• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.429-451
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• 2012

This paper examined eight novice elementary teachers' knowledge in terms of the types and sources of students' errors and teaching strategies on plane figures through a questionnaire and teachers' discussion. The teachers tended to predict students' diverse error types, but they attributed the sources of such errors mainly to their characteristics. The analysis of teachers' responses of teaching strategies revealed that they recognized the importance of the teacher's clear explanation and students' own problem-solving, while they were somewhat negative in presenting diverse examples and classifying, drawing, or constructing figures. Building on these results, this paper provides the implications for novice teachers' professional development programs.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.141-159
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• 2011

The purpose of the present research is to suggest implications on guidance of height concept understanding of figures by investigating concept understanding how sixth grade's elementary school students understand a height concept of figures. In order to achieve this research purpose, a height concept understanding test of figures was carried out with the target of 54 sixth grade students who already learned a height concept of plane figures and three-dimensional solid figures and thus this research analyzed characteristics and errors appeared there. When analyzing its characteristics and errors interviews with students were carried out for in-depth analysis. And as a result the following implications could be obtained. First, students felt more difficulty in measuring height in a figure that its lower base is not horizontal in questions measuring height of a plane figure. Second, there were cases that students associate a height concept of figures with experience of height experienced in daily life. Third, students were feeling difficulty in linguistically expressing a concept called height that oneself has. Expressing a concept linguistically plays an important role in understanding a concept clearly. Accordingly activities for raising this mathematical communication ability are required, Fourth, the present research can suggest implications in designing classes that students can clearly understand the height concept of figures.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

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