In this section, the study explored the meaning beyond the collected quantitative and interview data, and then compared them with the existing literature, to make a thorough discussion. In the following, a number of points worth noting, including the issue regarding AR representations instructional designs, also students’ varied perception, resulted from individual difference (i.e. prior knowledge), to the same AR treatment.
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4.2.1 Multiple representations facilitated by AR Representations
A paired t-test was conducted to verify whether any difference existed in AR Representations students’ pretest and posttest scores. As shown in Table 14, a significant difference was spotted in the comparison between their pretest and posttest scores.
Take a closer look at qualitative results, several transcriptions somehow explain these phenomena. For instance, students in AR groups reported that they thought AR was much more beneficial than traditional picture because they could saw the concept in different forms in addition to static pictures in textbooks.
“I learn faster with tablet than traditional picture. Because when I scan the object, the tablet would show pictures that make me understand the concept more easily.”
In that way, this mechanism made them understand much more easily. This results aligned with Chahine’ s (2011) study, which proved students learned with representation-based instructions outperformed those with traditional instructions. Along this line, the present study not only confirmed the previous results, but extended the results to a new device and display, that is, tablet and augmented reality.
4.2.2 “Concrete-Pictorial-Abstract” sequences of AR Representations
In addition to the number and forms of representations, it was also worth noting that the sequences of representations might make different impacts on students. According to students’
interview data, two AR Representations functions seemed to assist them to understand the fraction concept more easily: the scanning process and the stepwise displays.
As for the scanning process, the action of placing camera-embedded tablet onto the real-life objects somehow create a brand-new perspective from the naked eyes. During this process,
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they not only could aware how the real-life objects related to them handily, but also concentrate on the real-life object itself, without other distraction.
On the other hand, the stepwise displays would direct their attention to the very concepts they were learning at the moment.
“Also, the tablet shows the action step by step, so I realize how fraction is to equalize objects.”
By overlaying the display composed of simple geometric pattern, such as circle, square, rectangle, and simple lines, it was likely to shift their attention from the complex object to its’
sheer geometrical version. In other words, the AR Representations could transform a single concept from its complicated version to the lite version, which carry less details, on the very single tablet-screen. Consequently, the transitional process would be much more smooth, and so as students’ thinking fluency.
The results, aligned with Agrawal & Morin’s (2016), that the sequence of concrete-pictorial-abstract is beneficial for students to learn abstract concept, especially those who were suffered from mathematics difficulty.
4.2.3 High and low level of prior knowledge students’ perception to AR Representations As has been discussed, those finding further stressed the importance of the number and the sequence of representations. Furthermore, due to the individual difference, that is, levels of prior knowledge, inconsistency of perception to AR Representations were detected.
An independent t-test and an ANCOVA were conducted to verify whether the level of prior knowledge had effect on AR Representation students’ pretest and posttest scores. As shown in Table 18, a significant difference was spotted in the comparison between high and low students’ pretest scores. However, the result of ANCOVA with pretest as covariance
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indicated no significant difference between high and low prior knowledge students. It is highly reasonably to assume that AR Representations would equalize different level of prior knowledge students’ understanding.
Several interview data illustrated the quantitative results. The majority of high prior knowledge students only reported that it was entertaining. It seems that the higher ones tend to focus on the functional aspects of AR, rather than the content. However, contrary to the higher one, the low prior knowledge students seemed to focus on the content that presented on the tablet screen. For instance, the transitions of different overlays were highly valued by one of the low prior knowledge students.
However, this finding contradicts the previous research that high prior knowledge students would be much more likely to pay attention to the task-relevant details (Cook, Wiebe,
& Carter, 2008). According to the result of the present study, it seemed low prior knowledge students see the details of representations much closer than the higher ones. There is a likelihood that the higher ones’ viewpoints were somehow limited by the past learning experiences. They tend to take this AR Representations as another entertainment, rather than a learning material.
But to the lower ones, since it is their first time to learn about these fraction concepts, they would pay attention to the details that delicately arranged.
Furthermore, in comparison with other literature that explored low prior knowledge students’ characteristics on learning, especially about their attention, the AR Representations that created by the study somehow made an appropriate combination. For instance, since low prior knowledge heavily rely on pictures when they are learning, the AR Representations then overlay pictures on the real-objects, so as to meet their special needs. This result was identical with Moyer-Packenham & Suh’s (2012) research.
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4.2.4 Enhancement of analogical thinking with personal experiences
In picture group, most of the students’ answers to analogical reasoning, such as tomato, cakes, cucumber, apple, onion, and cookies, were merely either from examples in textbooks or the present study. While in AR Representations group, various examples were detected.
However, the distinction between high and low prior knowledge student was identified. The higher ones could hardly provide any examples, while the low ones could generate as many as examples that were not mentioned before, such as bun and donut.
Moreover, it is also necessary to draw much more attention to the answers of two low prior knowledge students from both pictures and AR Representations group. The student who learned with picture answered “watermelon and egg tart”. These answers shared much similar appearance with other examples mentioned in class, which was round. In the meanwhile, the other student came up with sandwich, which is triangle-shaped. Moreover, the real-life scenario was also brought out by the low prior knowledge students. He reported that he would make use of fraction concepts when he helps his family fill the bowls with rice during the meals.
Therefore, it’s likely that low prior knowledge students who learned with AR Representations seemed to equip much unique pattern of analogical thinking.
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CHAPTER FIVE
CONCLUSION AND SUGGESTIONS
In chapter five, the conclusion and suggestions are divided into four main sections. First of all, section 5.1 briefly outlines two major findings of the study. The contributions are delivered in section 5.2. Furthermore, in section 5.3 and 5.4, the limitations of the study and suggestions for future research are included.