## Introduction

Over the past few decades, information technology has infiltrated almost every aspect of our day-to-day lives including education. Due to the rapid advances in information technology and its inclusion in virtually every aspect of life, several types of research have been carried out on its applicability in education and with it, education technology has improved considerably over the years. E-learning technology includes software to enhance teaching, web-based libraries, and social networks where students can interact and share scholarly ideas.

According to Alexander (2006), the integration of information technology in education has enabled a more effective means of collaboration between teachers and students while at the same time allowing teachers to integrate the numerous technology-supported materials on the internet into the teaching-learning process. The internet has transformed the world into a global village; hence geographical confines cannot prevent the dissemination of information. The internet also contains vast storage of information collected from different people leaving in different parts of the world. Teachers and students can draw information from sources far away from them and thus improve their intellectual well-being (Gasser & Palfrey 2009). In the past, overhead projectors in conjunction with presentation software were the main form of e-learning. However, with the advent of more complex software, e-learning has taken the form of a more collaborative and engaging teaching process.

South Africa like the rest of the world has not been left behind with its e-learning efforts. Several schools in the country have adopted this new trend and achieved positive results. E-learning can support various platforms suitable for teaching different subjects. The most common subjects taught using e-learning are mainly non-mathematical (Droujkova 2009). This trend was developed during the onset of the e-learning technique and very little effort was taken to incorporate mathematical classes in e-learning.

Web 2.0 is a term used to describe modern computer applications that maximize the full potential offered by the internet allowing both collaboration and participation (Alexander 2006). It is an internet platform that enables users to create personalized content through sharing and participation. Unlike previous forms of e-learning platforms, Web 2.0 offers many tools that can be used to teach virtually any subject.

## Background and Context

Although e-learning technology has been adopted in many schools, most of the subjects taught are social subjects with very little attention being given to science subjects such as mathematics and physics. Although e-learning technologies advance at a fast pace, the teaching pedagogy is not increasing at the same pace. According to Ullrich (2008), the teaching pedagogy used for mathematical subjects has not been incorporated into most e-learning platforms.

The development of Web 2.0 platforms offers many tools for teaching mathematical subjects. However, most South African teachers still prefer using traditional teaching methods despite the availability of Web 2.0 in their schools. Teachers in rural schools find it particularly hard to adopt this new technology mainly because of a lack of understanding and inadequate facilities to offer effective services to their students. Another problem that has been noted by (Department of Education 2010) is what types of pedagogy should be utilized when incorporating technology into learning and how does this technology dictate what should be taught in schools. It is therefore important to develop a framework that may enhance the teaching and learning of mathematics using Web 2.0

## Scope and Objectives

This research sort to find out several things connected with e-learning. First, the research sort to find out the impact of technology on classroom teaching and learning. Secondly, it was also important to find out how Web 2.0 can be integrated into teaching mathematics in high schools. Lastly, the research aimed to deliver a suitable framework that could be used to teach mathematics using Web 2.0.

To achieve these objectives, certain questions needed to be answered. They include:

- What are some of the challenges encountered using classroom technologies for teaching and learning in high schools?
- What are the factors required to deploy Web 2.0 for teaching and learning mathematics subjects in high schools?
- How would Web 2.0 be deployed to enhance teaching and learning of mathematics subjects in high school?

## Methods

This research is qualitative and used mainly data collected from previous research on the subject and answers collected through the use of research tools; interviews and questionnaires. Two schools were chosen, one urban and one rural. The schools were compared on the amount of classroom technology they had, how they were integrated into the teaching curriculum and how mathematics faired as compared to other subjects in the e-learning environment. Using the results gotten from the interviews and questionnaires, vigorous research was carried out to find a solution for the poor application of e-learning technologies in teaching mathematical subjects. From various studies, it was possible to draw up a suitable recommendation in developing the right format for teaching mathematical courses.

## Mathematics Teaching Pedagogy

Teachers all over the world use various teaching styles to achieve the required results. The learning of mathematics is both a matter of teaching style and the student’s psychology (National Council of Teachers 2000). It has been discovered in the past that most students who have trouble solving mathematical problems are usually frustrated to the point of giving up (Brown, Collins & Duguid 1989). It thus became a norm for teachers to apply the direct approach to teaching whereby the teacher directly engages the students and if a need arises carries out a one-to-one discussion with a student having troubles (Hagsphil 2004).

From our research, mathematical subjects in South African schools use the one-to-one approach whereby teachers write problems on the blackboard and then engage the students to answer. During teaching, the teacher takes the step-by-step approach, writing on the board while explaining to the students what each step entails (Hagsphil 2004). This is common in both rural and urban schools with rural school teachers unwilling to defer from this style.

These traditional methods of teaching have recently come under attack as most critics argue that learning has become an on-site activity (Skemp 2009). Once the class ends, students rarely bother to revise or discuss amongst themselves what was learned. The students thus learn very little from the class and will most likely forget everything after some time. A commonly accepted modern approach to teaching mathematics is constructivism. This approach argues that learning cannot be transmitted rather it should be constructed by the student (Deubel 2006). The premise behind this approach is that learning is an active process of assimilating information with pre-existing knowledge (Ullrich 2008). Constructivism relies on both individual discovery and group collaboration.

As it was noted, the traditional forms of teaching mathematics involve teachers transmitting information to students and later testing them on their comprehension of what was taught/transmitted. This is highly ineffective as a student can rarely remember what was taught and usually after the test, the student purges all the information collected from their minds. Students also find mathematics complicated and boring and this negative mental also hinders the effectiveness of traditional forms of teaching mathematics (Hagsphil 2004).

Globalization poses another problem to traditional forms of teaching mathematics. New books and technologies are constantly being developed in the world. Relying on old methods of teaching hinders access to these wonderful teaching tools. Globalization has led to increased completion both in the work market and the education field. It is imperative therefore for schools to adopt any edge they can to perform better and provide their students a chance to pursue their dreams in a country whose job market is saturated with people, both local and foreigners, looking for work (Gasser & Palfrey 2009).

## Web 2.0 Technologies and Learning

Unlike other web-based applications that were mainly read-only, Web 2.0 applications make full use of the networking ability of the internet to allow both reading and writing (Eggers 2005). These applications are inherently open and encourage participation. Web 2.0 platforms are congruent with modern forms of teaching such as connectionism and constructivism (Hohenwarter & Preiner 2007). The availability of social sites, wikis, and blogs make Web 2.0 platforms very attractive to both students and teachers. Most traditional types of teaching are administrative, requiring teachers to constantly monitor students from the classroom. Web 2.0 however offers the opportunity for user-adaptive teaching whereby the student is just as important as the teacher in his learning process (Gray 2009).

To understand the application of Web 2.0 technologies in education, it is important to analyze the various principles of the platform from an educational perspective. Web 2.0 offers paradigm changes from traditional teaching methods hence understanding the principles behind the platform will enable one to navigate on how to include the changes into teaching mathematical subjects.

## Features of Web 2.0 platforms

The first inherent feature of Web 2.0 is individual creativity (Ullrich 2008). The Web 2.0 platform aids and encourages active user participation. The platform allows both writing and storage of textual information. Individual users can publish and save their information in terms of blogs while different users can collectively share information in terms of wikis (Zhao 2009). The advent of fiber optics has allowed for faster internet connections all over the world hence responses from user interfaces are now instantaneous. Web 2.0 platforms are usually geared for efficiency and usability hence they usually concentrate on the task they were designed for (Eggers 2005). Unlike traditional forms of teaching and the previous Web 1.0 platforms where users have to read then solve questions, Web 2.0 platforms allow users to participate directly, in real-time, and contribute to the subject under discussion. Pedagogically, these features of Web 2.0 bests support the constructivist method of teaching.

The next feature is the diverse data available on Web 2.0 platforms (Greenmeir & Gaudin 2010). There is a vast collection of information such as pictures, text, mapping data, and search indexes. The content available from this platform can be used in several ways, paving ways for the development of new pedagogies. First, teachers can utilize the available resources as the primary source of information (e.g. data from Wikipedia). Next, students can use active knowledge construction by using collective data as the foundation for collective participation (information mixing or mass-up).

The available resources from this platform are also very helpful in researching thus a student can find different ways of solving a problem from different books or past papers (Gasser & Palfrey 2009). Videos from sites such as YouTube could be used to offer a step to step guide to the student on how to solve problems and various dictionaries or encyclopedias could be used to explain terms that may cause problems to the student.

The final feature is individual access to data (Ullrich 2008). Web 2.0 platform was geared towards reaching as many people as possible. Data can be retrieved from game consoles, PDAs, and mobile phones. Due to the variety of input sources, student participation is greatly enhanced. Another advantage is that the information retrieved from these platforms can be used as per the client’s wishes. The various forms in which data can be retrieved allow online viewing or printing to get the data in a hard copy.

## Benefits and Drawbacks of Web 2.0 in teaching mathematics

These features offer greater advantages than traditional forms of learning. First, there is more active participation by students. Students can perform better due to the variety of learning materials on these platforms as well as collective participation, drawing knowledge from fellow peers (Droujkova 2009). Another advantage is that Web 2.0 platforms offer collective intelligence. In the past, teachers had to rely on a very limited amount of books to teach. The use of the author concept in disseminating information was highly flawed as learning depended on the author’s scope, accuracy, and method of delivering data. Web 2.0 platforms offer a variety of materials for the same subjects thus negating individual author errors (Hohenwarter & Preiner 2007).

The scope is magnified and a student can learn different techniques to handle a problem and not be restricted by a single author’s view. Students can also create a community whereby they interact to solve problems that they could not on their own. They can share resources, knowledge, and tactics as need are (Lemke & Coughlin 2009). The platform offers the student the ability to study at any time and to review their subjects. This has the added advantage in that the student feels in control thereby increasing his self-motivation. Collaboration also enables a student to learn what others are learning and where he lags or his weak points. With Web 2.0, rather than the content being composed, organized, and then packaged, the eLearning content is sought of syndicated, becoming more like a blog, podcast, or a post. There is more emphasis on community, sharing, and exchange of ideas in Web 2.0.

There are however several drawbacks connected with the use of Web 2.0 platforms in education. Having students in an unrestricted community may be counterproductive. Students may engage in activities not connected with the subject of focus (Lemke & Coughlin 2009). It is therefore important to find a means to teach the student how to use these platforms and at the same time how to self-regulate themselves.

Another drawback is that this platform may encourage destructive tendencies such as plagiarism (Greenmeir & Gaudin 2010). Students may develop the habit of taking data from the internet and claiming it as their own. The teacher therefore must instruct the student on the meaning of plagiarism, the consequences, and ways to avoid it. The final problem is that weak students may have a very difficult time assembling and analyzing the vast materials available on these platforms (Deubel 2006). They may also be unable to use available tools effectively thus learning very little in the process. This however can be rectified by collective sharing where weak students are guided by their counterparts who better understand the process (Deubel 2006). The teacher can also instruct the students regularly on how to use these services.

## Developing a Framework for the Use of Web 2.0 in Learning Mathematics

From the analysis of collected data, it is possible to develop a framework that may help in using Web 2.0 for teaching mathematics. The framework proposed here is a derivation of one developed by Droujka (2009), in which she states that learning should take community-related roles that include different events in the global, group, and family network levels. By ensuring that learning occurs at every step, Web 2.0 can be used very effectively in learning mathematics. The framework devised follows five routes

The first route is mathematical authoring (Droujika 2009). This involves creating mathematical resources geared for a particular group of students. Since most students in South Africa share the same age curriculum, the resources should be geared towards specific age groups. The created resource may include text, media, or mathematical games depending on the targeted age (Collins & Wellington 1997). The mathematical resources should also be created with consideration to mathematical tutors so that they can communicate, share ideas, and exchange resources. The content should be developed such that it is easily understandable to the targeted audience.

The second step is community mathematics. There should be a well-constructed communication platform to allow collective participation (Droujika 2009). Students from Rural South Africa and those from Urban can communicate and share ideas online. Competition, math clubs, and discussion sites should be set up to facilitate learning. Teachers may also create their learning platforms while at the same time helping their students develop theirs. There are various professional social networks that teachers can join to share ideas and resources (Eggers 2005).

The third step is Humanistic Mathematics. It involves supporting activities that the students can understand and enjoy. This may entail instilling mathematical content into artistic communities such as cartoons, games, or music (Gray 2009). As explained earlier, students feel mathematics is too complicated and boring. This mentality makes it harder for students to learn new things but this can be solved by this process (Hagsphil 2004).

The fourth step is executable mathematics. This involves using applications geared for mathematical problems (Droujika 2009). This may involve graph plotting applications, equation creators, and several interactive math tools. Some applications available in the market enable a student to input a question and the application offers a solution showing the possible step-by-step process in solving the problem.

The final step is the psychology of teaching and learning mathematics. This involves the incorporation of mathematical theories in the creation of Web 2.0 platforms and the general teaching using this platform (Ullrich 2008). As seen earlier, Web 2.0 requires a shift from traditional modes of teaching towards a more social model. One of the teaching methods presented in detail is connectivism whereby the responsibility for the teaching process shifts from the teacher to the student. The teacher acts as a facilitator and offers instructions and support (Skemp 2009). Connectivism relies heavily on networking as one of its foundations is collective participation. Students are empowered in the teaching process by finding resources and solutions to various mathematical problems (Zhao 2009). Teachers should therefore shift their teaching strategies and use the various metacognitive strategies available to them (Deubel 2006).

## Conclusion

Globalization has led to various changes all over the world. Innovations in information technology, global connectivity, and increased sharing of resources are just a few of the many changes brought about by globalization. It is therefore imperative that all schools in South Africa recognize the advantages that may be brought by Web 2.0 technologies and strive to implement them in their teaching profession.

Mathematics has usually been viewed as a complicated and boring subject. It is mainly due to this fact that many schools have trouble adapting it to their Web 2.0 e-Learning platforms. The paper has looked at the issues surrounding Web 2.0 and the teaching mathematics and a suitable platform for the teaching of mathematics in high school in the country has been proposed. A change in teaching pedagogy is also important. Teachers should abandon traditional teaching methods and adopt new methods that can better deliver services in this digital world. The availability of a variety of technological devices can prove to be a great asset to education if Web 2.0 platforms are better utilized.

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