• Communications of Mathematical Education
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• v.25 no.4
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• pp.693-734
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• 2011

The purpose of this research is to analyze the pedagogical content knowledge on the natural number concepts of Korean Elementary School Teachers. Shulman(1986b) had developed a tool in order to understand teachers' knowledge, as he defined three types of knowledge in teaching ; Subject Matter Knowledge, Curricular Knowledge, and Pedagogical Content Knowledge. Pang(2002) defined two types of elements including in the ways of teaching ; individual element, and sociocultural element. Two research questions are addressed; (1) What is the pedagogical content knowledge of Natural number Concepts for Korean Elementary School Teachers? ; (2) What factors are included in the pedagogical content knowledge of Natural number Concepts for Korean Elementary School Teachers? Findings reveal that (1) the Korean Elementary School Teachers had three types of the pedagogical content knowledge on the natural number concepts; (2) Teacher Factors were more included than Social-Cultural Factors in the pedagogical content knowledge on the natural number concepts of the Korean Elementary School Teachers. Further suggestions were made for future researches to include (1) a comparative study on teachers between ordinary teachers and those who majored mathematics education in the graduate school. (2) an analysis on the classroom activities about the natural number concepts.

• The Mathematical Education
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• v.42 no.1
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• pp.19-39
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• 2003

The purpose of this study is to find out effective ways to take care of the 8th and 10th graders' disposition causing math. disliking. To accomplish this goal, we proceeded as follows : First we categorized the 11 factors recognized as the reasons of math. disliking into 4 math. disliking causes such as psychological f: environmental cause, conceptual cause, relational cause and application related cause. Second, to take care of these tow causes, we developed materials which are closely related with the contents of the 8th and 10th graders' school mathematics. Third with these materials we taught the students who had proved to have the math. disliking trend, for one semester. As a consequence of this experiment we arrived at the following results. As for psychological & environmental causes, 35.7% of the 8th graders and 17% of the 10th graders proved to have been improved significantly. This result shows that the curing of the psychological & environmental causes is more effective in the 8th graders than in the 10th graders. i.e., the curing effects of the students' psychological & environmental cause for disliking math. decline as they get older. As for conceptual causes, 35% of the 5th graders and 30% of the 10th graders proved to have been improved significantly. In case of the 8th graders this ratio was similar to that of the other causes. But as for the 10th graders this ratio was a little low compared with that of the case of relation causes and application related causes. As for relational causes, 35% of the 5th graders and 49% of the 10th graders proved to have been improved significantly. Especially the 10th graders improved greatly. Among the four factors that compose this cause, especially hierarchy and connection factors were effectively cured. On application related causes, 47% of the 5th graders and 57% of the 10th graders proved to have been cured significantly. And among the four types of causes listed above, this was the most successfully cured one. Of the two factors of this cause, the basic application factor appeared to have been improved in all experimental groups. In connection with teaching methods, we found out the followings two facts. First, the more teachers push students to solve their tasks with their own efforts, the higher is the ratio of owe. Second, the more teachers teach students personally, the more effective are the teaching results.

• Journal of The Korean Association For Science Education
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• v.27 no.4
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• pp.346-353
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• 2007

In order to be efficient in teaching, a teacher should understand the current learner's level through diagnostic evaluation. This study has examined the major issues arising from the noble diagnostic assessment tool based on the theory of knowledge space. The knowledge state analysis method is actualizing the theory of knowledge space for practical use. The knowledge state analysis method is very advantageous when a certain group or individual student's knowledge structure is analyzed especially for strong hierarchical subjects such as mathematics, physics, chemistry, etc. Students' knowledge state helps design an efficient teaching plan by referring their hierarchical knowledge structure. The knowledge state analysis method can be enhanced by computer due to fast data processing. In addition, each student's knowledge can be improved effectively through individualistic feedback depending on individualized knowledge structure. In this study, we have developed a diagnostic assessment test for measuring student's learning outcome which is unattainable from the conventional examination. The diagnostic assessment test was administered to middle school students and analyzed by the knowledge state analysis method. The analyzed results show that students' knowledge structure after learning found to be more structured and well-defined than the knowledge structure before the learning.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.305-322
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• 2010

The epistemological obstacles in the area learning of plane figure can be categorized into two types that is closely related to an attribute of measurement and is strongly connected with unit square. First, reasons for the obstacle related to an attribute of measurement are that 'area' is in conflict. with 'length' and the definition of 'plane figure' is not accordance with that of 'measurement'. Second, the causes of epistemological obstacles related to unit square are that unit square is not a basic unit to students and students have little understanding of the conception of the two dimensions. Thus, To overcome the obstacle related to an attribute of measurement, students must be able to distinguish between 'area' and 'length' through a variety of measurement activities. And, the definition of area needs to be redefined with the conception of measurement. Also, the textbook should make it possible to help students to induce the formula with the conception of 'array' and facilitate the application of formula in an integrated way. Meanwhile, To overcome obstacles related to unit square, authentic subject matter of real life and the various shapes of area need to be introduced in order for students to practice sufficient activities of each measure stage. Furthermore, teachers should seek for the pedagogical ways such as concrete manipulable activities to help them to grasp the continuous feature of the conception of area. Finally, it must be study on epistemological obstacles for good understanding. As present the cause and the teaching implication of epistemological obstacles through the research of epistemological obstacles, it must be solved.

• School Mathematics
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• v.19 no.1
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• pp.137-151
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• 2017

This study aims to investigate the possibility of elementary students' generalization from three-digit numbers to multi-digit numbers in principles for addition and subtraction. One of main changes was the reduction of range of numbers for addition and subtraction from four-digit to three-digit. It was hypothesized that the students could generalize the principles of addition and subtraction after learning the three-digit addition and subtraction. To achieve the purpose of this study, we selected two groups as a sampling. One is called 'group 2015' who learned four-digit addition and subtraction and the other is called 'group 2016' who learned addition and subtraction only to three-digit. Because of the particularity of these subjects, this study covered two years 2015~2016. We applied our addition and subtraction test which contains ten three-digit or four-digit addition and subtraction items, respectively. We collected their results of the test and analyzed their differences using t-test. The results showed statistically meaningful difference between the mean score of the two groups only for four-digit subtraction. Based on the result, we discussed and made some didactical suggestions for teaching multi-digit addition and subtraction.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.21-45
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• 2011

It is the aim of this paper to find the requisites for the target problem solving process in reference to the base problem and to search the roles of those. Focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process, we tried to find the roles of them. We observed closely how four students solve the target problem in reference to the base problem. And so we got the following conclusions. The insight of structural similarity prepare the ground appling the solving method of base problem in the process solving the target problem. And we knew that the analytic activity can become the instrument which find out the truth about the guess. Finally the comparative activity can set up the direction of solution of the target problem. Thus we knew that the insight of structural similarity, the analytic activity and the comparative activity are necessary for similar mathematical problem to solve. We think that it requires the efforts to develop the various programs about teaching-learning method focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process. And we also think that it needs the study to research the roles of other elements for similar mathematical problem solving but to find the roles of the structural similarity, analytic activity and comparative activity.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.357-377
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• 2014

The purpose of this study is to identify whether math class with clip-type contents has a significant impacts on the academic achievement and attitude of students. To answer the questions, two classes of 4th graders at Sinlim Elementary School in Gwanak-gu, Seoul were selected as subjects; they were divided into experimental group and comparative group. They were confirmed as a homogeneous group at the significance level of 0.05 during a pre-test. The findings are as follows. First, math class with clip-type contents had positive influence on the academic achievement. Second, math class with clip-type contents had positive influence on the attitude towards learning. Furthermore, proper clip-type contents for class boost their understanding and enhance their mathematical thinking with multiple views. It led to their self-confidence in learning math, developing a positive attitude towards math. The benefits of the present research can be summarized as follows. First, the math class with clip-type contents benefited both teachers and students. For teachers, it helped them boost the quality of their teaching. For students, it helped them understand the class better, improving their academic achievement. Second, the diverse, interesting contents had a positive impact on the following of the students: self-concept of math; attitude towards math; learning habits.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.423-442
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• 2011

The purpose of this study was to examine the effects of tasks setting for mathematical modelling in the complex real situations. The tasks setting(MMa, MeA) in mathematical modelling was so important that we can't ignore its effects to develop meaning and integrate mathematical ideas. The experimental setting were two groups ($N_1=103$, $N_2=103$) at public high school and non-experimental setting was one group($N_3=103$). In mathematical achievement, we found meaningful improvement for MeA group on modelling tasks, but no meaningful effect on information processing tasks. The statistical method used was ACONOVA analysis. Beside their achievement, we were much concerned about their modelling approach that TSG21 had suggested in Category "Educational & cognitive Midelling". Subjects who involved in experimental works showed very interesting approach as Exploration, analysis in some situation ${\Rightarrow}$ Math. questions ${\Rightarrow}$ Setting models ${\Rightarrow}$ Problem solution ${\Rightarrow}$ Extension, generalization, but MeA group spent a lot of time on step: Exploration, analysis and MMa group on step, Setting models. Both groups integrated actively many heuristics that schoenfeld defined. Specially, Drawing and Modified Simple Strategy were the most powerful on approach step 1,2,3. It was very encouraging that those experimental setting was improved positively more than the non-experimental setting on mathematical belief and interest. In our school system, teaching math. modelling could be a answer about what kind of educational action or environment we should provide for them. That is, mathematical learning.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• Journal of the Korean School Mathematics Society
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• v.17 no.3
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• pp.359-384
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• 2014

The purpose of this study is inquire the reaction and adaptability of the mathematically gifted student, in the case of introduce learning materials based on GeoGebra in real class. The study program using GeoGebra consist of 'construction of fundamental figures', 'making animation with using slider tools' (graph of a function, trace of a figure, definite integral, fixed point, and draw a parametric curve), make up the group report after class. In detail, 1st to 15th classes are mainly problem-solving, and topic-exploring classes. To analyze the application effects of developed learning materials, divide students in four groups and lead them to make out their own creative products. In detail, guide students to make out their own report about mathematical themes that based on given learning materials. Concretely, build up the program to make up group report about their own topics in six weeks, after learning on various topics. Expert panel concluded that developed learning materials are successfully stimulate student's creativity in various way, after analyze of the student's activities. Moreover, those learning programs also contributed to the develop of the mathematical ability to thinking that necessary to writing a report. As well, four creative products are assessed as connote mathematically gifted student's creative thinking and meaningful elements in mathematical aspects.