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Prospective Teachers' Expectations of Students' Mathematical Thinking Processes in Solving Problems

prospective teachers' expectations mathematical thinking processes polya models mason theory

Mohammad Tohir , Maswar Maswar , Moh. Atikurrahman , Saiful Saiful , Diyah Ayu Rizki Pradita


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This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.

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10.12973/eu-jer.9.4.1735
Pages: 1735-1748
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12

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16

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The present study aimed to provide a digital story development experience for pre-service science teachers in the “instructional technologies and material development” course and to determine the impact of these experiences on their views on digital storytelling. Simultaneous parallel design, one of the mixed methods in which both quantitative and qualitative data were collected, was used in the study. Quantitative and qualitative findings are presented in different sections and both were interpreted in the discussion section. The quantitative study data were collected from 50 pre-service teachers, while the qualitative data were collected from 16 pre-service teachers. Quantitative data were collected by a survey and the qualitative data were collected in interviews. Descriptive/inferential statistics were employed in the analysis of the survey data. The steps of the analysis, coding, and categorization were adopted in the study for qualitative data. The positive effect of digital storytelling on the 21st-century skills of pre-service teachers was revealed by both quantitative and qualitative data. Furthermore, it was determined that pre-service teachers considered digital storytelling as advantageous since it provided meaningful and permanent learning, was fun and motivational; however, it also had disadvantages since it was time-consuming and required technological knowledge. It was revealed that they experienced certain difficulties in scriptwriting, finding the related images/videos and photographs, and finalizing the recording, and they considered that most, if not all, topics in the science course were suitable for digital storytelling. For pre-service teachers to acquire 21st-century skills, digital storytelling should be employed in several courses including the teaching practice course, and pre-service teachers should gain experience in preparing the students for digital storytelling.

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10.12973/eu-jer.10.1.97
Pages: 97-113
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1538
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1388
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23

Scopus
15

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This study aimed to investigate the degree to which teachers in Qatar implement differentiated instruction as well as the impact of years of experience, qualifications, grade, school subjects and training on teachers’ use of differentiated instruction. Also the study tried to explore the obstacles impeding the application of differentiate instruction. The study targeted all early childhood teachers (1,836) in 99 Qatar public schools spreading across the country. A random sample of 236 teachers, accounting for 12.9% of the population participated in the study. Following the mixed approach, the researchers used questionnaires and interviews to collect the data. The results showed no statistically significant differences among the respondents in the degree of application of differentiated instruction due to training and qualifications; however, statistically significant differences were detected in relevance to years of experience, grade, and the subject being taught. The study also found an agreement among teachers on the obstacles they face during their application of differentiated instruction, most notably the teaching load, class size, and time. The study concluded with recommendations for education providers, teachers and researchers.

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10.12973/eu-jer.10.1.127
Pages: 127-143
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4

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2

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This study seeks to develop a learning method based on local wisdom that is developed to support the learning process. One of the pearls of wisdom used in developing learning methods is the traditional games of the Sundanese people, namely the Bebentengan game. This study aims to see the improvement of student learning outcomes by implementing the Bebentengan learning method. The mix-method, quantitative data and qualitative data are described based on the research findings. It involves as many as 298 students at various levels; Elementary School (ES), Junior High School (JHS), and Senior High School (SHS) and nine teachers. Data analysis using ANCOVA. The results showed that there was no significant increase in learning outcomes at all levels (sig. 0.020 <α). There is a significant difference in the learning of students who get Sundanese local wisdom-based learning methods at each level (ES, JHS and SHS). Based on the comparison between ES and JHS (Sig = 0.079> α), can be concluded that the learning method is not effective to be applied in junior high schools. Then, between ES and SHS (Sig = 0.006 < α) so it can be concluded that the learning method is effective to be applied in elementary schools. The last comparison is between JHS and JHS or vice versa (Sig = 0.079> 0.314> α), can be concluded that the learning method is not effective to be applied in SHS. Therefore, this method is most effective at the primary level. We find that this learning method can improve student learning outcomes at all levels. Learning methods using local wisdom are effective enough to improve student learning outcomes. Thus, this method can be implemented more broadly. Still, it needs to be developed in the future. It does not rule out the possibility of learning methods based on local wisdom can be combined with technological advances.

description Abstract
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10.12973/eu-jer.10.1.199
Pages: 199-209
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603
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736
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4

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7

The Profile of Students' Social Skills of Bengawan Solo Elementary Nature School

social skills elementary school nature school

Moh Salimi , Achmad Dardiri , Sujarwo Sujarwo


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This study aimed to describe the profile of the students’ social skills of Bengawan Solo nature elementary school. The study was qualitatively conducted as a case study. The participants were teachers and students who were chosen by employing a purposive sampling technique. The data were obtained through observations, questionnaires, interviews, and document analysis. This study employed an interactive model data analysis included: data validating, data collection, data reduction, data display, and conclusion drawing. The conclusions of the study comprise: (1) the cooperation aspect, students can collaborate well; (2) the assertion aspect, students can get along with new friends and communicate with others; (3) the responsibility aspect, students understand their role and responsibility to the God, themselves, others, and society; (4) the empathy aspect, students can feel others' feeling and problem; (5) the self-control aspect, students can control their mental state so that they can avoid anger and bad influences.

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10.12973/eu-jer.10.1.211
Pages: 211-226
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955
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1560
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6

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5

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This study was conducted to determine the effectiveness of virtual laboratory based on semi second life (s-SL) on higher order thinking skills of general senior secondary school in chemistry learning process. The research design was adopted posttest-only design approach to a quasi-experimental. This study was conducted in the one of public general senior secondary school in 3T regions – Bangkalan City – one of the cities in East Java Province, Indonesia. There were 81 students in the grade 11 of natural science who involved in this study. The participants were divided into three groups, namely the students who did practical work by demonstration methods in chemistry real laboratory, the students who did practical work by experiment methods in virtual laboratory based on s-SL, and the students who did practical work by combination both of them (demonstration methods in chemistry real laboratory and experiment methods in virtual laboratory based on s-SL). The students in each group was tested by posttest of higher order thinking skills. The data was analysed with one-way ANOVA. The results of data analysis shows that there is a significance difference of each groups. Virtual laboratory based on s-SL has enough effect on the students’ higher order thinking skills.

description Abstract
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10.12973/eu-jer.10.1.261
Pages: 261-274
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473
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722
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2

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6

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A Descriptive-correlational study was sought to investigate the influence of metacognition on the academic achievement and learning style of undergraduate students. Using the survey method, data was collected from a sample of 150 undergraduate students selected through a stratified random sampling technique which includes 50 students each from the three schools namely School of Humanities and Social sciences (HSS), School of Engineering (SOE), and School of Sciences (SOS) of Tezpur University. The tools used are five-point Likert-type Metacognitive skills scale and five-point Likert-type Learning Style Inventory. Academic Achievement of the students was measured based on the semester grade point average SGPA obtained in the semester examination. The data were analyzed using percentage, simple regression, multiple regression and one-way ANOVA. The result showed that only 34-36% of the undergraduate students have above-average metacognitive skills. The undergraduate students have equal preferences in all the five learning styles rather than focusing on one learning style. There is a significant difference between metacognition levels and academic achievement of the undergraduate students of SOS, HSS and SOE. The metacognitive skill explicates only 43% variability of academic achievement of the undergraduate students which implies that the undergraduate student’s metacognitive skills influence and determines their academic achievement to some extent. However, the undergraduate student’s learning style doesn’t account for variation in metacognitive skills. Thus, it is suggested that metacognitive skills should be integrated into curricular components and learning strategy which will help the students to monitor and regulate their own learning to meet the challenges of academic society.

description Abstract
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10.12973/eu-jer.10.1.381
Pages: 381-391
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1285
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4

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6

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The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we were interested in how sixth-grade primary school students solve non-contextual and contextual problems involving the same mathematical content (in the contextual problems this content still needs to be recognised, whereas in the non-contextual problems it is obvious). The main guideline in the research was to discover the relationship between mathematical knowledge, which is the starting point for solving problems from mathematical literacy (contextual problems), and mathematical literacy. The empirical study was based on the descriptive, causal and non-experimental methods of pedagogical research. We used both quantitative and qualitative research based on the grounded theory method to process the data gathered from how the participants solved the problems. The results were quantitatively analysed in order to compare the success at solving problems from different perspectives. Analysis of the students’ success in solving the contextual and non-contextual tasks, as well as the strategies used, showed that the relationship between mathematical knowledge and mathematical literacy is complex: in most cases, students solve non-contextual tasks more successfully; in solving contextual tasks, students can use completely different strategies from those used in solving non-contextual tasks; and students who recognise the mathematical content in contextual tasks and apply mathematical knowledge and procedures are more successful in solving such tasks. Our research opens up new issues that need to be considered when developing mathematical literacy competencies: which contexts to choose, how to empower students to identify mathematical content in contextual problems, and how to systematically ensure – including through projects such as NA-MA POTI – that changes to the mathematics curriculum are introduced thoughtfully, with regard to which appropriate teacher training is crucial.

description Abstract
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10.12973/eu-jer.10.1.467
Pages: 467-483
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1576
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1245
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18

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15

Teaching and Learning Bucket Model: Experimented with Mechanics Baseline Test

mechanics tlb model mbt urce students

Kizito Ndihokubwayo , Pascasie Nyirahabimana , Théophile Musengimana


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Mechanics, as a large part of physics, shows the most basic concepts we encounter in our daily lives. With this regard, we implemented the mechanics baseline test (MBT) to the University of Rwanda - College of Education before and after the teaching mechanics module to track students learning. About 38 students participated in this study. We found the instructional strategies used to fit in a model we named "teaching and learning bucket" (lecturer backing and learners owning learning) during data analysis. The results showed that the performance occurred only in 12 out of 26 MBT items at a p<.001, and Cohen's D effect size of 1.26. Such analysis also allowed us to identify areas of mechanics that need teaching improvement, such as (a) constant acceleration, (b) average velocity, (c) the first law of Newton, (d) work and energy, and (e) energy conservation. There was also a positive correlation (r=0.58) between students' confidence in answering questions and correct answers provided and vice versa. Therefore, the research significantly informs lecturers to use various teaching approaches to effectively employ the teaching and learning bucket (TLB) model.

description Abstract
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10.12973/eu-jer.10.2.525
Pages: 525-536
cloud_download 953
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953
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1297
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6

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4

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This study aims to develop a standard instrument for measuring mental health among urban adolescents in Indonesia. The objective is to produce valid and reliable school adolescent mental health instruments to be used by agencies or schools to identify students' mental health. The survey was conducted in Jakarta and South Tangerang with a total of 1007 respondents divided into two experiments where the first trial was conducted on 597 students and the second trial was conducted on 410 students. Measurements were made using a Likert scale questionnaire. Instrument testing begins with a theoretical validity test by 4 experts and 20 panelists who test the instrument material in terms of construction, content and language. Experts analyze and correct the instrument qualitatively. The instrument was then reviewed and analyzed quantitatively by panelists using the Aiken index. At this stage, 44 items, 9 indicators and 3 variable dimensions were obtained. The next test is done by testing the validity empirically, by analyzing the measurement model using Confirmatory Factor Analysis (CFA) with the LISREL 8.80 Full Version program. By using the criteria for the SLF value ≥0.30 and t-value ≥1.96, and calculating the reliability with the construct reliability (CR) at the level> 0.70, the results of the second trial showed that 35 items were valid. The observations of the model fitness through Goodness-of-Fit test showed that there is a fitness between the theoretical model and the empirical model for the mental health instruments in this study.

description Abstract
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10.12973/eu-jer.10.2.729
Pages: 729-742
cloud_download 523
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523
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1016
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2

Scopus
1

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This study aimed to analyze the Research-Based Learning (RBL) model implementation in the natural sciences in improving students’ analytical thinking skills. This study employed a mixed-method with a sequential exploratory design. Data collection began with qualitative data and then continued with quantitative data. Qualitative data collection techniques used observation and interviews, while quantitative data collection used essay tests. Sampling was carried out before the research implementation. The samples were students of the PGMI IAIN Surakarta Study Program, Indonesia, which consisted of 34 pre-service elementary school teachers. The research was conducted in the odd semester of the 2019/2020 academic year. Quantitative data analysis techniques used a quasi-experimental design with one group pretest-posttest. Based on the results of four observations on the research treatments, the mean was 3.714, in which the values of preliminary activities were 3.625, core activities were 3.714, and closing activities were 3.75, used a rating scale (1-4) with the very good category. The RBL model implementation in the natural sciences in the concept of energy can improve the analytical thinking skills of students, as evidenced by the N-gain value was 56.57%in the medium category. This increase was obtained from the mean of the pretest score (46.84) and the post-test score (76.9), by using a rating scale (0-100). The research findings provide ideas to lecturers and researchers in improving the student's analytical thinking skills through the application of innovative learning models in the topic of the concept of energy.

description Abstract
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10.12973/eu-jer.10.3.1051
Pages: 1051-1062
cloud_download 1169
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1169
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1197
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5

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4

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This study examines the basic underlying structure of burnout experiences among teachers in Malaysia by discovering the challenges which lead them to experience burnout. Using interpretative phenomenological analysis, the current study explores the coping strategies that these teachers used to remain in their profession. Ten teachers from two public high schools participated in the study. The data was collected through in-depth semi-structured interviews and analysed using the constant comparison method. The findings revealed challenges that cause teachers to experience burnout, which are student misbehaviour, insufficient parental collaboration, occupational stress in the teaching environment, and negative emotions. The themes related to the coping strategies used to remain in the teaching profession are understanding teaching and learning, positive approach, individual factors, and support system. This paper lists some recommendations for managing the issue of teacher burnout and facilitate teacher retention is proposed, which includes providing training and development activities for teachers, increasing salaries, helping teachers develop coping strategies, and creating adequate support systems.

description Abstract
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10.12973/eu-jer.10.3.1075
Pages: 1075-1088
cloud_download 1090
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1090
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1142
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4

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2

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This study aimed to analyze the critical thinking skills of students in learning of environmental change material using e-learning madrasah. This study used explanatory sequential design by mixed-methods experiment. The data were collected by interviewing, observing, and essay testing that have indicators modified from critical thinking skills by Watson-Glaser, Facione, and Ennis. There were 67 participants in this study as 7th grade student at a junior high school in Sleman district. Quantitative data analyzed by determining average score and standard deviations and, qualitative data analyzed from interviews and observation. Quantitative analysis showed that there were 3 levels of student’s critical thinking skills which were 14 students (20.90%) in the high category, 38 students (56.72%) in the middle category, and 15 students (22.38%) in the low category. Qualitative analysis indicated learning model made students to learn actively, independently, and enthusiastically looking for several sources. This study provided information about student critical thinking skills in junior high school, especially in the environmental change matter which are still low. Thus, the alternative learning strategies to improve students critical thinking skills are very needed. Besides, information on the application of the discovery learning model with e-learning Islamic school was obtained in the COVID-19 pandemic.

description Abstract
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10.12973/eu-jer.10.3.1123
Pages: 1123-1135
cloud_download 748
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748
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1289
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9

Scopus
10

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The purpose of the study was to examine correlations between perceived teacher innovation (PTI) and self-regulated learning (SRL), where learning motivation, self-efficacy, and learning transfer help illustrate the interplay between and among influencing variables in the teacher-student relationship. This study gathered 213 valid questionnaires out of 355 participants in the Design Thinking for Data Scientists, which is one of the courses taught from a university in Taiwan. This study has analyzed the possible linkage in the Structural Equation Modeling (SEM) through the path coefficient. The ensuing data analysis study has shown that learning motivation, self-efficacy, and learning transfer not only served as the mediator effects in the PTI and SRL but also played small moderating effects. It appears that when learning motivation, self-efficacy, and learning transfer decrease, the interplay between PTI and SRL becomes stronger. It is necessary to increase the level of intrinsic motivation by the perception of greater innovation in teaching materials. By so doing, students would be more receptive and affective of course contents in the classroom and regulate themselves to achieve educational goals. The implications of teachers' perceptions of pedagogical innovation for learning motivation and learning experience are likewise discussed.

description Abstract
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10.12973/eu-jer.10.3.1317
Pages: 1317-1327
cloud_download 308
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308
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558
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Scopus
0

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Teachers who can adapt and be ready for all changes will also be able to provide a balance to increase the competence of vocational high school students. This is also not denied when teachers become assessors in student competency tests. The objectives of this study were to produce an instrument for the readiness of teachers as assessors; to knowing good grain reliability; to know the characteristics of the instrument; and to know the difficulty level of the item. The method used in this research is instrument development. Respondents were vocational school teachers who were candidates for competency test assessors. Data collection techniques using a questionnaire. Analysis of construct validity using Confirmatory Factor Analysis. Reliability using Cronbach’s alpha. Test the instrument items using the Rasch model. The results are the readiness instruments of the vocational teacher as an assessor has 19 indicators that have been grouped into 5 factors with consistency values being in the same construct (proven construct validity). The result of the calculation of the reliability of this instrument is 0.852, which means that the reliability coefficient is high; There are two items, namely numbers 24 and 18 which indicate the absence of a fit item in the overall item fit criteria; At the item difficulty level, items 8 and 6 have a difficulty score of more than 2, while this indicates that items 8 and 6 have a high difficulty level.

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10.12973/eu-jer.10.3.1471
Pages: 1471-1485
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293
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516
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5

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7

Mathematics Teachers’ Practices of STEM Education: A Systematic Literature Review

instructional approaches mathematics stem education

Noor Anita Rahman , Roslinda Rosli , Azmin Sham Rambely , Lilia Halim


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Science, technology, engineering and mathematics (STEM) education is regarded as one of the formulas to embracing many of our imminent challenges. STEM education benefits the learners by encouraging interest in STEM disciplines. This daunting task needs everyone’s concerted efforts in creating and innovating mathematics teachers’ classroom practices Therefore, a systematic review was conducted to identify best practices for STEM education following the guidelines of the Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) by Moher et al. (2015). The reviewed articles were published from 2016 to 2020 and accessed using the Scopus and Web of Science (WoS) databases. Three themes for best practices were identified namely (a) core competencies encompassing 21st-century teaching skills; (b) instructional designs; and (c) requisite STEM execution. Results of PRISMA determined the dominant STEM practices were critical thinking, communication, collaboration, problem-solving, research-based pedagogy, problem-based learning and project-based learning, technological integration, accessibility, professional development and learning support, evidence of effectiveness, access to materials and practitioner support, and scalability. Mathematics teachers should determine the best STEM practices to employ even though there is a lack of studies on integrated STEM domains. When more students are interested in venturing and exploring into the field of STEM, the high demand for STEM related careers could be met by the younger generation.

description Abstract
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10.12973/eu-jer.10.3.1541
Pages: 1541-1559
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1119
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1092
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14

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19

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The Coronavirus disease (COVID-19) pandemic outbreak in the Indonesians nowadays, the public education department established the policy of the online education system to all education levels. Most educators employ an online flipped learning method to support the policy. Research aimed to measure the effect of online based-flipped classroom learning between using Microsoft Team and WhatsApp and student engagement on reading comprehension skills. The research approach was a quasi-experimental model with a 2 x 3 factorial pre-test-post-test non-equivalent control group design. The sample of this investigation was early period undergraduates of the management economics study program. Data analysis employed a two-way ANOVA test. The result confirmed that the online flipped learning scheme using Microsoft Team was better than WhatsApp in improving student engagement and reading comprehension skills. We advise English lecturers to apply better online media services, pay attention to the completeness of the learning features and train their competence in implementing distance learning to use compatible synchronous flipped classroom teaching based on internet technologies.

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10.12973/eu-jer.10.4.1613
Pages: 1613-1624
cloud_download 12095
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12095
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12

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16

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The article mentions the impact of the Coronavirus disease (COVID-19) pandemic on online learning in Vietnamese higher education in 2020. This is a qualitative case study, by using in-depth interviews to explore the changes in the perception, methods, and orientation of online learning of students and lecturers at a key pedagogical university when experiencing the three COVID-19 outbreaks in Vietnam. The findings show that the COVID-19 pandemic has a positive impact on the developmental orientation of online learning at the Vietnamese higher education level. Even though at the time of an outbreak, opposition and dissatisfaction with online learning occurred; but through the three outbreaks, together with the efforts of lecturers and students, online learning in Vietnam has recorded remarkable achievements. This is a prerequisite for the development of online education and the innovation of digital technology in education.

description Abstract
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10.12973/eu-jer.10.4.1683
Pages: 1683-1695
cloud_download 2637
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2637
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1428
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9

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12

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The main topic of the presented article is the pedagogical concept of self-reflection of students of Social Education. The authors understand the pedagogical concept as primarily educational determinants that influence and shape students’ self-reflection. To identify this aim, the authors formulate the main research question: How do social education students reflect on themselves as students, and what are the determinants of study self-reflection for social pedagogy students? The authors used the qualitative research strategy, specifically The Grounded Theory, through which sixty self-reflecting essays were analysed. These written self-reflections were further complemented with six in-depth interviews in which we acquired clarifying information on self-reflection and self-assessment of social education students. It was ascertained that students’ self-reflection is shaped through an awareness of internal and external study factors, which subsequently influence the overall concept of their study, motivation to perform, study style, and self-assessment.

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10.12973/eu-jer.10.4.1793
Pages: 1793-1806
cloud_download 455
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455
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621
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2

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1

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Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on Action-Process-Object-Schema (APOS) theory. APOS theory is used to explore spatial thinking processes which consist of mental structures of action, process, object, and schema. This research is qualitative research with an exploratory method. It provided the students' opportunity to solve problems alternately until the method found the most appropriate subjects for the research objectives. The subjects were 2 students of Mathematics Education in the fourth semester of Universitas Muria Kudus Indonesia. The data collection techniques were started by distributing the validated and reliable spatial thinking questions, the cognitive style question, and the interview. The applied data analysis consisted of data reduction, presentation, and conclusion. The findings showed (1) spatial thinking process of holistic-external representation typed learners were indicated by the representative thinking element, abstract-illustrative figure expression to communicate and complete the tasks correctly, (2) spatial thinking process of the holistic-internal representation typed learners were indicated by the representative means, having ideas, connecting with the previous knowledge in the forms of symbols and numbers, and finding the final results correctly although incomplete.

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10.12973/eu-jer.10.4.1807
Pages: 1807-1823
cloud_download 580
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580
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621
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3

Scopus
5

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