• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.615-637
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• 2017

The purpose of this study is to analyze the actual realization of the opportunity to learn given to students by examining students' cognition for enrichment mathematics textbook tasks' levels of cognitive demand. First, we analyze characteristics and limitations based on the theoretical framework. Second, we examine students' cognition about the distribution of the mathematics textbook tasks' levels of cognitive demand. And we analyze how the opportunity to learn actually work. Third, in the sense that enrichment textbooks are textbooks for science school students, we analyze whether the opportunity to learn for gifted is offered. The conclusion is as follows: First, with respect to levels of cognitive demand, PNC tasks account most. Second, students also cognize that PNC tasks account most. Third, tasks for gifted are not offered and students also cognize that opportunity to learn for gifted is lacked.

• Research in Mathematical Education
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• v.23 no.2
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• pp.63-92
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• 2020

Student engagement in high-level, cognitively demanding instruction is pivotal for student learning. However, many teachers are unable to maintain such instruction, especially in instances of non-responsive students. This case study of three middle school teachers explores prompts that aim to move classroom discussions past student silence. Prompt sequences were categorized into Progressing, Focusing, and Redirecting Actions, and then analyzed for maintenance of high levels of cognitive demand. Results indicate that specific prompt types are prone to either raise or diminish the cognitive demand of a discussion. While Focusing Actions afforded students opportunities to process information on a more meaningful level, Progressing Actions typically lowered cognitive demand in an effort to get through mathematics content or a specific method or procedure. Prompts that raise cognitive demand typically start out as procedural or concrete and progress to include students' thoughts or ideas about mathematical concepts. This study aims to discuss five specific implications on how teachers can use prompting techniques to effectively maintain cognitively challenging discourse through moments of student silence.

• Research in Mathematical Education
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• v.16 no.3
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• pp.155-176
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• 2012

It is an important issue to explore classroom environments which are conducive to developing students' mathematical performance. This study explores the effects of different classroom environments (solution-demand and corresponding-time setting) on mathematical performances. Fourteen and eighteen prospective teachers were required to prove a task under different conditions respectively: a) Cognitive demand of multiple-solution corresponding time of three hours, and b) Cognitive demand of a right solution corresponding time of 20 minutes. We used SOLO as the assessment tool for mathematical performance from quality perspective. Significant differences were found in the quantity and quality of mathematical performance. The regular environment focusing on speed and accuracy were found to be directly linked to low levels of performance. The findings above provide implications to the cognitive benefits of multiple-solution demand and corresponding time setting.

• 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.

• 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.

• Education of Primary School Mathematics
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• v.10 no.2
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• pp.77-110
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• 2007

This study attempted to investigate how to students show high-level mathematical thinking in math classes. This paper describes how to setup the task for lead to a high - level of thinking out students and what efforts are required while a teacher tried to maintaining students's high-level cognition during the tasks implemented. The researcher as teacher analyzed the tasks of length measurement unit in 2-Ga elementary math textbooks, modified and created math tasks demanded students' high-level cognition, made instruction plans, and implemented those tasks maintaining the levels of cognitive demand of tasks. After that, the researcher reflected and analyzed the levels of cognitive demand of tasks of instruction and factors that cause to change intended high-level cognitive demand. After reflection, second roof of action research was conducted to 2-Na length measurement unit. This paper includes those results and reflections of practitioner.

• 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.

• Transactions of the Korean Society of Automotive Engineers
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• v.21 no.4
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• pp.62-69
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• 2013

Visual demands associated with in-vehicle display usage and text messaging distract a driver's visual attention from the roadway. To minimize eyes-off-the-road demands, voice interaction systems are widely introduced. Under cognitively distracted condition, however, awareness of the operating environment will be degraded although the driver remains oriented to the roadway. It is also know that the risk of inattentive driving varies with age, thus systematic analysis of driving risks is required for the older drivers. This paper aims to understand the age-related driving performance degradation and visual attention changes under auditory cognitive demand which consists of three graded levels of cognitive complexity. In this study, two groups, aged 25-35 and 60-69, engaged in a delayed auditory recall task, so called N-back task, while driving a simulated highway. Comparisons of younger and older drivers' driving performance including mean speed, speed variability and standard deviation of lane position, and gaze dispersion changes, which consist of x-axis and y-axis of visual attention, were conducted. As a result, it was observed that gaze dispersion decreased with each level of demand, demonstrating that these indices can correctly rank order cognitive workload. Moreover, gaze dispersion change patterns were quite consistent in younger and older age groups. Effects were also observed on driving performance measures, but they were subtle, nonlinear, and did not effectively differentiate the levels of cognitive workload.

• 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.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.103-123
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• 2017

Mathematical tasks in general introduce and deal with real-life situations, and they derive to students' thinking fluently in solving the given tasks. The tasks might be considered as an important and significant factor to lead a successful mathematical teaching and learning situation. MiC Textbook is a representative one showing such good examples and tasks. This study explores concretely and in detail the cognitive demand level of mathematical tasks, by the subject of MiC Textbook. To accomplish this, this study is to reconstruct more elaborately the analysis framework developed by Hwang and Park in 2013. The framework basically was set up utilizing 'the cognitive demand level' suggested by Stein, et, al. The cognitive demand level is divided into two levels such as low level and high level. The low level is comprized of two elements such as Memorization Tasks(MT), Procedures Without Connections Tasks(PNCT), and high level is Procedures With Connections Tasks(PWCT), and Doing Mathematics Tasks(DMT). This study deals with the tasks on the area of 'data analysis and statistics' in MiC 1, 2, 3 level Textbook. As a result, mathematical tasks of MiC Textbook led learners to deal with and understand mathematical content for themselves, and furthermore to do leading roles for checking and reinforcing the content. Also, mathematical tasks of MiC Textbook are comprized of the tasks suitable to enhance mathematical thinking ability through communication. In addition, mathematical tasks of MiC Textbook tend to offer more learning opportunity to learners' themselves while the level of MiC Textbook is going up.