• Research in Mathematical Education
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• v.9 no.2 s.22
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• pp.135-151
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• 2005

Further education for teachers is required for reforms of elementary education curricula and their career development. Principles of relevance, selectivity and hierarchy should be followed in the construction of further education curricula system for math teachers of senior high school. The following curricula should be included in the system: A. moral elevation and idea renewal curricula; B. theoretic curricula on math education; C. curricula on math education design; D. curricula on math education research; E. curricula on modern educational technology; F. curricula on knowledge renewal and extension.

• School Mathematics
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• v.12 no.2
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• pp.151-176
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• 2010

This research aims to conduct the teaching experiment based on the constructivism to elementary preservice teachers and report on how they construct and develop the mathematical knowledge on ratio concept. Furthermore, this research aims to examine the significances and difficulties of "constructivist teaching experiment" which are conceived by elementary preservice teachers. As the results of this research, I identified the possibilities and limits of mathematical knowledge construction by elementary preservice teachers in the "constructivist teaching experiment". And the elementary preservice teachers pointed out the significances of "constructivist teaching experiment" such as the experience of prior thinking on the concept to be learned, the deep understanding on the concept, the active participation to the lesson, and the experience of learning process of elementary students. Also they pointed out the difficulties of "constructivist teaching experiment" such as the consumption of much time to carry out the constructivist teaching, the absence of direct feedbacks by teacher, and the adaption on the constructivist lesson.

• The Mathematical Education
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• v.42 no.5
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• pp.607-622
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• 2003

The research was aimed at finding the dynamic aspects of the linguistic and social interaction with mathematical concept development using a graphing calculator in collaborative learning. This study was broadly divided into two categories: "Knowledge Construction Statement" for understanding how the verbal interaction works when a graphing calculator is used, and "Teacher's Instructional Role" for the research on the reaction of the students and on the teacher's role as a guide in helping students to construct their knowledge. This research used a case study in a collaborative learning environment. An attempt was made to show clearly how the students interacted with one another in a technology environment using a graphing calculator as a tool. A graphing calculator promoted the students' linguistic interaction and changed the characteristics of the linguistic interaction. Although it didn't show the different aspects completely, some changes of the linguistic traits were perceived.aits were perceived.

• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.125-136
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• 2008

There are different perspectives on a function graph. For instance, a parabola is defined by movement of a ball in physics and by quadratic function in mathematics. This study deals with the turtle motion, which is local and intrinsic, and the construction of function graphs with mathematical experiments in a microworld. This paper concerns with a function graph which is in the curriculum or in the history of mathematics. In view of pre-calculus, we introduce activities of mathematization about formalizing of length and area of function graphs without knowledge of calculus.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.299-312
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• 1998

In this study, we have investigated the meaning and mechanism of the 'construction' in the operational constructivism and the social constructivism. According to Piaget, a mathematical concept is the operational sch me, which is constructed through the reflective abstraction from a general coordination of activities and operations. The process of the reflective abstraction consists of 'reflechissement'and 'reflexion'. The reflechissement starting from 'intriorisation' concludes with 'thematisation', and the reflexion consists in the 'equilibration' of the result of reflechissement. The 'construction' in the social constructivism includes two process. One is the process from the individual, subjective knowledge of mathematics to the social, objective knowledge of mathematics, and the other is vice versa. The emphases is placed on the 'social interaction' and the 'representation' in this two processes. In this context, if we want to apply the social constructivism, we should clarify the meaning of 'society', and consider the difference between the society of mathematicians and the society of students.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• Journal of Korean Elementary Science Education
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• v.24 no.5
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• pp.558-570
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• 2005

The importance of teaching the nature of science (NOS) has been always emphasized in science education. However, the NOS is hardly taught in elementary science class. We are lacking in the strategies and materials for teaching NOS. So we designed the science drama teaching, and investigated the effects on pupils' perceptions about NOS. The subjects of this study were 185 third graders from a elementary school. The treatment group was provided with science drama lessons and the control group was provided with traditional lecture-type lessons. Their perceptions about NOS were investigated before/after the science lessons and after 3 months following them, and both of two groups were compared. The pretest results revealed that the pupils of both groups were found to have similar views on NOS. Dey had traditional views of the most items except for social construction of theories, mathematical knowledge and decision-making. After science lessons, they tended to change their views toward modem views, but the pupils of the treatment group showed more modem views than those of the control group on the observation, model, social construction of theories, predictions. After 3 months, the pupils of the control group tended to come back to their traditional views, but those of the treatment group showed tendencies that their changed views were kept up on the observation, scientific model, scientific knowledge, scientific methods, decision-making, social construction of theories, mathematical knowledge. Therefore this study suggests that science drama teaching could be one of the effective ways for teaching NOS.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.23-42
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• 2007

Learners who have taken learner-centered instruction is expected to construct conceptually mathematical knowledge which is. If so, they can have some ability to solve problems they are confronted with in the first time. To know this, First graders who have been in learner-centered instruction during 1 school year was given 7+52+186 which usually appears in the national curriculum for 3rd grade. According to the results, most of them have constructed the logic necessary to solve the given problem to them, and actually solve it. From this, it can be concluded that first, even though learners are 1st graders they can construct mathematical knowledge abstractly, second, they can apply it to the new problem, and third consequently they can got a good score in a achievement test.

• East Asian mathematical journal
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• v.36 no.2
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• pp.229-251
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• 2020

Problem Based learning(PBL) is a teaching and learning method to increase mathematical ability and help achieving mathematical concepts and principles through problem solving using the learner's mathematical prerequisite knowledge. In addition, the recent instructional situations or environments have focused on the learner's self construction of his learning and its process. In spite of such a quite attention, it is not easy to apply and execute PBL program actually in class. Especially, there are some difficulties in actually applying and practicing PBL in the areas of mathematics education in not only secondary school but also in college. Its reason is that in order to conduct PBL instruction constantly in real or experimental class there is no more concrete and detailed instructional content during the consistent and long period. However, to whom is related to mathematics education including instructors called scaffolders, investigation and recognition on the degree of the learner's acquisition of mathematical thinking skills and strategies is an very important work. By the reason, in this study, the instructional content was to be explored and developed to be conducted during 15 weeks in one semester, which was based on Problem Based Learning environment by the subject of the theories relevant to mathematics education in the college of education.