• The Mathematical Education
• /
• v.62 no.2
• /
• pp.257-268
• /
• 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
• /
• v.20 no.1 s.25
• /
• pp.117-145
• /
• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• Research in Mathematical Education
• /
• v.5 no.2
• /
• pp.87-98
• /
• 2001

The Center for Science Gifted Education (CSGE) of Chongju National University of Education was established in 1998 with the financial support of the Korea. Science & Engineering Foundation (KOSEF). In fact, we had prepared mathematics and science gifted education program beginning in 1997. It was possible due to the commitment of faculty members with an interest in gifted education. Now we have 5 classes in Mathematics, two of which are fundamental, one of which is a strengthened second-grade class gifted elementary school students, and one a fundamental class, and one a strengthened class for gifted middle school students in Chungbuk province. Each class consists of 16 students selected by a rigorous examination and filtering process. Also we have a mentoring system for particularly gifted students in mathematics. We have a number of programs for Super-Saturday, Summer School, Winter School, and Mathematics and Science Gifted Camp. Each program is suitable for 90 or 180 minutes of class time. The types of tasks developed can be divided into experimental, group discussion, open-ended problem solving, and exposition and problem solving tasks. Levels of the tasks developed for talented elementary students in mathematics can be further divided into grade 5 and under, grade 6, and grade 7 and over. Types of the tasks developed can be divided into experimental, group discussion, open-ended problem solving, and exposition and problem solving task. Also levels of the tasks developed for talented elementary students in mathematics can be divided into the level of lower than grade 5, level of grade 6, and level of more than grade 7. Three tasks developed and practiced are reported in this article.

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

• Research in Mathematical Education
• /
• v.6 no.1
• /
• pp.39-51
• /
• 2002

This study described an elementary teacher's practical knowledge of selecting and using mathematical tasks for promoting students' understanding and discourse. The informant of this ethnographic inquiry was a third grade teacher and has 10 years of teaching experience. According to the analysis of multiple data sources, this study showed that based on his beliefs about the development of understanding of mathematics and discourse, he continually employed two different types of tasks: open-ended tasks and tasks from students' mistakes and comments during discourse. Teachers' practical knowledge of teaching mathematics and the classroom norms for students' understanding and discourse are suggested to be given attention for further research on this area.

• Korean Journal of Cognitive Science
• /
• v.12 no.1_2
• /
• pp.65-76
• /
• 2001

This study investigated the relationships between hypermedia users information processing styles and navigational patterns. Three aspects of navigational patterns were investigated: (a) navigational breadth patterns which reveal how comprehensively users access, (b) navigational path patterns which display what sequences users follow. and (c) navigational method patterns which show what methods u users employ when using the system. Information processing styles were measured by the Human Information Processing Styles(HIPS) Survey. The subjects were 102 undergraduate students enrolled in management courses at a university. Participation was voluntary 34 students were selected for each of left, right, and integrated information processor group. The subjects interacted with A.g.i.l.e. TrainerTM program to complete two types of searching tasks 'open-ended and closed-ended tasks' Findings indicated that the information processing style seems to play an important role in how an individual interacts with the hypermedia systems.

• Journal of the Korean earth science society
• /
• v.25 no.8
• /
• pp.647-655
• /
• 2004

PISA (Program for International Student Assessment) 2003, the second cycle of PISA, collected data with respect to students' cross-disciplinary problem solving capabilities. Problem solving is defined as the ability to use cognitive processes to solve real cross-disciplinary problems. For the purpose of PISA 2003 assessment, three problem types were chosen: Decision Making, System Analysis and Design, and Trouble Shooting. For this paper a preliminary analysis on Korean students' responses to the PISA 2003 problem-solving items was conducted. The quantitative analysis mainly focused on the difficulties of the PISA 2003 items, while the quantitative analysis dealt with students' responses to open-ended items, which helped understand Korean students' cognitive style and reasoning processes. According to the item analysis result, Korean students had difficulty in representing their answers with pictures or graphs, and interpreting long and complex text. They also showed low achievement with relatively unfamiliar topics or tasks. The paper concluded with several suggestions on improve the quality of science education.