• The Mathematical Education
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• v.44 no.3 s.110
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• pp.375-396
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• 2005

This paper reports on the main results of 3 study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially sewing as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level

• Communications of Mathematical Education
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• v.28 no.3
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• pp.339-352
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• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.527-537
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• 2004

This paper deals with the asymptotic behaviour for the semi-linear differential systems x' (t) = A(t)χ + f(t, x). We give a detailed proof of known generalization of Coppel's result about the above mentioned system.

• Research in Mathematical Education
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• v.12 no.3
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• pp.193-200
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• 2008

In this study, an innovative computer support has been suggested to improve differential perception of the students. Research has been conducted on a calculus class which has 35 students. A semi-structured interview has been reported in the study. By this interview, it was tried to make differential concept more understandable by using Micro Soft Excel component of the well-known MS Office software. By this aim, students have been asked to integrate a simple function by using MS Excel. At the end of the study, it was observed that differential concept made more sense in students' minds than previous.

• Journal of Engineering Education Research
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• v.23 no.4
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• pp.37-51
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• 2020

This study examined the differential effects of High-Impact Practices(HIPs) on the career aspiration of STEM college students by gender. Through the theoretical lens of Social Cognitive Career Theory(SCCT), a two-level model analysis was conducted. A sample of 2,101 third- and fourth-year undergraduate students majoring in STEM at 38 universities, which had been collected from the National Survey on College Student Experiences and Learning Outcomes funded by the Korea Research Foundation, was used. This study found that the three HIP domains(learning with peers, faculty support, content relevancy) had different influences depending on gender. These findings suggest that HIPs can benefit the development of female students' career aspiration and have gender-differential effects on students in STEM majors. Based on those findings, this study also deduced implications about the roles of faculty members and higher-education institutions that might foster the retention of women in STEM.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.733-767
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• 2005

During the past decades, there has been a fundamental change in the objectives and nature of mathematics education, as well as a shift in research paradigms. The changes in mathematics education emphasize learning mathematics from realistic situations, students' invention or construction solution procedures, and interaction with other students of the teacher. This shifted perspective has many similarities with the theoretical . perspective of Realistic Mathematics Education (RME) developed by Freudental. The RME theory focused the guide reinvention through mathematizing and takes into account students' informal solution strategies and interpretation through experientially real context problems. The heart of this reinvention process involves mathematizing activities in problem situations that are experientially real to students. It is important to note that reinvention in a collective, as well as individual activity, in which whole-class discussions centering on conjecture, explanation, and justification play a crucial role. The overall purpose of this study is to examine the developmental research efforts to adpat the instructional design perspective of RME to the teaching and learning of differential equation is collegiate mathematics education. Informed by the instructional design theory of RME and capitalizes on the potential technology to incorporate qualitative and numerical approaches, this study offers as approach for conceptualizing the learning and teaching of differential equation that is different from the traditional approach. Data were collected through participatory observation in a differential equations course at a university through a fall semester in 2003. All class sessions were video recorded and transcribed for later detailed analysis. Interviews were conducted systematically to probe the students' conceptual understanding and problem solving of differential equations. All the interviews were video recorded. In addition, students' works such as exams, journals and worksheets were collected for supplement the analysis of data from class observation and interview. Informed by the instructional design theory of RME, theoretical perspectives on emerging analyses of student thinking, this paper outlines an approach for conceptualizing inquiry-oriented differential equations that is different from traditional approaches and current reform efforts. One way of the wars in which thus approach complements current reform-oriented approaches 10 differential equations centers on a particular principled approach to mathematization. The findings of this research will provide insights into the role of the mathematics teacher, instructional materials, and technology, which will provide mathematics educators and instructional designers with new ways of thinking about their educational practice and new ways to foster students' mathematical justifications and ultimately improvement of educational practice in mathematics classes.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.137-143
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• 2001

In this paper, we study the existence, uniqueness and norm estimate of solutions for the nonlinear delay integro-differential system.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.189-201
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• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• Journal of Practical Engineering Education
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• v.7 no.1
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• pp.1-9
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• 2015

STEM Education in the US and Korean STEAM are reviewed. The present STEM education focuses on K-12 and it does not concern STEM education in university. In this paper, we define a STEM education that can be made available in university and we establish a way of teaching and learning differential equations based on the STEM education. The class provides students with a chance to explore the capstone design projects that are developed by seniors and do hands-on activities. We introduce and set a Mobius strip with an instant delivery pathway to solve real problems as a symbol of STEM education.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.429-436
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• 2003

We study the asymptotic equivalence between the nonlinear differential system $\chi$'(t) = f(t, $\chi$(t)) and its variational system ν'(t) = f$\chi$(t, 0)ν(t) by using the comparison principle and notion of strong stability.