• School Mathematics
• /
• v.5 no.4
• /
• pp.401-420
• /
• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• School Mathematics
• /
• v.10 no.4
• /
• pp.625-648
• /
• 2008

We collected the data through the following process. 36 third-grade middle school students are selected, and we conducted ex-ante interviews for researching how they understand the nature of proof. Based on the results of survey, then we chose two students we took a lesson with the Branford's among the 36 samples. After sampling, historic-genetic geometry education, inspected carefully whether the Branford's method helps the students.

• School Mathematics
• /
• v.5 no.4
• /
• pp.555-572
• /
• 2003

In this study we analyze critically the educational studies on the history of mathematics, and the results of the questionnaires to the mathematics teachers and mathematics teacher educators and interviews with them in order to highlight the problems which ought to be settled for more efficient using the history of mathematics in the mathematics classes. We ought to deepen the understanding of the meaning of mathematical concepts and its essential viewpoints through the historical development of mathematics, going beyond the interest and motivation of learning mathematics. In this respect there are insufficient sides in the results of the educational studies in the history of mathematics and in the recognition of the mathematics teachers about using history of mathematics. And the teachings of the history of mathematics in the mathematics teachers education courses are not sufficient in that they just survey the history of mathematics, and it is the very important task to develop the historic-genetic materials in the school mathematics and study the historic-genetic approach to the mathematics texts.

• Management Science and Financial Engineering
• /
• v.20 no.1
• /
• pp.1-9
• /
• 2014

In multi-objective scheduling problems, the objectives are usually in conflict. To obtain a satisfactory compromise and resolve the issue of NP-hardness, most existing works have suggested employing meta-heuristic methods, such as genetic algorithms. In this research, we propose a novel data-driven approach for generating a single solution that compromises multiple rules pursuing different objectives. The proposed method uses a data mining technique, namely, random forests, in order to extract the logics of several historic schedules and aggregate those. Since it involves learning predictive models, future schedules with the same previous objectives can be easily and quickly obtained by applying new production data into the models. The proposed approach is illustrated with a simulation study, where it appears to successfully produce a new solution showing balanced scheduling performances.

• Journal of Educational Research in Mathematics
• /
• v.13 no.1
• /
• pp.25-55
• /
• 2003

In the school mathematics, the negative numbers have been instructed by means of intuitive models(concrete situation models, number line model, colour counter model), inductive-extrapolation approach, and the formal approach using the inverse operation relations. These instructions on the negative numbers have caused students to have the difficulty in understanding especially why the rules of signs hold. It is due to the fact that those models are complicated, inconsistent, and incomplete. So, students usually should memorize the sign rules. In this study we studied on the didactical phenomenology of the negative numbers as a foundational study for the improvement of teaching negative numbers. First, we analysed the formal nature of the negative numbers and the cognitive obstructions which have showed up in the historic-genetic process of them. Second, we investigated what the middle school students know about the negative numbers and their operations, which they have learned according to the current national curriculum. The results showed that the degree they understand the reasons why the sign rules hold was low Third, we instructed the middle school students about the negative number and its operations using the formal approach as Freudenthal suggest ed. And we investigated whether students understand the formal approach or not. And we analysed the validity of the new teaching method of the negative numbers. The results showed that students didn't understand the formal approach well. And finally we discussed the directions for improving the instruction of the negative numbers on the ground of these didactical phenomenological analysis.

• Journal of Korean Society of Transportation
• /
• v.32 no.5
• /
• pp.522-530
• /
• 2014

Spatio-temporal congestion evolution pattern can be reproduced using the VDS(Vehicle Detection System) historic speed dataset in the TMC(Traffic Management Center)s. Such dataset provides a pool of spatio-temporally experienced traffic conditions. Traffic flow pattern is known as spatio-temporally recurred, and even non-recurrent congestion caused by incidents has patterns according to the incident conditions. These imply that the information should be useful for traffic prediction and traffic management. Traffic flow predictions are generally performed using black-box approaches such as neural network, genetic algorithm, and etc. Black-box approaches are not designed to provide an explanation of their modeling and reasoning process and not to estimate the benefits and the risks of the implementation of such a solution. TMCs are reluctant to employ the black-box approaches even though there are numerous valuable articles. This research proposes a more readily understandable and intuitively appealing data-driven approach and developes an algorithm for identifying congestion patterns for recurrent and non-recurrent congestion management and information provision.