JOURNAL OF HIGHER EDUCATION CURRICULUM
Year:2016 | Volume:6 | Issue:12 |Papers Count:7

Educational challenges of geometric approach to Differential Equations (DE) is one of the important issues of undergraduate mathematics curriculum. Thus, a study was designed to investigate the breadth and depth of students’ understanding of DE.17 undergraduate students majoring in science and engineering, participated in the study. The data were collected via task- based interviews. Students were asked to solve a DE using geometric approach and then, compare the response curves with the given slope field and justify their answers. The analysis of the data helped to identify various challenges including their understanding of the relationships between [y, f (y)] and [t, y (t)], the number of roots of f (y) =0 and the number of equilibrium solutions, the number of intersection points of the graph of f (y) with the horizontal axis and the number of equilibrium solutions, the sign of f (y) and monotonicity of solution curves, phase line and labling of equilibrium solutions.

For proving and solving combinatorial theorems and problems, variety of creative methods are needed, as opposed to more classic fields such as algebra and analysis that their proving and solution methods are more routine. This charachteristic of combinatorics problems push many learners to find general methods by classifying its problems. Empirical evidence shows that at first, many students classify combinatorial problems and then, memorize one formula for each class. However, the difficulty becomes evident, when the number of classes become so big that a learner, is not able to use them as an efficient procedure. This study is a follow up to previous research on students’ conception of combinatorial concepts. In this paper, the use of combinatorial reasoning in teaching as last step in the combinatorial thinking, is investigated.

Faculty members are engaging with three important roles at university including teaching, research and services. However, the main focus of higher education on research has caused the neglect of teaching among faculty members. This is resulted in lack of information about what and how to develop teaching knowledge in different higher education disciplines. As well, teaching knowledge is practical in nature and that, contributed to the complexity of its study. Among different models, pedagogical content knowledge (PCK) model was chosen to study the nature of mathematics instructors’ teaching knowledge at higher education level. The data were collected through semi-structured interviews, with a number of university mathematics instructors. The data were analyzed using phenomenology. The analysis revealed that university mathematics teachers develop their pedagogical content knowledge, through some resources including model making, repeating courses, mathematics textbooks, students, colleagues, and their prior experiences as student, educational resources and mentoring. Moreover, the direction of PCK development is from content to learner and considering these resources towards the development of PCK, yet needs another factor as reflection on action, is influencial.

Investigating the historical development of Bachelor of Science (BSc.) in Mathematics in Iran, is a neglected and yet, much needed area of study. This is especially important since the number of undergraduate students in mathematics is soon shrinking and many infrastructures that have been established, will shortly be vacant, due to the decreasing the student population in Iran. Therefore, in the near future, drastic changes are needed to be responsive to the new societal and workforce need. To be responsive to this need, the purpose of this paper was to give a historical account of the development of BSc. Program of mathematics in Iran and then, using the case- study methodology, the paper has focused on the BSc. Program of mathematics at Sharif University of Technology taking the lead of so- called “educational reform”. To conclude the paper, few recommendations are presented for curriculum developers and planners at the higher education level. The history shows that in any curriculum change, the various needs of Iranian society should be taken into account.

Investigating the required knowledge for elementary teachers to teach mathematics, has a top priority of research in the field of mathematics teacher education. The reason is that all higher education institutes who have elementary education program leading to a professional degree or teacher certificate, are dealing with prospective elementary teachers who are generalists in nature and yet, responsible to set the foundation of mathematics learning of school children. Thus, the professional preservice and in- service of them is drastically different with those, who are subject specialists. Therefore, the main purpose of this research was to identify the essential mathematics knowledge for elementary teachers. So, a study was designed at three phase. At the 1st phase, a model was designed based of evidences from the research literature. At the 2nd phase, five questionnaires were developed based on the components of this model and were administered on 30 volunteer practicing elementary teachers. At the final phase, a focus group with same teachers was formed independent from other data. The analysis of the data collected via focus group, supported the findings from the analysis of the data gathered through five questionnaires. At the end, the model was modified. In this paper, part of this study is presented.

All students can learn to think mathematically and increase the depth and complexity of their ideas as the main goal of mathematics education. However, there are various challenges in achieving this goal extensively in mathematics classrooms due to the need for conceptual Account of mathematical thinking. Therefore, this study intends to give a more clear account of what are the challenges of mathematical thinking, why they matter and how they might be overcomed. For this purpose, different approaches to mathematical thinking were systematically and critically reviewed. Among those, the paper emphasized on mathematician’s account of mathematical thinking and the ways in which, it can be transferred into teaching- learning activities, has articulated. In addition, the challenges of developing mathematical thinking are discussed. This paper has aimed to depict a more clear perspective for educational researchers in general and mathematics education researchers in particular.

In this paper necessity of consideration of “application and modeling approach” in tertiary mathematics education will be introduced. After that history and different cycle of modeling in mathematics education will be explained. In the following, researches which carried on “application and modeling approach” in tertiary level will be reviewed. Then methodological details related to using this approach in teaching a tertiary level mathematics courses will be elaborated. In this regard, a modeling eliciting activity introduced to 39 engineer students and their strategies for solving this problem investigated upon seven steps modeling cycle. Finally, after introducing some of students’ answers to this real world problem and a typical correct answer, potential capacities and obstacles of using “application and modeling approach” in tertiary mathematics education will be discussed.