There are two mathematical models of Hepatitis C virus (HCV) being discussed; the original model of HCV viral dynamics (Neumann et al., 1998) and its extended model (Dahari et al., 2007). The key aspects of the mathematical models have provided resources for analysing the stability of the uninfected and the infected steady states, in evaluating the antiviral effectiveness of therapy and for estimating the ranges of values of the parameters for clinical treatment. The original model is considered to be a deterministic model because of the predictive nature of the antiviral therapy within the constant target cells. Numerical simulations are carried out in the extended model, to explain the stability of the steady states in the absence or existence of migration in hepatocytes and, drug efficacy in treating HCV infection.

A mathematics framework was developed to integrate problem-solving that incorporated simulation of real-life problems in the classrooms. The framework coined as the RECCE-MODEL emphasised understanding and thinking with a view on mathematics embedded in real-life. The RECCE which stands for Realistic, Educational, Contextual, Cognitive, and Evaluation encompass the underlying principles of teaching problem solving and guide teachers in planning, designing, developing, and facilitating real-life activity tasks in developing students’ problem-solving competencies in mathematics lessons. It also explores students’ cognitive competency in their application of abstract mathematical knowledge into real-life problems based on students’ developmental status of their thinking and reasoning skills correlating to Meanings, Organise, Develop, Execute and Link (MODEL). This study investigated the affective development of the students through activity tasks developed by the sampled teachers using the principles within the framework. In total, 94 students from two high schools in Brunei Darussalam responded to a students’ questionnaire constructed to address the MODEL aspect of the framework. In particular, the analyses involved the students’ affective competencies that corresponded to a 19-item instrument within the questionnaire.  The findings showed that Brunei high school students have stimulated beliefs and positive attitudes towards non-routine problem-solving in the learning of mathematics. Meanwhile, meaningful activities developed by the teachers encouraged the development of cognitive-metacognitive and affective competencies of the students. The RECCE-MODEL framework paved the way towards understanding the relationships between effective pedagogical approaches and students’ learning, and between attitudes and cognitive abilities, and also for teachers to make better-informed decisions in the delivery of the curriculum.

<p>Problem-Based Learning (PBL) is a constructivist, student-centered instructional strategy in which students work collaboratively to solve problems and reflect on their learning experiences to advance or gain new knowledge. PBL was originally developed in medical school programs at the McMaster University in Canada in the 1960s. Since then, much research has highlighted the benefits of PBL for developing students’ mathematical knowledge in more flexible and novel ways than traditional teacher-centered teaching approaches. However, there has been a lack of studies examining how PBL can be applied to mathematics teaching and learning, since studies that have investigated the implementation of PBL outside a medical context are sparse in Brunei Darussalam. Therefore, in this study, we attempted to fill this research gap by exploring the implementation process of PBL in a Year 9 mathematics classroom and its possible impact on students’ learning in mathematics in the context of Brunei Darussalam. The participants of the study consisted of 17 Year 9 students (ages 14-15) from a secondary school in Brunei Darussalam The findings from our study showed that the implementation of PBL helped motivate the students to collaboratively work as a group and learn from their peers and therefore, gradually reduced their dependence on the teacher during the course of the intervention. The results from the students’ performances on the pre-test and the post-test also provided evidence to show that the implementation of PBL could have a positive impact on the students’ learning in mathematics. Directions for future mathematical PBL implementation are also discussed and offered. </p>

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This study examined how Year 12 students use their inquiry skills in solving conditional probability questions by means of Inquiry-Based Learning application. The participants consisted of 66 students of similar academic abilities in Mathematics, selected from three classes, along with their respective teachers. Observational rubric and lesson observation checklist were used as the data collection instruments. The results obtained were analyzed and then quantitatively reported. Findings from the observational rubric revealed that Year 12 students were able to understand most of the questions during the activity, but they only select and use one previously learned method to solve the questions during the activity. In addition, these students rarely seek and asked probing questions during the activity. They only used words, diagrams and numbers to interpret the solutions to the questions and make connections between them but with few mistakes detected.