Facilitate and Monitor the Rollout of New Math and Reading Curriculums
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Enhancing achievement and interest in mathematics learning through Math-Island
Research and Practice in Applied science Enhanced Learning volume 14, Article number:v (2019) Cite this article
Abstract
Conventional instructor-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Nether such instruction, the teacher can rarely take care of all students. Many students may then keep to fall backside the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning mathematics. In fact, students in Taiwan generally take lower interest in learning mathematics compared to many other regions/countries. Thus, how to raise students' mathematics achievement and interest are two major problems, particularly for those depression-achieving students. This newspaper describes how we designed a game-based learning environs, chosen Math-Island, by incorporating the mechanisms of a construction direction game into the knowledge map of the simple mathematics curriculum. We also report an experiment conducted with 215 uncomplicated students for 2 years, from grade ii to form 3. In this experiment, in add-on to teacher-led instruction in the classroom, students were directed to larn with Math-Island past using their own tablets at school and at dwelling. Every bit a result of this experiment, nosotros found that at that place is an increase in students' mathematics achievement, particularly in the adding and word issues. Moreover, the achievements of depression-achieving students in the experimental school outperformed the low-achieving students in the control school (a control group in some other school) in word issues. Moreover, both the low-achieving students and the high-achieving students in the experimental schoolhouse maintained a rather high level of interest in mathematics and in the organisation.
Introduction
Mathematics has been regarded as a fundamental subject field considering arithmetic and logical reasoning are the footing of scientific discipline and technology. For this reason, educational authorities emphasize students' proficiency in computational skills and problem-solving. Recently, the results of the Program for International Pupil Assessment (PISA) and the Trends in Mathematics and Science Study (TIMSS) in 2015 (OECD 2016; Mullis et al. 2016) revealed a claiming for Taiwan. Although Taiwanese students had higher average functioning in mathematics literacy compared to students in other countries, there was still a significant percent of low-achieving students in Taiwan. Additionally, virtually Taiwanese students show low levels of interest and confidence in learning mathematics (Lee 2012).
The existence of a significant percent of depression-achieving students is probably due to instructor-led instruction, which however dominates mathematics classrooms in almost Asian countries. It should be noted that students in every classroom possess different abilities and hence demonstrate different achievements. Unfortunately, in teacher-led didactics, all the students are required to learn from the teacher in the same way at the same pace (Hwang et al. 2012). Low-achieving students, without sufficient time, are forced to receive knowledge passively. Barr and Tagg (1995) pointed out that it is urgent for low-achieving students to take more opportunities to larn mathematics at their own pace. Researchers suggested 1-to-one engineering science (Chan et al. 2006) through which every student is equipped with a device to learn in schoolhouse or at dwelling seamlessly. Furthermore, they can receive immediate feedback from Math-Island, which supports their individualized learning actively and productively. Thus, this may provide more opportunities for helping low-achieving students improve their achievement.
The low-interest problem for well-nigh all students in Taiwan is usually accompanied by low motivation (Krapp 1999). Furthermore, students with continuously low performance in mathematics may eventually lose their interest and refuse to learn further (Schraw et al. 2001). This is a severe problem. To motivate students to learn, researchers design educational games to provide enjoyable and engaging learning experiences (Kiili and Ketamo 2007). Some of these researchers institute that game-based learning may facilitate students' learning in terms of motivation and learning effects (Liu and Chu 2010), spatial abilities and attention (Barlett et al. 2009), situated learning, and problem-solving (Li and Tsai 2013). Given these positive results, we hope that our educational game tin raise and sustain the student's involvement in learning mathematics.
In fact, many researchers who endeavored to develop educational games for learning mathematics have shown that their games could facilitate mathematics performance, enjoyment, and cocky-efficacy (Ku et al. 2014; McLaren et al. 2017). Although some of the studies were conducted for every bit many as 4 months (due east.thou., Hanus and Pull a fast one on 2015), one may notwithstanding criticize them for the possibility that the students' interest could be a novelty effect—pregnant their interest will decrease as the feeling of novelty diminishes over time (Koivisto and Hamari 2014). Due to the limitations of either experimental fourth dimension or sample sizes, well-nigh studies could non finer exclude the novelty effect of games, unless they were conducted in a natural setting for a long time.
In this study, we collaborated with an experimental simple schoolhouse for more than two years. The mathematics teachers in the school adopted our online educational game, Math-Island. The students used their own tablet PCs to learn mathematics from the game in class or at home at their own stride. In particular, low-achieving students might have a take chances to catch up with the other students and start to feel interested in learning mathematics. Almost importantly, considering the online educational game was a part of the mathematics curriculum, the students could treat the game equally their ordinary learning materials like textbooks. In this paper, we reported a 2-year study, in which 215 2nd graders in the schoolhouse adopted the Math-Isle game in their daily routine. More specifically, the purpose of this paper was to investigate the effect of the game on students' mathematics achievement. Additionally, we were likewise concerned virtually how well the depression-achieving students learned, whether they were interested in mathematics and the game, and how their interest in mathematics compared with that of high-achieving students. In such a long-term study with a large sample size, it was expected that the novelty effect would be considerably reduced, allowing us to evaluate the effect of the educational game on students' achievement and interest.
The paper is organized every bit follows. In the "Related works" department, we review related studies on calculator-supported mathematics learning and educational games. In the "Design" section, the game mechanism and the organisation design are presented. In the "Method" department, we describe the research method and the procedures of this study. In the "Results" section, the inquiry results near students' achievement and interest are presented. In the "Discussion on some features of this study" department, we discuss the long-term study, knowledge map pattern, and the two game mechanisms. Finally, the summary of the current situation and potential time to come work is described in the "Decision and future work" section.
Related works
Computer-supported mathematics learning
The mathematics curriculum in elementary schools basically includes conceptual understanding, procedural fluency, and strategic competence in terms of mathematical proficiency (see Kilpatrick et al. 2001). Get-go, conceptual understanding refers to students' comprehension of mathematical concepts and the relationships between concepts. Researchers take designed various figurer-based scaffolds and feedback to build students' concepts and clarify potential misconceptions. For example, for guiding students' discovery of the patterns of concepts, Yang et al. (2012) adopted an anterior discovery learning arroyo to pattern online learning materials in which students were provided with similar examples with a critical attribute of the concept varied. McLaren et al. (2017) provided students with prompts to right their common misconceptions about decimals. They conducted a study with the game adopted as a replacement for seven lessons of regular mathematics classes. Their results showed that the educational game could facilitate better learning performance and enjoyment than a conventional instructional approach.
2d, procedural fluency refers to the skill in carrying out calculations correctly and efficiently. For improving procedural fluency, students demand to have cognition of calculation rules (e.g., place values) and practise the procedure without mistakes. Researchers developed diverse digital games to overcome the boredom of practice. For instance, Chen et al. (2012a, 2012b) designed a Cantankerous Number Puzzle game for practicing arithmetics expressions. In the game, students could individually or collaboratively solve a puzzle, which involved extensive calculation. Their study showed that the low-ability students in the collaborative status made the most improvement in calculation skills. Ku et al. (2014) adult mini-games to railroad train students' mental calculation ability. They showed that the mini-games could not only improve students' calculation performance but also increment their confidence in mathematics.
3rd, strategic competence refers to mathematical problem-solving ability, in particular, word trouble-solving in elementary education. Some researchers developed multilevel computer-based scaffolds to help students translate word problems to equations footstep by pace (e.g., González-Calero et al. 2014), while other researchers noticed the problem of over-scaffolding. Specifically, students could be likewise scaffolded and take trivial infinite to develop their abilities. To avoid this situation, many researchers proposed assuasive students to seek assistance during word problem-solving (Chase and Abrahamson 2015; Ringlet et al. 2014). For instance, Cheng et al. (2015) designed a Scaffolding Seeking system to encourage elementary students to solve word issues by themselves by expressing their thinking first, instead of receiving and potentially abusing scaffolds.
Digital educational games for mathematics learning
Because mathematics is an abstruse subject, elementary students easily lose interest in it, especially low-achieving students. Some researchers tailored educational games for learning a specific set of mathematical knowledge (e.grand., the Decimal Points game; McLaren et al. 2017), so that students could be motivated to learn mathematics. Yet, if our purpose was to support a consummate mathematics curriculum for simple schools, information technology seemed impractical to design various educational games for all kinds of knowledge. A feasible approach is to prefer a gamified content structure to reorganize all learning materials. For case, inspired by the pattern of near office-playing games, Chen et al. (2012a, 2012b) proposed a three-tiered framework of game-based learning—a game world, quests, and learning materials—for supporting elementary students' enjoyment and goal setting in mathematics learning. Furthermore, while a game world may facilitate students' exploration and participation, quests are the containers of learning materials with specific goals and rewards. In the game globe, students receive quests from nonplayer virtual characters, who may enhance social commitments. To consummate the quests, students accept to brand efforts to undertake learning materials. Today, quests accept been widely adopted in the pattern of educational games (due east.g., Azevedo et al. 2012; Hwang et al. 2015).
However, in educational games with quests, students still play the role of receivers rather than active learners. To facilitate elementary students' initiative, Lao et al. (2017) designed digital learning contracts, which required students to set weekly learning goals at the start of a week and checked whether they accomplished the goals at the cease of the calendar week. More than specifically, when setting weekly goals, students had to determine on the quantity of learning materials that they wanted to undertake in the coming calendar week. Furthermore, they also had to decide the average definiteness of the tests that followed the learning materials. To assist them set up reasonable and viable goals, the system provided statistics from the past 4 weeks. As a consequence, the students may reflect on how well they learned and and so brand appropriate decisions. Afterward setting goals, students are provided with a serial of learning materials for attempting to attain those goals. At the cease of the week, they may reflect on whether they accomplished their learning goals in the contracts. In a sense, learning contracts may not only strengthen the sense of commitment but also empower students to take more control of their learning.
In textbooks or classrooms, learning is usually predefined as a specific sequence, which students must follow to learn. Nevertheless, the construction of knowledge is not linear, but a network. If we could reorganize these learning materials according to the structure of cognition, students could explore cognition and discover the relationships among different pieces of knowledge when learning (Davenport and Prusak 2000). Cognition mapping has the reward of providing students concrete content through explicit knowledge graphics (Ebener et al. 2006). Previous studies accept shown that the incorporation of knowledge structures into educational games could finer raise students' achievement without affecting their motivation and self-efficacy (Chu et al. 2015). For this reason, this study attempted to visualize the construction of knowledge in an educational game. In other words, a knowledge map was visualized and gamified so that students could brand decisions to construct their own knowledge map in games.
Design
To enhance students' mathematics accomplishment and interests, we designed the Math-Isle online game by incorporating a gamified cognition map of the elementary mathematics curriculum. More specifically, nosotros adopt the mechanisms of a construction management game, in which every student owns a virtual island (a metropolis) and plays the role of the mayor. The goal of the game is to build their cities on the islands by learning mathematics.
Organization architecture
The Math-Isle game is a Spider web application, supporting cross-device interactions amid students, teachers, and the mathematics content construction. The system architecture of the Math-Island is shown in Fig. 1. The pedagogical cognition and learning materials are stored in the module of digital learning content, organized by a mathematical knowledge map. The students' portfolios almost interactions and works are stored in the portfolio database and the status database. When a student chooses a goal concept in the knowledge map, the corresponding digital learning content is arranged and delivered to his/her browser. Too, when the pupil is learning in the Math-Isle, the feedback module provides immediate feedback (east.g., hints or scaffolded solutions) for guidance and grants rewards for encouragement. The learning results tin too be shared with other classmates by the interaction module. In improver to students, their teachers can also access the databases for the students' learning information. Furthermore, the information consists of the students' condition (eastward.g., learning operation or virtual achievement in the game) and processes (e.grand., their personal learning logs). In the Math-Island, it is expected that students can manage their learning and monitor the learning results by the construction management mechanism. In the meantime, teachers tin can also trace students' learning logs, diagnose their weaknesses from portfolio analysis, and assign students with specific tasks to improve their mathematics learning.
The organization architecture of Math-Island
Knowledge map
To increment students' mathematics accomplishment, the Math-Isle game targets the complete mathematics curriculum of elementary schools in Taiwan, which mainly contains the four domains: numerical performance, quantity and measure, geometry, and statistics and probability (Ministry of Education of R.O.C. 2003). Furthermore, every domain consists of several subdomains with respective concepts. For instance, the domain of numerical functioning contains four subdomains: numbers, addition, and subtraction for the first and second graders. In the subdomain of subtraction, there are a series of concepts, including the meaning of subtraction, ane-digit subtraction, and 2-digit subtraction. These concepts should be learned consecutively. In the Math-Isle organisation, the curriculum is restructured as a cognition map, so that they may preview the whole structure of knowledge, recall what they have learned, and realize what they will acquire.
More specifically, the Math-Isle organisation uses the representational metaphor of an "island," where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. Equally shown in Fig. ii, for instance, in an expanse of numeral operation in Math-Island, there are many roads, such as an addition road and a subtraction road. On the addition road, the first edifice should exist the meaning of addition, followed past the buildings of 1-digit improver and so ii-digit improver. Students can choose these buildings to acquire mathematical concepts. In each edifice, the system provides a serial of learning tasks for learning the specific concept. Currently, Math-Island provides elementary students with more than than 1300 learning tasks from the offset grade to the sixth grade, with more than 25,000 questions in the tasks.
The knowledge map
In Math-Isle, a learning task is an interactive page turner, including video clips and interactive exercises for conceptual understanding, adding, and word trouble-solving. In each task, the learning procedure mainly consists of three steps: watching demonstrations, practicing examples, and getting rewards. Starting time, students learn a mathematical concept by watching videos, in which a human tutor demonstrates examples, explains the rationale, and provides instructions. Second, students follow the instructions to answer a serial of questions related to the examples in the videos. When answering questions, students are provided with immediate feedback. Furthermore, if students input incorrect answers, the organisation provides multilevel hints so that they could figure out solutions by themselves. Finally, after completing learning tasks, students receive virtual money according to their accuracy rates in the tasks. The virtual money is used to purchase unique buildings to develop their islands in the game.
Game mechanisms
In the Math-Isle game, there are two game mechanisms: construction and sightseeing (as shown in Fig. 3). The former is designed to assistance students manage their learning procedure, whereas the latter is designed to facilitate social interaction, which may further motivate students to better develop their cities. By doing so, the Math-Island can be regarded every bit ane's learning portfolio, which is a consummate record that purposely collects data about 1's learning processes and outcomes (Arter and Spandel 2005). Furthermore, learning portfolios are a valuable research tool for gaining an understanding about personal accomplishments (Birgin and Baki 2007), because learning portfolios tin can display one's learning process, attitude, and growth after learning (Lin and Tsai 2001). The appearance of the island reflects what students have learned and accept not learned from the noesis map. When students observe their learning status in an interesting way, they may exist concerned about their learning status with the enhanced sensation of their learning portfolios. Past keeping all activity processes, students tin can reflect on their efforts, growth, and achievements. In a sense, with the game mechanisms, the knowledge map can exist regarded equally a manipulatable open learner model, which non but represents students' learning status but also invites students to amend information technology (VĂ©lez et al. 2009).
Ii game mechanisms for Math-Island
First, the structure machinery allows students to plan and manage their cities by constructing and upgrading buildings. To exercise so, they have to decide which buildings they want to construct or upgrade. And then, they are required to complete corresponding learning tasks in the building to determine which levels of buildings they can construct. Every bit shown in Fig. 4, the levels of buildings depend on the completeness of a certain concept, compared with the thresholds. For example, when students complete one third of the learning tasks, the first level of a building is constructed. Later, when they complete two thirds of the tasks, the building is upgraded to the second level. After completing all the tasks in a building, they likewise consummate the last level and are allowed to construct the adjacent building on the road. Conversely, if students failed the everyman level of the threshold, they might need to sentry the video and/or practise the learning tasks again. By doing so, students can make their plans to construct the buildings at their ain pace. When students manage their cities, they actually attempt to improve their learning status. In other words, the construction mechanism offers an alternative way to guide students to regulate their learning efforts.
Screenshots of structure and sightseeing mechanisms in Math-Island
Second, the sightseeing mechanism provides students with a social stage to show other students how well their Math-Islands have been built. This mechanism is implemented as a public space, where other students play the part of tourists who visit Math-Island. In other words, this sightseeing mechanism harnesses social interaction to improve individual learning. Every bit shown in Fig. four, because students can construct different areas or roads, their islands may have unlike appearances. When students visit a well-adult Math-Island, they might take a positive impression, which may facilitate their self-reflection. Accordingly, they may be willing to expend more effort to amend their island. On the other paw, the educatee who owns the isle may also be encouraged to develop their island better. Furthermore, when students see that they take a completely constructed building on a road, they may perceive that they are good at these concepts. Conversely, if their buildings are small, the students may realize their weaknesses or difficulties in these concepts. Accordingly, they may be willing to make more than endeavour for comeback. On the other hand, the student who owns the island may also be encouraged to develop their island better. In a give-and-take, the visualization may play the role of stimulators, so that students may be motivated to better their learning condition.
Method
This paper reported a ii-yr study in which the Math-Island system was adopted in an elementary school. The written report addressed the post-obit ii enquiry questions: (1) Did the Math-Island organization facilitate students' mathematics achievement in terms of conceptual understanding, calculating, and give-and-take problem-solving? In particular, how was the mathematics achievement of the low-achieving students? (2) What was students' levels of involvement in mathematics and the arrangement, peculiarly that of low-achieving students?
Participants
The study, conducted from June 2013 to June 2015, included 215 second graders (98 females and 117 males), whose average age was 8 years old, in an simple schoolhouse located in a suburban region of a northern urban center in Taiwan. The school had collaborated with our research squad for more than 2 years and was thus called as an experimental schoolhouse for this study. In this school, approximately one 3rd of the students came from families with a low or eye level of socioeconomic status. It was expected that the lessons learned from this report could exist applicable to other schools with similar educatee populations in the future. The parents were supportive of this program and willing to provide personal tablets for their children (Liao et al. 2017). By doing then, the students in the experimental schoolhouse were able to employ their tablets to admission the Math-Island organisation every bit a learning tool at both schoolhouse and habitation. To compare the students' mathematics achievement with a baseline, this study also included 125 second graders (63 females and 62 males) from another school with similar socioeconomic backgrounds in the aforementioned region of the city equally a control school. The students in the command school received only conventional mathematics education without using the Math-Isle system during the 2-year menstruum.
Procedure
Before the first semester, a 3-calendar week training workshop was conducted to familiarize the students with the bones performance of tablets and the Math-Island arrangement. By doing then, information technology was ensured that all participants had similar prerequisite skills. The procedure of this study was illustrated in Table 1. At the beginning of the beginning semester, a mathematics achievement assessment was conducted as a pretest in both the experimental and the control school to examine the students' initial mathematics power as second graders. From June 2013 to June 2015, while the students in the control school learned mathematics in a conventional style, the students in the experimental school learned mathematics non merely in mathematics classes but too through the Math-Island system. Although the teachers in the experimental schoolhouse mainly adopted lectures in mathematics classes, they used the Math-Island system equally learning materials at school and for homework. At the same fourth dimension, they allowed the students to explore the cognition map at their own pace. During the ii years, every educatee completed 286.78 learning tasks on average, and each task took them 8.86 min. Given that there were 344 tasks for the second and third graders, the students could terminate 83.37% of tasks according to the standard progress. The data as well showed that the average definiteness rate of the students was 85.75%. At the end of the 2d yr, some other mathematics achievement assessment was administered as a posttest in both schools to evaluate students' mathematics power as third graders. Additionally, an interest questionnaire was employed in the experimental schoolhouse to collect the students' perceptions of mathematics and the Math-Island system. To empathise the teachers' opinions of how they feel nearly the students using the system, interviews with the teachers in the experimental schoolhouse were also conducted.
Data collection
Mathematics achievement assessment
To evaluate the students' mathematics power, this report adopted a standardized accomplishment cess of mathematics ability (Lin et al. 2009), which was developed from a random sample of simple students from dissimilar counties in Taiwan to serve equally a norm with appropriate reliability (the internal consistency was 0.85, and the test-retest reliability was 0.86) and validity (the correlation by domain experts in content validity was 0.92, and the concurrent validity was 0.75). Every bit a pretest, the assessment of the second graders consisted of 50 items, including conceptual understanding (23 items), calculating (eighteen items), and word problem-solving (nine items). As a posttest, the cess of the third graders consisted of 60 items, including conceptual agreement (18 items), calculating (27 items), and word problem-solving (15 items). The scores of the test ranged from 0 to 50 points. Because some students were absent during the exam, this written report obtained 209 valid tests from the experimental schoolhouse and 125 tests from the control school.
Interest questionnaire
The involvement questionnaire comprised ii parts: students' interest in mathematics and the Math-Isle organization. Regarding the first part, this study adopted items from a mathematics questionnaire of PISA and TIMSS 2012 (OECD 2013; Mullis et al. 2012), the reliability of which was sound. This part included three dimensions: mental attitude (xiv items, Cronbach's blastoff = .83), initiative (17 items, Cronbach's alpha = .82), and confidence (14 items Cronbach's blastoff = .72). Furthermore, the dimension of mental attitude was used to assess the tendency of students' view on mathematics. For example, a sample item of attitudes was "I am interested in learning mathematics." The dimension of initiatives was used to appraise how students were willing to learn mathematics actively. A sample item of initiatives was "I keep studying until I empathize mathematics materials." The dimension of confidences was used to assess students' perceived mathematics abilities. A sample particular was "I am confident virtually calculating whole numbers such as 3 + 5 × 4." These items were translated to Chinese for this study. Regarding the second part, this study adopted self-fabricated items to assess students' motivations for using the Math-Island system. This part included ii dimensions: attraction (8 items) and satisfaction (5 items). The dimension of allure was used to assess how well the system could attract students' attention. A sample item was "I experience Math-island is very appealing to me." The dimension of satisfaction was used to appraise how the students felt later using the system. A sample item was "I felt that upgrading the buildings in my Math-Island brought me much happiness." These items were assessed co-ordinate to a 4-point Likert calibration, ranging from "strongly disagreed (one)," "disagreed (2)," "agreed (iii)," and "strongly agreed (4)" in this questionnaire. Due to the absences of several students on the day the questionnaire was administered, there were simply 207 valid questionnaires in this study.
Instructor interview
This study also included teachers' perspectives on how the students used the Math-Isle system to learn mathematics in the experimental schoolhouse. This function of the study adopted semistructured interviews of eight teachers, which comprised the post-obit three main questions: (a) Do you take whatever notable stories about students using the Math-Island system? (b) Regarding Math-Isle, what are your teaching experiences that tin can be shared with other teachers? (c) Do yous have any suggestions for the Math-Island system? The interview was recorded and transcribed verbatim. The transcripts were coded and categorized according to the five dimensions of the questionnaire (i.e., the attitude, initiative, and confidence about mathematics, as well as the attraction and satisfaction with the system) as additional testify of the students' interest in the experimental school.
Information analysis
For the kickoff inquiry question, this study conducted a multivariate analysis of variance (MANOVA) with the schools every bit a between-subject variable and the students' scores (conceptual agreement, calculating, and discussion trouble-solving) in the pre/posttests every bit dependent variables. Moreover, this report also conducted a MANOVA to compare the low-achieving students from both schools. In addition, the tests were likewise carried out to compare achievements with the norm (Lin et al. 2009). For the 2nd enquiry question, several z tests were used to examine how the interests of the low-achieving students were distributed compared with the whole sample. Teachers' interviews were also adopted to support the results of the questionnaire.
Results
Mathematics achievement
To examine the homogeneity of the students in both schools in the first year, the MANOVA of the pretest was conducted. The results, every bit shown in Tabular array two, indicated that in that location were no pregnant differences in their initial mathematics achievements in terms of conceptual understanding, calculating, and discussion problem-solving (Wilks' λ = 0.982, F(3330) = 2.034, p > 0.05). In other words, the students of both schools had like mathematics abilities at the time of the get-go mathematics achievement assessment and could be fairly compared.
At the end of the fourth grade, the students of both schools received the posttest, the results of which were examined by a MANOVA. As shown in Tabular array 3, the event of the posttest on students' mathematics achievement was pregnant (Wilks' λ = 0.946, p < 0.05). The results suggested that the students who used Math-Isle for 2 years had better mathematics abilities than those who did not. The analysis further revealed that the univariate effects on calculating and give-and-take problem-solving were significant, simply the effect on conceptual understanding was insignificant. The results indicated that the students in the experimental school outperformed their counterparts in terms of the procedure and application of arithmetic. The reason may be that the system provided students with more opportunities to do calculation exercises and word problems, and the students were more willing to do these exercises in a game-based environs. Furthermore, they were engaged in solving various exercises with the support of firsthand feedback until they passed the requirements of every building in their Math-Island. However, the students learned mathematical concepts mainly by watching videos in the system, which provided only demonstrations like lectures in conventional classrooms. For this reason, the effect of the system on conceptual agreement was similar to that of teachers' conventional instruction.
Furthermore, to examine the differences betwixt the low-achieving students in both schools, another MANOVA was also conducted on the pretest and the posttest. The pretest results indicated that there were no significant differences in their initial mathematics accomplishment in terms of conceptual understanding, calculating, and give-and-take problem-solving (Wilks' λ = 0.943, F(3110) = 2.210, p > 0.05).
The MANOVA analysis of the posttest is shown in Table 4. The results showed that the effect of the system on the mathematics achievement of low-achieving students was significant (Wilks' λ = 0.934, p < 0.05). The analysis further revealed that only the univariate effect on word problem-solving was pregnant. The results suggested that the low-achieving students who used Math-Island for two years had ameliorate word trouble-solving power than those students in the control schoolhouse, but the event on conceptual agreement and procedural fluency was insignificant. The results indicated that the Math-Island system could effectively enhance low-achieving students' ability to solve word issues.
Because the mathematics achievement assessment was a standardized achievement assessment (Lin et al. 2009), the research team did a further analysis of the assessments past comparing the results with the norm. In the pretest, the boilerplate score of the control schoolhouse was the percentile rank of a score (PR) 55, but their average score surprisingly decreased to PR 34 in the posttest. The results confirmed the fact that conventional mathematics teaching in Taiwan might result in an M-shape distribution, suggesting that depression-achieving students required additional learning resources. Conversely, the average score of the experimental school was PR 48 in the pretest, and their score slightly decreased to PR 44 in the posttest. Overall, both PR values were decreasing, because the mathematics curriculum became more and more hard from the second grade to the fourth course. However, it should exist noted that the experimental school has been less affected, resulting in a significant departure compared with the control school (encounter Table 5). Notably, the average score of give-and-take trouble-solving in the posttest of the experimental school was PR 64, which was significantly college than the nationwide norm (z = twenty.8, p < .05). The results were consistent with the univariate effect of the MANOVA on word problem-solving, suggesting that the Math-Island system could assistance students learn to consummate discussion problems better. This may be because the learning tasks in Math-Island provided students with adequate explanations for various types of word issues and provided feedback for exercises.
Interest
To examine whether the low-achieving students had low levels of interest in mathematics and the Math-Island organization, the study adopted z tests on the information of the interest questionnaire. Table 5 shows the descriptive statistics and the results of the z tests. Regarding the interest in mathematics, the assay showed that the interest of the depression-achieving students was similar to that of the whole sample in terms of attitude, initiative, and confidence. The results were different from previous studies asserting that low-achieving students tended to have lower levels of interest in mathematics (Al-Zoubi and Younes 2015). The reason was perhaps that the low-achieving students were comparably motivated to acquire mathematics in the Math-Island arrangement. As a upshot, a instructor (#T-301) said, "some students would like to go to Math-Island after school, and a scattering of students could fifty-fifty complete up to forty tasks (in a day)," implying that the students had a positive mental attitude and initiative related to learning mathematics.
Another teacher (T-312) also indicated "some students who were frustrated with math could regain conviction when receiving the feedback for correct answers in the basic tasks. Cheers to this, they would not feel high-pressure level when moving on to current lessons." In a sense, the firsthand feedback provided the low-achieving students with sufficient support and may encourage them to persistently larn mathematics. Furthermore, past learning individually subsequently class, they could effectively set themselves for hereafter learning. The results suggested that the organisation could serve equally a scaffolding on conventional instruction for low-achieving students. The students could benefit from such a blended learning environment and, thus, build confidence in mathematics by learning at their own paces.
The depression-achieving students as a whole were also attracted to the system and felt satisfaction from information technology. Instructor (#T-307) said that, "At that place was a hyperactive and mischievous student in my class. However, when he was solitary, he would go on to Math-Island, concentrating on the tasks quietly. He gradually came to enjoy learning mathematics. It seemed that Math-Island was more attractive to them than a lecture by a instructor. I believed that students could be encouraged, thus improve their ability and learn happily." Some other teacher (#T-304) farther pointed out that, "For students, they did non merely experience like they were learning mathematics because of the game-based user interface. Conversely, they enjoyed the contentment when completing a chore, as if they were going aboard to join a competition." In teachers' opinions, such a game-based learning environment did not disturb their instruction. Instead, the organisation could help the teachers attract students' attention and motivate them to learn mathematics actively considering of its highly-seasoned game and joyful learning tasks. Furthermore, continuously overcoming the tasks might bring students a sense of achievement and satisfaction.
Discussion on some features of this study
In addition to the enhancement of achievement and interest, we noticed that there are some features in this study and our design worth some discussion.
The advantages of building a long-term written report
Owing to the limitations of deployment time and sample sizes, information technology is hard for most researchers to conduct a longitudinal report. Fortunately, we had a chance to maintain a long-term collaboration with an experimental school for more than than ii years. From this experiment, we detect that at that place are 2 advantages to conducting a long-term report.
Obtaining substantial testify from the game-based learning surroundings
The research environment was a natural setting, which could not be entirely controlled and manipulated similar near experiments in laboratories. Notwithstanding, this study could provide long-term evidence to investigate how students learned in a game-based learning surround with their tablets. It should be noted that we did not aim to supplant teachers in classrooms with the Math-Island game. Instead, we attempted to establish an ordinary learning scenario, in which the teachers and students regarded the game equally one of the learning resources. For example, teachers may assist depression-achieving students to improve their agreement of a specific concept in the Math-Island system. When students are learning mathematics in the Math-Island game, teachers may take the game every bit a determinative assessment and locate students' difficulties in mathematics.
Supporting teachers' instructions and facilitating students' learning
The long-term study not only proved the effectiveness of Math-Island but also offered researchers an opportunity to determine teachers' roles in such a computer-supported learning environment. For example, teachers may encounter difficulties in dealing with the progress of both loftier- and low-achieving students. How do they take care of all students with different abilities at the same time? Future teachers may require more instruction strategies in such a self-directed learning surroundings. Digital technology has an advantage in helping teachers manage students' learning portfolios. For example, the organization can go along track of all the learning activities. Furthermore, the organization should provide teachers with monitoring functions so that they know the average status of their class's and individuals' learning progress. Withal, it is still a challenge for researchers to develop a well-designed visualization tool to back up teachers' agreement of students' learning conditions and their choice of appropriate instruction strategies.
Incorporating a gamified cognition map of the elementary mathematics curriculum
Providing choices of learning paths
Math-Island uses a representational metaphor of an "island," where a virtual city is located and represents the cognition map. Furthermore, the isle comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. Considering the gamified knowledge map provides students with multiple virtual roads to learn in the system, every educatee may take unlike routes. For instance, some students may be more than interested in geometry, while others may be confident in exploring the rules of arithmetic. In this written report, we noticed that the low-achieving students needed more than time to work on basic tasks, while high-achieving students hands passed those tasks and moved on to the next ones. As a event, some of the high-achieving students had already started to learn the materials for the next grade level. This was possibly considering high-achieving students were able to respond well to challenging assignments (Singh 2011). Therefore, we should provide high-achieving students with more than circuitous tasks to maintain their interest. For example, Math-Isle should provide some authentic mathematical problems every bit advanced exercises.
Visualizing the learning portfolio
In this study, we demonstrated a long-term example of incorporating a gamified knowledge map in an uncomplicated mathematical curriculum. In the Math-Isle game, the curriculum is visualized equally a knowledge map instead of a linear sequence, every bit in textbooks. By doing so, students are enabled to explore relationships in the mathematics curriculum represented by the knowledge map; that is, the structure of the different roads on Math-Island. Furthermore, before learning, students may preview what will be learned, and after learning, students may also reflect on how well they learned. Unlike traditional lectures or textbooks, in which students could only follow a predefined order to learn knowledge without thinking why they take to acquire information technology, the cognition map allows students to understand the construction of knowledge and programme how to achieve advanced cognition. Although the guild of knowledge still remains the aforementioned, students accept primary control of their learning. In a sense, the knowledge map may liberate unproblematic students from passive learning.
Adopting the mechanisms of a construction management game
This 2-yr study showed that the accommodation of 2 game mechanisms, construction and sightseeing, into the uncomplicated mathematical curriculum could effectively improve students' learning achievement. The reason may be that students likely adult interests in using Math-Isle to learn mathematics actively, regardless of whether they are loftier- and low-achieving students.
Gaining a sense of achievement and ownership through the construction mechanism
Regardless of the construction mechanism, Math-Island allows students to plan and manage their cities by constructing and upgrading buildings. Math-Island took the advantages of construction management games to facilitate elementary students' agile participation in their mathematical learning. Furthermore, students may manage their knowledge by planning and constructing of buildings on their virtual islands. Like most construction management games, students fix goals and brand decisions so that they may accumulate their assets. These assets are not simply external rewards just also visible achievements, which may bring a sense of ownership and confidence. In other words, the organisation gamified the process of cocky-directed learning.
Demonstrating learning upshot to peers through the sightseeing mechanism
As for the sightseeing mechanism, in conventional instruction, elementary students usually lack the self-control to learn knowledge actively (Duckworth et al. 2014) or crave a social stage to show other students, resulting in low achievement and motivation. On the other hand, although previous researchers accept already proposed various cocky-regulated learning strategies (such as Taub et al. 2014), it is nonetheless hard for children to keep adopting specific learning strategies for a long fourth dimension. For these reasons, this study uses the sightseeing mechanism to engage elementary students in a social stage to testify other students how well their Math-Islands have been built. For example, in Math-Island, although the students recollect that they construct buildings in their islands, they programme the development of their noesis maps. Afterward learning, they may also reverberate on their progress past observing the appearance of the buildings.
In brief, owing to the construction machinery, the students are immune to cull a place and build their unique islands past learning concepts. During the process, students have to do the learning chore, become feedback, and get rewards, which are the iii major functions of the structure functions. In the sightseeing mechanism, students' unique islands (learning upshot) tin be shared and visited by other classmates. The pupil'south Math-Isle thus serves as a phase for showing off their learning results. The two mechanisms offer an incentive model connected to the game mechanism's forming a positive wheel: the more than the students learn, the more unique islands they can build, with more than visitors.
Conclusion and future piece of work
This study reported the results of a 2-yr experiment with the Math-Island system, in which a knowledge map with extensive mathematics content was provided to back up the complete elementary mathematics curriculum. Each road in Math-Isle represents a mathematical topic, such as addition. In that location are many buildings on each road, with each building representing a unit of the mathematics curriculum. Students may learn virtually the concept and exercise it in each building while being provided with feedback by the system. In improver, the construction management online game mechanism is designed to enhance and sustain students' involvement in learning mathematics. The aim of this study was not only to examine whether the Math-Island system could improve students' achievements but besides to investigate how much the low-achieving students would be interested in learning mathematics afterward using the organisation for 2 years.
Equally for enhancing achievement, the outcome indicated that the Math-Isle organization could effectively better the students' power to calculate expressions and solve word problems. In item, the low-achieving students outperformed those of the norm in terms of word problem-solving. For enhancing interest, we institute that both the low-achieving and the high-achieving students in the experimental school, when using the Math-Island organization, maintained a rather high level of interest in learning mathematics and using the system. The results of this study indicated some possibility that elementary students could be able to acquire mathematics in a self-directed learning fashion (Nilson 2014; Chen et al. 2012a, b) under the Math-Isle environment. This possibility is worthy of future exploration. For example, by analyzing pupil data, we can investigate how to support students in conducting self-directed learning. Additionally, because we have already collected a considerable amount of pupil information, we are currently employing machine learning techniques to ameliorate feedback to the students. Finally, to provide students appropriate challenges, the variety, quantity, and difficulty of content may need to be increased in the Math-Island system.
Abbreviations
- PISA:
-
Program for International Student Assessment
- PR:
-
The percentile rank of a score
- TIMSS:
-
Trends in Mathematics and Science Study
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The authors disclosed receipt of the following financial support for the enquiry, authorship, and/or publication of this article: The authors would like to thank the Ministry building of Science and Technology of the Commonwealth of China, Taiwan, for financial support (MOST 106-2511-Due south-008-003-MY3), and Research Eye for Science and Technology forLearning, National Central University, Taiwan.
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CYCY contributed to the study design, data acquisition and analysis, mainly drafted the manuscript and execution projection. HNHC was involved in data acquisition, revision of the manuscript and data assay.ZHC was contributed to the study idea and drafted the manuscript. CCYL of this research was involved in data acquisition and revision of the manuscript. TWC was project manager and revision of the manuscript. All authors read and canonical the final manuscript.
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Charles Y.C. Yeh is currently an PhD educatee in Graduate Institute of Network Learning Engineering at National Fundamental University. The inquiry interests include i-to-1 learning environments and game-based learning.
Hercy N. H. Cheng is currently an associate professor and researcher in National Applied science Research Center for E-Learning at Central China Normal University, Prc. His enquiry interests include i-to-one learning environments and game-based learning.
Zhi-Hong Chen is an associate professor in Graduate Institute of Information and Estimator Education at National Taiwan Normal University. His research interests focus on learning technology and interactive stories, technology intensive language learning and game-based learning.
Calvin C. Y. Liao is currently an Assistant Professor and Dean's Special Assistant in College of Nursing at National Taipei University of Nursing and Health Sciences in Taiwan. His research focuses on computer-based language learning for principal schools. His electric current research interests include a game-based learning environment and smart engineering science for caregiving & wellbeing.
Tak-Wai Chan is Chair Professor of the Graduate Constitute of Network Learning Technology at National Fundamental University in Taiwan. He has worked on diverse areas of digital technology supported learning, including bogus intelligence in pedagogy, computer supported collaborative learning, digital classrooms, online learning communities, mobile and ubiquitous learning, digital game based learning, and, most recently, engineering supported mathematics and language arts learning.
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Yeh, C.Y.C., Cheng, H.N.H., Chen, ZH. et al. Enhancing achievement and involvement in mathematics learning through Math-Island. RPTEL 14, v (2019). https://doi.org/x.1186/s41039-019-0100-9
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DOI : https://doi.org/10.1186/s41039-019-0100-9
Keywords
- Mathematics learning
- Noesis map
- Game-based learning
- Construction management games
Source: https://telrp.springeropen.com/articles/10.1186/s41039-019-0100-9
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