MOULDING POSITIVE CHARACTERS VIA INCULCATING VALUES IN MATHEMATICS TEACHING AND LEARNING

In this paper, I argue that it is pertinent to develop positive characters among all students as they are the future assets of a nation. A review of related literature shows that inculcating values and moulding character has been of great concern in the school mathematics curriculum of many countries. There are various categories of intrinsic values embedded in mathematics education. With careful and mindful integration into teaching and learning of mathematics, it is possible to inculcate positive values and thus produce positive characters of our future generation. Some suggestions on how to inculcate these values into mathematics teaching and learning at various school levels were discussed at the end of this paper. Keyword: mathematics teaching and learning; moulding character; values in mathematics educatio

A study on Malaysian Mathematicians’ Way of Knowing

“Can you name me a mathematician?” “Einstein??” “Do you wish to become a mathematician one day?” If these questions were asked to the public or any school students, the most likely answer to both questions might be a big ‘No!’. Why is this so? The director of the Public Understanding of Mathematics Forum, Gene Kloz (1996) claims that the mathematics profession is the most misunderstood in all of academia. According to him, the public thinks that mathematicians contemplate ancient proofs and work as lonely recluses. Moreover, the most common public image of a mathematician has been furnished by a physicist (example, Einstein) rather than a mathematician. Why is there such a lack of appreciation of mathematicians\u27 work by the public

Knowledge States in the Learning of “Time”: Comparison of Primary Six Pupils’ from Different Types of Schools in Penang

The findings in this paper were a part of a bigger study which aimed to develop a cognitive diagnostic assessment [CDA] for primary mathematics learning of “Time”. This paper aimed to discuss and compare the knowledge state of primary pupils from different types of schools in Penang. Knowledge state represented a pupil’s mastery level on a defined set of attributes. These attributes were assessed by using a set of items and the responses were observed to find out a pupil’s knowledge state. Two hundred and sixty-nine Primary Six pupils from 11 primary schools in Penang involved in the study. A set of CDA with 35 items consisting of four cognitive models were administered to the pupils. However, only three cognitive models were discussed in this paper. Students’ responses were analysed by using Artificial Neural Network [ANN] to find the attribute probability of every pupil on each attribute. This probability was then classified and this set of classified attribute probability represented knowledge state of a pupil. Finding out the knowledge state of pupils helps teacher to investigate pupils’ learning progress, identify pupils’ misconception and thus make effective instructional decision. Results showed that Chinese Vernacular School pupils performed better than National School and Tamil Vernacular School pupils. Besides, the most common knowledge state in each cognitive model for each type of school was quite similar. The findings of this paper could be a preliminary step to demonstrate the usability and practicality of using CDA to obtain meaningful instructional inferences

Teacher's Influence On Adult's Images Of Mathematics: Implications For Mathematics Teacher Education

Kertas kerja membincangkan sebahagian daripada hasil dapatan satu kajian penyelidikan yang telah dijalankan untuk mengenalpasti punca-punca pembentukan imej matematik di kalangan orang dewasa

Characterising the Pedagogical Practices in Mathematics Lessons among Selected Malaysian Primary Schools

This study aims to characterise the pedagogical practices of 45 observed primary mathematics lessons taught by 24 mathematics teachers in six national primary schools (SK) and six Chinese vernacular primary schools (SJKC). The data were collected using two video cameras, one focused on the teacher while the other camera focused on the pupils’ activities. The qualitative data were analysed based on two main activities in the classroom, which are teacher’s activities and pupils’ activities. The findings show that mathematics lessons conducted by SK teachers tended to engage the pupils in individual seatwork so as to assess pupils’ understanding. Conversely, SJKC teachers were focused more on explaining mathematical concepts to help the pupils build up their conceptual understanding. By characterising the pedagogical practices of mathematics lessons in various schools, the researcher hopes that the findings of this study will contribute to better understanding of the teaching and learning process in SK and SJKC mathematics classrooms. The results serve as a documentation of pedagogical practices in Malaysia to enable implementation of suitable programmes to help in improving teachers’ pedagogical practices from different types of primary schools. While the results are interesting and provide some directions, a much larger study would be needed to determine if the results are due to the teachers’ enthusiasm, geographical differences, cultural or social differences, or what is known as the Hawthorne Effect

A View through a Different Lens: Elicitng Pupils’ Conception of a Good Mathematics Lesson Using Photovoice

The purpose of this paper is to share our experience in using photovoice to explore what is a good mathematics lesson as conceived by the primary pupils. Photovoice is a participatory method of research that can be used as a reflection technique among children who developmentally are less inclined to engage in language-based data gathering methods.In the study, six 11-year old pupils were chosen to participate. The objective of the study was to gauge the effectiveness of photovoice as an alternative method to capture reflection. Pupils were asked to take photographs with digital camera the most effective moment in their mathematics lesson. Photo-elicited individual interviews were conducted. On the methodology perspective, result of the study shows that photovoice does enhance learner’s critical reflection. However, the interpretation of photovoice data faces some validating issues such as personal judgment and multiple interpretations. We believe that by employing triangulation of different data sources may help to solve the problems. The analysis of the case study data using photovoice showed that primary pupils valued “concrete examples”, “drill and practice”, and “board work” as characteristics of a good mathematics lesson. This study supported photovoice as another viable approach for researchers to capture and elicit pupils’ voice. In particular, the marginalized groups can be led to reveal their own perspectives on what they learned about a good lesson in mathematics

Implementation of lesson study as an innovative professional development model among Malaysian school teachers

Purpose – This qualitative study explored the implementation of Lesson Study, a kind of teacher-directed and bottom-up approach of the Japanese model of teacher professional development in the Malaysian education context.It seeks to answer the question of how implementation of lesson study as an innovative professional development model among Malaysian school teachers influences teachers’ pedagogical content knowledge, and what school-based factors support or hinder the implementation of lesson study in the Malaysian context. Methodology – The case study method was employed involving two secondary schools in the state of Kedah.Each school set up a lesson study group as a case.Case A had 9 teachers while case B had 8. The participants of both cases engaged themselves in the lesson study process for a period of 12 months. Each lesson study cycle required the participants to collaboratively plan, discuss, teach, observe and reflect on a particular lesson. Due to various constraints, at the end of this study, case A conducted three lesson study cycles while case B conducted only two cycles. Multiple data sources were gathered through in-depth interviews, observations, group discussions and reflections as well as participants’ journal writing.Findings – The analysis of the qualitative data indicated that the lesson study group setting provided an encouraging opportunity and venue for the participants to collaborate, discuss and share their teaching knowledge and experiences. Consequently, the participants expressed that their content knowledge and pedagogical content knowledge were enhanced.They became more reflective and keener in promoting active student participation in their lessons.Significance – This study revealed that the degree of knowledge enhancement was dependent upon each participant’s attitude and commitment towards the teaching profession.However, when provided with sufficient supporting factors such as positive support from the school administrators, committed and dedicated group leaders and strong collegiality among the lesson study team, lesson study could be successfully implemented as an effective and innovative mode of teachers’ professional learning

Abstracting common errors in the learning of time intervals via cognitive diagnostic assessment / Phei-Ling Tan, Liew-Kee Kor and Chap-Sam Lim

This study engaged the cognitive diagnostic assessment (CDA) to abstract the common errors in the learning of time intervals based on pupils’ knowledge states. CDA is a feasible testing tool that can inform us where a test taker may be prone to making errors in the tests. In this study, a cognitive diagnostic model with six attributes and 12 test items was created to evaluate pupils’ performance in a diagnostic test on “duration of two inclusive dates”. A total of 269 primary six pupils from 11 elementary schools participated in the study. The diagnostic test scores were analyzed using the Artificial Neural Network which generated 12 knowledge states (KS). Result shows that “100000” was the leading KS. The common errors associated with this KS in hierarchical order of prominence were: (i) exclude starting date as a day in duration; (ii) error in regrouping; (iii) compute incorrectly the sum of the two given dates; and, (iv) express incorrectly the time measurement in months and days. These identified common errors would provide a valuable basis for remedial teaching of the topic “Time”. It also allows mathematics teachers to identify the inadequacy of an earlier teaching strategy and to engender an improved approach to help struggling learners shore up their basic skills

Enhancing Primary Pupils' Geometric Thinking Through Phase-Based Instruction Using The Geometer's Sketchpad

The purpose of this study was to enhance primary pupils' geometric thinking through phase-based instruction using The Geometer's Sketchpad (GSP) based on the van Hiele theory of geometric thinking. Specifically, it sought to examine Year Four pupils' van Hiele levels of geometric thinking about equilateral triangle, square, regular pentagon and regular hexagon before and after phase-based instruction using GSP, and whether there was any significant difference in the pupils' van Hiele levels of geometric thinking about the regular polygons after the intervention. The researchers employed an exploratory case study research design and purposeful sampling to select a class of 26 mixed-ability Year Four pupils from a primary school in Selangor. A van Hiele level test based on Mayberry's (1981) test and scoring criteria was devised and administered to the pupils before and after the intervention to assess their van Hiele levels of geometric thinking about the regular polygons. The results of the pre-test showed that the pupils' initial van Hiele levels were predominantly at Level 0 (Pre-recognition) for regular pentagon and regular hexagon but at Level 1 (Recognition) for equilateral triangle and square. However, the results of the post-test revealed that the pupils' van Hiele levels after the intervention were predominantly at Level 2 (Analysis) for all the regular polygons. In addition, the results of the Wilcoxon test showed that there was a significant difference in the pupils' van Hiele levels of geometric thinking for all the regular polygons after phasebased instruction using GSP. The median van Hiele level in the post-test was higher than the median van Hiele level in the pre-test for all the regular polygons, indicating that the intervention had significantly enhanced the pupils' geometric thinking about the regular polygons

Use Mathematical Writing as a Practical Approach to Increase Students’ Problem Solving Skills: A Case Study

In mathematical problem solving, students’ written work mostly reveals their mathematical algorithm skills and has very little information about their reasoning skills of the problem solving process. This study extends the features of mathematical writing that integrate the language and mathematical thinking to increase students’ mathematical problem solving skills. The main feature of this study is the use of mathematics writing workbook as a practical approach to guide the students in the problem solving process. Thirty Foundation students in Engineering participated in a six weeks of writing to solve mathematical problems. An exploratory case study analysis was used to examine the written contents of the participants’ mathematical writing workbook, the performance of their formal test as well as their perceptions of mathematical writing. The trace of work in the workbooks showed that mathematical writing has somehow given some impact on these students to visualize, aware and recognize their problem solving behaviors in words