• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.465-486
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• 2010

Studying the definition and building a foundation about variables during elementary school is a crucial factor before students study the variable in depth in middle school. So, forming a basis for understanding variable in this period should be treated with importance, because it is the first step in forming a clear understanding of the concept of variables. According to analysis of the types of letters used in current textbooks, we can see that too much emphasis was placed on type 1(letter evaluated), type 3(letter used as an Object). By not utilizing the various types of letter usage we reduce the situation to one which is removed from the context and an automatous style of learning. Therefore, the purpose of this study was the development about early algebra learning materials which use diverse types of letters. We have analyzed the types of letters used from the 4-ga to 6-na mathematics textbooks and the 4-ga to the 6-na workbooks. To make learning materials for well-balanced letter use, we developed learning materials focused on early algebra with the 6-ga and the 6-na textbooks.

• Communications of Mathematical Education
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• v.20 no.2 s.26
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• pp.147-177
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• 2006

The 7th curriculum sets a basic direction based on learner centered teaching, with the aim of allowing students to develop their mathematical ability. Teachers' manuals are provided to help teachers fallow the basic direction and achieve the curriculum aims, but in practice they are not always helpful. Therefore, we reconstructed parts of a teachers' manual. This involved analyzing the contents of units 6, 7 and 8 of the elementary mathematics textbook 4 na to identify and outline the problems; introducing more detailed teaching methods and activities; and developing teaching learning materials. We tested the new version in several real classes and analysed the responses 6f teachers and students to examine the possibility of its practical use. The results suggest that the reconstructed version of the teachers' manual for units 6, 7 and 8 of textbook 4 na is of greater practical utility.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.543-567
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• 2008

The current 2007 Mathematics Curriculum in Korea emphasizes mathematical problem solving, advanced mathematical thinking and effective mathematical communicating. Therefore, in order to assess and evaluate these important thinking attributes, performance evaluation using descriptive and essay type of assessments are emphasized. In this paper, analysis of the elementary mathematics curriculum is used to develop descriptive assessment problems and grading rubrics that could be used objectively and consistently by teachers of the grade 6 school mathematics. The assessment problems were developed, pilot tested, revised, implemented and analyzed in detail to understand the overall effectiveness of the descriptive evaluation method in school mathematics.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.335-352
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• 2008

The purpose of this research was to investigate the descriptive evaluation method that focuses on the problem solving process of the student. The goal was to evaluate the students' understanding of the subject rather than the students' ability to find the final answer. The descriptive evaluation is being suggested as a way of examining the thought process of the student by performing a structured analysis of the problem solving process. Today, there are not enough descriptive evaluation resources available for teachers to effectively carry out this alternative assessment method in the elementary school mathematics curriculum. This research is a case study on the development of resources for descriptive evaluation in grade 4 mathematics. We designed the development process for descriptive evaluation and its rubric for all 8 units of the 4-Na level of mathematics in the elementary school curriculum. Three descriptive problems were developed for each of the 8 units for a total of 24 problems. The rubric consisted of three areas of assessment, 1) understanding of the problem, 2) problem solving, and 3) mathematical communication. The problems were first pilot tested in two 4th grade classes. Modified problems were then tested in a different 4th grade classroom. The study showed that the three defined areas of evaluation framework (problem understanding, problem solving and mathematical communication) were measurable and analyzable using the developed grading rubric. We then conclude that he descriptive evaluation could be used as an effective tool for improving teacher performance in elementary school mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.1-15
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• 2009

This research is to provide a useful reference for the future revision of textbook by comparative analysis with the textbook in the 4th grade of elementary school in Japan. The results from this research is same as follows: First, Korean curriculum is emphasizing the reasonable problem-solving ability developed on the base of the mathematical knowledge and skill. Meantime, Japanese puts much value on the is focusing on discretion and the capability in life so that they emphasize each person's learning and raising the power of self-learning and thinking. The ratio on mathematics in both company are high, but Japanese ensures much more hours than Korean. Second, the chapter of Korean textbook is composed of 8 units and the title of the chapter is shown as key word, then the next objects are describes as 'Shall we do$\sim$' type. Hence, the chapter composition of Japanese textbook is different among the chapter and the title of the chapter is described as 'Let's do$\sim$'. Moreover, Korean textbook is arranged focusing on present study, however Japanese is composed with each independent segments in the present study subject to the study contents. Third, Japanese makes students understand the decimal as the extension of the decimal system with measuring unit($\ell$, km, kg) then, learn the operation by algorithm. In Korea, students learn fraction earlier than decimal, but, in Japan students learn decimal earlier than fraction. For the diagram, in Korea, making angle with vertex and side comes after the concept of angle, vertex and side is explained. Hence, in Japan, they show side and vertex to present angle.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.