CHAPTER 3: THEORETICAL FRAMEWORK
3.9 The Development process of integrating technologies into mathematics
The emergence of new technologies demands that teachers rethink its acceptance especially in mathematics teaching and learning. It also necessitates rethinking content and pedagogies.
Niess et al. (2009) observed teachers going through the five stages of the development process which they described as follows:
Table 3: The five-stage development process Source: Niess et al., 2009 p. 9
The five stages of the development process
1. Recognising (knowledge) - where teachers can use the technology and recognize the alignment of the technology with mathematics content yet do not integrate the technology in teaching and learning of mathematics.
2. Accepting (persuasion) -where teachers form a favourable or unfavourable attitude toward teaching and learning mathematics with an appropriate technology.
3. Adapting (decision) - where teachers engage in activities that lead to a choice to adopt or reject teaching and learning mathematics with an appropriate technology.
4. Exploring (implementation) - where teachers actively integrate teaching and learning of mathematics with an appropriate technology.
5. Advancing (confirmation) - where teachers evaluate the results of the decision to integrate teaching and learning mathematics with an appropriate technology.
The five stages are discussed in detail by Niess and other researchers are;
52 Stage 1 - Recognising
With the introduction of technologies in schools, researchers believe that there is a process in which teachers gain mathematics TPACK knowledge. Initially, Rogers explained an innovation decision process describing the sequence of how one decides to adopt or reject innovation. This idea was further developed by Niess, Sadri and Lee in 2007. Niess et al.
(2009) believe that classroom practitioners undergo five stages of development namely recognising, accepting, adapting, exploring and advancing which lead them to technology adoption. These researchers reformed the idea in terms of teachers learning how to integrate tools that have not yet been integrated into teaching mathematics. The process shows how teachers develop mathematics TPACK knowledge through the five stages.
During the first stage the teacher can use the technology tools however he/she strongly retains core beliefs about how students learn mathematics. In most cases this may be through memorisation of rules, formulas, algorithms and following certain procedures without necessarily using technology. Such beliefs hinder the teacher from exploring and experimenting with technology-based tools. The teacher may resist changes brought by the innovative tools even though there is recognition that mathematical concepts can be displayed with technology. Most lessons are delivered in lecture format followed by repetition in order to consolidate ideas. At this stage the teacher views most technology activities as focused on learning about technology within a mathematics context, rather than teaching mathematics concepts with technology.
Stage 2 - Accepting
This is the persuasion stage where attitudes (favourable or unfavourable) related to the use of technology-based tools in teaching mathematics are formed. The teacher accepts that some technologies can be useful for teaching and learning mathematics and desires to use them to teach mathematics. Technology- based tools are only seen as appropriate teaching tools rather than learning tools. This simply means that technology-based tools are viewed as effective tools only when they are utilised by the teacher and not necessarily by learners to form concepts. Integrating technology-based tools is believed to take away important time for teaching mathematics. Furthermore, teachers usually raise concerns about learners’
attention being diverted to the technology tools themselves instead of the concept being taught. Even though some technologies are useful, teachers may find it difficult to identify topics which may be aligned to these technology- based tools.
53 Stage 3 - Adapting
During the third stage, the teacher is aware of some of the benefits of incorporating technology-based tools with regard to teaching and learning mathematics. There is belief that the tool is used primarily as a means of implementing new teaching strategies and does not necessarily enhance the teaching of mathematics. Technology-based tools are known to be enhancing mathematics ideas that learners already possessed prior to the use of the tools.
The teacher may show the desire to explore and experiment using the tools for the purposes of both teaching and learning. Failure to implement technology integration may sometimes be restricted by challenges (for example; classroom management, fewer resources, technology glitches), which may arise during technology integration. At this stage the teacher may question how students think when technology-based tools are used for teaching and learning mathematics. Teachers at this stage can decide to adopt or reject incorporating appropriate technology-based tools.
Stage 4 – Exploring
In the fourth stage, teachers are excited about integrating the tools into mathematics lessons and they explore them in different ways. They accept that technology -based tools can be effectively used for teaching and learning specific topics in the syllabus. Planning, implementation and reflecting on teaching and learning is done using technology tools however there is a concern for guiding learners to understand mathematics concepts using technology-based tools. At this stage teachers are willing to explore various instructional strategies and are willing to learn and expand on new ideas for integrating technology in the classroom. Even though challenges for teaching mathematics with technology-based tools are recognised, the teacher strives to use other strategies and ideas which may minimize the impact of these challenges. The teacher presents technology enhanced activities which fully engage learners as he/she guides them. Most lessons are a success as the teacher puts maximum effort with tools that he / she has.
Stage 5 – Advancing
The last stage of the development process is whereby teachers have accepted the integration of the tools and are actively exploring them in a consistent manner. All available technological resources are utilized in a maximum way and teachers explore ideas for
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teaching and learning mathematics with different technologies. Tools engage learners in a variety of high-level thinking activities like problem-solving and mathematics projects.
Their motivation to use the tools is reflected in the lessons that are well planned and prepared for in advance. Plans to resolve challenges brought by technology-based tools during teaching time are planned for in advance. At this stage teachers can explore and experiment different strategies that accurately translate concepts in a creative way. Teachers in this stage firmly believe that integrating technology tools into mathematics lessons helps students to understand mathematical concepts in a better way.
Teachers require several competencies to build innovative teaching and learning environments designed to accommodate social constructivist views of learning. It is through various interactions that learners internalise knowledge. Teacher competencies, which include knowledge of technology integration, knowledge of different teaching methods and content knowledge, are necessary skills needed for the 21st century teachers hence cannot be ignored in the learning institutions. Basic understanding of different types of knowledge needed for integrating technologies can assist teachers assisting learners in grasping mathematical concepts. The TPACK framework also give guidance as to how teachers can incorporate technology in their classrooms in a successful manner.