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Humanizing Mathematics: An Amalgamation of Constructionist Theory and Situated Cognition in the Mathematics Classroom.

机译:数学的人性化:建构主义理论与数学课堂中的情境认知的融合。

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摘要

A primary contributor to facilitating student learning in mathematics includes the mathematics teacher. The design of instructional delivery, presentation of engaging activities and analysis of student feedback are the key responsibilities that mathematics teachers are tasked with in order to present learning opportunities to the students. The approach to satisfying these responsibilities is contingent on the teachers' values and beliefs regarding the various aspects of mathematical proficiency. In this study, I have investigated teachers' valuation of two of these aspects: procedural fluency and conceptual understanding. The literature on these two aspects of mathematical proficiency has focused almost exclusively on elementary teachers. Research studies have uncovered a proclivity of elementary teachers toward procedural learning despite the abstract nature of mathematical processes. Elementary teachers have been found to possess a certain aversion toward a deeper conceptual understanding of mathematics. With regard to secondary teachers, the research is more focused on instructional strategies that emphasize mathematical concepts, but neglect the relationship that these concepts may have to the robust procedures that allow students to process known values as they attempt to discover solutions to both prescribed and unique problems. This study examined the values that secondary teachers place upon two learning constructs within the framework of mathematical proficiency, and how these values influence their approach to teaching. "How do secondary mathematics teachers value procedural fluency and conceptual understanding in their instructional practices?" is the fundamental question of this study. The study reaches beyond this initial question to also examine the root causes of the establishment of these values by asking "how do teachers develop their value-system of procedural fluency and conceptual understanding in their instructional practices?". This study consisted of two phases. In phase one, teachers completed a 27-item survey instrument in order to gather responses about their beliefs regarding conceptual understanding, procedural fluency and a blend of the two constructs. Phase two consisted of a focus group interview of teachers to delve deeper into the source of the various belief systems that serve as the foundation for mathematics instruction in secondary schools in southeastern Pennsylvania.
机译:促进数学学生学习的主要贡献者包括数学老师。教学设计,参与活动的介绍和学生反馈的分析是数学老师要承担的主要职责,以便向学生提供学习机会。履行这些职责的方法取决于教师对数学熟练度各个方面的价值观和信念。在这项研究中,我研究了教师对以下两个方面的评价:程序流畅性和概念理解。关于数学熟练度这两个方面的文献几乎都集中在基础教师上。尽管数学过程具有抽象性质,但研究发现小学教师倾向于程序学习。人们发现小学教师对更深层的数学概念理解有一定的反感。对于中学教师,研究更多地集中在强调数学概念的教学策略上,而忽略了这些概念与稳健程序之间的关系,这些程序允许学生在尝试发现规定的和独特的解决方案时处理已知的值问题。这项研究检查了中学教师在数学熟练度框架内对两种学习结构的价值观,以及这些价值观如何影响他们的教学方法。 “中学数学教师如何在他们的教学实践中重视程序的流畅性和概念性理解?”是这项研究的基本问题。该研究超出了这个最初的问题,还通过询问“教师如何在他们的教学实践中发展其程序流畅性和概念理解的价值体系?”来研究建立这些价值观的根本原因。这项研究包括两个阶段。在第一阶段,教师完成了一项27项调查工具,目的是收集有关他们对概念理解,程序流利程度以及两种结构的融合的信念的回应。第二阶段包括对教师进行的焦点小组访谈,以更深入地探究各种信念系统的来源,这些信念系统是宾夕法尼亚州东南部中学数学教学的基础。

著录项

  • 作者

    Reilly, Brian M.;

  • 作者单位

    Drexel University.;

  • 授予单位 Drexel University.;
  • 学科 Mathematics education.;Educational philosophy.;Secondary education.
  • 学位 Ed.D.
  • 年度 2017
  • 页码 142 p.
  • 总页数 142
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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