• Research in Mathematical Education
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• v.1 no.1
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• pp.75-85
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• 1997

One of the main objectives of school mathematics education is to develop a student' intuition and logical thinking [11]. But two -valued logical thinking, in fact, is not sufficient to express the concepts of a student's mind since intuition is fuzzy. Hence fuzzy -valued logical thinking may be a more natural way to develop a student's mathematical thinking.

• The Mathematical Education
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• v.53 no.3
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• pp.413-434
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• 2014

Logic lays the foundation of Mathematics and the development of Mathematics is dependent on critical thinking. So it is important that school mathematics helps students develop their logical and critical thinking ability for both mathematics learning and problem solving in general. MINDSTORMS, a LEGO based programming activity kit, is an effective teaching and learning tool that can be used to enhance logical and critical thinking in students. This study focused on measuring the growth of students' ability to think logically and critically when they used MINDSTORMS activities to learn programming. In addition, we investigated how the students' logical and critical thinking changed from the MINDSTORMS learning experience. The study confirmed that the programming activities using MINDSTORMS help to enhance logical and critical thinking in students. The students attitude about logical and critical thinking became more positive and the activities helped to engage students to think logically and critically. This type of programming activities should be valuable in mathematics education and it should be included in a general mathematics curriculum.

• Korean Journal of Child Studies
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• v.29 no.1
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• pp.15-32
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• 2008

The logical and mathematical thinking of 1- to 3-year-olds was studied by age groups at 6 month intervals; logical-mathematical thinking was examined by the two physical knowledge activities of cylinder rolling and making a slope. Results showed that in their early 1st year infants failed in both tasks. Infants in their late 2nd year showed understanding of 'rolling things' and 'non-rolling things' by comparing cylinders and cubes in the cylinder rolling activity and they showed 'spatial inference' by adjusting the position and direction of the cylinder so that the cylinder could roll properly and by adjusting the board on a block in the slope making activity. Three-year-old children rolled a cylinder and made a slope without difficulty.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1101-1110
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• 2008

The present paper investigates about the formation of the logical thinking and the intuitive thinking in mathematical concepts with reference to secondary talented students (students aged 16$\sim$17 years). As a main result, we conclude that their preference between the logical and the intuitive thinking does not related to the distinction of the school level and sex, while their consistence between them relates.

• Research in Mathematical Education
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• v.17 no.4
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• pp.291-307
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• 2013

Piaget's revolutionary study on the cognitive development of children has focused on the development of logic. Logical operations and a variety of classifications based on the set of accepted rules involve convergent thinking. Children and adults have logical and creative thinking which deal with a reality of thinking. This study aims to examine a cognitive structure of students, which is closely related to the Piaget's cognitive development theories of students when creative thinking. Students were given an open mathematical problem and were expected to be able to take advantage of sensitivity, fluency, flexibility, originality, and elaboration which can be seen as clearly of their structure cognitive.

• Journal of Korea Society of Industrial Information Systems
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• v.14 no.4
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• pp.198-204
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• 2009

It is one of important and interesting topics in mathematics education to study the process of the logical thinking and the intuitive thinking in mathematical problem-solving abilities from the viewpoint of mathematical thinking. The main purpose of the present paper is to investigate on this problem with reference to secondary talented students (students aged 16~17 years). In particular, we focus on the relationship between the preference of mathematical thinking and their problem-solving abilities for logical-type problems by applying logistic regression analysis.

• Journal of Fisheries and Marine Sciences Education
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• v.25 no.5
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• pp.1020-1030
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• 2013

The purpose of this study was to develop the STEAM educational program based on the computer programming. STEAM education has been recently attracted to a lot of people. We had a focus of computer science in STEM fields. We used the programming language f or learning KODU. We selected appropriate topics for STEAM education and learning programming. We developed the educational program of 30 hours about selected topics and had classes for 4th and 5th grade elementary students. In order to verify the effectiveness of the educational program, we analyzed the results of pre- and posttest about GALT(Group Assessment of Logical Thinking), TTCT(Torrance Tests of Creative Thinking), science-related affective domain, and mathematical interests and attitudes tests. In the analysis results, the education program we developed had positive impacts on creativity, logical thinking, and science-related affective domain of elementary school students.

• The Mathematical Education
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• v.48 no.2
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• pp.149-167
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• 2009

This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

• Research in Mathematical Education
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• v.23 no.1
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• pp.47-62
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• 2020

Learning through "recreational mathematics" has become a meaningful outlet to children of all ages. The Edumatrix set is a didactic tool for the development of logical and abstract reasoning among students. In this paper, we provide several illustrative exercises involving Edumatrix that teachers can utilize in their classrooms. We formulate students' expected learning outcomes by aligning each exercise to the CCSSM content standards as well as examining which Standards for Mathematical Practices (SMP) our proposed exercises promote.

• The Mathematical Education
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• v.52 no.2
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• pp.203-215
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• 2013

We explored implications of storytelling in learning and teaching mathematics and examined examples of storytelling for deep understanding of the educational meanings of storytelling and new direction of storytelling approach to mathematics teachers. Mathematics had been commonly considered as the subject irrelevant to the narrative mode of thinking and only relevant to the paradigmatic mode of thinking that has rigorous logical forms and independent from human mind. As a result, this common sense forced a transmission pedagogy of mathematics: only the teachers as owners of the objective and logical truth of mathematics could transmit mathematical truths to students. Storytelling is highlighted as an alternative to the common teaching practices of mathematics focused only on the paradigmatic mode of thinking. Although a lot of research about the educational uses of storytelling mainly focused on the development and modification of stories, we suggested that the educational interest about storytelling should move to the elements or techniques for the positive effect of storytelling.