• Communications of Mathematical Education
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• v.33 no.4
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• pp.471-488
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• 2019

This paper aims to examine how mathematical history is used in $ textbooks according to the 2015-Revised Curriculum. We analyze the distribution and characteristics of making use of the mathematical history in the nine textbooks, using the framework suggested by Jankvist (2009) on the whys and hows of using historical tasks. First, the tasks related to mathematical history in the textbooks are mostly used as an affective tool, while few tasks are used as a cognitive tool. Second, most of the historical tasks of the type of an affective tool are introducing the anecdotes of mathematicians or in the history of mathematics, and only one case is trying to show human nature of mathematics by illuminating the difficulties mathematicians were faced with. Third, all the mathematical history tasks used as affective tools and goals are illumination materials, while only two out of the ten tasks in the category of a cognitive tool are illumination materials, yet eight others are modular ones. Considering the importance and value of using mathematical history in the math education, this paper recommends that more modular materials on mathematical history tasks in the category of cognitive tools and goals should be developed and their deployment in the textbooks or courses should be promoted. $

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.461-488
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• 2005

This article presents new perspectives for classification of students' mathematical errors on the basis of experiential structuralism. Experiential structuralism's mechanism gives us new insights on mathematical errors. The hard core of mechanism is consist of 6 autonomous capacity spheres that are responsible for the representation and processing of different reality domains. There are specific forces that are responsible for this organization of mind. There are expressed in terms of a set of five organizational principles. Classification of mathematical errors is ascribed by the theory to the interaction between the 6 autonomous capacity spheres. Different types of classification require different autonomous capacity spheres. We can classify mathematical errors in the domain of linear function problem solving comparing cognitive psychological mechanism of experiential structuralism.

• 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.

• 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.13 no.1
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• pp.129-160
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• 2002

대학수학 수업에서 틈틈이 유아 교육과 유아 수학교육에 관한 기본적인 내용을 대학수학(미분적분학의 이해, 생활과 수학) 수업 내용과 관련이 있는 경우 설명을 하여주고, 놀이를 통한 유아 교육과 유아 수학교육 과제(216가지, 105가지)를 각각 한 가지씩 내어준 다음 과제들에 대해 직접 실습을 하고 그 결과를 보고서 형태로 제출하도록 하였다. 그리고 유아 수학교육과 대학수학에 대한 태도가 변화되었는가를 유아 수학교육 기초 조사를 통하여 조사하여 알아보고 분석하였다.

• 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.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.4
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• pp.773-778
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• 2020

In this paper, we analyzed the effects of musical stimuli on humans in performing mathematical tasks through EEG measurements. The musical stimuli were divided into preferred music and non-preferred music, and mathematical tasks were divided into memorization task and procedure task. The data measured in the EEG experiments was divided into frequency bands of Theta, SMR, and Mid-beta because of the concentration. In our results, preferred music causes more positive emotional response than no music and non-preferred music regardless of the type of mathematical task.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.117-134
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• 2011

The purpose of this research was to analyze mathematical task types to enhance creativity. Creativity is increasingly important in every field of disciplines and industries. To be excel in the 21st century, students need to have habits to think creatively in mathematics learning. The method of the research was to collect the previous research and papers concerning creativity and mathematics. To search the materials, the researcher used the search engines such as the GIL and the KISTI. The mathematical task types to enhance creativity were categorized 16 different types according to their forms and characteristics. The types of tasks include (1) requiring various strategies, (2) requiring preferences on strategies, (3) making word problems, (4) making parallel problems, (5) requiring transforming problems, (6) finding patterns and making generalization, (7) using open-ended problems, (8) asking intuition for final answers, (9) asking patterns and generalization (10) requiring role plays, (11) using literature, (12) using mathematical puzzles and games, (13) using various materials, (14) breaking patterned thinking, (15) integrating among disciplines, and (16) encouraging to change our lives. To enhance students' creativity in mathematics teaching and learning, the researcher recommended the followings: reshaping perspectives toward teaching and learning, developing and providing creativity-rich tasks, applying every day life, using open-ended tasks, using various types of tasks, having assessment ability, changing assessment system, and showing and doing creative thinking and behaviors of teachers and parents.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.85-104
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• 2019

The purpose of this study is to analyze the tasks developed through task development activities with emphasis on mathematical connectivity, and to provide implications for teacher education to enhance teacher's competence. For this purpose, I analyzed the task developed by 52 pre-teachers through the activities. As a result, they combined mathematics with 'other subjects', 'mathematics', 'phenomenon', 'technology' and 'real life'. And they also made various internal connections of 'Different representation', 'Part-whole relationship', 'Implication', 'Procedure', and 'Instruction-oriented connection'. From the point of view of teacher knowledge, the study revealed that CCK and SCK were positive in terms of 'logical' and 'expression', and KCT as 'strategic' was meaningful but disappointing in diversity; however in terms of 'level', the KCS was limited due to tasks that did not meet the level of students. As such, this analysis reveals that teachers continue to struggle with understanding students' level, but exhibit little difficulty with 'logic', 'expression' and 'strategy. This being the case, teacher education needs to place additional emphasis in understanding students' levels and planning corresponding activities.

• Journal of the Korean School Mathematics Society
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• v.14 no.1
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• pp.31-42
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• 2011

The purpose of this study is to explore how elementary mathematics teachers' adaptations of a reform-oriented mathematics curriculum material in the USA, Everyday Mathematics, influence elementary students' opportunities to learn mathematics. I illustrate how elementary mathematics teachers alter the curriculum material and how such alterations influence their students' opportunities to learn mathematics in their mathematics classrooms. Results suggest that the teachers with Everyday Mathematics did not appear to maintain the cognitive demand of mathematical tasks as appeared in the curriculum material, as set up by the teacher, and as enacted in the classrooms. The results also show that the teachers seemed to omit components including important tasks and suggestions in the curriculum material. As a consequence, the students did not have an opportunity to think and understand mathematics conceptually and meaningfully; they were exposed and encouraged to learn mathematics procedurally.