• The Mathematical Education
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• v.44 no.2 s.109
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• pp.307-323
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• 2005

The purpose of this study was to develop a program to cultivate mathematical creativity based on open-ended problem and to investigate its effect. The major features of this innovative program are (a) breaking up fixations, (b) multiple answers, (c) various strategies, (d) problem posing, (e) exploring strategies, (f) selecting and estimating, (g) active exploration through open-ended problems. 20 units for 7th grade mathematics were developed. This study hypothesizes that experimental students may develop more divergent thinking abilities than their traditional counterparts. The participants were 7th grade students attending middle schools in Seoul. Instruments were pre and post tests to measure mainly divergent thinking skills through open-ended problems. The results indicated that the experimental students achieved better than the comparison students on overall and each component of fluency, flexibility, and originality of divergent thinking skills, when deleting the effect of covariance of the pretest. The developed program can be a useful resource for teachers to use in enhancing their students' creative thinking skills. Further this open-ended approach can be served as a model to implement in classes. This study suggests that further investigations are needed in order to examine effects on affective domains such as motivation and task perseverance which are also considered as important factors of creativity.

• Research in Mathematical Education
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• v.22 no.4
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• pp.261-282
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• 2019

The research related to testing pupils' achievement in the field of Measurement and Measure in initial teaching of geometry points to an insufficient adoption of the basic components of the length measurement concept among pupils. In order to discover the cause, we looked at the basic components on which the procedure of measuring length using a ruler is based, highlighted the possibilities of introducing the procedure in measuring length, and determined pupils' achievement during the procedure of measuring length using a ruler. The research sample consisted of 145 pupils, out of which 72 were the 2^nd grade pupils and 73 were the 4^th grade pupils. A descriptive method was applied in the research. The technique we used was testing, and for the statistical data processing we used a χ² test. The results of the research show that, when drawing a straight line of a given length using a ruler, there is no statistical difference in achievement between the 2^nd and 4^th grade pupils, nor in the pupils' knowledge regarding drawing a ruler independently, while drawing a straight line of a given length using a "broken" ruler 4^th grade pupils are statistically better. The results of the research indicate that pupils' achievement is better in doing standard tasks than in non-standard ones, given that the latter require conceptual knowledge. The components of the concept of length measurement using ruler have not been sufficiently developed yet, and these include: zero-point, partitioning a measured object in a series of consecutive measurement units and their iteration. We shed more light on the critical stage in the procedure of length measurement - the transition from non-standard to standard units and the formation of the length measurement scale. For further research, we propose to look at the formation of the concept of length measurement using the ruler through all its components and their inclusion in the mathematics curriculum, as well as examining the correlation of pupils' achievement in the procedure of measuring length with their achievement in measuring area (and volume).

• Communications of Mathematical Education
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• v.24 no.1
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• pp.123-143
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• 2010

The Skeleton Tower problem is an example of a curriculum that integrates algebra and geometry. Finding the number of the cubes in the tower can be approached in more than one way, such as counting arithmetically, drawing geometric diagrams, enumerating various possibilities or rules, or using algebraic equations, which makes the tasks accessible to students with varied prior knowledge and experience. So, it will be a good topic which can be used in the elementary grades if we exclude the method of using algebraic equations. The purpose of this paper is to propose some points which can be considered with attention by gifted children education teachers by analyzing the 4th Skeleton Tower problem solutions made by 3rd and 4th graders in their selection test who applied for the education of gifted children in math at J University for the year of 2010.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.541-563
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• 2014

The purpose of this study is to investigate how the curriculum, in which pre-service teachers experience mathematical process and develop assessment items and standards through the process experience in a mathematical essay course, affects the pre-service teachers and suggest its implications for teacher education. Fourty nine pre-service teachers, registered at a mathematical essay course in a K university in Seoul, developed mathematical essay problems and their assessment standards, and their developed processes were analyzed. According to the analysis results, first, mathematical essay problems developed by the fifty students reflect components of mathematical processes. Especially, one characteristic in revising assessment items shows that pre-service teachers considered not only justification process through different levels of difficulty and mathematical reasoning, but also logical descriptions through problem solving, when they worked on group discussions and examined middle school and high school students' responses. Second, while pre-service teachers developed rubrics for their assessment items and revised the rubrics based on students' responses, they established assessment standards which employed mathematical process by focusing on problem solving process rather than results and considering students' unexpected problem solving. The results imply a concrete method in planning and executing a mathematical essay course which makes use of mathematical process in teacher education.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.179-199
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• 2007

The purpose of this study was to discover differences between mathematically gifted students (MGS) and non-gifted students (NGS) when making probability judgments. For this purpose, the following research questions were selected: 1. How do MGS differ from NGS when making probability judgments(answer correctness, answer confidence)? 2. When tackling probability problems, what effect do differences in probability judgment factors have? To solve these research questions, this study employed a survey and interview type investigation. A probability test program was developed to investigate the first research question, and the second research question was addressed by interviews regarding the Program. Analysis of collected data revealed the following results. First, both MGS and NGS justified their answers using six probability judgment factors: mathematical knowledge, use of logical reasoning, experience, phenomenon of chance, intuition, and problem understanding ability. Second, MGS produced more correct answers than NGS, and MGS also had higher confidence that answers were right. Third, in case of MGS, mathematical knowledge and logical reasoning usage were the main factors of probability judgment, but the main factors for NGS were use of logical reasoning, phenomenon of chance and intuition. From findings the following conclusions were obtained. First, MGS employ different factors from NGS when making probability judgments. This suggests that MGS may be more intellectual than NGS, because MGS could easily adopt probability subject matter, something not learnt until later in school, into their mathematical schemata. Second, probability learning could be taught earlier than the current elementary curriculum requires. Lastly, NGS need reassurance from educators that they can understand and accumulate mathematical reasoning.

• School Mathematics
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• v.16 no.1
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• pp.19-37
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• 2014

This study investigated the degree of understanding pre-service teachers' random variable concept, based on the attention and the importance for developing pre-service teachers' ability on statistical reasoning in statistics education. To accomplish this, the subject of this study was 70 pre-service teachers belonged to three universities respectively. The teachers were given to 7 tasks on random variable and requested to solve them in 40 minutes. The tasks consisted of three contents in large; 1) one was on the definition of random variables, 2) the other was on the understanding of random variables in different/diverse conditions, and 3) another was on problem solving relevant to random variable concept. The findings are as follows. First, while 20% of pre-service teachers understood the definition of random variable correctly, most teachers could not distinguish between random variable and variable or probability. Second, there was a significant difference in understanding random variables in different/diverse conditions. Namely, the degree of understanding on the continuous random variable was superior to that of discrete random variable and also the degree of understanding on the equal distribution was superior to that of unequality distribution. Third, three types of problems relevant to random variable concept dealt with in this study were finding a sample space and an elementary event, and finding a probability value. In result, the teachers responded to the problem on finding a probability value most correctly and on the contrary to this, they had the mot difficulty in solving the problem on finding a sample space.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.107-138
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• 2022

This study is a study that developed class materials that can apply Process-Focused Assessment to classes by paying attention to feedback using teacher learning community programs centered on teachers belonging to the same school in the field. In particular, this study was conducted with the aim of developing class materials applicable to actual classes. At this time, We thought about how to provide appropriate feedback when applying course-based evaluation in school field classes. It was conducted according to the procedure of data development research by Lee & Ahn(2021). As for the procedure of data development itself, an evaluation plan was established by establishing a strategy to reconstruct achievement standards and confirm understanding based on curriculum analysis. Next, an evaluation task, a scoring standard table, and a preliminary feedback preparation table were developed. In addition, based on these development materials, a learning guidance plan that can predict scenes when applying actual classes was developed as a result. This study has value as a practical study that can contribute to providing a link between theory and field schools. It is also meaningful in that it considered how the teacher would grasp when to provide feedback in performing rocess-Focused Assessment. Likewise, in providing feedback by teachers, it is meaningful in that it reflects in the data development how to prepare in advance and take classes according to the characteristics of the subject. Finally, it seems that the possibility of field application can be improved in that the results of the 4th class developed in this study are presented in a form applicable to the class directly in the field.

• Journal of Science Education
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• v.36 no.2
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• pp.381-393
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• 2012

This study was analyzed that what kind of elements for STEAM, except scientific commonsense, are contained in 2009 revised chemistry textbooks I for high school students. So first, elements of STEAM in textbooks were examined by following three sections; by publishing company, each unit and area of textbook. For reference, new sub-elements of STEAM were set because existing elements of STEAM is incongruent with current textbooks. As a result, most chemistry textbooks included elements of STEAM properly for inter-related learning with the other fields. Every textbook had its unique learning methods for utilizing elements of STEAM and they were unified as one way. Depending on textbooks, learning methods were little bit different from the others. Also, detailed elements of STEAM contained in textbooks were classified just 14 types. And they were even focused on a few elements according to sort of textbook. Thus, it seemed that there was a certain limitation of current education of STEAM in chemistry Field. By the unit, according to the curriculum, contained elements of STEAM were different. Almost all elements of STEAM were located in I section. Consequently, it is difficult to include elements of STEAM if mathematics or history were not existed in curriculum. Lastly, by the area, most of all elements of STEAM were included in reference section. Almost all elements of STEAM were focused on art and culture. Thus, STEAM was used for utilization about chemical knowledge in substance. Otherwise, convergence training for approach method was not enough in chemical knowledge.

• Journal of the Korean earth science society
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• v.23 no.3
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• pp.207-220
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• 2002

The purpose of this study was to verify the trends of Korean students' achievement of earth science, especially the gender differences, in recent two international comparative studies, TIMSS-R (The Third International Mathematics and Science Study-Repeat) and PISA 2000 (Programme for International Student Assessment). To achieve this purpose, the 33 earth science items in TIMSS-R and 13 earth and environmental science items in PISA 2000 were analyzed. As a result of the comparison between Korean- and international percent correct, Korean students showed especially higher achievement in close-ended items or items required 'understanding of simple information.' Korean students, in particular Korean male students, also showed higher achievement in items of data interpretation. On the other hand, Korean students, in particular Korean female students, showed relatively lower achievement in astronomy items. The serious gender differences occurred in all aspects of items, regardless of item content, item format, and performance expectations.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.499-514
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• 2007

In modern mathematic education, the development of mathematical ability based on the understanding of mathematical concepts has been emphasized in curriculum and teaching methodology. Also, in schools, most math teachers stress the importance of mathematical concepts in doing math well. Thus, in this paper, we outlined the development of mathematical concepts through the literature survey. And then, based on the Sfard's definition of mathematical concepts, which classifies math concepts into the operational approach and structural approach, we analyzed the math concepts of exponential function and logarithmic function units in three highschool math textbooks. As the result, we found that the textbook authors used different approach for the same concepts, and, at the same time, they used both approaches to help develop the students' math concepts.