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Kemahiran Penyelesaian Masalah Berayat Matematik Melalui Model Bar: Sorotan Literatur Bersistematik (Malaysian Journal of Social Sciences and Humanities)
Abstract
Model Bar merupakan lukisan model atau kaedah model dengan membina gambar rajah daripada masalah berayat matematik. Justeru, kajian ini bertujuan untuk mengkaji trend pelaksanaan strategi Model Bar dalam menyelesaikan masalah berayat dalam matematik berdasarkan empat kriteria. Empat kriteria merupakan kriteria pangkalan data, tahun penerbitan artikel, lokasi kajian dijalankan dan skop kajian. Terdapat empat pangkalan data iaitu Web of Science (WOS), Scopus, Semantic Scholar dan Lain-lain pangkalan data jurnal digunakan dalam saringan artikel-artikel kajian lepas. Prosedur sorotan literatur bersistematik (SLR) digunakan merangkumi reka bentuk, strategi dan kata kunci pencarian artikel, kriteria pemilihan artikel, proses pemilihan artikel serta proses pengumpulan dan penganalisisan artikel. Terdapat 20 buah artikel dianalisis dan telah dipilih dalam kajian ini dengan berlandaskan empat kriteria tersebut. Dapatan kajian menunjukkan bahawa keberkesanan penggunaan strategi Model Bar banyak dikaji di negara-negara luar seperti Indonesia, Australia, United State, Amerika, Brunei dan Filipina. Namun demikian, kajian ini kurang penerbitan dalam masa lima tahun yang terkini. Maka, tempoh tahun penghasilan artikel yang berkaitan dipanjangkan sehingga 10 tahun yang terkini. Pangkalan data Semantic Scholar menyumbang paling banyak artikel dalam kajian ini. Tiga skop kajian telah dianalisis iaitu keberkesanan penggunaan Model Bar terhadap penyelesaian masalah matematik, persepsi guru dan murid terhadap penggunaan Model bar dalam penyelesaian masalah matematik dan perbezaan antara penggunaan strategi Model Bar dengan pendekatan konvensional terhadap pencapaian murid. Cadangan kajian lanjutan yang boleh dibuat ialah dengan mendedahkan Model Bar kepada murid konteks lain melalui teknik visualisasi secara lebih holistik.
... Although the findings demonstrate the proficiency of students in the PSDMB method in mastering the construct of algebraic thinking skills in arithmetic generalization, the results also indicate that the proficiency of arithmetic generalization among MB students is superior to that of the CPS method. This study is supported by the findings of Wong et al. (2020) study, which indicate that the bar model can enhance students' ability to construct mathematical models based on their understanding of arithmetic concepts compared to conventional methods of problem solving. This is because the use of the bar model assists students in solving high-level mathematical problems. ...
... As such, this method serves to bridge the divide between the concrete and the abstract. Wong et al. (2020) contended that the bar model provides a more efficient and widely accepted approach to the instruction of mathematics. In instances where conventional teaching methods prove ineffective, it becomes imperative to periodically introduce innovative interventions. ...
There is a dearth of empirical data to support the positive effects of problem solving (PS) combined with digital technology in the classroom, despite claims that these activities improve students' algebraic thinking abilities. Therefore, the purpose of this study was to evaluate how the teaching method known as Polya's problem solving with digital bar model (PSDMB) affected the seventh graders' ability to think algebraically. Ralston's framework, which covers Generalised Arithmetic, Function, and Modelling within the topic of Linear Equation, served as the foundation for the evaluation of algebraic thinking abilities. A quasi-experimental pre-test and post-test control group design was employed. A total of 90 seventh graders, aged twelve- to thirteen-year-olds, from a secondary school in Tambunan, Sabah, Malaysia, made up the sample. Three teaching groups were formed out of these randomly chosen students: PSDMB (n = 30), Bar Model (MB) (n = 30), and Conventional Problem Solving (CPS) (n = 30). Both the pre- and post-algebraic thinking tests were taken by students. The post-test results were analysed using MANCOVA with the students' pre-test results acting as covariates. The results indicated that students in the PSDMB group performed notably better in Generalised Arithmetic, Function, and Modelling than those in the MB group, who, in turn, outperformed those in the CPS group. These results imply that incorporating digital bar model into problem-based learning is a successful strategy for improving seventh graders' algebraic thinking abilities. Keywords: algebraic thinking skills, digital bar model, Polya's problem solving, seventh graders
... In the context of mathematics learning in Malaysia, students are required to solve sentence-based mathematics problems by applying mathematical concepts learned at the end of each topic. Two types of sentence-based mathematics problems are presented when teaching mathematics: routine and non-routine (Wong and Matore, 2020). According to Nurkaeti (2018), routine sentence-based math problems are questions that require the students to solve problems using algorithmic calculations to obtain answers. ...
... This statement also aligns with Wilson's (1997) opinion that solving non-routine sentence-based mathematics always involves high-order thinking skills (HOTS). To solve non-routine and HOTS fundamental sentence-based math problems, a student is required to know various problem-solving strategies for solving the problems (Wong and Matore, 2020). This situation has indirectly made the mastery of sentence-based mathematics problem-solving skills among students more challenging (Mahmud, 2019). ...
Sentence-based mathematics problem-solving skills are essential as the skills can improve the ability to deal with various mathematical problems in daily life, increase the imagination, develop creativity, and develop an individual’s comprehension skills. However, mastery of these skills among students is still unsatisfactory because students often find it difficult to understand mathematical problems in verse, are weak at planning the correct solution strategy, and often make mistakes in their calculations. This study was conducted to identify the challenges that mathematics teachers face when teaching sentence-based mathematics problem-solving skills and the approaches used to address these challenges. This study was conducted qualitatively in the form of a case study. The data were collected through observations and interviews with two respondents who teach mathematics to year four students in a Chinese national primary school in Kuala Lumpur. This study shows that the teachers have faced three challenges, specifically low mastery skills among the students, insufficient teaching time, and a lack of ICT infrastructure. The teachers addressed these challenges with creativity and enthusiasm to diversify the teaching approaches to face the challenges and develop interest and skills as part of solving sentence-based mathematics problems among year four students. These findings allow mathematics teachers to understand the challenges faced while teaching sentence-based mathematics problem solving in depth as part of delivering quality education for every student. Nevertheless, further studies involving many respondents are needed to understand the problems and challenges of different situations and approaches that can be used when teaching sentence-based mathematics problem-solving skills.
... Terdapat dua jenis masalah matematik berayat yang sering digunakan dalam pengajaran matematik iaitu masalah rutin dan masalah bukan rutin (Wong & Matore, 2020). Masalah matematik berayat bersifat rutin adalah jenis soalan yang mempunyai jalan penyelesaian yang mudah di mana pelajar hanya mengaplikasikan operasi asas dalam menyelesaikan masalah. ...
... Keadaan ini turut wujud dalam kalangan pelajar di luar negara di mana hasil dapatan kajian Sumule et al. (2018) dan Wildani (2020) turut menunjukkan pelajar luar negara juga kerap melakukan kesilapan dalam memahami soalan dan kesilapan dalam mentransformasi bahasa ke dalam bentuk operasi. Pendek kata, penyelesaian masalah bukan sahaja memerlukan seseorang pelajar mencari jawapan akhir malah pelajar perlu menguasai strategi penyelesaian masalah yang kompleks (Raifana et al., 2016) secara tidak langsung telah menyebabkan kemahiran penyelesaian masalah itu satu konsep matematik yang sukar dan menimbulkan kesukaran dalam kalangan pelajar (Wong & Matore, 2020). ...
Problem solving skills are one of the important aspects and become a necessity in mathematics curriculum around the world. In the context of Malaysia, students have been exposed to various methods to solve sentence-based math problems that are related to daily life through the latest revised KSSR Mathematics Curriculum. However, there are still many students who have difficulty in mastering these skills have been proven through past studies. This situation is supported by the mathematical performance of students in the international assessments of PISA and TIMSS which is still below the average score. This happening occurs because the problems posed are in the form of complex reasoning and problem solving. Thus, this paper discusses the literature of the types of errors that students frequently make while solving sentence-based
... Sorotan Literatur Bersistematik (SLR) adalah kajian yang dilaksanakan untuk menjawab persoalan kajian dengan mengenal pasti, menganalisis, merumus serta membuat penilaian secara kritikal terhadap isu yang ingin dikaji dalam kajian-kajian lepas yang releven (Ting & Effendi, 2020). Garis panduan gambar rajah aliran Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) telah digunakan dalam pemilihan artikel yang bersesuaian dengan persoalan kajian. ...
Pelbagai kaedah teknologi telah digunakan secara meluas untuk membantu dalam pendidikan matematik. Salah satu kaedah terkini ialah Flipped Classroom yang merupakan satu inovasi dalam pengajaran dan pembelajaran Matematik. Justeru, kajian literatur yang sistematik ini dijalankan untuk mensintesiskan data empirikal yang berkaitan tentang pelaksanaan kaedah flipped classroom dalam pendidikan matematik dalam tempoh 2017 - 2021. Tujuan kajian ini adalah untuk mengenal pasti tahap pencapaian pelajar serta persepsi guru dan pelajar terhadap penggunaan flipped classroom dalam matematik. Pangkalan data SCOPUS dan WOS digunakan untuk mendapatkan artikel yang berkaitan tentang penggunaan flipped classroom dalam pendidikan matematik. Lima kriteria dalam kajian ini adalah tahun penerbitan, jenis bahan rujukan, bahasa, metodologi serta bidang kajian artikel jurnal. Terdapat 21 artikel dianalisis dan telah dipilih berlandaskan lima kriteria tersebut. Kata kunci seperti flipped classroom, mathematics flipped classroom dan inverted classroom digunakan dalam kajian ini. Persepsi guru dan pelajar turut dikaji dari segi penggunaan, sikap, amalan dan penglibatan dalam penggunaan flipped classroom bagi mata pelajaran matematik. Analisis kajian menunjukkan penggunaan flipped classroom dalam matematik banyak dikaji di negara-negara luar seperti Indonesia, Spain dan Switzerland. Dapatan kajian menunjukkan bahawa penggunaan flipped classroom meningkatkan pencapaian pelajar dalam matematik. Guru dan pelajar turut menunjukkan persepsi yang positif terhadap penggunaan flipped classroom dalam matematik. Hasil kajian ini diharapkan memberi maklumat yang jelas tentang keberkesanan penggunaan flipped classroom dalam pengajaran dan pembelajaran matematik.
This experimental research was conducted to assess the effectiveness of using the Singapore Bar Model Approach in improving the Math performance of the 60 Grade VI pupils of Loboc Central Elementary School of the S.Y. 2016-2017. It also aimed to assess the acceptability level of the experimental respondents towards the Singapore Bar Model Approach in terms learning of objectives, learning outcomes, learning experiences and learning activities. This study also sought to determine the performances of the following: pretest and posttest of the experimental group taught using the Singapore Bar Model Approach and the control group using the traditional method, the significant difference of the pretest-posttest of the control group, pretest-posttest of the experimental group and the posttests of both groups. Relevant data were gathered and subjected to statistical treatment, analyzed and interpreted through the use of weighted mean and t-test. This study concluded that both the traditional method and the Singapore Bar Model approach were effective in improving the academic performances of the respective respondents. The experimental group also indicated a positive attitude towards the use of Singapore Bar Model approach. It is recommended that the Singapore Bar Model may be used as an alternate teaching approach especially in topics where it is more appropriate.
Background:
The massive abundance of studies relating to tropical medicine and health has increased strikingly over the last few decades. In the field of tropical medicine and health, a well-conducted systematic review and meta-analysis (SR/MA) is considered a feasible solution for keeping clinicians abreast of current evidence-based medicine. Understanding of SR/MA steps is of paramount importance for its conduction. It is not easy to be done as there are obstacles that could face the researcher. To solve those hindrances, this methodology study aimed to provide a step-by-step approach mainly for beginners and junior researchers, in the field of tropical medicine and other health care fields, on how to properly conduct a SR/MA, in which all the steps here depicts our experience and expertise combined with the already well-known and accepted international guidance.We suggest that all steps of SR/MA should be done independently by 2-3 reviewers' discussion, to ensure data quality and accuracy.
Conclusion:
SR/MA steps include the development of research question, forming criteria, search strategy, searching databases, protocol registration, title, abstract, full-text screening, manual searching, extracting data, quality assessment, data checking, statistical analysis, double data checking, and manuscript writing.
With Brunei's participation in the PISA starting 2018, there is a need to improve students' mathematics competencies, particularly their problem solving skills. The Bar Model is a distinctive problem-solving strategy introduced in Singapore and is one of the key to Singapore's success in PISA 2012 Problem Solving. This action research examined the use of Bar Model to help fifty Year 9 students in one government school in Brunei in solving word problems involving profit, loss and discount. Paired-sample t-test revealed significant difference in the mean score at p < 0.0 5 between the pre-test (M = 4.76) and post-test (M = 6.10) after intervention lessons. Despite the mean mark of post-test still lower than the passing mark, there is an overall increase in the number of students who improved in the post-test compared to the pre-test. In item-by-item analysis, improvements were observed in most questions; however questions on percentage calculation of profit, loss and discount still indicated small improvement, with two items decreased in the post-test performance. With more practice and guidance, particularly to overcome similar common errors done by students in the post-test, the Bar Model is a valuable problem-solving strategy in attempting word problem question, and help enhance students' problem-solving competencies.
Previous studies revealed that many students cannot perform well when it comes to word problem-solving questions. There are various problem-solving strategies that can be applied to help students to overcome the problem. Visualisation techniques in learning have been used to help students enhance their conceptual understanding of the mathematical problem-solving and the use of bar model visualisation technique is one of the strategies. This study aims to investigate students’ achievement in mathematical problem-solving after applying the Bar Model and to explore students’ experiences while applying the technique. This study employed a pre-experimental design of the quantitative research. There were 32 participants of year three students. The instrument used in this research consists of questions of pre-test and post-test and a semi-structured interview. Data were analysed using SPSS 20.0 software and thematic analysis. The test results showed that there is a significant difference in participants’ mathematical problem-solving achievement. The analysis of semi-structured interview transcripts revealed that level of understanding and motivation influence students’ performance. Findings of this study showed that students perform better after the implementation of the Bar Model in mathematical problem-solving. This study can provide an alternative or guidance for teachers to improve students’ mathematical problem-solving skills.
Mathematics is one of the challenging subjects in the Brunei education system. Achievement rate in this subject is often low especially among males. Both barriers and enablers of success need to be identified early to help fix the problem. The present field survey (N = 254 randomly selected Year 7 students, 144 males and 110 females) examined the: (1) attitudes and perceptions of students towards the Bar Model Method (BMM) of teaching and learning mathematics; (2) predictors of achievement in mathematics; and (3) effectiveness of the BMM in teaching and learning mathematics. Both genders and age-groups had positive attitudes and perceptions towards the BMM. In addition, the majority of participants (all genders, age-groups and districts) stated that the BMM was effective and liked the strategy. Furthermore, the participants’ Word Problem-Solving Achievement Test (WPSAT) posttest scores did not differ significantly by gender and age-group. However, students in Brunei-Muara and Kuala Belait districts scored significantly higher at the posttest level than those in Tutong. Two implications were drawn from this finding. First, schools in Tutong might not be well-resourced like those in the other two districts. Second, more BMM work with students was required in Tutong to facilitate mastery of the strategy.
This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem–solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction in drawing bar diagrams to represent problem components. Results suggest the intervention package was effective for improving the fraction word problem solving of students with learning disabilities and that effects were maintained 2 and 4 weeks after intervention. Implications of these findings and indications for future research are discussed.
Discrepancy of knowledge among students, teachers and schools to some extent has contributed in developing the negative attitude that says mathematics is hard. Therefore, the author tries to explain a method for teaching mathematics (especially for elementary school students), to be easily understood by students. As a result, mathematics is no longer perceived hard. One good method of learning mathematics is the use of models (bar modeling). The author conducted research by providing two different treatments, without bar modeling and with bar modeling, to the elementary school students. The result showed that the use of bar modeling has increased students’ scores significantly. Bar modeling is not the only method of teaching at the elementary level, and it is easier for elementary school students in learning mathematical concepts of symbolization in problem solving.
Kajian tindakan ini dijalankan bertujuan untuk meninjau pelaksanaan pendekatan kaedah model bar dalam penyelesaian masalah berayat operasi tolak dalam kalangan murid Tahun Empat di daerah Seremban, Negeri Sembilan dalam menyelesaikan masalah operasi tolak. Objektif kajian ini adalah untuk mengenalpasti pelaksanaan kaedah model bar dalam meningkatkan pencapaian murid dalam penyelesaian masalah berayat Matematik operasi tolak dan sejauh mana kaedah bar model menaik minat murid dalam menjawab soalan penyelesaian masalah berayat Matematik operasi tolak. Metodologi kajian ini menggunakan kajian tindakan yang mengaplikasikan model Kemmis & Mctaggart (1988). Pendekatan yang digunakan dalam kajian ini ialah Ujian Pra, Ujian Pasca 1 dan Ujian Pasca 2 digunakan untuk membandingkan pencapaian murid sebelum dan selepas diajar pendekatan model bar. Borang soal selidik juga digunakan untuk mengetahui perasaan dan tahap minat murid terhadap penggunaan kaedah model bar. Dapatan kajian menunjukkan 100% berjaya mencapai tahap minimum dalam Ujian Pasca 2. Tahap minat murid terhadap kaedah model bar meningkat lebih daripada 50% dari segi kefahaman dan pengaplikasian kaedah model bar.
This article describes how to teach fraction and percentage word problems using a model-drawing strategy. This cognitive strategy places emphasis on explicitly teaching students how to draw a schematic diagram to represent the qualitative relations described in the problem, and how to formulate the solution based on the schematic diagram. The step-by-step procedures for using the model-drawing strategy are described. In addition, the results of an action research study applying the model-drawing strategy with high school students who have learning disabilities are reported.
In a 1981 diagnostic test, the Ministry of Education in Singapore found its country facing a challenge: Only 46 percent of students in grades 2-4 could solve word problems that were presented without such key words as "altogether" or "left." Yet today, according to results from the Trends in International Mathematics and Science Study (TIMSS 2007), Singapore students continue to place among the best mathematical problem solvers in the world. How did this small country improve its students' performance? It all began with an approach, developed by a team of educators, which advocated a concrete-to-pictorial-to-abstract strategy. The "model method," as it is known in Singapore, has students draw a pictorial model to represent quantities and their relationships. The model puts the focus back on the relationships and actions presented in the problem, and helps students choose both the operations and sequence of steps that are needed to solve a problem. In this article, the author explores the possibilities of the model method in her third-grade class and discusses the results of this method. In conclusion, the Singapore model method provides a visual approach to help future astronauts, engineers, and other workers focus on mathematical relationships, operations, and actions. Posttest questions and an answer key are appended. (Contains 5 tables and 9 figures.)
This study took place at a mid-sized, Midwestern university located in a mid-sized town. The researchers developed the BAR model to teach mathematics methods both in the classroom and in the field. The preservice teachers took Enochs, Smith, and Huinker's Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) on the first and last day of class. A total of 297 responses were collected from the pre- and posttests, with 280 matching responses, which were then used for data analysis. Mixed methods were used to analyze qualitative and quantitative data. The researchers sought to determine if the specific teaching methods from the BAR model led to positive changes in preservice teacher efficacy beliefs. They also explored if efficacy beliefs changed as a result of field experiences. Preservice teachers' efficacy scores changed positively on every item on the MTEBI. The researchers also determined that there was an increase in preservice teachers' outputs as a result of their field experiences.
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