• School Mathematics
• /
• v.11 no.3
• /
• pp.351-368
• /
• 2009

This study presents data from a year-long teaching experiment which illustrate how two seventh graders modified their multiplicative thinking and interacted with their representing symbols in the context of combinatorial problem situations. Damon was at the process of construction of recursively multiplicative thinking by modifying his multiplicative reasoning, but Carol appeared to remain at the stage of a binary multiplicative scheme. The two students' struggles with their representing symbols or represented symbols by the teacher show that even well-organized symbolic systems from teachers' perspective do not necessarily help students advance their mathematical capacity.

• Research in Mathematical Education
• /
• v.18 no.4
• /
• pp.273-288
• /
• 2014

In recent years, coding education has been globally emphasized and the Free Semester System will be executed to the public schools in Korea from 2016. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this research aims to design 'learning environment' in which learners can design and construct mathematical objects through computers and print them out through 3D printers. Furthermore, it will design learning mathematics by constructing the figurate number patterns from 'soma cubes' in the playing context and connecting those to algebraic and combinatorial patterns, which will allow students to experience mathematical connectivity. It is expected that the activities of designing figurate number patterns suggested in this research will not only strengthen CT capacity in relation to mathematical thinking but also serve as a meaningful program for the Free Semester System in terms of career experience as 3D printers can be widely used.

• Journal of The Korean Association For Science Education
• /
• v.29 no.4
• /
• pp.437-449
• /
• 2009

The purpose of the study is to meta-analyze research results on Korean students' logical thinking ability. The results of meta-analysis on the research studies between the year 1980 and the year 2000 show that about 40-50% of Korean middle school students have conservation reasoning, proportional reasoning and combinatorial reasoning abilities, and that about 25-30% of them have control of variables and probability reasoning abilities. In addition, only 8% of the Korean middle-school students have correlational ability. When comparing their logical thinking ability results with those of Japanese and American middle-school students, The ratio (32.6%) of Korean middle-school students who have formal thought ability is a little higher than that of American students (30.6%), but much lower than that of Japanese students (50.1%).

• Journal of The Korean Association of Information Education
• /
• v.14 no.4
• /
• pp.555-560
• /
• 2010

The purpose of this study is to investigate the effect of learning algorithm which uses real-life examples including the concept of algorithm on the logical thinking of elementary school students. For this purpose, the experiment was performed by pre-GALT test, a case selection of algorithm which can be taught in real-life, experiment treatment after completing teaching plan, post-GALT test, and paired sample t-test on the results of pre and post GALT in order. As a result, changes in the degree of logical thinking ability and in five sub-regions(conservative logic, proportional logic, combinatorial logic, probabilistic logic, controlling variables) composing of logical thinking obtained statistically significant results in .05 significance level but changes in the correlational logic couldn't obtain the significant results.

• Journal of Educational Research in Mathematics
• /
• v.26 no.4
• /
• pp.635-662
• /
• 2016

Combinatorics, the basis of probabilistic thinking, is an important area of mathematics and closely linked with other subjects such as informatics and STEAM areas. But combinatorics is one of the most difficult units in school mathematics for leaning and teaching. This study, using the designed combinatorial models and executable expression, aims to analyzes the eye movement of graduate students when they translate the written combinatorial problems to the corresponding executable expression, and examines not only the understanding process of the written combinatorial sentences but also the degree of difficulties depending on the combinatorial semantic structures. The result of the study shows that there are two types of solving process the participants take when they solve the problems : one is to choose the right executable expression by comparing the sentence and the executable expression frequently. The other approach is to find the corresponding executable expression after they derive the suitable mental model by translating the combinatorial sentence. We found the cognitive processing patterns of the participants how they pay attention to words and numbers related to the essential informations hidden in the sentence. Also we found that the student's eyes rest upon the essential combinatorial sentences and executable expressions longer and they perform the complicated cognitive handling process such as comparing the written sentence with executable expressions when they try the problems whose meaning structure is rarely used in the school mathematics. The data of eye movement provide meaningful information for analyzing the cognitive process related to the solving process of the participants.

• Journal of The Korean Association of Information Education
• /
• v.16 no.4
• /
• pp.463-474
• /
• 2012

The necessity of computer science education has been increased in the society which has been changing rapidly by the development of information science. But most elementary school teachers don't realize its necessity and don't recognize the notion of computational thinking which is the fundamental principle of computer science. In this research, we designed and implemented an algorithm learning program based on computational thinking with using Logo, which was for pre-service elementary school teachers to be able to realize the necessity of computer science education and recognize computational thinking. As the findings analyzed between pre- and post-test, the averages of correlational reasoning, combinatorial reasoning and the sum of overall logical thinking increased significantly. Also, participants' awareness of computer science education and computational thinking changed positively.

• The Journal of Korean Association of Computer Education
• /
• v.13 no.2
• /
• pp.1-14
• /
• 2010

Previous researches on the improvement of logical thinking in Informatics subject have used general logical thinking test and only limited improvement of logical thinking by programming learning result. In this study, the operational definition of the logical thinking in problem-solving process on Informatics education is different from the general logical thinking and the logical thinking of the other subjects. Firstly, we suggested the operational definition of components of logical thinking using the open questionnaire by expert and research team discussion. Also, we suggested the relationship between the operational definition and contents of the 'problem-solving methods and procedure' section in secondary Informatics subject. Finally, this study developed the evaluation contents based on the operational definition of components of logical thinking. The components of logical thinking which was required in problem-solving process on Informatics subject were ordering reasoning, propositional logic, controlling variables, combinatorial logic, proportional reasoning. We suggested the relationship between operational definition and problem-solving process and assessment of logical thinking in problem-solving process on Informatics subject. This paper will give meaningful insight to supply the guideline of the teaching strategy and evaluation methods for improving the logical thinking in Informatics education.

• Research in Mathematical Education
• /
• v.16 no.1
• /
• pp.79-90
• /
• 2012

This research investigated if the embodied symbol using a turtle metaphor in a microworld environment works as a cognitive tool to mediate the learning of combinatorics. It was found that students were able to not only count the number of cases systematically by using the embodied symbols in a situated problem regarding Permutation and Combination, but also find the rules and infer a concept of Combination through the activities manipulating the symbols. Therefore, we concluded that the embodied symbol, as a bridge that connects learners' concrete experiences with abstract mathematical concepts, can be applied to introduction of various mathematical concepts as well as a combinatorics concept.

• Journal of the Korean School Mathematics Society
• /
• v.5 no.1
• /
• pp.13-19
• /
• 2002

In this experiment we emphasized the cooperative small group learning and the members of my group worked together to succeed and communicate their mathematics ideas freely. The researcher(teacher) became an observer and facilitator of small group interaction, paying attention to the ongoing learning process, Sometimes the researcher suggested some investigation approach(or discovery)being written by computer software or papers. In this experiment we provided 6 activities as follows : (1) changing the conditions in given problem. (2) operating the meaningful heuristics with the problem sets. (3) creating the problem situations related to understanding (4) creating the Modeling situations. (5) creating the problem related to combinatorial thinking in real world. (6) posing some real problem from real world. we could observed several conjectures First, Attitude and chility to interpret the problem setting is highly important to pose the problem effectively. Second, Generating the understanding can be a great tool to pose the problem effectively. Third, Sometimes inquiry approach represented by software or programmed book could be some motivation to enhance the posing activities. Forth, The various posing activities relate to one concept could give the students some opportunity to be adaptable and flexible in the their approach to unfamiliar problem sets.

• Journal of The Korean Association For Science Education
• /
• v.14 no.3
• /
• pp.312-320
• /
• 1994

The purpose of this study is to analyze the relationship of logical thinking skills and integrated process skills, and to investigate the differences in general tendency of subskills by grade level and gender between Korean middle school students and Japanese one. The performance level of skills was measured using GALT and TIPS II. The results are compared with those of Japan (Mattheis et al., 1992). Summary of the results are as follow. 1. Percentages of formal and transitional stage of males are more than females in developmental level. It has been found out that the males attained significantly higher scores of logical thinking skills than the females in middle school stage. The significant differences in scores by gender show a good correlation with those for Japanese middle school students. Developmental level of Korean middle school students shows a remarkable improvement as they move up from 8th grade to 9 one. The significant differences in developmental level by grade also show a good correlation with those for Japanese middle school students. Total scores of GALT for Japanese middle school students are higher than Korean one, but it has been found nearly same scores for 9th grade in both countries. Scores of subskills of logical thinking skills, except correlational reasoning, for Korean students show lower than those for Japanese students. It could be noted that the combinatorial reasoning is considered to be easiest and the correlational reasoning to be most difficult in both countries. 2. It also has been found out similar pattern for integrated process skills in both countries because the males and females did not examplify significant differences, although males gain somewhat higher scores than females in Korea. Scores of subskills of integrated process skills for Japanese middle school students show higher them Korean one. It could be noted that the identifying variables is considered to be easiest and stating hypothesis to be most difficult in both countries. 3. There was a significant relationship (r= .65) between logical thinking skills and integrated process skills, and there were statistically significant differences of the integrated process skills for developmental level. In integrated process skills, the students who belong to the higher grade levels acquired better score than who belong to the lower grade level. It has been also found remarkable improvement between 8th and 9th grade, and there are significant differences for grade level in both countries.