The reform movements of current mathematics education have based on several major ideas, in order to provide a new vision of the teaching and loaming of mathematics. Of the ideas, the motto of communication of mathematics appears to be a significant factor to change teaching practices in mathematics classroom. Through Vygotsky's sociocultural theory, the psychological background is presented for both supporting the motto and extracting important suggestions of the reform of mathematics education. The development of higher mental functions is explained by internalization, semiotic mediation, and the zone of proximal development. Above all, emphasis is put on the concepts of scaffolding and inter subjectivity related to the zone of proximal development. Seven implications are proposed by Vygotsky's sociocultural theory for the new forms of the teaching and learning of mathematics.

This article introduces a proposed lesson to help younger or lower level mathematics students conceptualize area. The objective for the proposed lesson was for the student to demonstrate an understanding of the concept of area by identifying the area, in square units, of polygons drawn on computer dot board constructed by computer software, Geometer's Sketchpad. The concept of covering is the key to develop the concept of the area. The article proceeded from rectangular figures, to right-triangular figures, to non-right triangular figures, then to polygons to find the area and develop the formula for the area of the figures. It is meaningful that this kind of materials can be developed within interactive computer environment since students feel successful in loaming and teachers use them directly in their measurement classes.

To improve the elementary student's ability to classify the data and obtain the information from the data through graphics, it is necessary to use the teaching and learning material which encourage the student to study with interest and is adjacent to the student's environment. In this thesis. several materials to satisfy the condition is proposed together with some remarks to direct the teaching. These materials is recommended to use for the maturity learning and teaching in grade 6.

The purpose of this study is to examine meaning, factors, and diagnostic method of underachievers in mathematics and to propose the idea of the individualized teaching method for underachievers. For the first purpose, previous literatures on underachievers are reviewed. For the second purpose, this study described the procedure of developing the individualized instructional program, and the method of diagnosing and prescribing errors in mathematics. In the future, individualized instructional program need to be developed based on correct diagnosis of factors effecting under achievement for the effective teaching of underachievers.

When the game is used in mathematics loaming, students take pleasure of game in themselves and communicate through interaction with other students naturally. It is important because the game is activity for intellectual growth and social development. Also students have had affirmative attitude about mathematics by Emu. The communication in mathematics loaming helps that linking informal and intuitive thinking of students with abstract and basic mathematical language and that it also helps changing from the dependent situation to teacher to the self-directive teaming of students. The purpose of this thesis is to effect on extension of mathematical communication ability to the second grade of elementary school students by applying of computational-strategy games. It has conclusion as follows. Application of computational-strategy games had effected on extension of mathematical communication ability importantly. When students have mathematical communication through computational-strategy games, at the beginning, the words which students used was long, incorrect, and unnecessary words. But at the later, students became to use clear, correct concise words as they connect their routine language with mathematical symbol. Therefore we can make sure that mathematical communication ability of the second grade students' is extended by applying of computational-strategy games.

The Assessment using the observation is one of the common ways to know what the student knows and dose not. Using the obserbational Assessment, Teachers, analyzing student's growth, provide appropriate feed-back, and so they try to record every activities. but, accumulatively recording the result of observational assessment face time·spacial limits. and it is difficult to apply in a real classroom situation. Taking these into consideration, I'd like to take a look at the idea of check-list assessment that could record data observing student and contrive a practical ways of application.

We have performed a series of tests on 3rd, and 4th graders to estimate their understandings of some mathematical concepts. We found some noticeable differences between 3rd and 4th graders on fractional concepts, logical classifications. But for spatial, sense age didn't help much. Lower graders need to work with concrete shapes to improve their spatial concepts. For the fractional concepts, they also need to deal with various problems before they move on to fractional operations. In general feed-back is important and the curriculum needs to be reconstructed to help this matter. We haven't found any significant age deceleration fur children to arrive at the abstract operating stage compared to Piagetian research.