• 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.

• Journal of the Korean Chemical Society
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• v.57 no.5
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• pp.640-655
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• 2013

The purpose of this study is to analyze the cognitive demands level of the description about 'changes of state' and 'kinetic theory' on the 'science 1' textbooks by the 2007 revised curriculum. The three types of curriculum analysis taxonomy have been used to analyze the cognitive demands level of those contents on the 6 kinds of 'science 1' textbooks. The most higher level of cognitive demands about the concepts have been discussed here due to the focus of the concepts. The first, the cognitive demand level about 'three states of substances' depending on the motion of their particles in 6 textbooks is a early formal operational stage because of using by the application of kinetic theory. The second, the cognitive demand level about 'diffusion' and 'evaporation' is a early formal operational stage, because the particles move around faster so they can change their position. The third, the cognitive level of the pressure and volume in a gas is a early formal operational stage because of explaining only phenomena in simple correspondence with formal model of kinetic theory. And simple functional relationships beyond linear on the graph of the volume and pressure of gas, the volume and temperature of gas is also a early formal operational stage. The fourth, the cognitive level of the energy of heat by a change of the state is also a early formal operational stage because kinetic theory picture accepted as providing explanation by the change of the state. And functional relationships beyond linear on the graph of the explanation of boiling point of water in water is also a early formal operational stage.

• 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.

• 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.

• 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.15 no.1
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• pp.37-59
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• 2013

The purpose of this study was to examine and analyze the mathematical tasks in the high school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the textbooks. We adopted the framework for mathematical task analysis suggested by Smith & Stein (1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at low level and the rest at high level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures.

• Journal of the Korean Chemical Society
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• v.43 no.5
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• pp.578-588
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• 1999

The purpose of this study is to develope the more effective chemistry teaching strategy through analyzing the demanded cognitive levels of contents in high school chemistry I textbooks and the cognitive levels of students who learn these textbooks. For this purpose, the levets of cognitive development stages of 821 second grade students of high schools in Seoul City were anaIyzed using the GALT short version test. The demanded cognitive levels of understanding the contents of chemistry I textbooks in high school were analyzed using the curriculum analysis taxonomy developed by CSMS (Concept in Secondaly Mathematics and Science) program of the Great Britain. The resuIts showed that the proportion of students in the concrete operational stage, the transition stage, and the formal operational stage was l0.7%, 43.0% and 46.3%, respectively. The demanded levels of textbook contents were mostly the early formal operational stages. The concepts demanded the level of the late formal operational stage were 'atomic and molecular weight', 'stoichiometry of chemical reaction', and 'periodic properties of elements'. The results will be helpful for teachers in knowing what concepts are difficult for students to understand and in planning strategies for teaching those concepts. To demonstrate the application of the results obtained in this study, an example of developing teaching strategy which includes the adjustment of cognitive level of contents was shown.

• 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 Korean Elementary Science Education
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• v.22 no.1
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• pp.1-14
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• 2003

This study investigated the effects of the cognitive acceleration program devised for accelerating the development of formal reasoning ability of students. ‘Thinking Science’ activities developed by the Cognitive Acceleration through Science Education(CASE) project were implemented to 420 students in 5th grade aged 10+ in four elementary schools over a period of two yea. Homogeneity between the experimental group and control group was tested with SRT II, and the improvement of formal reasoning ability of the students was tested with SRT III. The results were analyzed by treatment, gender, and cognitive levels of the students. Statistically significant gains were shown in the CASE group compared with those in the control group. Cognitive level of girls in the CASE group increased as compared with the control group, while there was moderate effect in boys for the primary school. These results implied that the thinking science activities were effective in cognitive acceleration of girls aged 10+. It was shown that much more CASE students in concrete operational level shifted to formal operational level as compared with the control group while there were no significant effects in the other levels for primary school.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.899-925
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• 2013

The purpose of this study was to examine how constructive-response questions in regular test was in aligned with the nature and goals of 2007 Curriculum Amendment. For this purpose, data were collected and analysed by using the framework for mathematical task and the cognitive demand of tasks suggested by Smith & Stein(1998) and mathematical proficiency suggested by National Research Council(2001). In particular, it aimed to reveal the overall picture of the level of cognitive demand and the proportion of mathematical proficiency of constructed-response items created by secondary mathematics teachers. The findings from the analysis showed that 70 percent of the constructed-response items were at low-level and the rest at high-level in terms of cognitive demand. Also, the constructed-response assessment focused on conputing (89%), understanding(45%), applying(30%) and least reasoning(17%). Most of the constructed-response items included computing and were algorithmic.