• School Mathematics
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• v.15 no.1
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• pp.101-120
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• 2013

International comparative studies of students' performance in mathematics have shown that Korean students possess very negative attitudes toward mathematics, while they are ranked as one of the highest in the cognitive achievement of mathematics. This has prompted mathematics educators to seek for a way to improve the quality of mathematics education. In this context, this research has been conducted to investigate the learning style of Korean middle school students under the assumption that it is of essence to understand the characteristics of our students as mathematics learners. For the purpose, in-depth interview had been conducted and sixteen middle students participated in the interview. The students were chosen to represent the average group of their age-cohorts based on their performance in mathematics and their SES. The interview was designed as a semi-structured clinical interview. In the interview, the students were given mathematical tasks dealing with central themes in the domain of function. Each student was given about 30 to 50 minutes to solve the tasks. After an interviewee finished the tasks, s/he was asked to explained how s/he solved the tasks. The researchers asked additional questions to clarify the students' understanding of the mathematical themes in the tasks and to identify their strategies for learning mathematics. The analysis of the in-depth interview has primarily identified the characteristics of the students' understanding of the main themes in function and then has been extended to investigate their characteristic styles for learning mathematics. The analysis of the interview identified the learning styles of the students as 'inductive learning based on prototypical cases', 'repeated practice of exemplar mathematics problems', 'disengaged learning', and 'double standards in learning mathematics'. Based on the results of the analysis, this research presents the implications for the improvement of mathematics education.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.227-246
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• 2024

The purposes of this study were to analyze the levels of cognitive demand and questioning types in tasks of 'Data and Chance' presented in elementary mathematics textbooks in Korea, the United States, and Australia. The levels of cognitive demand of textbook tasks were analyzed according to the knowledge and process and thinking types required in the tasks. The tasks were also analyzed for questioning types, answer types, and response types. As a result, in terms of knowledge and process and thinking types in tasks, all three countries had something in common: the percentage of tasks requiring 'representation' and process was the highest, and the percentage of tasks requiring 'basic application of skill/concept' was also the highest. From a thinking types perspective, differences were found between textbook tasks in the three countries in graph and chance learning. The results of analyzing questioning types showed that in all three textbooks, the percentage of observational reasoning questions was highest, followed by the percentage of factual questions. The proportions and characteristics of the constructing questions included in the U.S. and Australian textbooks differed from those in the Korean textbooks. Based on these results, this study presents implications for constructing elementary mathematics textbook tasks in 'Data and Chance.'

• School Mathematics
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• v.14 no.1
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• pp.109-134
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• 2012

The purpose of this study is to develop authentic assessment model and example tools of mathematics teaching and learning. By reviewing literature researches, we set up the definition of authentic assessment in mathematics education, checked the criterian of authentic assessment tasks and mathematical activities. We searched various assessment models of mathematics teaching and learning, project assessment proceeding model, and criterian of project assessment, and checked various project tasks of the authentic assessment. And we developed authentic assessment model and example tools of mathematics teaching and learning. The model is applied project tasks in the form of being integrated with class to high school students, with high school mathematics especially. Furthermore, we carried the test of content validity for a validity of developed tasks for experts in studies of mathematics education. The result is that authentic assessment model and example tools of mathematics teaching and learning has an significance in mathematics education and can be used to judge whether students are doing 'real' mathematics or not, keeping the applicability in the form of being integrated with class.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.347-366
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• 2015

There are a lot of causes of under-achievement in elementary mathematics, one of which may be lack of previous learning elements. We focus on the understanding of place value. The purpose of this study is to analyze underachievers' levels of understanding of place value concepts and to find the types of place value tasks that they have had special difficulty. For this purpose, an individual test called as "the Six Tasks of Place Value(SToPV)"was applied to ten third grade mathematics underachievers in elementary school. The test is a type of place value concept tests and requires one-on-one interview with some preparation materials. The participants' reactions were analysed according to the framework by Berman(2011). The result of analysis shows that third grade mathematics underachievers tend to have a great difficulty understanding the place value concepts. Also the types of difficult tasks were various from individual to individual. Based on the test results and discussion, we suggested some implications for diagnosing place value concepts of mathematics underachievers.

• Journal of the Korean School Mathematics Society
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• v.22 no.3
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• pp.241-256
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• 2019

In this paper, we analyzed the types of tasks presented in the 'Probability and Statistics' textbooks and how the cognitive competences required to perform the tasks provide students with opportunity-to-learn. To this end, the analysis of the 9 books of the 'Probability and Statistics' test textbooks according to the 2015 revised mathematics curriculum showed that the context-based tasks(CF type, RE type) ranged from 67.5% to 78.0% of the total number of tasks in each textbook, but the ratio of relevant and essential tasks related to real life is from 0.4% to 2.0%, it was found that most of the context-based tasks presented in the textbooks were disguised as real life materials. The cognitive competences of context-based tasks ranged from 29.6% to 50.0% in reproduction category, from 33.8% to 54.3% in connection category, and from 8.8% to 20.0% in reflection category. As a result, there was not enough opportunity-to-learn for students to experience reflective cognitive processes.

• Education of Primary School Mathematics
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• v.22 no.1
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• pp.95-111
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• 2019

This study searched for the possibility of tangram activities through modifying the tasks of elementary school mathematics textbooks into content based open tasks. As a result of analyzing previous researches, it was confirmed the educational effect of the mathematical tasks transformation and the educational value of tangram activities. The analysis of the textbooks revealed that the tangram activities presented in the textbooks are likely to be at the level of play. It was tried to modify 2015 revised curriculum textbook-tasks into content based open tasks. Based on this study, it could be expected advantages of task modification such as improvement of teachers' expertise and expectation of diverse reactions of students.

• School Mathematics
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• v.19 no.2
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• pp.289-317
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• 2017

This study aims to explore how Korean middle-school mathematics textbooks on functions provide students an opportunity-to-learn [OTL]. For this purpose, we investigate 3 textbooks in terms of mathematics content and practice, the level of cognitive demands of mathematical tasks, types of student responses, types of context-based tasks, and connections among the tasks. The findings from the data analysis suggest as follows: a) an opportunity-to-learn to connect procedures to functional concepts and new ideas of functions to the existing one is very limited; b) the textbooks seem to provide students an OTL to understand functions as definitions, rules and conventions and to experience repeatedly procedural executions through worked examples and mathematics tasks; c) students may not experience to explain their own ideas/thinking by using mathematical sentence or justify their own cognitive processes; and d) students can be exposed to get a sense of mathematics as a set of fragmented and isolated facts or procedures, rather than to encourage to expand and deepen their understanding of functions.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.155-173
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• 2015

The purpose of this study is to offer the implication for elementary school mathematics teaching by analyzing teachers' reflection on the cognitive demands of mathematical tasks they give in class. During the setup phase and the implementation phase in math class, the researchers analyzed the change of cognitive demands on mathematical tasks and the factors which had influence on such changes. After teachers' reflection on teaching, the researchers analyzed the change of cognitive demands on mathematical tasks and the factors which had influence on such changes in math classes. As a result, before teachers' reflection on the cognitive demands of mathematical tasks, the higher-level demands of mathematical tasks had a tendency to decline. However, after teachers' reflection on the cognitive demands of mathematical tasks, higher-level demands of mathematical tasks were maintained.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.621-641
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• 2017

The purposes of this study were to identify the characteristics of students with different cognitive styles in the communication process according to the types of mathematical tasks and investigate the effects of their cognitive styles and types of mathematical tasks on their mathematical communication. For this, the investigator selected subjects according to the field dependent-field independent cognitive style by Witkin et al.(1977, p. 7). Mathematical tasks were developed in the areas of numbers and operations, regularity, and measurement according to the four types of Stein & Smith(1998, p. 269), which include the Memorization, Procedures without Connections, Procedures with Connections, and Doing Mathematics tasks. The selected students were divided into homogeneous groups according to their cognitive styles, and their communication processes according to the four types of mathematical tasks were observed through participation and videotaped. The videotapes were then transcribed and analyzed in protocols. The conclusions is that mathematical tasks of high cognitive level had positive effects on the activation of significant mathematical communication among the students and that differences in approaches to tasks according to their cognitive styles influenced their communicative activities in speaking and listening.