• Research in Mathematical Education
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• v.24 no.1
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• pp.1-27
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• 2021

For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.

• Research in Mathematical Education
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• v.24 no.4
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• pp.279-311
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• 2021

In this paper, we report the types of teaching moves a mathematics teacher educator attempted in his teaching of third-grade students at an urban elementary school in South Korea over two months. We analyze the lesson videos to find the patterns of teaching moves and speculate the link between the teaching and students' mathematical proficiencies recommended in the Common Core State Standards for Mathematical Practices. Closely related teaching moves to the students' development of a certain mathematical proficiency would imply the exemplary practices that teachers-both inservice and preservice teachers-can implement in their classrooms.

• Knowledge Management Research
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• v.17 no.3
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• pp.207-225
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• 2016

Recently, flipped learning is being highlighted especially at the college of engineering because of its self-directed learning which direction matches that of the engineering education system. Although many engineering professors have tended to apply the flipped learning to their classes, they experienced a number of significant problems and challenges in practical implementing. By using TRIZ method as a tool for creative problem solving, that have been developed and applied in many fields ranging from engineering as well as management, this study aims to solve the education dilemma between learning efficiency and learning effectiveness, create a new concept of the flipped learning based on the solutions, and then explore its educational feasibility for successfully adopting it to engineering courses. This study suggests an instructional design for implementing the flipped learning according to the characteristics of engineering classes and then designs a new model of the flipped learning according to that procedure. Also, based on the empirical results in applying a new flipped learning model to the applied mathematics, this paper proposes several guidelines for the successful application of flipped learning in the future.

• Journal of the Korean School Mathematics Society
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• v.3 no.2
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• pp.195-215
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• 2000

Illinois issues the following standard teaching certificates : Early Childhood (birth-grade 3), Elementary (grades K-9), High School (grades 6-12) Special (grade K-12), School Service Personnel, and Administrative. Any of the preceding certificates can be issued on a provisional (maximum of two fiscal years) basis to qualifying individuals. Other certificates issued are : Substitute, Provisional Vocational, Temporary Provisional Vocational, Part-Time Provisional, and General. To obtain an Early Childhood, Elementary, High School, or Special certificate in Illinois, you must either complete an approved teacher education program or be an experienced, licensed teacher seeking a subsequent certificate through transcript evaluation. You must meet all other requirements for the particular certificate you are seeking, For school Service Personnel and Administrative certificates you must have completed a state approved program before you may apply. The Standard Elementary Certificate, High School Certificate, and Special Certificate are valid for four years for teaching. These certificates may be issued to graduates with a bachelor's degree from a recognized college who have successfully completed the required certification examinations and who present certified evidence of having earned credits. All individuals receiving certificates must be of good character and in good health, and be at least 19 years of age and a citizen of the United States or legally present and authorized for employment.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.183-198
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• 1999

Let $\mathcal{F}(B)$ be the Fresnel class on an abstract Wiener space (B, H, ${\omega}$) which consists of functionals F of the form : $$F(x)={\int}_H\;{\exp}\{i(h,x)^{\sim}\}df(h),\;x{\in}B$$ where $({\cdot}{\cdot})^{\sim}$ is a stochastic inner product between H and B, and $f$ is in $\mathcal{M}(H)$, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an $L_p$ analytic Fourier-Feynman transform ($1{\leq}p{\leq}2$) and a convolution product on $\mathcal{F}(B)$ and verify the existence of the $L_p$ analytic Fourier-Feynman transforms for functionls in $\mathcal{F}(B)$. Moreover, we verify that the Fresnel class $\mathcal{F}(B)$ is closed under the $L_p$ analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the $n$-repeated $L_p$ analytic Fourier-Feynman transform on $\mathcal{F}(B)$. Finally, we show that several results in [9] come from our results in Section 3.

• East Asian mathematical journal
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• v.39 no.4
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• pp.455-478
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• 2023

Expectations and interests in blended learning are increasing as universities respond to the educational flow of transition to e-lernring. This study tried to explore and understand the meaning of and the properties of blended instruction. In addition, through the literature review, this study was to find out how bleanded learning affected in teaching and learning situation. Particularly, it was to find out students' preference to the type of blended instruction. Those types are the mixed of or the unique of class instruction(off line), on line, and recorded instruction. To investigate learners' preference to the type of the instruction and also the reason of the preference, in this study, the 27 undergraduate students of the fourth grade in the major of mathematics education in the C university located in G area. By the result, most students preferred the mixed type of instruction involving off line and recorded instruction. The reason is that they could attend to the class while participating in the group activity positively and understand the content through the communication in depth and the instructor's feedback. Because of this reason, they did not prefer to the only one type insturction such as the recorded type.

• Journal of the Korea Convergence Society
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• v.9 no.6
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• pp.209-215
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• 2018

The college liberal arts mathematics is opened as a required course in science and engineering field, but students with low achievement experience difficulty in learning. Therefore, flip learning, which is well known as an effective teaching method based on self-led and learner, is suggested as an alternative. However, some problems are pointed out in this pedagogy. As an alternative to flip learning, we apply flip PBL classes that apply PBL to flip learning to general math subjects to supplement the problems of existing flip learning classes and increase interest in mathematics I want to know the effectiveness of whether it can be done. In this study, we investigated the educational effectiveness of the comparison study between the experimental group applying flip PBL class and the control group applying the existing flip learning class. First, the experimental group showed higher than the control group by 22 points Second, in the reflection journal analysis, in contrast to the control group, there was a positive effect on the improvement of the interest of the mathematics in the experimental group, It is expected that it will be applied as a teaching method that can complement the learning.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.327-344
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• 2009

In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale $\mathbb{T}$ $$\{{{{{{x^{\bigtriangleup\bigtriangleup}(t)+f(t,\;y(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}\atop{y^{\bigtriangleup\bigtriangleup}(t)+g(t,\;x(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}}\atop{\alpha_1x(a)-\beta_1x^{\bigtriangleup}(a)=\gamma_1x(\sigma(b))+\delta_1x^{\bigtriangleup}(\sigma(b))=0,}}\atop{\alpha_2y(a)-\beta_2y^{\bigtriangleup}(a)=\gamma_2y(\sigma(b))+\delta_2y^{\bigtriangleup}(\sigma(b))=0,}}$$ where $\alpha_i$, $\beta_i$, $\gamma_i\;{\geq}\;0$ and $\rho_i=\alpha_i\gamma_i(\sigma(b)-a)+\alpha_i\delta_i+\gamma_i\beta_i$ > 0(i = 1, 2), f(t, y) may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems $x^{\bigtriangledown\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangledown}(t)$ + g(t, x(t)) = 0, $x^{\bigtriangleup\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangleup\bigtriangledown}(t)$ + g(t, x(t)) = 0, and $x^{\bigtriangledown\bigtriangleup}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangleup}(t)$ + g(t, x(t)) = 0 satisfying similar boundary conditions.

• Journal of Engineering Education Research
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• v.5 no.2
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• pp.22-35
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• 2002

The main purpose of this study is to prepare an outline for developing the Contents Systems that achieve self-study systems to make the students adopt themselves into new study atmosphere and maximize the result of study on technical college in Electric-Electronic field. Questionnaire posed to analyze the demand of teaching materials to the students, and professors and also to find characteristics of students in technical college. The SPSSWIN/PC+ statistics Package was used to assay the collected answers. And simple frequency with percentage, average, and standard deviation were calculated to check the entire trend and actual state of each question. The primary outcomes of this study are as follows i) The students in the technical college prefer self-directed learning to lecturer-oriented teaching. ii) It is difficult to offer the technical college students normal education systems since the students?interest and motivation towards study are very low. iii) The lack of capability of foreign language and basic mathematics are considered as obstacles for many students technical college to study. iv) The professors in technical college still depend on traditional method to teach the students without organized research of the intellectual levels and attitude the students. v) Teaching materials in currently use are not appropriated to induce the motivation and interest of study from the students. Also, the teaching materials in use now were discovered not to have enough originality, practical application, andwere text based. Therefore, the improvement of the existing teaching materials was demanded while the fundamental ability to study of general students is declining. Consequently, it is necessary to introduce new teaching materials which are simple, easy, and organized to offer the studen ts study desire and interest.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.123-131
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• 2014

The purpose of this paper is to study the perturbation analysis of the matrix equation $X=I-A^*X^{-1}A+B^*X^{-1}B$. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.