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Using a neo-Piagetian framework for learning and teaching mathematical functions.

机译：使用新的Piagetian框架来学习和教授数学函数。

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摘要

Using the framework of Case's theory of cognitive growth, an age-related developmental sequence for students' understanding of mathematical functions is proposed. An experimental curriculum designed to foster that development is also presented. Studies at Grades 6, 8, and 10 investigated (1) whether the experimental instruction better fosters students' learning of functions than textbook approaches and (2) whether experimental students' understandings develop according to the predicted sequence.; Results indicate that the experimental groups' understanding of functions continually improved across Grades 6, 8, and 10. Moreover, students in each successive grade had a mean respective gain score approximately equidistant from that of the grade below. Analyses of the experimental students' correct and partially correct strategies showed few qualitative differences in the ways these students approached problems. However, students at different levels of development exhibited difficulties with the mathematical intricacies of operating with rational numbers, integers, and with algebraic notation. Thus, there appeared to be some grade-related limits to students' learning that resulted from a combination of their experiences with these mathematical intricacies and with their developmental level.; Results also showed that the Grade 8 and 10 experimental groups performed significantly better on the functions test than did control groups at these same grades. Furthermore, the Grade 6 experimental group outperformed the Grade 8 control group, and performed equally to the Grade 10 control students. Analyses of students' solution strategies on each test item indicated that students in the experimental groups demonstrated a better understanding of how the graphic, tabular, and algebraic representations of a function are connected.; Results show that a model of development and instructional approach that share an emphasis on developing children's understandings of how and why different representations of a function are connected, foster a deeper conceptual understanding of functions than do traditional approaches to the topic. The experimental curriculum's use of a familiar context, technology, and theory-driven activities helped participants learn concepts important for functions. Furthermore, only the experimental group demonstrated that they had integrated these functional concepts into a rich conceptual network for their current and future learning of functions.
机译：利用凯斯认知增长理论的框架，提出了与年龄有关的发展顺序，以供学生理解数学功能。还介绍了旨在促进这种发展的实验课程。对6、8、10年级的研究进行了调查（1）实验教学是否比教科书方法更好地促进了学生的功能学习;（2）实验学生的理解是否根据预测的顺序发展了;结果表明，实验组在6、8和10年级之间对功能的理解不断提高。此外，每个后续年级的学生平均各自的平均成绩与以下年级的平均成绩相等。对实验学生的正确和部分正确策略的分析表明，这些学生处​​理问题的方式几乎没有质的差异。但是，处于不同发展水平的学生在用有理数，整数和代数符号进行运算的数学复杂性上表现出困难。因此，学生的学习似乎存在一些与年级相关的限制，这是由于他们的经验与这些数学错综复杂以及他们的发展水平相结合的结果。结果还显示，在相同的等级上，第8年级和第10年级的实验组在功能测试中的表现明显优于对照组。此外，6年级实验组的成绩优于8年级对照组，并且与10年级对照组的学生表现相同。对学生在每个测试项目上的解决方案策略的分析表明，实验组的学生表现出对函数的图形表示，表格表示和代数表示如何连接的更好理解。结果表明，一种发展和指导方法的模型，其重点在于发展儿童对功能的不同表示如何以及为什么相互联系的理解，与传统的方法相比，它对功能的理解更深入。实验课程使用熟悉的上下文，技术和理论驱动的活动帮助参与者学习对功能很重要的概念。此外，只有实验组证明他们已经将这些功能概念整合到一个丰富的概念网络中，以用于当前和将来的功能学习。

著录项

  • 作者

    Kalchman, Mindy Susan.;

  • 作者单位

    University of Toronto (Canada).;

  • 授予单位 University of Toronto (Canada).;
  • 学科 Education Mathematics.
  • 学位 Ph.D.
  • 年度 2001
  • 页码 186 p.
  • 总页数 186
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 O1-4;
  • 关键词

  • 入库时间 2022-08-17 11:47:20

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