This study sought to answer the three research questions stated in Chapter One. The impact of ICT on a Learning Study on students' performance on the topic Conversion of Travel Graphs was investigated. Students' misconceptions were identified through observation during the intervention, interview transcripts and from analysing their answers from pre-test and post-test. Teacher's perspectives on ICT and Learning Study had been discussed based from the interview transcripts. All of which are presented in Chapter Four and to be concluded in the next section.
Conclusions and Implications of the Study
The difference between this Cycle Three with Cycle One and Two was that ICT had been integrated in the research lesson. In it, Geometer's Sketchpad was used as part of the students' activity, two videos downloaded from YouTube was shown and Interactive White Board was used to show the Power Point slides for teaching purposes. In addition to that, a rubric was used to assess the students' performance on the post-test. Rubrics were not designed then in Cycle One and Two. Scoring was limited as there were only three items to be assessed in the pre-test and post-test for both cycles. Despite this limitation, comparisons of the results were still made in order to be sure of the practicality of ICT in improving students' performance.
The students' results that were discussed in Section 4.2.1 exhibited significantly higher scores in the post-test. Question 1 was the most scored by the students. This implied that students managed to grasp the concept from the first research lesson. This lesson was on introducing the five graphical conversions from distance-time graphs to speed-time graphs. Moreover, there was an improvement in an overall performance when compared to Cycle One and Two. This improvement might have been the result of the impact of ICT during the lesson.
Looking further at the rubrics results, students have shown better improvement in their scoring for each assessed dimension after their post-test. Perhaps, ICT might have improved the students' Knowledge and Understanding on Conversion of Travel Graphs. Students also achieved better standards in the Problem Solving dimension although weaker still at their Communication Skill in which they were still having difficulties in reasoning out their own mathematical working. In response to RQ1, with the overall statistical analysis that was reported in Chapter Four, Section 4.2, it was found that the use of ICT in a Learning Study may have given a positive impact on the academic performance for all 17 students.
In answering RQ2, this study managed to discover the different types of misconceptions. Based from the observation and interview transcripts, the misconceptions can be accumulated to six interrelated attributes. They are:
Misleading graphical feature
Though it may not be applicable to some students, teachers will be able to use the above list as guidelines in minimising the possible errors that students will make when learning this particular topic.
The first misconception on common problems is possibly the most difficult to get rid of. It is usually up to the teachers to plan and manage their lessons so that they are effective and meaningful for the students in order for them to grasp the concept and be able to apply them in the tasks event. As stated by Klemm (2007), "Students cannot apply what they understand if they don't remember it" (p. 61). If meaningful learning can be achieved, then there may be possibilities that all three misconceptions on Coordinates confusion, Formula dependency and Gradient-Area confusion can be avoided. Of course students also need to play their role as an active learner where one should pay attention and seek through the underlying concept of the object of learning. In other words, the process of teaching and learning is a reciprocal relationship in order to achieve a meaningful learning. Perhaps, in this way, the common problems of forgetting concepts and stating incorrect formulas can be avoided.
Apart from that, teachers also need to educate their students in the habit of checking their work to prevent miscalculations. A local study by Noorelawati (2011) who emphasised that "Not only can it increase the students' confidence in their own answer, but it can also save the students from spending unnecessary time in each question worrying about their answer" (p. 73).
Perhaps, the most universal problem that teachers have always come across to is the word 'misinterpretation'. Be it Mathematics, Science or even English Language, as a second language learners, students tend to interpret certain words differently. This is true because according to Latu (2005), "One of these [linguistic] difficulties arises when their first language does not have the vocabulary to express the mathematical ideas that they learn in the classroom" (p. 483). Obviously there are many ways to tackle this problem. One example that can be given here is that teachers need to explain new terms or unfamiliar keywords during the lesson and perhaps, even at the beginning of a lesson. Once this can be avoided, then it is possible for the students to develop the ability of drawing a correct response for any conversion graph.
For the last research question, RQ3, this study aims to seek the teachers' perspectives on Learning Study. Two teachers who are members of this Learning Study were interviewed. Based from the interview transcripts, it could be concluded that these two teachers have shown positive changes after experiencing all three cycles. Both have emphasised on the need of collaboration between their colleagues in designing meaningful research lessons in order for Learning Study to be carried on effectively.
Teachers' ability in using Variation Theory is also improving; one tried to implement it in his classroom through discerning several of exercises given to his students, the other used it in her teaching to analyse the critical learning features that students tried or developed. According to Lo and Marton (2011):
In addition, it provides a theoretical grounding to understand some of the necessary conditions of learning, so that we can make wise pedagogical decisions. Learning Study also contributes to Variation Theory by providing a platform for testing and further developing it as a source of pedagogical principles (Lo & Marton, 2011, p. 21).
Based from the results discussed earlier, the performance of the students in Cycle Three Learning Study was better than the previous cycles. This has shown that with teachers' collaboration and Variation Theory, a better systematic design research lesson can affect students' understanding of a mathematical concept. Teachers should be aware and understand what Variation Theory is about in order to implement Learning Study. The discernment in the items of the activity of lesson content will help students to conceptualise a general principle. With this, meaningful learning can be encouraged, as Edwards (2006) stated "We can structure the learning environment to ensure students experience the variations of the information searching experience; by doing so, we may encourage learning" (Variation Theory section, para. 3).
Another perspective that this study had focused on is on the integration of ICT in a Learning Study. Initially, both teachers were asked to discuss the pros and cons where in terms of the disadvantages, both claimed that designing ICT lessons with unfamiliar software are time consuming. Limited ICT equipments and other problems encountered while using computer for example, slow internet connection and computer crash are few of the drawbacks that they talked about. Many advantages were also mentioned briefly. According to them, ICT saves a lot of time in delivering lessons and that the pace can be sped up as teachers do not have to write the lesson on the board.
Furthermore, ICT can help attract students' attention. This is expected as ICT lessons provide visuals and students find that fun and interesting. Such interactive lessons can be found from the internet. Moreover, free mathematical software can be downloaded easily and can be used during a lesson so that students will be able to explore the concept of this topic freely in their own time. Many interactive activities, lesson plan and even lesson notes are now made readily available to be shared for teachers internationally on many websites. Teachers can now effortlessly access these lessons with just 'one-click away'.
With the above positive reviews, one might agree with the fact that ICT could be used as a pedagogical tool in a Learning Study. With the current trend of global education reform, teachers are encouraged to implement the use of ICT in their teaching. Oliver and Trigwell (2005) supported the idea of mixing teaching with technologies in which they referred this as blended learning. They stated that, "Blends of e-learning with other media may make it easier to help students experience the variation in the critical aspects of the topic being learnt" (p. 23).
This is true to some extent as admitted by the two teachers. They commented that ICT can be integrated in a lesson to certain Mathematics topics only. In this case, it is suitable to integrate ICT when teaching this particular topic. Overall, it could be implied that the teachers are well aware of the importance of ICT. The idea of moving forward in changing their procedural pedagogical approach is in the back of their mind. If these teachers are given chances to participate in ICT workshops or be trained using any Mathematical software, surely they will be able to divert their ways into creating ICT based lessons and teach confidently and comfortably in a different teaching environment.
Overall, there are four main interrelated themes in this study and they are: Learning Study, technology, meaningful research lessons and the topic chosen, Conversion of the Travel Graphs. It can be summarised that the process of Learning Study may help out in improving teaching and learning of the topic chosen. Meaningful research lessons may also be accomplished through collaboration of teachers in designing the activities. This of course relates to Learning Study as well since it promotes sharing of ideas and experiences. To improve Learning Study with the integration of ICT, teachers should be exposed to series of professional development.
Professional development is essential in supporting the ICT implementation to be successful. Fullan (1991) stated that "continuous development of all teachers is the cornerstone for meaning, improvement and reform" (p. 315). Additionally, teachers should also be open minded in accepting the change in the teaching and learning environment. Positive attitude on the use of ICT in their lesson and being creative in designing the lesson will further help to enhance meaningful learning. As supported by Thorburn (2004), "teachers need to be convinced that whatever change is being proposed will positively impact student learning" (Summary section, para. 1).
Professional development is needed so that teachers will be proficient enough to use any technology. This is important because teachers will facilitate students during a lesson especially if they are using ICT incorporated in their teaching. It helps further for teachers to be more confident in designing creative lessons provided that the professional development focuses on pedagogical techniques. Pedagogical approach using Learning Study should also be shared during professional development. With it, teachers will be able to implement Variation Theory so that Learning Study in Brunei can be continued throughout the years to come.
Recommendations for Further Study
The results that had been discussed in this study originated from a small number of sample size and thus, must not be generalised for the whole Brunei. It is recommended that in the future, a further study with a much larger sample with different level of abilities should be taken into consideration in order to investigate the impact of the students' performance after such intervention. With this being said, the results of students in the post-test also do not portray much of their actual concept on the topic Conversion of Travel Graphs as it was administered two days after the intervention. The plan was to distribute the post-test a week after the intervention however due to the cancellation of two of their afternoon classes during Ramadhan and that the students were behind in their syllabus, the post-test had to be advanced to two days.
This study can further be improved if the multimedia software programs are readily available. These software programs namely microcomputer-based laboratory (MBL), calculator-based laboratory (CBL) and calculator-based ranger (CBR) were used mainly in many international studies for this particular topic in Mathematics or Physics subjects. It is suggested that, these multimedia can be used in future research lessons. Comparisons of results can be made since there had been many reviews such as from Lapp and Cyrus, Yenni and Heck, Urban-Woldron and others, written in relation to the use of this multimedia.
Meanwhile students' misconceptions can also be explored further if more students are to be interviewed. Perhaps, few misconception facts can be ruled out from the list as the existing ones may only be applicable to the interviewee.
A wider perspective on the teachers' collaboration should also be asked during the interview to avoid any biasness that may lead researchers into thinking that there is only positive action and reactions. Such perspective should fit the six keys of collaboration as stated by Welborn (2012). They are: clarity of purpose, individual commitment, time, understanding how to collaborate and communicate, supportive administrators and freedom to explore. In this study, the collaboration was only based on discussions during meeting and sharing of responsibilities while designing the research lessons. It is recommended for further research to investigate whether teachers are able to achieve the six attributes whilst planning the research lessons.