Zaleha Ismail

Malaysian students' misconceptions about measures of central tendency: An error analysis

Earlier studies revealed that students encountered difficulties in understanding the concept of measures of central tendency. However, there is negligible empirical support concerning this problem in Malaysian context. Thus, the purpose of this study is to identify misconceptions held by tenth grade students from Malaysian secondary schools regarding measures of central tendency. The instrument used was a statistical reasoning test. It was administered to 412 tenth grade students from nine different schools. Overall, the results demonstrated that tenth grade students held considerable misconceptions about measures of central tendency. Interestingly, some misconceptions were new which had not been identified in previous research. This study provides implications for instructors and researchers planning learning goals as well as designing instructional activities and assessments for future studies.

A Framework for Assessing High School Students' Statistical Reasoning

Based on a synthesis of literature, earlier studies, analyses and observations on high school students, this study developed an initial framework for assessing students’ statistical reasoning about descriptive statistics. Framework descriptors were established across five levels of statistical reasoning and four key constructs. The former consisted of idiosyncratic reasoning, verbal reasoning, transitional reasoning, procedural reasoning, and integrated process reasoning. The latter include describing data, organizing and reducing data, representing data, and analyzing and interpreting data. In contrast to earlier studies, this initial framework formulated a complete and coherent statistical reasoning framework. A statistical reasoning assessment tool was then constructed from this initial framework. The tool was administered to 10 tenth-grade students in a task-based interview. The initial framework was refined, and the statistical reasoning assessment tool was revised. The ten students then participated in the second task-based interview, and the data obtained were used to validate the framework. The findings showed that the students’ statistical reasoning levels were consistent across the four constructs, and this result confirmed the framework’s cohesion. Developed to contribute to statistics education, this newly developed statistical reasoning framework provides a guide for planning learning goals and designing instruction and assessments.

Computing in Differential Equations with Mathematical Thinking Approach among Engineering Students

Differential equations are indispensible for engineers as they help to produce models which to study various phenomena. Research has shown that students experience difficulty in interpreting graphical solutions of differential equations and symbolic solutions. Therefore, mathematical thinking powers should be developed in differential equations in classrooms as the current situation in differential equations is concerned with procedural knowledge such as finding symbolic solutions with an emphasis on conceptual knowledge rather than procedural knowledge. However, very few studies have investigated how engineers use differential equations in real situations. This study reports the computation of real life problems, applying differential equations. Data was collected through in-depth interview with seven engineering students from chemical engineering faculty at a public university in Malaysia. Findings showed that to solve real life problems, students needed both procedural and conceptual knowledge of differential equations. Moreover, they used software packages, specifically a computer algebra system, to compute the problems and to interpret the solutions using their mathematical thinking powers such as specializing, generalizing, conjecturing, and convincing. The findings may lead to an examination of the current situation in differential equation classrooms to ensure a balance between procedural, conceptual, and technological knowledge with mathematical thinking approach.

A framework for integrating cooperative learning and creative problem solving in engineering mathematics

Creative problem solving (CPS) is a multi-step method for solving problems in various disciplines that can support students in the learning of mathematics. Although CPS is cooperative in nature and is most productive when done as a team, CPS cannot utilize the full potential of teamwork to connect and share ideas among groups in the process of solving problems. Cooperative learning (CL) has additional elements designed to develop groups into a learning community. Both CL and CPS elements are combined to create a problem solving framework to guide students through the CPS cycle according to CL principles and to transform group discussions to class discussions. The main objective of this study is to propose a cooperative creative problem solving (CCPS) framework to support student problem solving in engineering mathematics. The designed framework can encourage engineering students to learn mathematics in their teams and overall class discussion.

LEARNING DIFFERENTIAL EQUATIONS: A METASYNTHESIS OF QUALITATIVE RESEARCH

Teaching methodology is continually developing over time. There is a need to revise the methods that have been planned and examined. This research explores the development of Differential Equations teaching methods from the year 2000 onwards. The methodology used in this paper is metasynthesis research. In the last chapter, the researchers proposed using online learning as a new method of teaching.

Mathematical problem solving skills among high achiever students

This study aims to examine the problem solving skills among form four high achievers in a boarding school. 52 students from two classes were purposively chosen based on their mathematics achievement in mid-year examination and PT3 results. As this study was to test students’ problem solving skills with the daily life problem, the Mathematical Problem Solving Skills Test (UKPMM) was created for this purpose. The items in this test were adapted from PISA mathematics questions and consists of ten multiple answer questions and eight openended questions. Data was analyzed using descriptive statistics. Results showed that high achiever students have problems in solving mathematics questions especially in real life context. Most of the students managed to extract important information from the questions but possess limited ability to utilize and manipulate the information to solve the problem given. The students have tendency towards finding the correct solution rather than processing the information during the thinking process. Therefore, there is a need to introduce an alternative way of teaching approach to enhance problem solving skills among high achievers.

Teaching mathematical structures in differential equations using a computer algebra system to engineering students

Engineers often need to make sense of mathematical structures in differential equations to deal with real life problems. However, students showed difficulties in grasping them. This study presents the teaching of mathematical structures in differential equations using a computer algebra system. The computer algebra systems played the role as a pedagogical tool to enhance teaching mathematical structures. Findings showed the nature of the problems, prompts and questions assisted engineering undergraduates to make sense of mathematical structures. Explanations and links were the most frequent type of mathematical structures employed in solving real life problems. While techniques and representations were the most frequent mathematical structures adopted during solving procedural problems. This study implies that instructors should use computer algebra systems strategically to teach meaningful mathematics.