대한수학교육학회지:수학교육학연구 (Journal of Educational Research in Mathematics)
- 제15권3호
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- Pages.251-272
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- 2005
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- 2288-7733(pISSN)
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- 2288-8357(eISSN)
수학 교수${\cdot}$ 학습 과정에서 과제의 인지적 수준 분석 - 초등학교 '비와 비율' 단원을 중심으로 -
An Analysis of Cognitive Demands of Tasks in Elementary Mathematical Instruction: Focusing on 'Ratio and Proportion'
- Kim, Hee-Seong (Sang-in Elementary School) ;
- Pang, Suk-Jeong (Korea National University of Education)
- 발행 : 2005.08.01
초록
수학 수업에서 핵심적인 역할을 하는 과제의 인지적 수준은 교수
Given that cognitive demands of mathematical tasks can be changed during instruction, this study attempts to provide a detailed description to explore how tasks are set up and implemented in the classroom and what are the classroom-based factors. As an exploratory and qualitative case study, 4 of six-grade classrooms where high-level tasks on ratio and proportion were used were videotaped and analyzed with regard to the patterns emerged during the task setup and implementation. With regard to 16 tasks, four kinds of Patterns emerged: (a) maintenance of high-level cognitive demands (7 tasks), (b) decline into the procedure without connection to the meaning (1 task), (c) decline into unsystematic exploration (2 tasks), and (d) decline into not-sufficient exploration (6 tasks), which means that the only partial meaning of a given task is addressed. The 4th pattern is particularly significant, mainly because previous studies have not identified. Contributing factors to this pattern include private-learning without reasonable explanation, well-performed model presented at the beginning of a lesson, and mathematical concepts which are not clear in the textbook. On the one hand, factors associated with the maintenance of high-level cognitive demands include Improvising a task based on students' for knowledge, scaffolding of students' thinking, encouraging students to justify and explain their reasoning, using group-activity appropriately, and rethinking the solution processes. On the other hand, factors associated with the decline of high-level cognitive demands include too much or too little time, inappropriateness of a task for given students, little interest in high-level thinking process, and emphasis on the correct answer in place of its meaning. These factors may urge teachers to be sensitive of what should be focused during their teaching practices to keep the high-level cognitive demands. To emphasize, cognitive demands are fixed neither by the task nor by the teacher. So, we need to study them in the process of teaching and learning.
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