CGI에 기초한 유아 수세기와 연산활동의 개발 및 적용

Abstract

In this study, we developed CGI-based counting and arithmetic operation activities for young children, applied them to an early childhood class, and investigated the changes in children's mathematical thinking and exploration attitudes displayed in that process. We also examined the effects of the developed activities for children's understanding of numbers and their abilities to perform arithmetic operations. For these purposes, we selected 23 children in a 5-year old class of D kindergarten in Busan Metropolitan City and their class teacher as research participants. To develop the activities for counting and arithmetic operations, we carried out an extensive domestic and foreign literature exploration on mathematics education for young children and the CGI (Cognitively Guided Instruction). The developed activities were supplemented reflecting the parents' demands collected through the questionnaire surveys and revised through the review of early childhood education experts and field teachers. A total of 29 activities were developed, the first 14 activities for counting and the next 15 activities for arithmetic operations. All activities have the form of problem-solving within realistic contexts. To promote peer interactions in the process of problem-solving, we paired children so that two children with different ability levels belonged to one team. To investigate the changes in children's mathematical thinking and exploration attitudes, we collected qualitative data through participant observations of the researcher, interviews of children and teachers, consultation between teachers and researcher, and records of activities of children. We conducted an inductive qualitative analysis of the collected data. Also, to examine the effects of the activities on children's counting and arithmetic operation abilities, we applied One-Factor Repeated Measures ANOVA to three evaluation results taken at the beginning, in the midst, and at the end of the activities, and used Bonferroni method to perform paired comparisons between three time-points. We also divided the children into three groups, upper (30%), middle (40%) and lower (30%) level groups, according to the results of the preliminary evaluation of the children's understanding of numbers. We performed the Friedman Test to analyze the differences between the groups and used the Wilcoxon Signed Rank Test for paired time-points comparisons within each group. The results of this study are as follows. First, the developed CGI-based counting and arithmetic operation activities are aimed to form an understanding of the basic concepts of numbers of children and to enhance arithmetic operation abilities of them. The goals are to improve the understanding of numbers, the ability of counting, problem-solving strategies, and the abilities to perform arithmetic operations including addition, subtraction, multiplication, and division. To achieve these goals, we selected oral counting, object counting, addition, subtraction, multiplication, and division as the central contents of the activities. Teaching and learning methods were designed based on the following six principles: engaging children in problem-solving activities based on their understanding and interest, learning with the focus on understanding, use of manipulation tools, providing questioning-centered interactions to promote reflections, and constructing exploration community. To implement these principles, we conducted each activity in five stages: opening the mind, understanding the problem, exploring and solving problems, sharing thoughts, and looking back on ideas. Second, the changes of children's thinking in the counting activities were appeared as transitions "from counting one by one to skip counting with various units," "from monotonous counting to counting using additions," and "from counting to developing the understanding of place values." We interpreted those changes as developing from "counting based on fragmented knowledge" to "counting based on relational understanding." The changes of children's thinking in arithmetic activities were appeared as a progress from "relying on concrete objects" to "solving with knowledge of numbers and counting," "diversifying problem-solving strategies," and "having flexibility in mathematical thinking." We analyzed these changes in terms of the development of problem-solving strategies. The changes in children's exploration attitudes in counting and arithmetic activities were appeared as "deliberately and persistently working on it," "thinking and trying myself," "reaching perfect understanding through rumination," and "realizing through talking and debating with each other." Third, the effects of the developed activities on children's counting and arithmetic operation abilities were found to be significant for all levels of children. Besides, the problem-solving abilities of the children in word problems were significantly improved in all sub-categories. The children in the high-level group showed significant improvements in division operation, the middle-level group children showed significant improvements in all categories except for the mixed type, and the low-level group children showed significant improvements in all categories of word problems. In other words, the counting and arithmetic operation activities for young children based on CGI are effective in improving children's mathematical abilities and can be most useful for middle and lower level children. In conclusion, young children's counting and operation activities based on CGI can be considered effective in promoting fundamental understanding of numbers, problem-solving strategies, mathematical exploration attitudes, and abilities to perform arithmetic operations of young children. This study suggested that it is meaningful to apply CGI principles to early childhood mathematics education regarding its applicability and effectiveness. The future studies might provide more comprehensive viewpoints and insights by looking for the changes in the teachers' beliefs about teaching and learning and the children's accompanying changes in their abilities.