Changing attitudes to university mathematics through problem solving

University mathematics is often presented in a formal way that causes many students to cope by memorising what they perceive as a fixed body of knowledge rather than learning to think for themselves. This research studies the effects on students' attitudes of a course encouraging co-operative problem-solving and reflection on the thinking activities involved. The attitudinal questionnaire was shown to the students' teachers who were asked to specify the attitudes they expect from their students and the attitudes they prefer. This was used to give a ‘desired direction of change’ from expected to preferred. Before the course, half the students responded that university mathematics did not make sense. A majority declared negative attitudes such as anxiety, fear of new problems and lack of confidence. During the problem-solving course the changes were almost all in the desired direction. During the following six months of standard mathematics lecturing, almost all changes were in the opposite direction

Thinking mathematically : a framework for developing positive attitudes amongst undergraduates

This thesis tests the hypothesis that problem-solving activities caused positive changes in students attitudes towards mathematics. A pilot test, carried out in a problem-solving course at the University of Warwick, tested possible questions that would indicate change of attitudes. The findings indicate that the course affected students attitudes to mathematics in what was considered a positive manner. Using that experience gained through the pilot study, the main study was carried out at Universiti Teknologi Malaysia (UTM) in which data was collected from 44 students who took the course in problem-solving taught by the researcher. A pre-test, post-test and a delayed post-test (six months later) were administered, which included interviews with selected students and staff. To establish what might be considered a positive change, the staff at the Mathematics Department were asked what attitudes they would expect students have as a result of the mathematics teaching at the University, and then specify the attitudes they would prefer students to have. The direction of change between the two responses were considered to be positive, and this is defined as the "desired direction of change". The results show that the problem-solving course affected students attitudes such that the change, identified as the difference between pretest and post-test results, was largely in the desired direction of change. However, when students return to normal mathematics lectures many of the indicators reverted in the opposite direction; away from what the staff preferred

Modeling the spread of dengue fever by using SIR model

The establishment and spread of dengue fever is a complex phenomenon with many factors that interact with each other. This report present a study on a mathematical model, the SIR (Susceptible, Infected and Recovered) that serve as a framework for understanding the spread of the infectious dengue fever. We begin with a brief discussion of the origin and historical development of the disease. This is followed by a review on the relation between the three compartments, susceptible, infected and recovered. The modeling steps that lead to the SIR model using ordinary differential equation is explained in detail. The solution gives the basic reproduction number R_0, and this basic reproduction number is use to determine whether the dengue fever will dies out or persists in human population in the long run. The disease-free equilibrium point is determined and R_0 is used to determine whether the disease free equilibrium is stable or unstable. Establishing the endemic equilibrium point determines when the dengue fever will become calm

Developing effective students communication in engineering mathematics

The Malaysian workplace needs graduates with employability skills such as critical thinking, problem solving and ability to communicate. In 2006, Universiti Teknologi Malaysia (UTM) has integrated these goals in undergraduate education but studies at UTM have indicated that the goals have not been translated into successful implementation. In this presentation, we will share how we had implemented an integrated approach which addressed students’ knowledge, thinking, problem solving and generic skills, in particular, communication. We had developed a framework which was used to guide our instructions in Engineering Mathematics I since 2009/2010 session, in Engineering Mathematics II since 2010/2011, and in Differential Equations since 2012/2013 session. The same strategies were implemented in Malaysia Japan International Institute of Technology (MJIIT, UTM KL) in Engineering Mathematics III for the 2011/2012 and 2013/2014 sessions

Engineering Mathematics Obstacles and Improvement: A Comparative Study of Students and Lecturers Perspectives Through Creative Problem Solving

AbstractThis study is part of a project concerned with the students’ obstacles in face-to-face Engineering Mathematics classrooms through mathematical thinking approach. The main data collection for this study was carried out through students’ structured questionnaires of three classes at Universiti Teknologi Malaysia (UTM) in the end of semester. The findings showed that the students’ obstacles from students’ and lecturers’ perspectives are approximately the same and the majority of each group separately believed that two main obstacles in the learning of Engineering Mathematics are imaging and sketching in the 3-dimensions. The analysis showed that for both groups different thinking skills and tools from Creative Problem Solving (CPS) are less important methods that can help students to overcome learning obstacles

Systematic qualitative data management (SQDM) during an interpretive action research

This paper presents the systematic way of data management in an action research to explore the interplay of mathematical thinking processes and mathematical sense making experiences of first year engineering students. The transitional impact of future engineers from school mathematics to engineering mathematics is explored by collecting data through multiple techniques and methods. The interpretivist epistemology and constructivist theoretical perspective during this action research demanded a rigorous qualitative research process and extensive data collection using emergent methods and techniques. This paper would address the queries like what data to collect and manage and how to manage it during this research process. Data management became vital for securing and utilizing the data in a proper way throughout our research. Managing the data effectively also enabled us to risk free data, accuracy, verifiability, and improved productivity of the research. Properly managed data would easily be preserved and reanalyzed in future with new analysis techniques. During this research, the digital and nondigital data, documentation and meta-data were also collected. We used multiple softwares e.g. Microsoft Excel, Word and NVivo10 to manage the data. Documentation helped us to be precise and holistic to further utilize the data for interpretive analysis

A Conceptual Framework for Mathematical Ability Analysis through the Lens of Cultural Neuroscience

AbstractThis paper present a conceptual framework that will be used for analyzing divergence in mathematical thinking, skills, abilities, processes and achievements in mathematics through the lens of cultural neuroscience. The bidirectional interface between mathematical thinking and cultural neuroscience is used to explore different learning styles, cognition patterns and neural activities in response of mathematical thinking influenced by culture. Research questions are emerged as how do innate mathematical abilities, plasticity of the young brains and the mathematical cultural environment contribute to mathematical thinking? Why do a group of students from one ethnicity tend to achieve higher scores in mathematics than a group of students from another ethnicity? How does cultural neuroscience report the differences in mathematical thinking and learning trajectories? How does culture accelerate the mathematical thinking?

Supporting Students Mathematical Thinking in the Learning of Two-Variable Functions Through Blended Learning

AbstractIn multivariable calculus, the concept of multivariable function is one of the most difficult for undergraduate students to study. The main objective of this study is to establish a model of teaching and learning to support students’ mathematical thinking in the learning of two-variable functions through a blended learning environment. The impact of this environment on students’ learning of two-variable functions and in overcoming students’ obstacles are put forward. Findings revealed that blended learning supports students’ mathematical thinking and helps in overcoming additional obstacles in mathematical learning. Poor mathematical knowledge of single-variable functions and poor algebraic manipulations are still the main reasons behind student obstacles in learning two-variable functions

The Relationship Between Emotional Intelligence and Mathematical Competency Among Secondary School Students

Anxiety towards mathematics among secondary school students have been reported. Anxiety creates strong negative emotions and can hinder a person's cognitive, learning and academic performance. Fear of mathematics came early in the educational process and if this is not handled properly, it will negatively affect the students to adulthood. In learning mathematics, emotional intelligence (EI) impacts on how a person deals with emotions, mathematics and the general self-regulations strategies that the person adopts. A study was carried out to access secondary students' EI and their mathematical competency (MC). The EI was tested using an EI questionnaire for adolescents (IKEM-R/MEQI) consisting of 7 domains, while the MC was tested using selected questions from PISA (Programme for International Student Assessment) 2012 released items. Analysis shows that EI predict significantly students MC, but with low correlational value. Most of the respondents have moderate level of EI in all 7 domains whereby self awareness and self-regulation are the two domains with lowest scores. On the other hand, most of the students' MC are poor. This particular research shows that EI is not a good predictor of MC which contradicts other reports. However it is suggested that the data collection can be improved by examining students' EI while they are engaging in activities that call for MCs rather than doing it before or after the tasks

Fostering Mathematical Creativity Among Engineering Undergraduates

This research is used to study engineering undergraduates fostering their mathematical creativity during creative problem solving. This was an exploratory research carried out in a public university as to find out the impact of CPS towards mathematical creativity among the engineering undergraduates. A case study was used to provide deep exploration of how the engineering undergraduates using their creative methods to solve open-ended mathematical problems creatively. Qualitative research design was applied in order to understand in depth the engineering undergraduates working collaboratively to generate their creative ideas during mathematical problem solving. Three final years engineering undergraduates took part in the study.  They had to use their divergent and convergent thinking to generate creative methods to solve twelve open-ended mathematical problems. Qualitative research design of case study was used in this study to explore the engineering undergraduates using creative methods to solve open-ended mathematical problems during creative problem solving processes. By analyzing the data collected from the case study can provide in-depth and detail understanding of the creative processess and products of the research. Observation and recording sheets were used to collect all the data. SCAMPER was also used as a guideline for them to spark their creaivity. All the qualitative data of drawing from documents, videotape from observation and snapshot texts from recording sheets were collected and then analyzed. They were coded and categorized into different themes in order to find out the mathematical creativity among the engineering undergraduates. The results in this study shows that the engineering undergraduates were able to generate different creative methods with the help of the SCAMPER