Teaching Mathematics. Computer-Based Technologies.

Introduction

With the rapid increase in the use of the computers and other forms of ICT in virtually all the sectors, the education docket too, has embraced these emerging trends. Consequently, the curricula of many institutions have been revised to embraces this change (Wallace 2004). This has then ensured that ICT now becomes an integral part of any school curricula.

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In using computers to teach mathematics, a strong link between computers and mathematics has emerged, given that mathematics teachers were the first teaching professional to handle computer work in schools (Papert 1993). The indication of this is that ICT too, is an integral part in as far as the teaching and learning of mathematics is concerned. According to Papert (1993 p. 183), computers will not only be viewed at as objects in peoples’ everyday lives, but shall also be utilized daily in the teaching and learning of mathematics (Goos 2005).

According to Ittigson and Zewe (2003), technology is an essential tool in both the teaching and learning of mathematics. ICT not only helps to improve the way mathematics is taught, but also enhances the understanding of basic concepts to the same by students (Russell, Bebell, O’Dwyer & O’Connor 2003). Becta (2003) offers a summary of the key benefits of using ICT in mathematics: promotion of an enhanced collaboration between students and teachers, and an encouragement on both communication and knowledge sharing. ICT also gives a rapid and accurate feedback, hence offering motivation to students.

Further, ICT enables students to be more focused on interpretations of answers and the strategies to getting these, as opposed to spending more time on the computations and calculations (Kelleher 2000). Furthermore, student through the use of ICT, are better able to explore and understand mathematics concepts, thus promoting better strategies for problem solving (Ittigson & Zewe 2003). According to a study published in 2004, it was shown that 37 percent of high-school teachers in Italy regularly use their PCs in their preparation of lessons, while a further 20 percent use the technology to make classroom presentations (Midoro 2005).

Another study at two universities in Italy attempted to explore the use of technology in the teaching of mathematics (Monaghan 2005). This research was undertaken based on two hypotheses. According to the first hypothesis, there is a lack of perception by mathematics teachers on the possible changes that would accompany the use of ICT in teaching mathematics; in as far as pedagogical practice is concerned. According to the second hypothesis, there is a lack of realization by teachers that technology calls for a regular update in order to achieve ‘adequate competencies’ in teaching (Verillon & Rabardel 1995).

Theoretical framework

According to research, ICT is useful in the strengthening of procedural knowledge. In a school environment, ICT is mostly used in the capturing, processing and interpretation of data, multimedia software, computer projection technology, and in the provision of publishing and presentation tools (Lagrange & Artigue 2003). Newton and Rogers (2003) opines that by using ICT technology in the study of mathematics, benefits are accrued in two ways. Firstly, the intrinsic properties of ICT help in time saving, as well as the handling of data. Secondly, the manner in which ICT is used in classrooms, offers potential learning benefits to the students. In this regard, one would need to possess operational skills to be able to exploit ICT properties (Osborne & Hennessy 2003).

On the other hand, ICT benefits can only be exploited by way of application skills (Lagrange & Artigue 2003). The use of ICT in schools enhances and reinforces student-centered learning. This then ensures that there is a didactic pedagogy shift from teacher-centered learning, to a constructivist pedagogy student-centered form of learning (Laborde 2002). Consequently, ICT integration into the classroom has in essence enabled teachers to focus more attention to informed activities, courtesy of constructivist learning theories (Brousseau 1997).

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However, this is not reason enough to guarantee a full grasp of the ICT integration in teaching. Perhaps a reason for this is as a result of compartmentalized coursework that offers little connection between theory and practice (Laborde 2002). When teachers lack a student-centered learning environment to support ICT learning, then they resort to a teacher-centered approach of teaching when embracing the use of ICT. According to Kuhn (1962), people always find it culturally difficult to embrace a paradigm in the face of scientific revolution. From this angle then, one can rightly be hypothesise that owing to teacher’s ‘partial perception’ of ICT, they are not able to completely utilize it.

However, the continuous spread of technology has seen to it that this paradigm shift does occur. According to Bottino (2000), one can attain learning environments that are innovative, by integration of educational and cognitive theories, teaching and learning needs, as well as technological opportunities. Indeed, technological tools support both the teaching and the learning process, by creating a conducing environment for both teachers and students, thus helping promote the meaning of the objects of mathematics (Fasano & Casella 2001).

According to Laborde (2002), the integration of technology into teaching is time consuming. First, they have to accept the technology, and then be able to create ideal learning situations. Goos (2005) is of the opinion that technologies ought to be viewed at as cultural tool that re-organize cognitive processes, while at the same time transforming social practices at the classroom. However, the attainment of an adequate perception of ICT, and the awareness about its potential in mathematics education, needs to be achieved (Simonsen & Dick 1997).

Factors encouraging/ hindering the use of computer-based technology

As much as the use of ICT is touted as a paradigm shift in learning methods, its use in learning institutions has however been not without challenges (Vérillon & Rabardel 1995). One of these challenges is the barriers encountered at the teacher level. First, some teachers are lacking in ICT formal training (Simonsen & Dick 1997). Secondly, others do not have a self-directed exploration of the ICT teaching methodology (Artigue 1998). Kelleher (1997) also attributes lack of time to prepare ICT resources for the lessons as another barrier at the teacher level. Other teacher are also lacking in confidences, in as far as the use of ICT in schools is concerned (Monaghan 2005).

Others have had a previous negative experience in the use of ICT (Artigue 1998). Some teachers are also plagued with embarrassment when standing in front of students, while also fearing for a loss of status, and a possible degradation of professional skills (Russell & Bradley 1997). Still, another group of teachers is unable to manage the classroom, especially in case whereby pupils have to share ICT facilities owing to scarcity (Simonsen & Dick 1997).

Incase of a technical problem occurring, majority of the teachers lacks the knowledge to resolve such problems (Brousseau 1997).

While some teachers may be lacking in management skills to embrace personal change, others are of the perception that learning is not enhanced thorough technology (Labored 2002). Brousseau (1997), is of the opinion that some teachers have the perception that computers are too difficult for them understand how to use. At the school level, some institutions may be lacking in ICT facilities (Kelleher 1997) while the acquiring, maintenance and usage costs of ICT resources is beyond the affordability of others. Some students are also not able to access ICT equipment, owing to the institutions organization factors, as well as obsolete hardware and software (Papert 1993), and equipment which are unreliable (Verillon & Rabardel 1995).

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A deficiency in technical and administrative support is another hindrance to the use of ICT in learning institutions (Goos 2005). When poor leadership and planning occurs in an institution, teachers are unable to implement changes, such as the use of ICT. Lack of institutional support will also result in teachers who are lacking in ICT training, meaning that they are only focused in the basic teaching skills (Verillon & Rabardel 1995).

Despite the inhibiting factors to the use of ICT in classrooms, computer use at school has however, also had a profound effect on the teachers. According to (Papert 1993), computers are not only able to challenge the technical abilities if teachers, they also place a high demand on both their energies and time. Moreover, computers will also require teachers to adopt and embrace teaching strategies, to their benefits and that of the students (Goos 2005).

Teacher educators’ perception on preparing student teachers to use technologies in teaching mathematics

With technology having permeated our educational experiences, educators are seeking viable ways through which they can tap this technology to enrich the learning experience. The use of technology in pedagogical teaching ought to be more involving that a mere mastery of skill (Goos 2005). It is important when training teachers to embrace technology, that due regard is given to their beliefs and perception, courtesy of their teacher training programs (Simonsen & Dick 1997).

Consequently, a paradigm shift and behaviour modification is necessary in teachers and administrators, as well as the students, in a bid to successfully embrace the use of ICT in learning institutions (Becker 1991, p. 8). Research findings have confirmed that teachers normally teach as they were taught (Osborne & Hennessy 2003) and that pre-service teachers are more likely to rely more on the experiences and knowledge of school-based teachers as opposed to educators (Becker 1991).

In the training of mathematics teachers to make use of ICT, focus should be on the didactical reflection, in order to help students and teachers alike to utilize the technology to the fullest not only in teaching, but also as a learning activity (Osborne & Hennessy 2003). In this regard, ICT learning tools such as multimedia, internet and spreadsheet, ought to be utilized. Cabri, which is mathematics-specific software, also needs too be used (Goos 2005). However, use of technology-enhancing tolls, per se, is not a guarantee that students will be directly brought into mathematical thinking (Laborde & Capponi, 1994).

According to Brousseau (1997), introducing students to ‘theory of situations’, while devoting particular attention on the role played by a-didactical milieu, is a useful indicator of the perceived usage of ICT in learning by students. Given that most student teaching experience gets lost during internship owing to diverging opinions and a lack of direction and focus, teacher educators needs to provide pre-service teachers with the opportunity to not only observe, but also participate in appropriate technology practices. This, way the teachers will be motivated to enrich their student teaching experiences (Lagrange et al 2003).

Work cited

Artigue, Michael. Teacher training as a key issue for the integration of computer technologies, study of thought in relation to instrumented activity”. European Journal of Psychology of Mathematics, Florida: Chapman & Hall, 1998.pp.121-129.

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Becta. What the Research Says about Using ICT in Maths. UK: Becta ICT Research, 2003.

Bottino, Robert. Advanced Learning Environments: Changed views and future perspectives, in M.Ortega & J. Bravo (Eds.), Computers and Education: towards an interconnected society, The Netherlands, Dordrecht: Kluwer Academic Publishers, 2000, pp 11-27.

Brousseau, Gerald. Theory of Didactical Situations in mathematics. Dordrecht: Kluwer Academic Publishers, 1997.

Fasano Michael and Casella Francis. The didactic laboratory as a place to experiment models for the interdisciplinary research, in M. Michelini (Ed.), Proceedings of the International Conference Developing formal thinking in physics, Udine, Italy, 2001, pp. 399-403.

Goos, Margaret. “A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology”, Journal of mathematics teacher Education, 8 (2005): 35-59.

Ittigson, Rachel. & Zewe, John. Technology in the mathematics classroom. In Tomei, L.A. (Ed.). Challenges of Teaching with Technology across the Curriculum: Issues and Solutions. Hershey: Information Science Publishing, 2003. Pp.114-133.

Kelleher, Rueben. “A review of recent developments in the use of information communication techologies (ICT) in science classrooms”. Australian Science Teachers’ Journal, 46.1 (2000): 33-38.

Kuhn Timothy. The Structure of Scientific Revolution, 1st Ed., Chicago: The University of Chicago Press, 1962.

Laborde Charles. “Integration of Technology in the Design of Geometry tasks with Cabri-Geometry”, International Journal of Computers for Mathematical Learning 6.3 (2002): 283-317.

Lagrange John, Artigue Michael., Laborde Charles, and Trouche, Lawrence. Technology and mathematics Education, in A. Bishop et al (Eds.), Second International Handbook of mathematics Education: Part two, Dordrecht: Kluwer, 2003, pp. 237-269.

Midoro, Vincent. European teachers towards the knowledge society, Cortona, Italy: Menabò, 2005.

Monaghan, Jonathan. Thinking algebraically: Manipulative Algebra. In Johnston­ Wilder, S. and Pimm, D (Eds) (2005) teaching Secondary Mathematics with ICT. Maidenhead: Open University Press.

Newton, Lawrence, and Rogers, Lindsay. “Thinking frameworks for planning ICT in science lessons. School Science Review, 84 (2003): 113-120.

Osborne, James, and Hennessy, Samuel. (2003). “Literature review in science education and the role of ICT: Promise, problems and future directions”. A report for NESTA Futurelab (Report 6).

Papert, Simon. Mindstorms: Children, Computers and Powerful Ideas. Basic Books Brighton: Harvester, 1993.

Russell, Michael, Bebell, David, O’Dwyer, Lawrence and O’Connor, Kent. “Examining teacher technology use: Implications”. Journal of Teacher Education, 54.4 (2003): 297-310.

Simonsen, Lawrence, and Dick, Thomas.” Teachers’ perceptions of the impact of graphing calculators in the Mathematics classroom”. Journal of Computers in Mathematics and Science16.3 (1997): 239-268.

Wallace, Robert. “A framework for understanding teaching with the Internet. American Educational Research Journal, 41(2004): 447-488.

Vérillon, Patrick, and Rabardel, Paul. “Cognition and artifacts: a contribution to the study of, thought in relation to instrumented activity”. European Journal of Psychology of Education 10.1 (1995): 77-101.

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