• Journal of Gifted/Talented Education
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• v.20 no.1
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• pp.31-59
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• 2010

Previous studies reported that gifted students' capacity on mathematics had high correlations with results of the performance assessment. However, there have been few studies that develop recommending tools through the assessment that can be used to identify mathematically gifted students or analyse their applications. Then it is difficult to use them to identify mathematically gifted students practically. Therefore, this study developed the tasks and evaluation tables for the tools. And one of them was applied for four students in Grade 1 of a middle school to simulate the assessment and characteristics assessment teachers showed were analysed. As the results, the extensive and specific information on the giftedness of the students was obtained through using the tool. The gifted capacity grasped from the order, speed, and attitudes of problem-solving was identified as observing the process of solving the task.

• The Mathematical Education
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• v.40 no.2
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• pp.253-263
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• 2001

Developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recent performance based on assessment has focused on the teaching and learning environment in school, emphasizing student's self construction of their learning and its process. Because of this reason, people related to mathematics education including math teachers are taught to recognize the fact that the degree of students'acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) should be estimated formally in math class. However, due to the lack of an evaluation tool for estimating the degree of their thinking skills, efforts at evaluating student's degree of mathematics thinking skills and strategy acquisition failed. Therefore, in this paper, mathematical thinking was studied, and using the results of study as the fundamental basis, mathematical thinking process model was developed according to three types of mathematical thinking - fundamental thinking skill, developing thinking skill, and advanced thinking strategies. Finally, based on the model, evaluation factors related to essential thinking skills such as analogy, deductive thinking, generalization, creative thinking requested in the situation of solving mathematical problems were developed.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.299-316
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• 2023

With the importance and necessity of using AI in the field of education, this study aims to explore elementary school teachers' perceptions of using Artificial Intelligence (AI) in mathematics education. For this purpose, we conducted a survey using a 5-point Likert scale with 161 elementary school teachers and analyzed their perceptions of mathematics education with AI via four categories (i.e., Attitude of using AI, AI for teaching mathematics, AI for learning mathematics, and AI for assessing mathematics performance). As a result, elementary school teachers displayed positive perceptions of the usefulness of AI applications to teaching, learning, and assessment of mathematics. Specifically, they strongly agreed that AI could assist personalized teaching and learning, supplement prerequisite learning, and analyze the results of assessment. They also agreed that AI in mathematics education would not replace the teacher's role. The results of this study also showed that the teachers exhibited diverse perceptions ranging from negative to neutral to positive. The teachers reported that they were less confident and prepared to teach mathematics using AI, with significant differences in their perceptions depending on whether they enacted mathematics lessons with AI or received professional training courses related to AI. We discuss the implications for the role of teachers and pedagogical supports to effectively utilize AI in mathematics education.

• The Mathematical Education
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• v.47 no.1
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• pp.27-47
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• 2008

In this paper, we study the effect of writing activity as mathematical communication on the students's mathematics achievement, learning attitude, and mathematical tendency. For this purpose, we construct a experimental class and then analyze the students' change in those aspects after applying three-divided-note writing activity and colleague feedback on their works those students are in the experimental class. As a result of the experiment, we find that three-divided-note writing activity and colleague feedback made some significant changes on the students achievement in mathematics, learning attitude, but does not affect on mathematical tendency. We also offer some suggestions for further research. Firstly, the mathematical communication ability must be stressed in mathematics education. For this purpose, we need to develop the teaching and the evaluation method to use not only writing but also reading, speaking, and listening skills so that many teachers can apply this method easily to their classes. Second, we need to fix some realistic problems such as fair evaluation , the numbers of students per class, the numbers of lesson, and too much extra-work, and so on. Thirdly, we suggest to explore some methods for extending three- divided-note writing activity to evaluate mathematical essay and to study educational effects of colleague feedback on mathematics performance assessment.

• Research in Mathematical Education
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• v.14 no.2
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• pp.173-194
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• 2010

This study examines the differences and similarities of mathematics teachers' subject matter knowledge among England, the Chinese mainland and Hong Kong. Data were collected from a ten-item test in the SKIMA subject matter audit instrument [Rowland, T.; Martyn, S.; Barber, P. & Heal, C. (2000). Primary teacher trainees' mathematics subject knowledge and classroom performance. In: T. Rowland & C. Morgan (eds.), Research in Mathematics Education, Volume 2 (pp.3-18). ME 2000e.03066] from over 500 participants. Results showed that participants from England performed consistently better, with those from Hong Kong being next and then followed by those from the Chinese mainland. The qualitative data revealed that participants from Hong Kong and the Chinese mainland were fluent in applying routines to solve problems, but had some difficulties in offering explanations or justifications.

• Education of Primary School Mathematics
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• v.6 no.1
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• pp.11-28
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• 2002

The purposes of this study were to analyze elementary school mathematics textbooks developed in accordance with the 7th national amended curriculum and to find implications for the development of a new revised curriculum to meet the needs of the knowledge-based society. Elementary school mathematics textbooks and accompanying practice books were analyzed. Teacher's manuals were also studied to examine the intentions of the textbook developers. The two major questions were sought. First, to what degree do elementary school mathematics textbooks and practice books match with the intentions of the national curriculum\ulcorner Second, how do elementary school mathematics textbooks and practice books facilitate student's learning for understanding mathematics\ulcorner The findings were as follows. First textbooks, practice books, and teacher's manuals appeared not to reflect the intentions of the 7th amended curriculum to the full extent. Second, characteristics and roles of textbooks, practice books, and teacher's manuals were not clearly defined and therefore, they were not very feasible for teaming for understanding mathematics. The recommendations for a new revised curriculum were suggested. First, regarding the contents presented in the textbooks, the idea of structure of subject matter need to be considered in order to help students to understand connections of concepts and relationships between concepts and functions in mathematics. Second, more ill defined problems should be presented to develop problem solving ability in real life contexts in students. Third, contents for relearning and enrichment need to be reorganized to reflect students' real ability. Fourth, uses of the concrete and the manipulative need to be more realistically suggested. Fifth, more prototypes of performance assessment tasks, scoring rubrics, and portfolios need to be presented in a more teacher-friendly manner. Sixth, characteristics and roles of textbooks and practice books need to be more discernible.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.1-22
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• 2010

The purpose of this study was to examine the relationship between teacher's role and interaction patterns in mathematics classrooms. Teacher's role was divided into usual practices with students, usual practices with content and usual practices with students and contents, and interaction patterns were classified into report, inquiry and discussion. The subjects in this study were teachers and students in three fourth- grade classes in T elementary school located in Seoul. After the classes of every math teacher were observed, three teachers who played distinctively unique roles were selected in accordance with the results of the first-semester autonomous supervision, of open class for parents and of the instructional observation. Thus, there was a close relationship between the teacher roles and interaction patterns. And it's concluded that students are able to have a more discussion on each other's ideas in the student-centered classroom, and that teachers should perform active roles in that process. Given the findings of the study, there are some suggestions: First, the teachers appeared to fulfill consistent roles when their videotaped classes, study aids and performance assessment materials were analyzed, and they should play more active roles in mathematics class. Second, they should try to create the kinds of climate that encourages students to come up with ideas in an active manner. Third, earlier studies had focused on student-teacher interaction patterns, but this study found that the roles of the teachers depended on interaction with not only students but study aids and performance assessment materials, and that the interaction patterns hinged on their roles as well. Therefore more profound research efforts should be directed into this issue.

• 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.

• The Mathematical Education
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• v.39 no.2
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• pp.81-99
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• 2000

The Purpose of this study is to develop and implement an alternative secondary mathematics curriculum to enhance creative problem-solving abilities. The curriculum consisting of three main elements-content knowledge, process knowledge and creative thinking sills-as developed. Lessons were taught by a problem-based-learning method in an experimental group. In order to examine the effect of the curriculum, performance assessment was developed and used for pre and post.. There were significant group differences in the creative problem-solving abilities, so we could examine the effect of developed program and confirm the group differences in the attitude for lessons. But there were no significant group differences in motive for learning, a study skill and the achievement test.

• School Mathematics
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• v.3 no.2
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• pp.373-399
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• 2001

The function is a basic and key concept to understand mathematical problems. However, many students have difficulties to expand the knowledge to other related concepts and to transfer the knowledge to real world problems. The reasons for the problem may be that the concept of function is taught by simplified and abstracted formula without fully understanding of the reasoning process. Also, the examples for the concepts are artificial and not related to students' experiences. Situated learning theory provides great implications to solve these problems. So, this study was designed to teach the concept of function more meaningful to students by appling situated learning theory. Thirty-eight middle school students were participated in this study. Students were provided the instruction designed according to the principles of situated learning theory. Then, they were asked to complete attitude survey questionnair and a performance assessment task. The result showed that the instruction based on situated learning theory was useful to Promote students' understanding and motivation for learning. More implications of the study was provided in the paper.