivate students towards becoming more interested in the exploration, investigation, conjecturing, creation, and discovery of principles which helps students to become mathematical problem-solvers, while at the same time making sure that the conceptual understanding of geometry is enhanced (Van de Walle et al., 2013).
A particular technology tool that can be used with students to increase their understanding of points, lines, planes, and angles is the Dynamic Geometry Software (DGS). This technology tool is particularly a wonderful tool used to teach Geometry to students in a discovery mode (Chandler, 2011). Chandler (2011) contends that this is attributed to the fact that it allows students to create and manipulate geometric figures while at the same time encouraging them towards making conjectures on the basis of what they see. The students can also modify the constructed figures by dragging points around the screen, while not changing the underlying relationships. Therefore, through recognition of the aspects remaining constant while doing the modifications, students are able to identify geometric concepts (Chandler, 2011).
It is quite evident that DGS provides more opportunities for the concentration of students on abstract structures in comparison to traditional approach of paper-pencil (Van de Walle et al., 2013). Thus, with this new approach, it is easy for students to enter the research setting, and engage in investigating, hypothesizing, testing, rejecting, formulating, or explaining these hypotheses (Beckmann, 2013). Hence DGS has revolutionized the nature of teaching and instruction in geometry because it can help to discover mathematical relationships with induction, while enabling them to draw simple to relatively complex figures, conduct analysis on them, and subsequently express their own hypotheses in form of a theorem (Beckmann, 2013). However, the most significant feature of DGS which helps students to increase their understanding of points, lines, planes, and angles is its ability to drag individual elements of a figure or the figure as a whole. This feature can be used by students to observe the dynamics of some of the figures’ properties because some changes while others remain constant (Van de Walle et al., 2013).
The main challenge encountered using DGS is that it initially requires close supervision from the teacher in order to ensure that students grasps all the details. Geometer’s Sketchpad program is a particular DGS technology tool which might be used to solve real-world geometry problems (Van de Walle et al., 2013). This is mainly because it gives very good results, and it can be practically used by students to quickly learn how to construct segments, circles, parallel and perpendicular lines as well as many other geometric figures (Chandler, 2011). The Sketchpad can also practically used as a measuring tool specifically because it only makes available all the measuring tools that are applicable to highlighted figures (Chandler, 2011).
This technology tool can be used to present students with geometric experiences that will foster their advancement through the van Hiele levels because students progress through levels based on their experiences, and it is imperative that teachers might use this technology tool to provide tasks and experiences so that students are capable of developing along this continuum (Breyfogle & Lynch, 2010). Breyfogle & Lynch (2010) show that DGS which is applicable in Van Hiele geometric model can be used to support deductive proof because it usually show empirical evidence as proof. Furthermore, DGS not only provides empirical data for confirmation or rejection of a conjecture, but also provides ideas leading to a proof (Breyfogle & Lynch, 2010).
References
Beckmann, S. (2013). Mathematics for elementary teachers with activities (4th ed.). Boston, MA: Pearson.
Breyfogle, M. L., & Lynch, C. M. (2010).Van Hiele revisited. Mathematics Teaching in the Middle School, 16(4), 232–238.
Chandler, S. (2011). Dynamic Geometry Software. Retrieved from Maths RUs website: http://mathr.us/welcome/2011/03/31/dynamic-geometry-software/ (Accessed on January 14, 2014).
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
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