• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.83-103
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• 2014

The purpose of this paper is to find a method of measuring mathematical creativity reasonably. In the pursuit of this purpose, we designed four multiple solution tasks that consist of two kinds of open tasks; 'tasks with open solutions' and 'tasks with open answers'. We collected data by conducting an interview with a gifted fifth grade student using the four multiple solution tasks we designed and analyzed mathematical creativity of the student using Leikin's model(2009). Research results show that the mathematical creativity scores of two students who suggest the same solutions in a different order may vary. The more solutions a student suggests, the better score he/she gets. And fluency has a stronger influence on mathematical creativity than flexibility or originality of an idea. Leikin's model does not consider the usefulness nor the elaboration of an idea. Leikin's model is very dependent on the tasks and the mathematical creativity score also varies with each marker.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.505-530
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• 2017

Although mathematically gifted students have potential and creative productivity, they might not manifest group level creative synergy. To manifest group creativity among them, the manifestation process should be facilitated and the process losses should be minimized. The purpose of this study is looking for the method to facilitate the manifestation process of group creativity and minimize the process losses of it. To do this, a case study method was adopted. The products and process losses of the manifestation process of group creativity was analysed. In conclusion, the processes and products of group creativity were concretized and the process losses were analysed by social/motivational and cognitive factors. In addition, the justification and agreement were necessary for the manifestation process of group creativity among mathematically gifted students.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.331-368
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• 2018

This study is derived from a student who can add without knowing the addition principle. To understand where the student's response come from, we came to analyse the curriculum contents of natural numbers, decimals and fractions addition principle. At the same time, we surveyed two different school of forty six sixth grade participants with questionnaires to determine whether it is a problem of the student or an universal one. As a result, we found that there is a room for improvement in the addition and connections of addition. We propose appropriate instructional method regarding connections of addition and addition principle of natural numbers, decimals and fractions. The conclude there is a close relation and differences among the principles of natural numbers, decimals and fractions in the proposed instructional method. Therefore, we need to consider and instruct the differences of the number expansion.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.369-384
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• 2018

Multiplication is able to be described by using repeated addition, a Cartesian product, a scalar operation, rectangular array and area in many various context. Multiplication in various problem situations is learned by various of the teaching method and the order of teaching more than any other mathematical concepts and operations in elementary school. Nevertheless, the context of multiplication leaves further room for improvement. The purpose of this study is to examine the similarities and differences between the conceptual aspects of multiplication through the literature and to analyze the appropriateness of the teaching method and the order of teaching through textbook analysis. As a result of the study, it was found that multiplication of a scalar operation was introduced too early and did not properly reflect of meaning of multiplication as a scalar operation. There is also a need to use the concept of the rectangular array or area as a meaning of multiplication two quantities.

• The Mathematical Education
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• v.60 no.3
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• pp.321-340
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• 2021

As many changes in the future society represented by the age of artificial intelligence(AI) are expected to come, efforts are being made to draw the shape of the future education and various research methods are being employed to support the attempts. While many research studies use methods for deriving generalized results such as expert survey and trend analysis in along with a review of literature, there are attempts to apply the scenario methodology to explore ideas and information needed within a changing context. A scenario method, one of the experiential learning strategies, aims to seek various and alternative approaches by establishing a plan from the present conditions considering future changes. In this study, in-service teachers' perceptions and expectations of the interactivity between human and AI teachers were visualized by applying the role-play presentation technique that grafted the concept of role-play game to the scenario method. In addition, the mandal-art method was introduced to support in conducting productive discussion during the teachers' collaboration. This method appeared to help to depict teachers' perceptions of AI teachers in the detailed and concrete form, which may flow in the abstract otherwise. Through analyses of the teachers' role-play presentations with the implementation of the madal-art method it was suggested that most teachers would want to collaborate with an AI teacher for improved instruction and individualized student learning while they would take the instructional authority over the AI teacher in the classroom.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.59-81
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• 2021

This study aimed to investigate how the learners' mathematics learning processes change with repeatedly reading mathematical text. As a way to teach and learn mathematics, we also wanted to examine the effect of repeated reading and to explore the implications for a more efficient teaching and learning strategy. To help us with this study, we mainly used eye tracking and heart rate (HR) measurement. There were four cycles in a cycle of repeated reading, and the number of repeated readings for all cycles was fixed to three times. Eight prospective mathematics teachers in the Department of Mathematics Education of a National University in South Korea participated. Data were analyzed in five aspects: (1) the total reading time per round, the total reading time per slide; (2) the change trends of total reading time per round and slide; (3) the order of slides read; (4) the change trends of HR per round. We found that most participants read in a similar pattern in the first reading, but the second and third reading patterns appeared more diverse for each learner. Also, the first reading required the most time regardless of the repeat cycle, and the time it took to repeatedly read afterward varied depending on the individual. Based on the findings of this study, the most primary conclusion is that self-directed mathematics learning by using repeated reading is effective regardless of cycle. In addition, we suggested four strategies to improve the efficiency of this teaching and learning method.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.509-522
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• 2009

This study aims to identify the effects of math education for the aged as part of active measures to the aging society with its growing elderly population which is one of the greatest changes in our society. Developing and disseminating materials of silver math with a role as a program for intelligent needs and physical and spiritual health of the aged presents evidence for development of more systemic and scientific method at this point of time when the importance of education of the aged increases to help the old enjoy qualitatively successful lives in later years in the perspective of lifelong education. The effectiveness of 'Silver Math' are explored by applying developed materials to the aged. Also, the influence of mathematical activities of learners capable of computing basic numbers on improvement of cognitive power are identified. Finally, the impact of 'Silver Math' on interaction with younger generations or communications is raised and the influence on brain activities is analyzed through examination of brain waves.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.21-45
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• 2011

It is the aim of this paper to find the requisites for the target problem solving process in reference to the base problem and to search the roles of those. Focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process, we tried to find the roles of them. We observed closely how four students solve the target problem in reference to the base problem. And so we got the following conclusions. The insight of structural similarity prepare the ground appling the solving method of base problem in the process solving the target problem. And we knew that the analytic activity can become the instrument which find out the truth about the guess. Finally the comparative activity can set up the direction of solution of the target problem. Thus we knew that the insight of structural similarity, the analytic activity and the comparative activity are necessary for similar mathematical problem to solve. We think that it requires the efforts to develop the various programs about teaching-learning method focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process. And we also think that it needs the study to research the roles of other elements for similar mathematical problem solving but to find the roles of the structural similarity, analytic activity and comparative activity.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.315-318
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• 2006

In this paper we present the simple updating formulas for a sum of product and a sum of cross product when a new value is added on or a specific value is eliminated from the original data. The sample variance and correlation for the new data set are derived by new computing formulas. Any statistic which is a function of the sum of product and a sum of cross product also can be updated by proposed method even though the original data is not available.