In this paper, possibility of practical use of cryptarithmetic problems in teaching and learning of mathematics is discussed. There might be seven cases to use them practically like followings: (1) Cryptarithmetic problems might be used for deepening the mathematical knowledges. (2) Cryptarithmetic problems might be used for fostering mathematical thinking abilities. (3) Cryptarithmetic problems might be used for fostering problem solving abilities. (4) Cryptarithmetic problems might be used as open ended problems. (5) Cryptarithmetic problems might be used as materials for personalized learning. (6) Cryptarithmetic problems might be used as materials for cooperative learning. (7) Cryptarithmetic problems might be used as materials for problems posing.

This study aims to develop performance assessment tools for mathematics in the primary school. In order to achieve this aim, it reviews the tics in the primary school. In order to achieve this aim, it reviews the meaning and the purpose of mathematics performance assessment, and the characteristics of performance assessment tasks. Then the framework for portfolio developed in this study is introduced. This portfolio is called 'mathematical thinking and applying'. It aims at balanced assessment for improvement of mathematics instruction. It is composed of journal writhing, problem by the student, constructed task, work samples, written test, self assessment, teacher's comment and parents' comment. The criteria of performance tasks is categorized in impact, reasoning, accuracy and communication. The procedures of development of these tasks are as follows: the analysis of mathematics curriculum for the primary school, the design of performance tasks with considering teaching unit goals, designing rubrics, discussing these tasks with teachers in primary school, modifying them when is needed, observing the process of children's task performing, interviewing with teachers and final modifying. After performance assessment tasks are implemented, the answers by the students is analyzed using rubrics. Then anchor papers are selected. Also, the errors of children are analyzed. Through the process, teachers can obtain the information of children for improvement of mathematics instruction. Finally in order to generalize this study, I suggest that we need to cooperate with the field of education and to establish expert assessment groups.

The purpose of the study is to introduce how elementary mathematics pre-sevice teachers in pre-service teacher program could use and integrate poster, a kind of instructional media, to connect mathematics knowledge to real worlds. Poster examples include such as connection to mathematicians and mathematical connections to real world as well as nature. Further, future study will continue to foster students and teachers to try to construct their alive mathematics knowledge.

In this study, we tried to suggest a meaningful teaching method that is a mathematical thinking-oriented. After referring to the recent trend of mathematics education, we examined the direction that school mathematics should go. Next, we considered previous studies that deals with teaching methods focusing on the mathematical thinking. On the basis of the above examination, we accomplished case studies that aims at mathematical thinking-oriented teaching. And we explained that these case studies reflects the key points didactics of mathematics such as the education of ‘open mathematics’, constructivism etc. Finally, we proposed the necessity of mathematical thinking-oriented teaching in the current state of school mathematics.

This study amis to develop an instrument to measure the behavior characteristics of the mathematically gifted children. The checklist represents 6 factors of characteristics - aptitude, attitude, inclination, general metal ability, creative ability and reflective ability in mathematics - which are from 36 items by factor analysis.

It has been said that concrete materials are useful and necessary when children learn mathematics. But it has been proved by several researches teachers don’t often use them even if they agree that they are useful. This article focuses on the lack of systematic and applicable research on manipulatives. Therefore, it tries to identify the state of current research and to present the concrete domains which need more study in the future, in order to induce both qualitative and quantitative research. The following nine domains cover almost all the research on manipulatives so far affect of manipulatives on achievement. types of learners, mathematical topics, subjects of operation, variety of mainipulatives, instructional method, degree of involvement of mainpulatives in class, selection criteria, and place for use.

As a result of carrying out t-test against the learning activity that used the learning materials designed by level, significant disparity was found. Thus, it was found that hte effect of this learning activity became more visible with lapse of time. But the major cause by which there appeared small significant disparity as a result of testing is that the units of experiment were limited and that the period of using the learning materials was not long. In an analysis on the results of interest test, the experimental class also appeared to show the average score that was higher than that of the comparative class by 0.10 after converting a decimal point. The outcome of attitude test was that the experimental class showed a higher average score by 0.11, as a result of converting a decimal point, than that of the comparative class. So, a large number of students showed an improved reaction. But, there seemed some problems of the learning materials or the method of progressing the activity in changing under achievement students or students who avoided studying math. When the effect of the level-based learning activity was investigated, more than 80% of the experimental class’s students showed a positive reaction. Thus, it could be judged that students, who felt some burden at studying math, might be served more largely, not by teacher’s uniform instruction, but by an individual learning using the level-based learning materials that enabled them to do a systematic self-learning for themselves.

With the increased use of computational technology, many educators question about spending large amount of class time for dealing with computational algorithms in elementary school math classroom at the expense of more holistic aspects of mathematics such as number sense, spatial sense, problem solving and data management. This paper introduce the new method for learning addition and subtraction so called ‘Mrs. Weill’s Hill’, which is believed as a suitable remedial method for children with mathematical learning disabilities, with perceptual problems, or with limited working memory capacities. This method provides children with external memory strategies by allowing them to solve the addition and subtraction problems in a stage by stage fashion with as many steps as they require. It also gives the child greater flexibility in the solution process and thus helps reduce anxiety.

The purpose of this paper is to study the present situation of the performance assessment having been introduced for recent years as a new system to measure students' mathematical power as well as their achievement in mathematics by analyzing math teachers' recognition about the assessment. The specific research questions are as follows: (1) what is the difficulty in the administrative process of the assessment\ulcorner (2) what is mathematics teachers' recognition about the assessment with respect to its nature and purpose\ulcorner (3) what is the situation of the in-service program for the newly introduced assessment\ulcorner (4) what is the administrative procedure of the assessement\ulcorner (5) what is mathematics teachers' recognition about the effectiveness of the assessemtn\ulcorner (6) What support is requried to improve the assessemt?