Literature review
Level 4 Rigor
2.5 Technology
2.5.2 Applets and Virtual manipulation and Kinetics
Living in a three dimensional world allows one to possess a remarkable amount of natural or untaught geometric knowledge (Lisi &Weatherall, 2014; Wohlhuter, 2013). From childhood, a person is constantly interacting with and making sense of space and shapes around them. As noted by Van Hiele (1982), the intuitive notions that children reveal when exposed to spatial situations should be capitalised. Thus, the teaching of three dimensional shapes using resources like text books and the chalkboard gives rise to a lack of in-depth learning of three dimensional shapes. This has a temporary impression on learners' minds as it does not
provide a concrete foundation and negatively impacts on their mathematical careers. A degree of spatial awareness and related meanings are essential for mathematics (Yarmohammadian, 2014), especially geometry (Weckbacher & Okamoto, 2015;
Yegambaran, 2009). A person learns best by doing. Hackathorna, Solomonb, Blankmeyerb, Tennialb and Garczynskib (2011) note that when learners are actively engaged, this promotes deeper levels of thinking which facilitate genuine encoding, longer storage, and quick retrieval, in contrast to a traditional chalk and talk lesson. Learners' interaction would result in authentic learning, allowing them to experience their learning rather than playing a passive role in the learning process.
More importantly, active learning enables learners to investigate issues that concern them, such as learning more about a current event, an experiment, scientific discoveries or exploring the Ice Age. One can use the Internet to investigate the topic at hand, participate in a virtual field trip to the event, and watch it as it unfolds without leaving one's comfort zone.
Bansilal and Naidoo (2012) remark that visualisation promotes investigation and discovery through the use of concrete manipulations, models and diagrams. In addition, when learners are actively engaged, they construct knowledge from a combination of simulations like visuals and movement; hence knowledge is developed in a structured manner (Pettigrew &
Shearman, 2014). This is important since the ability to imagine and manipulate forms in space plays a fundamental role in problem solving, especially in STEM subjects (Goldsmith, Simmons, Winner, Hetland, Hoyle &Brooks, 2014).
Ndlovu, Wessels and De Villiers (2011) note that technology is being integrated into mathematics education in many countries around the world. As a conceptual subject, face-to- face contact is regarded as necessary to convey mathematical concepts (Engelbrecht &
Harding, 2005). Woo and Reeves (2007) maintain that learning that involves interaction is difficult as the use of technologies is more time-consuming than face-to-face contact.
However, virtual manipulation will create a more concrete learning experience (Pettigrew &
Shearman, 2014) because the visual and touch senses play a key role.
Applets are small programs that run on Java when accessed online via the Internet. They can be described as programs that run on the Internet allowing user interaction and thus virtual manipulation and visual simulation. Goose (2010) points out that "dynamic geometry packages and web-based applications that offer virtual learning environments, have changed the mathematics teaching and learning terrain" (p.67). Applets designed with dynamic
properties allow for objects to be virtually touched and moved one by one, which can be used to introduce or reinforce a mathematical concept. This creates an environment where learners can pose and solve their own problems, by forming links between concepts and receiving immediate feedback, thus allowing for reflection (Arnold, 2013). The learner is actively involved in the learning process. Applets can be set up in stages using scaffolds. This is exemplified in the applet named Getting to know the circle (Appendix S). Designing applets around previous knowledge is important, as this offers support in grooming new knowledge.
This led to the coining of the term Zone of Proximal Development (ZPD) (Bodrova, Germeroth, &Leong, 2013; Vygotsky, 1978). Thus, learning that starts from the known and moves to the unknown with the assistance of the applet would exhibit ZPD.
With regard to the applet design, Human-Computer Interaction (HCI) enables one to directly interact and manipulate objects, changing mathematical properties that are instantaneously represented on the screen. A level of confidence is achieved as one's visual senses are fed information (De Villiers, 2012), by noticing a change in measurement or orientation of the objects under study. Feeling in control and involved with the objects that are being manipulated immerses one in the learning environment.
In South Africa, adult illiteracy stands at just over 20% for young adults and school leavers (Wedekind, 2015). The language of instruction is undoubtedly an essential tool in the classroom as it promotes communication between the learner and teacher. According to De Villiers (1987), second language speakers find it difficult to shift from concrete to abstract levels of thinking. Geometry stresses the use of correct mathematical language with appropriate vocabulary to express the unique properties of the object under study (Atebe &
Schafer, 2010; Jamison, 2000). If a learner finds it difficult to define geometry's specialised terminology, poor performance results (De Villiers, 1987). Instruction via virtual manipulation offers more effective communication than traditional classroom instruction, where the teacher leads the learning process by reading out the instruction. Through visualisation, learners acquire the correct technical terms since they are able to see the definition and experience the meaning. Language will not pose a barrier to teaching and learning, as emphasis is placed on visualisation, allowing for the clear communication of geometry concepts. However, manipulatives can potentially be confusing if presented in a haphazard and disorganised way that lacks proper guidance (Arnold, 2013).
As noted by Bansilal and Naidoo (2012), research among high school students in the United States resulted in the identification of five types of imagery: concrete, kinaesthetic, dynamic, memory and pattern. It was found that dynamic imagery was the most effective but least used.
The use of kinaesthetic and dynamic imagery has proven effective in the learning and reasoning process of geometry as the visual and touch/movement senses are exercised, bearing in mind that the human body is most responsive to these senses (Robles-De-La-Torre, 2006).