Good Mathematics Teaching: Perspectives of Beginning Secondary Teachers

What is good mathematics teaching? The answer depends on whom you are asking. Teachers, researchers, policymakers, administrators, and parents usually provide their own view on what they consider is good mathematics teaching and what is not. The purpose of this study was to determine how beginning teachers define good mathematics teaching and what they report as being the most important attributes at the secondary level. This research explored whether there was a relationship between the demographics of the participants and the attributes of good teaching. In addition, factors that influence the understanding of good mathematics teaching were explored. A mixed methodology was used to gather information from the research participants regarding their beliefs and classroom practices of good mathematics teaching. The two research instruments used in this study were the survey questionnaire and a semi-structured interview. Thirty-three respondents who had one to two years of classroom experience comprised the study sample. They had graduated from a school of education in an eastern state and had obtained their teacher certification upon completing their studies. The beginning mathematics teachers selected these four definitions of good teaching as their top choices: 1) have High Expectations that all students are capable of learning; 2) have strong content knowledge (Subject Matter Knowledge); 3) create a Learning Environment that fosters the development of mathematical power; and 4) bring Enthusiasm and excitement to classroom. The three most important attributes in good teaching were: Classroom Management, Motivation, and Strong in Content Knowledge. One interesting finding was the discovery of four groups of beginning teachers and how they were associated with specific attributes of good mathematics teaching according to their demographics. Beginning teachers selected Immediate Classroom Situation, Mathematical Beliefs, Pedagogical Content Knowledge, and Colleagues as the top four factors from the survey analysis that influenced their understanding of good mathematics teaching. The study's results have implications for informing the types of mathematical knowledge required for pre-service teachers that can be incorporated into teacher education programs and define important attributes of good mathematics teaching during practicum

Exploring Secondary Students\u27 Modelling Competencies

Mathematical modelling is a very important component in the teaching and learning of mathematics. In Malaysia, educators require more exposure to mathematical modelling it is still a new pedagogical method in classrooms. Modelling tasks that require students to construct a mathematical model would be a good start in developing modelling competencies. In this study, the authors investigate three mathematical modelling competencies of secondary students in the state of Selangor through a qualitative analysis of 20 students (divided into four groups) responses based on one modelling task developed by the researchers. The three modelling competencies we focus in this study are (1) making assumption; (2) computing and interpreting solution; and (3) mathematical reasoning. Our findings indicate that most students were basic users while a small percentage reached the proficient users level. With more engagement with the modelling tasks, students would able to acquire the modelling competencies and also develop their modelling skills. This would contribute to the meaningful learning of mathematics

Obstacles Faced by College Students in Solving Probability Word Problems

There are many difficulties that can be identified when students solve mathematic problems especially in solving probability word problems. This study was conducted to identify the major obstacles faced by matriculation college students while solving the probability of an event word problems. Seven college students were the sample for this case study. Clinical interviews are used as a data collection. This data collection technique was selected based on the researcher’s observation on the participants as they answered the probability word problem task. The task was given during the interview session. Semi structured interviews are used to obtain in depth information. Think-aloud analysis involves observations leading to individual behaviours in the oral or nonverbal form of participants and the researcher’s field notes. Participants were found to have difficulty interpreting probabilities. There are three categories of difficulties that have been identified, namely not knowing the meaning of the word, not knowing the nature of the probability and not being able to identify the goal of the probability word problem

Penaakulan perkadaran murid tahun lima dalam topik nisbah dan kadaran

Kajian ini bertujuan untuk mengenal pasti tahap penaakulan perkadaran murid sekolah rendah semasa menyelesaikan masalah berkaitan perkadaran. Kajian kes kualitatif ini melibatkan tujuh murid tahun lima (berumur 11 tahun) yang dipilih melalui pensampelan bertujuan. Data kajian yang telah dikumpulkan melalui teknik temu bual klinikal dapat memaparkan strategi dan justifikasi murid secara mendalam bagi setiap aktiviti yang ditunjukkan. Artikel ini hanya membentangkan analisis terhadap respons murid terhadap tugas berkaitan masalah membandingkan nisbah. Dapatan kajian ini menunjukkan bahawa tahap penaakulan perkadaran murid konsisten dengan tahap yang dikemukakan oleh beberapa pengkaji lepas yang mana murid sekurang-kurangnya mempunyai tahap penaakulan perkadaran tidak formal, manakala tahap penaakulan perkadaran kuantitatif merupakan tahap tertinggi. Namun dapatan juga menunjukkan bahawa terdapat respons murid yang tidak boleh dikategorikan dalam mana-mana tahap menyebabkan wujud satu tahap antara tahap penaakulan perkadaran tidak formal dan tahap penaakulan perkadaran kuantitatif. Dapatan kajian ini dapat membekalkan informasi kepada guru matematik sekolah rendah bahawa setiap murid mempunyai tahap penaakulan perkadaran yang berbeza dan guru perlu mempelbagaikan aktiviti yang menggalakkan murid berfikir secara perkadaran

Mediating Role of Metacognitive Awareness Between Self-Efficacy and Mathematics Reasoning Among Education Undergraduate Students During Pandemic

This research aimed to examine the contribution of metacognitive awareness as a moderator in the relationship between self-efficacy and mathematical reasoning among education undergraduates during the Covid-19 Pandemic. The analysis included 184 undergraduate students in one public university around Klang Valley, Malaysia. The researcher distributes mathematics reasoning assessment, metacognitive awareness, and self-efficacy questionnaires to collect research data. Statistical Package for the Social Sciences version 25 analyzes the mediating influence of metacognitive awareness in the correlation between self-efficacy and mathematics reasoning. The findings revealed that undergraduate mathematics and science education students had better mathematical reasoning abilities than undergraduates of nonmathematics and science education. However, the result indicated that mathematics and science education undergraduate students have high metacognitive awareness and utilize more strategies in mathematics reasoning assessment. This research suggested that further analysis can measure other populations, such as secondary school students’ metacognitive awareness and self-efficacy in mathematics reasoning

Self-Regulation Test-Taking Strategies for Mathematics

The present study aims at exploring various self-regulation test-taking strategies used by the grade 11 students for their mathematics tests which is observed from three aspects, they are before, during, and after test-taking. The data were collected from 86 students in a private school which located in Malaysia. The goal-setting and planning, help-seeking, seeking information, rehearsal, memorization, reviewing, peer pressure, adult influence, self-consequences, self-motivated, and environment setting were the strategies that is used for test preparation. Outline formulas, recall and identify key information, keep trying, and checking were the strategies used during test-taking. In addition, correction and self-evaluation were the strategies used after the test-taking. The study further examined differences of various test-taking strategies used across three performance groups, high, medium, and low achievers, and also for male and female students. The results showed that there were statistical differences in goal-setting and planning, help-seeking, keep trying, checking, and correction strategies among high, medium, and low achievers. There were also statistical differences in goal-setting and planning, rehearsal, self-motivated, outline formulas, checking, and correction strategies between male and female students. The result of this research showed that the groups of using goal-setting and planning, rehearsal, help-seeking, recall and identify key information, keep trying, checking, and correction strategies have higher scores in mathematics performance rather than those groups which do not use these strategies

Pengetahuan Matematik Untuk Pengajaran Dalam Kalangan Guru Pra Perkhidmatan di IPG

Pengetahuan yang dimiliki oleh seseorang guru berperanan memastikan pelaksanaan aktiviti pengajaran dan pembelajaran yang berkesan dan seterusnya mampu meningkatkan prestasi matematik murid. Tahap penguasaan pengetahuan matematik untuk pengajaran (PMUP) yang rendah dalam kalangan guru secara tidak langsung akan menyumbang kepada pelaksanaan proses pengajaran dan pembelajaran matematik yang kurang berkesan. Tujuan kajian ini dijalankan adalah: (1) untuk menguji tahap PMUP dalam kalangan guru pra perkhidmatan di Institut Pendidikan Guru (IPG), (2) untuk mengenal pasti faktor-faktor yang mempengaruhi penguasaan PMUP dalam kalangan guru pra perkhidmatan di IPG. Ini merupakan kajian awal, dan seramai empat puluh orang guru pra perkhidmatan terlibat di dalam kajian ini. Tahap penguasaan PMUP telah diukur dengan menggunakan ujian pensel dan kertas, manakala pengujian hipotesis telah dijalankan bagi mengenal pasti faktor-faktor yang mempengaruhi penguasaan PMUP. Dapatan daripada ujian pencapaian PMUP menunjukkan tahap penguasaan PMUP dalam kalangan guru pra perkhidmatan di IPG adalah pada tahap sederhana. Selain itu, didapati terdapat dua faktor utama yang mempengaruhi penguasaan PMUP dalam kalangan guru pra perkhidmatan di IPG secara langsung, iaitu peluang untuk menjalani latihan mengajar (β=0.383, p˂0.01) dan peluang untuk mengikuti program pendidikan guru koheren (β=0.557, p˂0.01). Manakala faktor kepercayaan efikasi pengajaran matematik (KEPM) didapati tidak mempunyai hubungan yang signifikan dengan penguasaan PMUP. Dapatan daripada kajian ini boleh dijadikan sebagai panduan di dalam merangka program pendidikan guru yang mampu melahirkan guru matematik yang kompeten selari dengan visi yang telah ditetapkan, iaitu “IPG Peneraju Kecemerlangan Pendidikan Guru”. Kata kunci: pengetahuan matematik untuk pengajaran; peluang untuk belajar; kepercayaan efikasi pengajaran matematik; pengetahuan kandungan; pengetahuan pedagogikal kandungan

Impact of Fathom on Statistical Reasoning among Upper Secondary Students

The teaching and learning of statistical reasoning is becoming challenging due to the change in the perspective emphasizing on the deeper understanding rather than basic statistics computations. As suggested by researchers, implementing technologies able to develop student interest in the topics leads to deeper understanding. Hence, this study used dynamic software, Fathom for teaching statistical reasoning. The purpose of this study is to examine the statistical reasoning understanding among upper secondary students after using dynamic software, Fathom. The sample consists of seventy -two students randomly assigned to control and experimental groups. The experimental group underwent an intervention where they learnt statistical reasoning using Fathom while the control group learnt statistical reasoning using traditional learning method not involving Fathom. Statistical Reasoning Assessment (SRA) was used in this study as the instrument for measuring statistical reasoning. The research hypothesis data were analyzed using MANCOVA test. The findings showed a significant difference across four statistical reasoning constructs namely Describing Data, Organizing Data, Representing Data and Analyzing and Interpreting Data between students in the control and experimental groups. Furthermore, the results of the analysis emphasized that the students who learned statistical reasoning using Fathom performed better than students in the control group. In brief, the upper secondary students’ statistical reasoning enhanced after implementing Fathom