• Communications of Mathematical Education
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• v.33 no.3
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• pp.395-423
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• 2019

The purpose of the study is to analyze the levels of cognitive demands and components of the reasoning process presented in the mathematical sequence section of three high school mathematics textbooks in order to provide implications for the development of reasoning tasks in the future mathematics textbooks. The results of the study have revealed that most of the reasoning tasks presented in the mathematical sequence section of the three high school mathematics textbooks seemed to require low-level cognitive demands and that low-level cognitive demands reasoning tasks required only a component of one reasoning process. On the other hand, only a portion of the reasoning tasks appeared to require high-level of cognitive demands, and high-level cognitive demands reasoning tasks required various components of reasoning process. Considering the results of the study, it seems to suggest that we need more high-level cognitive demands reasoning tasks to develop high-level cognitive reasoning that would provide students with learning opportunities for various processes of reasoning, and that would provide a deeper understanding of the nature of reasoning.

• 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.

• School Mathematics
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• v.17 no.4
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• pp.633-652
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• 2015

The purpose of the present study is twofold: one is to understand secondary mathematics teachers' capacity to sort out given tasks based on Stein & Smith(1998)'s Cognitive Demands of Mathematical Task Framework; the second is to examine how the teachers assess the levels of cognitive demand indicated in students' reponses and how they modify the tasks to elicit the students' higher levels of cognitive activity. The analysis of 45 teachers' responses to the survey indicates that the teachers, in general, could select appropriate tasks for the given goal of the lessons but some made the decision merely by their appearances. Even though the teachers chose a particular level with different reasons amongst each other, most teachers could correctly evaluate the levels of cognitive demand of the students' responses. Finally, teachers could pose cognitively demanding tasks using various methods, but a number of them felt challenged in creating word problems that were realistic and aligned with curriculum.

• Journal of Science Education
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• v.36 no.2
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• pp.216-234
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• 2012

This study examined the characteristics of verbal interactions presented in TS activities with different tasks' openness levels by the cognitive levels of students through the implementation of TS program to 14 fifth graders in gifted class. Results of this study revealed that the open-type TS activities showed higher percentages of verbal interactions than the guiding-type TS activities showed and that the higher the open level of tasks was, the more high-level verbal interactions occurred. These results were showed in almost all subcomponents of verbal interactions. The results according to the students' cognitive levels showed that the higher the cognitive level of students was, higher frequency of interactions, high-level verbal interactions and a variety of verbal interactions occurred. The influence of both cognitive level of students and the task's openness on verbal interactions among students seemed to be interactive, however. In guiding-type activities, the percentage of high-level verbal interactions was not high although the cognitive level of students was high. And students in low level of cognition showed far lower frequency of interactions and their percentage of high-level verbal interactions was low even though the openness of the tasks was high. The results of this study meant that although open-type activities drew higher level verbal interactions by stimulating students' thought, the effects would be limited owing to their low cognitive level. Based on these findings, an implication was suggested that it is important to design instructional strategies and adjust openness level of TS activities to students' cognitive level so as to stimulate the thinking of students in lower cognitive level and to highten their engagement in activities.

• The Mathematical Education
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• v.60 no.1
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• pp.61-76
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• 2021

The purpose of this study is to analyze the errors and difficulties which pre-service secondary teachers shows during the task modification in consideration of the cognitive demand and to provide significant implications to the pre-service teacher education program related to the modification of the mathematical tasks. In the pursuit of this purpose, tasks were selected from perpendicular bisector units and 24 pre-service teachers were asked to modify the tasks to higher and lower level tasks. After the modification activities, opportunities for reflection and modification were provided. The findings from analysis are as follows. Pre-service teachers had a difficulty to distinguish between PNC tasks and PWC tasks. Also, We identified the interference phenomena that pre-service teachers depended on the apparent elements of the task. Pre-service teachers showed a tendency to overlook the learning objectives and learning hierarchy during the task modification, and to focus on some types of task modification. However, pre-service teachers were able to have meaningful learning opportunities and extend the category of tools to technology including Geogebra through self-reflection and correction activities on task modification. The above results were summed up and we presented the implications to the task modification program in the pre-service secondary teacher education.

• The Mathematical Education
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• v.62 no.2
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• pp.257-268
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• 2023

The purpose of the study is to analyze the characteristics of open-ended tasks in terms of cognitive demands. For this purpose, we analyzed characteristics of open-ended tasks presented in the sequence units of three high school mathematics textbooks. The results of the study have revealed that low cognitive demand levels of open-ended tasks had characteristics including procedures within previous tasks or within those tasks. On the other hand, high cognitive demand levels of open-ended tasks had characteristics of actively exploring new conditions to gain access to what is being sought, requesting a basis for judgement, linking various representations to the concepts of sequences, or requiring a variety of answers. These results are significant in that they not only specified the characteristics of open-ended tasks with high cognitive demands in terms of the intended curriculum, but also provided a direction for the development of open-ended taks with high congitive demands.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.387-408
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• 2015

The purpose of this research is to analyze the mathematical tasks of length measurement in two different perspectives, the level of cognitive demands and learning trajectories, and restructure the mathematical tasks so that the students' conceptual learning is promoted and students are able to have opportunities to think more broadly. Ten lessons with the restructured mathematical tasks were implemented for a class of 2nd grade elementary students. Also a qualitative and in-depth study was conducted with 4 students of the target group. The study shows that firstly, the restructured tasks requiring high level of cognitive skills, had positive effects in increasing the students' level of thinking and reasoning. Secondly, the tasks modified according to the learning trajectories of Szilag, Clements & Sarama(2013) in length measurement, have proven to promote students' concept learning and elaborate the students' level of thinking.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.281-300
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• 2015

The purpose of this research is to analyze cognitive demands, answer types, and storytelling types on the basis of mathematical tasks in five different mathematics textbooks based on 2009 revised curriculum in order to suggest directions for the development and use of storytelling mathematics textbooks in school. Results show that first, PNC (Procedures without Connections) task was the largest category in cognitive demands of all mathematical tasks, Low-Level task was larger than others in cognitive demands of mathematical content tasks, and High-Level task was larger than others in cognitive demands of mathematical activity tasks. Second, a short-answer type was the largest category in answer types of all mathematical tasks, the majority of mathematical content tasks were a short-answer type, and the majority of mathematical activity tasks were both short-answer and explanation-answer types. Finally, storytelling connected to real-life was the largest category in storytelling types, and the number of mathematical activity tasks was less than that of mathematical content tasks. However, in the tasks reflected on storytelling, the percentage of mathematical activity tasks was higher than that of mathematical content tasks. Based on the results, while developing storytelling mathematics textbooks and using storytelling textbooks in school, it suggests to consider the need for balance and diversity in cognitive demands, answer types, and storytelling types according to mathematical tasks.

• School Mathematics
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• v.18 no.4
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• pp.749-771
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• 2016

The purpose of this study is to analyze mathematical tasks of Korea and the USA textbooks focused on conditions for parallelograms. In this study, structures of task, types of proof and reasoning, and levels of cognitive demand are investigated. The conclusion is as follows: First, with respect to structures of task, structures presented in the USA textbooks are more diverse. Second, with respect to types of proof and reasoning, Korea and the USA prefer IC task and DA task. And task types presented in the USA textbooks are more diverse. Third, with respect to levels of cognitive demand, in both Korea and the USA textbooks, PNC task and PWC task account most. And compared to the USA, Korea prefer algorithms. In addition, we find out implications for reconstruction of Korea textbook. It is as follows: First, with respect to structures of task and types of proof and reasoning, the diversity of composition needs to be raised. Second, with respect to levels of cognitive demand, the concentration in PNC task needs to be declined. And levels of cognitive demand on types of tasks need to be reconsidered. Third, with respect to tasks' topic and material, internal and external connectivities of mathematics need to be strengthened.

• Journal of the Korean School Mathematics Society
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• v.22 no.2
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• pp.95-113
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• 2019

In this paper, we analyzed the levels of cognitive demand of the tasks for developing t he mathematical core competencies presented in the "Mathematics" textbook of the first y ear of high school developed according to the 2015 revised mathematics curriculum. "Mathematics" textbook included 4999 mathematics tasks, of which 703 were tasks for developing the mathematical competency. Analysis of 703 mathematical tasks according to the analysis framework of Stein, Smith, Henningsen, and Silver (2000) showed that 61.5% of students required high cognitive levels, 38.5% required low cognitive levels, and the types of tasks were as follows: Low-M 1.0%, Low-P 37.5%, High-P 57.8%, High-D 3.7%. It w as found that most of the tasks for the purpose were tasks that led to understanding mathematical concepts, principles, and processes along procedural processes.