Undergraduate Mathematics Enhanced With Graphing Technology.

The School of Mathematical Sciences at University Sains Malaysia has offered a laboratory course on the integration of hand-held technology into the teaching and learning of mathematics since the beginning of the 2001/2002 academic year

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

Teacher communication and the role of language use in the primary mathematics classroom discourse / Liew Kee Kor and Chap Sam Lim

Language is central to learning and acts as a medium or a tool through which new learning is assimilated and defined.The teaching and learning of mathematics which mediated by language is complicated in a multilingual context. This paper reports a study that explored the communication and language use in a multicultural Malaysian primary mathematics context. The aim of this study was twofold. Firstly, it investigated the language use by teachers in the mathematics classroom discourse, and secondly, it studied the roles of language use by the teachers in teaching mathematics. Six mathematics teachers from three types of primary schools participated in this study. Data were collected by video recording 12 classroom lessons and interview with each teacher after each lesson. Results showed that language use in the three types of primary schools mathematics classroom reflects the ethnicity of the pupils in the schools. In the weaker classes, both novice and expert teachers, in particular, those from the Chinese schools switched from English to pupils’ spoken language to teach for understanding. It was also observed that language use assumed different roles in the mathematics discourse. The three important roles identified are: for explaining, questioning and discussing among peers. This paper concludes with some implications for language use in primary school mathematics within a bi/multilingual context

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

Application of fuzzy technique for order preference by similarity to the ideal solution in the selection of candidates / Mohd Ariff Ahmad Taharim and Kor Liew Kee

Selecting the right candidate for the right cause is similar to identifying the most compromising solution of multi-criteria decision making (MCDM) problem. In real life the selection criteriamay involve vague and incomplete data which cannot be expressed in precise mathematical form or numerical values. Apparently fuzzy-based technique can be applied to describe and represent these data in fuzzy numbers. This paper presents a MCDM fuzzy TOPSIS based model designed to solve the selection problemfor allocation of government staff quarters. Result shows that the proposed model is suitable and appropriate. It was also found that the MCDM model which uses single decision maker rating process can also be applied to multiple decision makers. It is recommended that the application of fuzzy TOPSIS can be extended to other selection processes such as vendor selection, training evaluation or group marking of project works

Diagnosing Primary Pupils Learning of the Concept of After in The Topic Time Through Knowledge States by Using Cognitive Diagnostic Assessment

Purpose - Knowledge state specifies pupils mastery level and informs about their strength and weaknesses in the tested domain. This study attempted to diagnose primary pupils learning the concept of after through their knowledge states by using Cognitive Diagnostic Assessment (CDA). Methodology - This study employed a survey research design to gauge pupils' knowledge states for the concept of finding the date after a specific number of days from a given date [abbreviated as the concept of after]. Quantitative data from the pupils pattern of response to the items in Cognitive Diagnostic Assessment (CDA) were collected and analyzed. Items in the CDA were designed by three experienced Mathematics Education researchers and content validated by a panel of seven expert primary mathematics teachers. It was then administered to 238 Grade Six pupils from 11 primary schools in Penang, Malaysia. The pupils item responses were interpreted into knowledge states and mastery levels. Findings - The overall analysis showed that there were 18 knowledge states diagnosed in the concept of after. This large number of knowledge states indicated the specificity of pupils mastery level and thus provided detailed information about their strengths and weaknesses in the concept of after. The findings of this study imply that primary pupils face different levels of difficulty when they are learning the topic of Time. Significance - This method of diagnosing pupils knowledge in terms of mastery level of each attribute tested is different from a conventional diagnostic test which provides only the final score for each pupil. By knowing the pupils knowledge states, teachers can make use of this fine-grained information to enable them to carry out differentiated instructional planning and other remedial work more effectively. Pupils can also use this information to monitor their own learning by maintaining their strengths and overcoming their weaknesses to cope with their own studies

Vee-mapping integral calculus / Kor Liew Kee and Mohd Rijal Illias

Improving student achievement in calculus is a mounting and challenging task especially when it is a prerequisite course for most the undergraduate students. Undeniably mathematics instructors have continuously faced problems of high failure rates in calculus. This study investigated the impact of Vee mappings creative and unique approach to an old integral problem on a sample 70 calculus undergraduate participants using an experimental-control research design. The result of t-test showed that the mean scores for Quiz and Test for the experimental group were both significantly higher than the control group. The large effect size for Quiz (d= 2.016) and Test (d = 0.816) constituted a strong supportive empirical evidence for the above result. Both values confirmed that students in the experimental group who have used Vee mapping performed significantly better in lntegral Calculus than those of their counterparts in the control group at p < .05. Further analysis revealed that participants who favoured using model or diagram in learning correlated moderately high (r = .421, p < .01) with their confident in solving problem about integration and vice versa. Likewise, those who were confident in drawing Vee maps correlated highly with those who were confident in solving integration problems (r = .741, p < .001) and those who were proficient in using the Vee maps to visualize the connection between what they knew and what they could apply in doing integration^ = .846, p < .001) and vice versa. The regression analysis showed “Confidence in drawing Vee maps” predicted most highly (Beta = .756, t = 3.525, p < .05) the “Confidence in doing integration”. Result also showed that “Beliefs” contributed significantly to students’ confidence in solving integration problems (Beta = .514, t = 4.684, p < .05). In other words, participants who were confident in using Vee map were confident in doing integration problem. Furthermore, those who believed that they are competent in mathematical problem solving techniques were also confident in solving integration problem. In addition to investigating the impact of Vee mapping, this study extracted five salient factors in the Mathematics Attitude Questionnaire (MAQ). These five factors were mathematics anxiety, motivation, values, beliefs and confidence. It is hope that Vee mapping can be presented to more calculus students as another viable teaching and learning tool to enable more active and meaningful learning. In so doing, students’ attitude must not be overlooked when introducing new technique into the classroom. Future mathematics instructors can subsequently explore the effectiveness of such tool through the MAQ. Lastly, it is the desire and joy to all mathematics educators to witness more learners who are successful in the Calculus course

Using graphics calculator (GC) in the mathematics classroom: students’ perception/ Kor Liew Kee…[et al.]

This study explores students" perception on using graphics calculator (GC) to learn mathematics. The results were obtained from a sample of 244 students enrolled in the local institutes of higher learning. In this study, the term "perception" is conceptualised as a combination of confidence in using GC to learn mathematics"and "classroom organization and practice" in a GC-enhanced classroom. The '‘confidence" attribute is presumably influenced by cognitive, affective, values and tool competency. "Classroom organization and practice” is a manifestation of students' actions and behaviour through their interaction with the teachers, peers and the tool in the classroom. "Perception” on the whole comprises skills, knowledge, beliefs, attitudes, feelings and actions that are related to mathematics learning experiences with GC. Quantitative data from the survey questionnaire and qualitative data from the open-ended questions were collected and analysed. The reliability coefficients for the five variables (MatGC, cognitive, affective, values and tool) in the 45-item questionnaire were a = .7740, .8480, .7938 .7488 and .7505 respectively. Results from the tests of significance showed that males and females did not show any significant difference in their perception on using GC to learn mathematics and age has no significant influence on the confidence in using GC to learn mathematics at p<.05.However, there was a significant difference between the achievement grade in the SPM Additional Mathematics and the confidence in using GC to learn mathematics at p<.05. Students in the grade A and C category were reported to acquire a higher confidence in using the tool to learn. Result from the multiple regressions showed that “cognitive”, “affective”, “values” and “tool competency” contributed significantly to the “confidence” attribute with “values” top the list. Written remarks from the four open-ended questions showed that there are differences in the “cognitive competence”, “affect” and “values” between those who claimed to like GC-technology and those who claimed to dislike GC-technology Notably, most of the respondents remarked that using GC to learn mathematics is challenging, exciting, and motivating. In contrast, the group that encountered difficulty using GC to learn mathematics attributed failure to their lack of technical ability or not able to follow instruction to operate GC correctly. Although limited in generalisability, these findings suggest that the use of GC in learning mathematics is well received by the students. The benefits of inclusion of technology in the mathematics curriculum may need time to be proven. Nonetheless, the results of this study may help to bring awareness to all the mathematics educators about a new way in the learning of mathematics with the graphics calculator

Operationalizing computerized testing in mathematics competition

This chapter seeks to take a modest and yet formative approach in proposing computer-based test (CBT) as the inevitable next wave in digital assessment. The major section reports on the practical design of developing and administering CBT in a mathematics competition by HOTS educational innovation development (HEID) in a mathematics competition. This chapter describes the CBT developmental process undertaken by HEID, which focuses on constructing multiple-choice test items, administering CBT, and scoring the test. While CBT offers the possibility of improving assessment, the process of preparing items and conducting online competition have nevertheless encountered several challenges such as getting quality test items, school and teacher readiness, seat time in front of computer, computer compatibility, and internet speed. As with many other educational reforms at infancy, more research in the area of implementing CBT to facilitate international competitions is needed in landscaping the assessment platform of Education 4.0