• School Mathematics
• /
• v.18 no.2
• /
• pp.257-275
• /
• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.14 no.2
• /
• pp.119-126
• /
• 1996

TM projection is widely used for surveying and mapping. However, the complicated computations and process are required and, moreover. the different results of computation may occur according to different formulae and coefficients. In this study, the transformation formulae are classified into 4 categories and the computations are executed according to the categories. The computations are also made to different value of the circular constant, $\pi$. The result of test shows that the enough number of items in formular have to be used for precise computation and the circular constant has to calculate down the 13 places of decimals in order to obtain the precision of 1mm on the ground scale.

• KIISE Transactions on Computing Practices
• /
• v.22 no.11
• /
• pp.559-566
• /
• 2016

Excel is a commercially available computer program that is used worldwide. Excel is widely utilized; it is helpful in household ledgers, corporate tax calculations, management of academic grades or reports, etc. However from the beginning, inaccuracies and errors in calculations have constantly been identified, so the program is updated regularly. Decimal-to-binary conversion is a simple and repetitive task. So, use of a computer program to do this calculation is suitable. Errors in decimal-to-binary conversion are surprising and are not easily understood. Therefore, it is important to identify the flaws in Excel, which unfortunately still exist today. It is necessary to determine the cause of this type of error, and I hope for a fix to be implemented quickly.

• School Mathematics
• /
• v.4 no.4
• /
• pp.643-655
• /
• 2002

In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

• School Mathematics
• /
• v.14 no.1
• /
• pp.45-64
• /
• 2012

The purpose of the present study was to investigate middle grades (Grade 5-7) mathematics teachers' knowledge of partitive fraction division. The data were derived from a part of 40-hour professional development course on fractions, decimals, and proportions with 13 in-service teachers. In this study, I attempted to develop a model of teachers' way of knowing partitive fraction division in terms of two knowledge components: knowledge of units and partitioning operations. As a result, teachers' capacities to deal with a sharing division problem situation where the dividend and the divisor were relatively prime differed with regard to the two components. Teachers who reasoned with only two levels of units were limited in that the two-level structure they used did not show how much of one unit one person would get whereas teachers with three levels of units indicated more flexibilities in solving processes.

• School Mathematics
• /
• v.19 no.1
• /
• pp.209-228
• /
• 2017

Understanding decimal numbers is important in mathematics as well as real-life contexts. However, lots of students focus on procedures or algorithms of decimal numbers without understanding its meanings. This study analyzed teaching method related to decimal numbers in a series of mathematics textbooks of Korea, Japan, Singapore and the US. The results showed that three countries except Japan introduced the decimal numbers as another name of fraction, which highlights the relation between the concept of decimal numbers and fractions. And limited meanings of decimal numbers were shown such as 'equal parts of a whole' and 'measurement'. Especially in the korean textbooks, relationships between the decimals were dealt instrumentally and small number of models such as number lines or $10{\times}10$ grids were used repeatedly. Based these results, this study provides implications on what and how to deal with decimal numbers in teaching and learning decimal numbers with textbooks.

• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.263-279
• /
• 2015

The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.

• The Mathematical Education
• /
• v.59 no.3
• /
• pp.217-235
• /
• 2020

This study examined Korean fourth-grade students' performance by gender on the Trends in International Mathematics and Science Study(TIMSS) 2011 and 2015 mathematics assessment. We first identified items which had significantly higher mean scores by gender to decide which gender did better on a certain domain(domain-level analysis). Then, we examined the content of items(item-level analysis) to understand which items lead to gender differences in mathematics achievement. Our findings showed that about 80% of the items on both assessments did not show statistically significant differences between males and females. However, there were meaningful gender differences in the other 20% items. On both assessments, females had more items with significantly higher mean scores than males on the Shapes domain, and males had more those items on the Numbers and Measurement domains and all cognitive domains(Knowing, Applying, and Reasoning). In particular, females outperformed males on items related to identifying two- and three-dimensional shapes and drawing lines and angles and identifying them. Conversely, males had higher performance than females on items related to the pre-algebraic thinking, fractions and decimals, estimation of number differences, unit of length, and measuring time, height, and volume. The effect sizes for each item ranged from .12 to .33 and the mean effect size of all items across both assessments was .20, which indicated significant gender differences but small.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.12
• /
• pp.1079-1085
• /
• 2012

For precise motion control, S-curve velocity profile is generally used but it has disadvantage of relatively long calculation time for floating-point arithmetics. In this paper, we present a new generating method for velocity profile to reduce delay time of profile generation so that it overcomes such disadvantage and enhances the efficiency of precise motion control. In this approach, the velocity profile is designed based on the gamma correction expression that is generally used in image processing to obtain a smoother movement without any critical jerk. The proposed velocity profile is designed to support both T-curve and S-curve velocity profile. It can generate precise profile by adding an offset to the velocity profile with decimals under floating point that are not counted during gamma correction arithmetic operation. As a result, the operation time is saved and the efficiency is improved. The proposed method is compared with the existing method that generates velocity profile using ring buffer on a 8-bit low-cost MCU. The result shows that the proposed method has no delay in generating driving profile with good accuracy of each cycle velocity. The significance of the proposed method lies in reduction of the operation time without degrading the motion accuracy. Generated driving signal also shows to verify effectiveness of the proposed method.

• Journal of the Korean School Mathematics Society
• /
• v.18 no.4
• /
• pp.353-370
• /
• 2015

This study was conducted as a qualitative case study that explored how gifted 3rd-grade elementary school children who had learned the primary concepts of division and fraction, when they studied contents about decimal, formed the transformed primary concept and transformed schema of decimal by the learning of accurate primary concepts and connecting the concepts. That is, this study investigated how the subjects attained relational understanding of decimal based on the primary concepts of division and fraction, and how they formed a transformed primary concept based on the primary concept of decimal and carried out vertical mathematizing. According to the findings of this study, transformed primary concepts formed through the learning of accurate primary concepts, and schemas and transformed schemas built through the connection of the concepts played as crucial factors for the children's relational understanding of decimal and their vertical mathematizing.