微积分基本定理:数学任务的认知需求与学习限制

Q3 Multidisciplinary
Jenny Patricia Acevedo Rincón, Elisabeth Ramos-Rodríguez
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引用次数: 0

摘要

背景:大学数学教学任务通常有很大的认知需求,而没有考虑到这些任务对学生的限制。目的:对微积分教学中提出的四项任务,特别是微积分基本定理的教学局限性和认知需求进行理论分析。设计:根据所收集数据的性质,采用描述-解释方法的定性范式。背景和参与者:研究在哥伦比亚大学进行,在第二学期工程专业学生的“微积分II”课程中,教授设计了在本课程中实施的任务。数据收集和分析:数据与教授的课程计划相对应,其中包括主要数学任务的陈述。这些计划是根据可用性和可访问性来选择的。进行内容分析,以每个学校数学任务陈述的段落或段落集为分析单位。结果:大多数被提议的任务符合高认知需求(连接过程和数学建构),只有一个低需求(记忆)。此外,每个任务都有自己的认知需求和一些学习约束,其中一些与已公开的文献一致。结论:这项工作的目的是对高等教育产生影响,因为考虑一个更好的教学方法的教学建议是必要的,以配置课程计划,调动工程中的数学学习,但从使用具有不同认知需求的任务,其中将从少到多变化,并导致有意义的学习新任务的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fundamental Theorem of Calculus: Cognitive Demands and Learning Limitations on Mathematical Tasks
Background: Mathematical tasks for university teaching are generally of great cognitive demand, without thinking about the limitations they imply for their students. Objectives: To develop a theoretical analysis of the teaching limitations and cognitive demand of four tasks proposed for teaching calculus, specifically, the Fundamental Theorem of Calculus. Design: Qualitative paradigm, with a descriptive-interpretive approach, according to the nature of the data collected. Setting and Participants: The study is framed in a Colombian University, in the subject “Calculus II” for second-semester engineering students, where a professor designs the tasks to be implemented in this course. Data collection and analysis: The data correspond to the professor's lesson plans the statements of the main mathematical tasks within them. These plans were chosen based on availability and accessibility. A content analysis was conducted, considering as units of analysis the paragraphs or sets of paragraphs of the statement of each school mathematics task. Results: Most of the proposed tasks correspond to high cognitive demand (procedures with connections and mathematical construction) and only one was of low demand (memorisation). Moreover, each of the tasks presents its own cognitive demand and several learning constraints that, some of them, agree with the exposed literature. Conclusions: The work aims to have implications for higher education, since to think of a didactic proposal for a better approach to teaching is necessary to configure lesson plans that mobilise the learning of mathematics in engineering, but from the use of tasks with different cognitive demands, in which will vary from less to more, and lead to meaningful learning for the approach of new tasks.
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来源期刊
Acta Scientiae
Acta Scientiae Multidisciplinary-Multidisciplinary
CiteScore
0.70
自引率
0.00%
发文量
43
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