• Research in Mathematical Education
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• v.15 no.2
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• pp.159-179
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• 2011

This paper reports on the learning journeys in mathematical problem solving of 21 teachers enrolled on a Masters of Education course entitled Discrete Mathematics and Problem Solving. It draws from the reports written by these teachers on their personal journeys: the commonalities and differences among them in terms of how they look at their own problem solving experiences, what language they employ in talking about problem solving, and what impact the course has on their views about problem solving. One particular aspect of problem solving instruction, a pedagogical innovation called the Practical Worksheet, is addressed in some detail. These graduate students are full-time mathematics teachers with at least two years of classroom experience. They include primary and secondary teachers.

• The Mathematical Education
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• v.43 no.3
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• pp.233-255
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• 2004

Problem solving in math education is of great importance. The interest on problem solving in math education is growing all over the world. Problem solving ability is important throughout the fourth-sixth national curriculum in Korea and this is also necessary in the seventh national curriculum. The writer has implemented a proper model for problem posing and this is also necessary in the seventh national curriculum that emphasizes self-leading for improvement in the classroom. This model has advantages to cultivate a good habit of students who tries to solve the problems with concrete strategies, to take part in the problem solving activity and to change their mathematical attitude.

• The Mathematical Education
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• v.54 no.2
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• pp.195-206
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• 2015

The purpose of this study is to examine the effects of teacher on fourth-grade students' attitudes toward mathematics using data from TIMSS 2011. Students' attitudes toward mathematics included interest in learning mathematics, interest in mathematics lessons, and confidence in their mathematics ability. Teacher factors included mathematics professional development, confidence in teaching mathematics, teacher-centered mathematics instruction, and enhancing student mathematical thinking. The two level Hierarchical Linear Model was employed to analyze the relationship between teacher factors and student attitudes. Results showed that teacher-centered mathematics instruction significantly and positively predicted students' confidence about their mathematics ability. The findings suggest that school systems and mathematics educators need to provide teachers with the curriculum, assessment, and research-based practices and knowledge to overcome the obstacles to change their mathematics classroom.

• Journal of KSNVE
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• v.3 no.3
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• pp.231-243
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• 1993

The dynamic characteristics of two types of mathematical models for a rigid body suspension system are analyzed and compared in this paper. One is a linearized model which is commonly used in the engine mount system analysis, the other is a nonlinear model which usually applied to the pendulum type system. The typical 3 d.o.f's mathematical model, for convenience, is chosen as a simulation model, because it has fundamental dynamic characteristics of suspension system. Time responses and unbalance responses of the rigid body, transmitted forces and torques are simulated by using the mathematical model. From the results of computer simulation, it is approved that he nonlinear model is valid and the linearized model gives erroneous results in the case of the pendulum type suspension system. In addition, in this study the effects of design change on the dynamic characteristics of the suspension system are investigated. Mount locations, mount angles, lengths, stiffness and damping coefficients of suspension bars are chosen as design parameters.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1371-1385
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• 2019

Given a topological space X and a non-negative integer k, ${\varepsilon}^{\sharp}_k(X)$ is the set of all self-homotopy equivalences of X that do not change maps from X to an t-sphere $S^t$ homotopically by the composition for all $t{\geq}k$. This set is a subgroup of the self-homotopy equivalence group ${\varepsilon}(X)$. We find certain homotopic tools for computations of ${\varepsilon}^{\sharp}_k(X)$. Using these results, we determine ${\varepsilon}^{\sharp}_k(M(G,n))$ for $k{\geq}n$, where M(G, n) is a Moore space type of (G, n) for a finitely generated abelian group G.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• The Mathematical Education
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• v.58 no.4
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• pp.545-566
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• 2019

The purpose of this study is to show that research community activities can contribute to the professional development in respect of average concepts and mathematical creativity. In the community, activities were undertaken to transform the existing task into the task that contributes to the manifestation of creativity. In this process, researchers tried to connect the theory with the practice of the class, and the teacher acted as an active learner. The findings show that the teacher who had difficulty in teaching average could overcome difficulties, and also derived the way of task modification and strategies necessary for teaching average. The modified task induced improvements in students' achievement levels, which led to change in teachers' perspective on the relationship between mathematical creativity and learning. Research community activities have been shown to have contributed to improvements with regard to both teaching the average and promoting mathematical creativity.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.103-122
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• 2016

The purpose of this study was to analyze the sentences related with mathematical modeling in the third and fourth grade mathematics textbooks in accordance with changing of Korean mathematics curricula. In the preliminary analysis, the researchers used the criteria that Kim(2010) had analyzed Mathematics in Context[MiC], and analyzed South Korean textbooks from the perspective of mathematical modeling. The researchers revised them for the analysis criteria among South Korean elementary mathematics textbooks and employed them as the analysis framework of the present study. From the mathematical modeling perspective, the study reached the following conclusions in accordance with the change of textbooks from the 7th curriculum to the 2009 revised curriculum. The contexts of real-world situations presented in the textbooks are increased in all areas except Probability and Statistics areas, the methods of expression of mathematical model are diversified in all areas except Patterns area, and the communication types are also diversified and frequencies increased in all areas except Patterns area. Based on this research, several suggestions were made for the development of future textbooks.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.55-66
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• 1999

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, ′the process of the length of curve being equal to the sum of the vectors when intervals get smaller′ and ′the process of calculating volume of spinning curve by using definite integral.′ Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Also it can help students with solving mathematical problems intuitively. Consequently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the application of definite integral", which exists in mathematical curriculum the second and third grade of high school. When this study is used for students as assisting materials, it is expected the following educational effect. 1. Students will have precise concepts because they can understand what they learn intuitively. 2. Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 3. It is possible to change the teacher-centered instruction into the student-centered instruction. 4. Students will understand the relation between velocity and distance correctly because they can see the process of getting the length of curve by vector through the monitor. For the purpose of increasing the efficiencies and qualities of mathematics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, teachers have to use the CIA program carefully.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.519-536
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• 2018

This study is intended to develop a numeracy program for late-adult learners. For this study, firstly, characteristics of numeracy were analyzed and based on those characteristics, numeracy learning contents for late-adult learners were selected. Also, teaching and learning materials were developed by linking the mathematics contents selected to experience-based real lives of late-adult learners. When this numeracy program was applied to late-adult learners, it was observed that there was a change in the affective domain like interest at the early stage of learning and that as learning continued, mathematical elaboration occurred by way of mathematical formalization. In conclusion, this study has significance by re-defining arithmetic for late-adults from a perspective of numeracy, based on experience of late-adults, and making a contribution to mathematical elaboration of late-adult learners so non-formal problem-solving processes of lat-adult learners can be justified as elaborate mathematical problem-solving.