Malaysian Online Journal of Educational Sciences, 2017
In this study, different factors affecting students’ differential equations (DEs) solving abiliti... more In this study, different factors affecting students’ differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students’ differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that combination of four factors; “epistemological math problem solving beliefs, belief about usefulness of mathematics, self-regulated learning (SRL) strategies and goal orientations” have great potential to enhance differential equation problem ability. Based on these findings, a conceptual model was developed and presented in this paper to enhance differential equation problem solving ability. This study has provided several important implications for the curriculum designers and teachers to enhance conceptual understanding in differential equation problem solving, particularly in the developing countries..
Pertanika Journal of Social Sciences and Humanities
This study investigates goal orientations, and self-regulated learning (SRL) strategies, particul... more This study investigates goal orientations, and self-regulated learning (SRL) strategies, particularly for differential equations (DEs) based problem-solving. Two adapted self-designed questionnaires for goal orientations, and SRL and an assessment test containing five self-developed DEs tasks were distributed among 430 students studying in inter-colleges. Collected data was further examined through SPSS and Smart PLS software. Initially, direct effects of goal orientations (mastery, performance, and avoidance goal) and SRL (elaboration and critical thinking) were considered. Findings revealed that mastery, avoidance goals, and elaboration had a significant direct effect on DEs’ problem-solving. However, no such effect was observed for performance goals and critical thinking. Similarly, it was revealed that only elaboration had the role of mediation for both mastery and performance goals. Likewise, in the case of critical thinking, no significant effects were observed. The current st...
In this study, role of context familiarity in students’ differential equations (DEs) solving was ... more In this study, role of context familiarity in students’ differential equations (DEs) solving was explored at pre-university level. An assessment test containing three self-developed DEs tasks were distributed among 430 students, studying in inter-colleges. Collected responses were analyzed using a scoring rubric containing three main stages (understanding, planning towards the solution and getting answer).Findings revealed that context familiarity positively affected students’ problem solving. Students showed better problem-solving skills in physics based problem as compared to biological related problem. Surprisingly, in solving compound interest related problem, students’performance was even better than physics related problem. Beside the positive affect of context familiarity, students have shown lower performance in getting answer and the increasing trend of errors was found in answering to logical questions. From the findings of this study, it may be concluded that context fami...
Differential equations (DEs) have an essential role in mathematics and have been at the center of... more Differential equations (DEs) have an essential role in mathematics and have been at the center of calculus for centuries. The study of differential equations started in the late 17th century with Sir Isaac Newton, who sought information about motion of planets indirectly through the analysis of rate of change equations (Rasmussen et al., 2000). The concept of DE is used to model and understand real life problems. Therefore, these provide opportunities to formulate the application of phenomena from other discipline of science and social science fields such as Physics, Astronomy, Biology, and Economics. Teaching and learning of differential equation is the most difficult part of the mathematics course, particularly at pre-university level. This is because, the topic of differential equation along with differentiation and integration is introduced first time at 12 th year of study, and the students have no previous knowledge and understandings of this topic (Rehman et al., 2012). In addition to it, students' special attention, efforts and learning strategies are required to solve problems containing differential equations, particularly non-routine problems because these problems are typically concerned with unanticipated, unusual, and strange solutions (Polya, 1981; Rehman et al., 2012).Even talented calculus problem solver sometimes became unable to solve these non-routine problems(Dawkins et al., 2014). So it is common for students to avoid the essential part of mathematics, which leads to sever understanding problems at higher levels of education, when they correlate the real life problems. From the teaching point of view, most important aspects of the recent studies in mathematics education were to find competent strategies for teaching differential equation course. Within the case of differential equation, various kinds of scheme have been come out to deal with the concepts related to them(Raychaudhuri, 2008). Generally, three different approaches (algebraic, numerical and graphical) are employed to solve differential equations (Arslan, 2010b; Artigue, 1989). In traditional differential equation teaching and learning, algebraic approach predominates, while recently, graphical and numerical approaches are more emphasized to facilitate the conceptual learning of differential equations. In a traditional differential equation environment, Selahattin (2010b) reported that nature of students' learning is procedural and is restricted to mastering and applying a few algebraic techniques. Artigue (1989) supported these results in a sense, so as to learner do not have understanding of differential equation concept (Boyce, 1994; Rasmussen, 2001). The main difficulties that students found when handling the algebraic based solutions of differential equations are related to the unsuitable choice of the method of solution or an incorrect process of integration (Camacho-Machín et al., 2012b).
International Electronic Journal of Mathematics Education
Teaching and learning of differential equations (DEs) have a prominent role in all the fields of ... more Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with differentiation and integration is only introduced first time at the 12th year of study or at pre-university level, and the students have no previous knowledge and understandings of this topic. Therefore, the aim of current study is to determine whether teaching and learning of DEs is a challenging task and also, to find out the ways these challenges can be tackled to develop a better understanding for differential equations problem solving. Results showed that teaching and learning of differential equation is not only a difficult part of the mathematics as compared to algebra, trigonometry but also demand high level of conceptual understanding and special efforts for solving differential equation problem. Addition of non-routine problems has been found major factor to enhance teaching and learning. Teacher should also be properly equipped and trained, so that they may educate both routine and nonroutine differential equation problem.
Uploads
Papers by Aisha Bibi