• Journal of Elementary Mathematics Education in Korea
• /
• v.15 no.3
• /
• pp.619-640
• /
• 2011

The study aims the introducing the items for the assessment of mathematical thinking including mathematical reasoning, problem solving, and communication and the analyzing on the responses of the 5th grade pupils. We categorized the area of mathematical reasoning into deductive reasoning, inductive reasoning, and analogy; problem solving into external problem solving and internal one; and communication into speaking, reading, writing, and listening. And we proposed the examples of our items for each area and the 5th grade pupils' responses. When we assess on pupil's mathematical reasoning, we need to develop very appropriate items needing the very ability of each kind of mathematical reasoning. When pupils solve items requesting communication, the impact of the form of each communication seem to be smaller than that of the mathematical situation or sturucture of the item. We suggested that we need to continue the studies on mathematical assessment and on the constitution and utilization of cognitive areas, and we also need to in-service teacher education on the development of mathematical assessments, based on this study.

• Communications of Mathematical Education
• /
• v.24 no.1
• /
• pp.159-175
• /
• 2010

In this paper we make a new problem solving model using the principle of the lever. Using the model we solved many word problems related with consistency. We suggest new problem solving method using the lever model and describe some characteristics of the method.

• School Mathematics
• /
• v.6 no.2
• /
• pp.135-151
• /
• 2004

This study investigated children's realistic response on problematic word problems focused on number operations. Even though word problems and problem solving should be considered in terms of realistic context, results indicates that children's responses didn't show realistic consideration in solving problems. Also, children showed their tendency of mindless or mechanical operation in solving problems and modeling problems

• Communications of Mathematical Education
• /
• v.19 no.2 s.22
• /
• pp.327-344
• /
• 2005

솔리테르(solitaire) 중 간단한 게임인 자리바꾸기 문제에 대해 학습자로 하여금 다양한 해결방법을 산출 하도록 한 후, 그 과정에서 학생들의 수학적 창의성의 발현 과정을 추적해 본다. 제시한 문제 해결 과제에 대한 학습자들의 반응과 해답을 분석함으로써 수학적 창의성에서의 인지적 구성요소인 확산성, 유창성, 논리성, 유연성, 독창성과 정의적 구성요소에 해당하는 적극성, 독자성, 집중성, 정밀성 등이 어떻게 나타나고 있는가를 살펴본다. 또한 그렇게 함으로써 각 구성요소의 의미와 특성을 규명하고자 하며, 나아가 이들 구성요소를 판별할 수 있는 방안에 대한 기초 자료를 제공하고자 한다.

• Education of Primary School Mathematics
• /
• v.24 no.4
• /
• pp.175-187
• /
• 2021

The purpose of this study is to investigate the effects of solving multi-strategic mathematics problems on mathematical creativity and attitudes of the 6th grade students. For this study, the researchers conducted a survey of forty nine (26 students in experimental group and 23 students in comparative group) 6th graders of S elementary school in Seoul with 19 lessons. The experimental group solved the multi-strategic mathematics problems after learning mathematics through mathematical strategies, whereas the group of comparative students were taught general mathematics problem solving. The researchers conducted pre- and post- isomorphic mathematical creativity and mathematical attitudes of students. They examined the t-test between the pre- and post- scores of sub-elements of fluency, flexibility and creativity and attitudes of the students by the i-STATistics. The researchers obtained the following conclusions. First, solving multi-strategic mathematics problems has a positive impact on mathematical creativity of the students. After learning solving the multi-strategic mathematics problems, the scores of mathematical creativity of the 6th grade elementary students were increased. Second, learning solving the multi-strategy mathematics problems impact the interest, value, will and efficacy factors in the mathematical attitudes of the students. However, no significant effect was found in the areas of desire for recognition and motivation. The researchers suggested that, by expanding the academic year and the number of people in the study, it is necessary to verify how mathematics learning through multi-strategic mathematics problem-solving affects mathematical creativity and mathematical attitudes, and to verify the effectiveness through long-term research, including qualitative research methods such as in-depth interviews and observations of students' solving problems.

• School Mathematics
• /
• v.8 no.4
• /
• pp.379-396
• /
• 2006

The purpose of this study is to analyze characteristics of problem solving in mathematics for gifted students through case study on solving the mathematical problem for gifted students, and to investigate what are relationships with the cognitive and affective characteristics. To this end, this study was to analyze the characteristics on the problem solving in mathematics by using qualitative research method after it selected two students who had specific education for brilliant students. As a result, this study has shown that it had high preference for question with clear answer, high preference for individual inquiry learning, high adhesion to answer for question, and high adhesion for assignment on characteristics of process of problem solving, but there was much difference in spirit of competition. As to the characteristics of thoughts in problem solving, this study has shown that it had high grasp capacity, intuitive insight, and capacity for visualization, but there were differences in capacity for generalization and adaptability. However, both two students had low values in deductive thought. In addition, as to the home environment and cognitive and affective characteristics, they were not related to the characteristics on problem solving directly, but it has shown that it affected each other indirectly. As to the conclusion of this study, this researcher thinks that it will be valuable documentation in order to improve curriculum, development of textbooks, and teaching method for special education for the gifted students and education for secondary mathematics.

• Journal of Elementary Mathematics Education in Korea
• /
• v.7 no.1
• /
• pp.23-44
• /
• 2003

The purpose of the study is to examine the phenomenon presented the process of problem solving activities of students with the mathematical context information accompanied problem based on Freudenthal's mathematizing theory and Realistic Mathematics Educations about cognitive and emotional aspects. In conclusion, taking a look at the results of study, open-ended contextual problem was had to offer in order to pull out various solutions. Teachers should help students develop their own methods, discuss their methods with others' and reinvent formal mathematics and its constructive process under the guidance of the teachers.

• Journal of the Korean School Mathematics Society
• /
• v.13 no.4
• /
• pp.655-678
• /
• 2010

In the elementary mathematics, geometric education emphasize spatial sense and understandings of figures through development of intuitions in space. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and methods in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. First, we investigate visualization methods for plane problem solving and space problem solving respectively, and analyse in diagram form how progress understanding of figures and visualization process. Next, we derive constituent factor on visualization process, and make a check errors which represented by difficulties in visualization process. Through these analysis, this paper aims at deriving an influence of visualization on geometric problem solving in the elementary mathematics.

• School Mathematics
• /
• v.11 no.4
• /
• pp.665-683
• /
• 2009

The purpose of this study is to improve forward mathematics study by analyzing the effects of the teaching and learning process applied situation-based mathematical problem posing activity on problem solving ability and mathematical attitudes. For this purpose, the research questions were established as follows: 1. How the situation-based mathematical problem posing activity(WQA activity) changes the problem solving ability of students? 2. How the situation-based mathematical problem posing activity(WQA activity) changes the mathematical attitudes of students? The results of the study were as follows: (1) There was significant difference between experimental group and comparative group in problem solving ability. This means that situation-based mathematical problem posing activity was generally more effective in improving problem solving ability than general classroom-based instruction. (2) There was not significant difference between experimental group and comparative group in mathematical attitudes. But the experimental group's average scores of mathematical attitudes except mathematical confidence was higher than comparative group's ones. And there was significant difference in the mathematical adaptability. The results obtained in this study suggest that the situation-based mathematical problem posing activity can be used to improve the students' problem solving ability and mathematical attitudes

• Education of Primary School Mathematics
• /
• v.16 no.3
• /
• pp.285-301
• /
• 2013

The purpose of the study is to analyze the 4th graders' visual representation in mathematics problem solving process and to find out how to teach the visual representation in mathematics problem solving process. on the basis of the results, this study gives several pedagogical implication related to the mathematics problem solving. The following were the conclusions drawn from the results obtained in this study. First, The achievement level of students and using visual representation in the mathematics problem solving are closely connected. High achieving students used visual representation in the mathematics problem solving process more frequently. Second, high achieving students realize the usefulness of visual representation in the mathematics problem solving process and use visual representation to solve mathematical problem. But low achieving students have no conception that visual representation is one of the method to solve mathematical problem. Third, students tend to especially focus on 'setting up an equation' when they solve a mathematical problem. Because they mostly experienced mathematical problems presented by the type of 'word problem-equation-answer'. Fourth even through students tried visual representation to solve a mathematical problem, they could not solve the problem successfully in numerous instances. Because students who face a difficulty in solving a problem try to construct perfect drawing immediately. But generating visual representation 2)to represent mathematical problem cannot be constructed at one swoop.