• School Mathematics
• /
• v.17 no.2
• /
• pp.309-329
• /
• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.4
• /
• pp.655-676
• /
• 2016

The purpose of this study is to examine the effects of teaching on functional thinking, one of the algebraic thinking in sixth grade students level. For this study, we developed functional thinking based-teaching through analyzing mathematical curriculum and preceding research, which consisted of 12 classes, and we investigated the effects of teaching through quantitative and qualitative analysis. In the results of this study, functional thinking based-teaching was statistically proven to be more effective in improving algebraic reasoning skills and lower elements which is an algebraic reasoning as generalized arithmetic and functional thinking, compared to traditional textbook-centered lessons. In addition, the functional thinking based-teaching gave a positive impact on the functional thinking level. Thus functional thinking based-teaching provides guidance on the implications for teaching and learning methods and study of the functional thinking in the future, because of the significant impact on the mathematics learning in six grade students.

• Journal of Elementary Mathematics Education in Korea
• /
• v.5 no.1
• /
• pp.77-98
• /
• 2001

This study has a purpose to find out how the problem posing activity by presenting the problem situation effects to the mathematical problem solving ability. It was applied in two classes(Experimental group-35, Controlled group-37) of the fourth grade at ‘D’ Elementary school in Bang Jin Chung nam and 40 Elementary school teachers working in Dang Jin. The presenting types of problem situation are the picture type, the language type, the complex type(picture type+ language type), the free type. And then let them have the problem posing activity. Also, We applied both the teaching-teaming plan and practice question designed by ourself. The results of teaching and learning activities according to the type of problem situation presentation are as follows; We found out that the learning activity of the mathematical problem posing was helpful to the students in the development of the mathematical problem solving ability. Also, We found out that the mathematical problem posing made the students positively change their attitude and their own methods for mathematical problem solving.

• School Mathematics
• /
• v.10 no.2
• /
• pp.139-154
• /
• 2008

The primary purpose of this study was to investigate how sixth grade elementary school students react to the types of letters use, what levels of understanding letters students are in and what difficulties are in understanding letters, and to raise issues about instructional methods of algebra. A descriptive study through pencil-and- paper tests was conducted. The test instruments consisted of 18 questions with 6 types of letters use. According to the results of testing, students' types of letter use and the levels of understanding letters were classified. The conclusions from the results of this study were as follows: First, the higher the types of letters use, the more sixth grade elementary school students had low scores on the types. Therefore, teaching methodologies of letters and expressions in the classroom need to encourage for students to improve their ability of using and understanding letter. Second, approximately 40% of students were categorized in level 3. Accordingly it is necessary to have a program of teaching and learning to improve their understanding levels of letters. Third, approximately 15% of students were categorized in level 0. In order to develop understanding of letters, it is important that students use letter evaluated and letter used as an object. Fourth, students had the difficulties in understanding letters. It is informative for teachers to understand these students' difficulties and thinking processes. Finally, we must treat the different uses of letters and introduce them successively according to the student's understanding levels of letters.

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.3
• /
• pp.395-411
• /
• 2013

There are two concepts of division: measurement division and partitive or fair-sharing division. Students are expected to understand comprehensively division algorithm in both contexts. Contents of textbooks and teachers' guidebooks should be suitable for helping students develop comprehensive understanding of algorithm for whole-number division in both contexts. The results of the analysis of textbooks and teachers' guidebooks shows that they fail to connect two division contexts with division algorithm comprehensively. Their expedient and improper use of two division contexts would keep students from developing comprehensive understanding of algorithm for whole-number division. Based on the results of analysis, some ways of improving textbooks and teachers' guidebooks are suggested.

• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.1
• /
• pp.161-194
• /
• 2017

The aim of this study is to look into sub-factors of spatial sense that can be contained in spatial sense of solid figure of mathematics curriculum and offer suggestions to improve teaching spatial sense of solid figures in the future. In order to attain these purposes, this study examined the meaning and sub-factors of spatial sense and the relations between spatial sense of solid figure and sub-factors of spatial sense through a theoretical consideration regarding various studies on spatial sense. Based on such examination, this study compared and analyzed textbooks used in South Korea, Finland and the Netherlands with respect to contents of mathematics curriculum and textbooks in grades, sub-factors of spatial sense, and realistic contexts for spatial sense of solid figure. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching spatial sense of solid figures in elementary schools in Korea as follows: extending contents regarding spatial sense of solid figures in mathematics curriculum and considering continuity between grades in textbooks, emphasizing spatial orientation as well as spatial visualization, underlining not only construction with blocks but also mental activities in mental rotation and mental transformation, comparing strength and weakness of diverse plane representations of three dimensional objects, and utilizing various realistic situations and objects in space.

• Journal of Elementary Mathematics Education in Korea
• /
• v.23 no.1
• /
• pp.169-192
• /
• 2019

This study investigates how well grade 4, 5, and 6 students understand graphs before formal education is done on graphs. For this, we analyzed students' understanding of graphs by classifying them into 'reading data', 'finding relationships between data', 'interpreting data', and 'understanding situations' based on previous studies. The results show that the students have good understanding of graphs that did not have formal education. This suggests that it is necessary to consider the timing of the introduction of the graph. In addition, when we look at the percentage of correctness of each graph, it is found that the understanding of the line graph is weaker than the other graphs. The common error in most graphs was that students relied on their own subjective thoughts and experiences rather than based on the data presented.

• Journal of Educational Research in Mathematics
• /
• v.17 no.1
• /
• pp.67-90
• /
• 2007

The purpose of this study is to understand students' thinking process in the algebra problem solving, on the base of the works of Vinner(1997a, 1997b). Thus, two middle school students were evaluated in this case study to examine how they think to solve algebra word problems. The following question was considered to analyze the thinking process from the similarity-based perspective by focusing on the process of solving algebra word problems; What is the relationship between similarity and the characteristics of thinking process at the time of successful and unsuccessful problem solving? The following results were obtained by analyzing the success or failure in problem solving based on the characteristics of thinking process and similarity composition. Successful problem solving can be based on pseudo-analytical thought and analytical thought. The former is the rule applied in the process of applying closed formulas that is constructed structural similarity not related with the situations described in the text. The latter means that control and correction occurred in all stages of problem solution. The knowledge needed for solutions was applied with the formulation of open-end formulas that is constructed structural similarity in which memory and modification with the related principles or concepts. In conclusion, the student's perception on the principles involved in a solution is very important in solving algebraic word problems.

• Journal for History of Mathematics
• /
• v.20 no.1
• /
• pp.33-44
• /
• 2007

This paper examines a historical case- the French Revolution- of conceptual change in mathematics. The case that is a space of possibility gave birth to a new community of mathematical practitioners. Carnot and Monge shared the particular conceptions of the problems, aims, and methods of a field and contributed to found Ecole Polytechnique. I intend to show how Carnot's and Monge's mathematical endeavours responded to social, political and technological developments in French society.

• Journal of the Korean Chemical Society
• /
• v.61 no.6
• /
• pp.378-387
• /
• 2017

In this study, we analyzed the causes of decrease in the number of students taking Chemistry ? in the College Scholastics Ability Test (CSAT) by analyzing the adequacy of the Chemistry I question in the CSAT and the recognition survey of students and teachers about the Chemistry I choice. We analyzed some questions in Chemistry I of the CSAT from the year 2014 to 2016. The questions were analyzed to determine whether they were appropriate to the curriculum content, achievement standard, and achievement level. The target of the survey for perception was 452 senior high school students and 68 science teachers. The result of the study showed that the questions in Chemistry I are somewhat difficult compared to the depth and achievement level required by the curriculum, and it also requires mathematical thinking ability. Students recognized the mathematical thinking and complex mathematical skills are needed to solve problems in Chemistry I. Teachers also thought that the choice of Chemistry I is unfavorable in aspect of meeting the minimum academic ability standard, and accordingly, they did not actively recommend students to take Chemistry I. Moreover, most of the teachers recognized that it is necessary to improve the direction of writing questions for Chemistry I. Therefore, setting questions that can be solved using chemical knowledge, not mathematical ability need to be addressed.