• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.93-113
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• 2017

This research analyzed the cases of math competencies-oriented assessment, integrating assessment and instruction, which had been conducted in an elementary school whose assessment system involves frequent tests from a formative perspective on assessment. The research outcome is as follows: First, the competencies-oriented assessment of integrating instruction made possible for curriculum restructuring and competencies-oriented teaching, whereas more emphasis needs to be focused on the assessment feedback. Second, assessment on math competencies involves multiple dimensions; therefore, it needs to be managed to prevent problems arising due to overlap between different competencies. Third, though it has been identified that with evaluation it is possible to recognize and gradually improve the areas short of competency, more practical studies need to be conducted in this regard. Fourth, even with the fact that various types of evaluation ensure its fairness, make an accurate interpretation of the evaluation result before arriving at a comprehensive assessment.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.657-673
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• 2015

In this study, we are interested in the teachers' MCK about '$N{\div}0$' and MPCK in relation to the proper ways to teach it. Even though '$N{\div}0$' is not on the current curriculum and textbooks of elementary school mathematics, a few students sometimes ask a question about it because the division of the form '$a{\div}b$' is dealt in whole number including 0. Teacher's obvious understanding and appropriate guidance based on students' levels can avoid students' error and have positive effects on their subsequent learning. Therefore, we developed an interview form to investigate teachers' MCK about '$N{\div}0$' and MPCK of the proper ways to teach it and carried out individual interviews with 30 elementary school teachers. The results of the analysis of these interviews reveal that some teachers do not have proper MCK about '$N{\div}0$' and many of them have no idea on how to teach their students who are asking about '$N{\div}0$'. Based on our discussion of the results, we suggest some didactical implications.

• 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.

• Education of Primary School Mathematics
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• v.5 no.2
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• pp.121-142
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• 2001

The goal of the National Assessment of Educational Achievement(NAEA) 2001 was to affirm the accountability of school education, to scientifically manage and elevate the quality of education at the national level, and to articulate the final design of the NAEA. It was implemented on June 28th of the year 2001. The assessment frame for NAEA includes the achievement standards, the assessment standards, the instruction for the item development, and the grading policy for mathematics subject. Most of items are multiple-choice types, but the performance-based items should be at least thirty percent of the total items, also 30% in case of mathematics. Approximately 1% of students among entire population of the Grades 6 were randomly selected. Therefore, the finally sampled examines were 8023 at Grade 6. The result of the analysis of the NAEA revealed that Grade 6 students was labelled as ‘average’ level in general (Number and Operation: average, Geometric figures: average, Patterns and Functions: excellent, Measurements: average, Letters and Expressions: average, Probability and Statistics: average). The most characteristic finding was that except for Grade 6(its average is 69.92), most secondary students obtained low test scores and its average of each grade is below 50 out of 100. Especially, the scores on the performance-based items were by and large very low. This finding implies that Korean students are not familiar with the kind of test items which requires expression of ideas and feelings and they are rather familiar with the multiple-choice items. Another interesting finding was that the students in small towns and remote areas showed significantly low scores in all four skills compared with Seoul, metropolitan cities and medium and small cities. This may be attributed from the fact that the remote areas do not have equal learning environment with regard to social and cultural experience, supply of various teaching materials, extracurricular lessons which are directly related to teaching and learning. These findings may be utilized as a reliable resource fur improving curriculum and teaching and learning in Mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.23-42
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• 2007

Learners who have taken learner-centered instruction is expected to construct conceptually mathematical knowledge which is. If so, they can have some ability to solve problems they are confronted with in the first time. To know this, First graders who have been in learner-centered instruction during 1 school year was given 7+52+186 which usually appears in the national curriculum for 3rd grade. According to the results, most of them have constructed the logic necessary to solve the given problem to them, and actually solve it. From this, it can be concluded that first, even though learners are 1st graders they can construct mathematical knowledge abstractly, second, they can apply it to the new problem, and third consequently they can got a good score in a achievement test.

• The Mathematical Education
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• v.60 no.3
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• pp.265-279
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• 2021

In this study, by analyzing of types and functions of questions presented in Data and Chance area of the mathematics textbooks for grades 1-6 of the 2015 revised curriculum, the characteristics of the questions presented in the textbook were identified, and implications for teaching and learning related to the questions in this textbook were obtained. Types and functions of the presented questions showed different proportions of appearance according to the grade clusters, and this seems to be related to the learning contents for each grade clusters and the characteristics of grade clusters. In addition, it can be seen that the functions of questions are related to the types of questions. Teachers should have pedagogical content knowledge about Data and Chance area as well as developmental characteristics for each grade clusters. In addition, the teacher should present an suitable question for the level of grade clusters and the nature of the content to be taught so that effective learning can be achieved based on the understanding of the characteristics and functional characteristics of each type of questions. The results of this study can contribute to statistical teaching in a progressive direction by providing a foundation for textbook writing and teaching/learning.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.135-157
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• 2023

Double scale models have been introduced in elementary mathematics textbooks under the 2015 revised mathematics curriculum. However, few studies have examined in detail how students understand or utilize such models. In this study, we analyzed how 154 sixth-grade students who had learned the division of fractions from textbooks containing double scale models understood such models. The results showed that the students tended to identify the components of the model relatively well, but had difficulties exploring the unit or the meaning of the bottom number line of a model. They also had a lot of difficulties using the double scale model to complete the computation process and explain the computation principle. Based on these findings, we discuss the implications of teaching double scale models.

• The Mathematical Education
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• v.63 no.2
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• pp.369-385
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• 2024

With the advancement of digital technology, a variety of digital materials are being utilized in education. For their appropriate use of digital resources, teachers need to be able to evaluate the quality of digital resource and determine the suitability for teaching. This study explored how preservice teachers evaluate TocToc-Math, an Artificial Intelligence (AI)-based math support system. Based on an evaluation framework developed through prior research, preservice teachers evaluated TocToc-Math with evidence-based criteria, including content quality, pedagogy, technology use, and mathematics curriculum alignment. The findings shows that preservice teachers positively evaluated TocToc-Math overall. The evaluation tendencies of preservice teachers were classified into three groups, and the specific characteristics of each factor differed depending on the group. Based on the research results, we suggest implications for improving preservice teachers' evaluation abilities regarding the use of digital technology and AI in mathematics education.

• The Mathematical Education
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• v.62 no.3
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• pp.363-380
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• 2023

This study analyzed the difficulties and mathematical modeling knowledge improvement that an elementary school teacher experienced in modifying a mathematics textbook task to a mathematical modeling task. To this end, an elementary school teacher with 10 years of experience participated in teacher-researcher community's repeated discussions and modified the average task in the data and pattern domain of the 5th grade. The results are as followings. First, in the process of task modification, the teacher had difficulties in reflecting reality, setting the appropriate cognitive level of mathematical modeling tasks, and presenting detailed tasks according to the mathematical modeling process. Second, through repeated task modifications, the teacher was able to develop realistic tasks considering the mathematical content knowledge and students' cognitive level, set the cognitive level of the task by adjusting the complexity and openness of the task, and present detailed tasks through thought experiments on students' task-solving process, which shows that teachers' mathematical modeling knowledge, including the concept of mathematical modeling and the characteristics of the mathematical modeling task, has improved. The findings of this study suggest that, in terms of the mathematical modeling teacher education, it is necessary to provide teachers with opportunities to improve their mathematical modeling task development competency through textbook task modification rather than direct provision of mathematical modeling tasks, experience mathematical modeling theory and practice together, and participate in teacher-researcher communities.

• The Mathematical Education
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• v.59 no.4
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• pp.313-329
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• 2020

The purpose of this study was to develop an integrated teaching model that integrates mathematics and ethics with social justice theme centric approach. To solve the research problems, the investigator conducted literature studies on the 2015 revised mathematics curriculum, 2015 revised mathematics 3rd to 6th grade textbooks, and the 2015 revised ethics curriculum.. Based on the results of analysis, the mathematics and ethics integrated model for social justice was devised by using the three axes of mathematics subject, ethics subject, and social justice. The integrated class of mathematics and ethics for social justice consists of the steps of problem recognition (ME 1), analysis (ME 2), discussion (ME 3), inquiry and practice (ME 4), and it can be implemented in a total of 27 ways. In order to confirm the effectiveness of the integrated model, two classes of sixth grade were selected as experimental and comparative classes. As a result of the study, the integrated class of mathematics and ethics can be used as a tool to improve the value perception of mathematics, However, it should be conducted with full consideration of students' mathematical tendencies in advance. Also, it can improve students' social consciousness. However, practice and experience-oriented classes are effective to overcome 'reserved agency' problem. Finally, it can improve students' perception of integrated classes and their creative thinking and critical thinking skills.