• Education of Primary School Mathematics
• /
• v.20 no.2
• /
• pp.177-192
• /
• 2017

In theory, mixed methods that incorporate both quantitative and qualitative approaches can maximize strengths of each method while minimize the short comings of each. Mixed methods research is a feature of educational research nowadays, and the number of studies applied mixed methods research has been gradually increasing. This study investigates how mixed methods research was applied in the field of mathematic education, especially focusing on how qualitative and quantitative methods are combined to best address their research questions. With this in mind, this study carefully selects and analyzes 4 research articles that used mixed methods and were published by Journal of Elementary Mathematics Education in Korea in 2015. This study provides detailed result of qualitative analysis on mixed methods research while other a few previous analysis on mixed methods research were tend to focusing on quantitative analysis, producing numeric quantitative information. The result of this study provides practical and in-depth analysis on how to improve validity and possibility of mixed methods research, addressing alternative ways to combine two different research methods and key elements to take into account.

• Journal of the Korean Home Economics Association
• /
• v.44 no.9
• /
• pp.1-8
• /
• 2006

The purposes of the present article are to suggest pragmatism as offering a philosophical paradigm for mixed methods research, to explain the fundamental principles of mixed methodology, and to present examples of research for understanding how to apply it to family studies. Mixed methods research is the class of research where the researcher mixes or combines quantitative and qualitative techniques, methods, approaches, concepts or language into a single study. Mixed methodology has its roots in pragmatism, which is a new philosophical paradigm to criticize the traditional dualism and to endorse eclecticism and pluralism. The present article argues that mixed methods research has the potential to answer a broader and more complete range of research questions, and to provide strong evidence for a conclusion through convergence and corroboration of the qualitative and the quantitative methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.7 no.2
• /
• pp.95-111
• /
• 2003

BDM mixed methods are obtained for a good approximation of velocity for flow equations. In this paper, we study an implementation issue of solving the algebraic system arising from the BDM mixed finite elements. First we discuss post-processing based on the use of Lagrange multipliers to enforce interelement continuity. Furthermore, we establish an equivalence between given mixed methods and projection finite element methods developed by Chen. Finally, we present the implementation of the first order BDM on rectangular grids and show it is as simple as solving the pressure equation.

• Journal of Korea Multimedia Society
• /
• v.24 no.1
• /
• pp.155-165
• /
• 2021

With the continuous development and progress of science and technology, the field of mixed reality applications has involved scientific research, medicine, entertainment, education, information dissemination, and people's daily lives; This paper will focus on the application of mixed reality in the field of education and teaching, relying on the characteristics of mixed reality technology. This article will use the combination of mixed reality and smart glasses to fully consider the characteristics of photography darkroom teaching, design and produce a mixed reality photography darkroom teaching software, and explore the feasibility of the application of mixed reality in teaching. This paper will use literature research methods, practical research methods, and survey methods as the main methods of research topics to determine the importance, feasibility, and necessity of the relevant theories studied in this paper. The application of mixed reality technology in photography darkroom teaching can not only solve many problems in the existing darkroom teaching methods, but also develop and expand students' Independent learning ability. It is concluded from this that mixed reality teaching software has the feasibility of sustainable development, which brings particular application value to the development and research of other education and art discipline software.

• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.125-134
• /
• 2003

Standard estimation methods for linear mixed models are sensitive to influential observations. However, tools and concepts for linear mixed model diagnostics are rudimentary until now and research is heavily demanded in linear mixed models. In this paper, we consider two diagnostics to evaluate the effects of individual observations in the estimation of fixed effects for linear mixed models. Those are Cook's distance and COVRATIO. Results of our limited simulation study suggest that the Cook's distance is not good statistical quantity in linear mixed models. Also calibration point for COVRATIO seems to be quite conservative.

• Communications of Mathematical Education
• /
• v.28 no.3
• /
• pp.303-320
• /
• 2014

The purpose of research is to analyze research trends and methods in a total of 709 studies published in five domestic mathematics education journals issued by Korea Citation Index (KCI) for the last 10 years (2003-2013) and strands in stages of research methods among mixed methods studies. As a result, the majority of articles in the five journals used either qualitative or quantitative methods and mixed methods research was less than 10 % of the total number of studies. The majority of mixed methods was research equally mixing qualitative and quantitative methods. The mixed methods research consisted primarily of quantitative with descriptive statistics and very little qualitative with conceptual framework based on theoretical background. Our results provide not only trends of the current research methods, but also implications for various future research paradigms in mathematics education.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.321-341
• /
• 2013

In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k(k{\geq}0)$. Using mixed elliptic reconstruction method, a posterior $L^{\infty}(L^2)$-error estimates for both the state and the control approximation are derived. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.6 no.1
• /
• pp.1-15
• /
• 2002

Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.1127-1144
• /
• 2013

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order $k(k{\geq}1)$. $L^2$ and $L^{\infty}$-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for fourth order elliptic control problems.

• Honam Mathematical Journal
• /
• v.42 no.1
• /
• pp.17-35
• /
• 2020

In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the fixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.