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Postsecondary developmental mathematics: An interactive problem-solving approach.

机译:中学后发展数学:一种交互式的问题解决方法。

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摘要

This investigation involved the development, implementation, and evaluation of an interactive problem-solving approach to teaching developmental mathematics. The strategy, based on findings from cognitive research and recommendations from the National Council of Teachers of Mathematics, emphasized conceptual understanding and group problem-solving. A quasi-experimental study was conducted to compare students taught using this method with students in a control group taught with a conventional lecture-demonstration approach that emphasized computational skill. The experimental group performed as well as the control group on a computational test, indicating that a focus on interactive problem-solving activities does not jeopardize students' development of computational skill.;Pre/post assessments of conceptual understanding were administered in both treatment groups. While the experimental group scored slightly higher than the control group, differences were not statistically significant and both groups had low scores. Because the concept portion of examinations throughout the semester did not affect examination scores, students may not have taken the concept posttest seriously.;Students in both treatment groups completed self-assessment measures of mathematics anxiety, perceived value of mathematics, and expectancy for success in mathematics. Mathematics anxiety levels were lowered in both groups, but no significant differences between groups were detected. Perceived value of mathematics and expectancy for success in mathematics remained stable from beginning to end of semester for students in both groups. It was theorized that one semester is probably insufficient time to effect changes in attitudes developed over periods of twelve years or more.;An informal post-course attitude survey conducted in the experimental group revealed a highly favorable response to the teaching approach used. Students felt that emphasis on conceptual understanding and small-group interaction increased the effectiveness of the class.;Recommendations for further research include: (1) replication of the study incorporating a more realistic assessment of conceptual understanding, tests of problem-solving skill and confidence, and a measure of attitude toward and beliefs about mathematics; (2) qualitative studies that investigate student characteristics that might account for varying responses to developmental mathematics classes; and (3) longitudinal studies to determine the effectiveness of the experimental approach in preparing students for subsequent college-level mathematics courses.
机译:这项研究涉及开发性数学的交互式问题解决方法的开发,实施和评估。该策略基于认知研究的结果和国家数学教师委员会的建议,强调概念理解和小组问题解决。进行了一项准实验研究,以比较使用这种方法教授的学生和对照组的学生,而对照组则采用强调计算技能的传统演讲示范方法。实验组和对照组在计算测试中的表现均好于对照组,这表明对交互式问题解决活动的关注不会损害学生的计算技能发展。在两个治疗组中均进行了概念理解的前后评估。尽管实验组的得分略高于对照组,但差异无统计学意义,并且两组的得分均较低。因为整个学期的考试概念部分不会影响考试成绩,所以学生可能没有认真对待概念后测。两个治疗组的学生均完成了数学焦虑的自我评估措施,数学的感知价值以及对成功的期望。数学。两组的数学焦虑水平均降低,但两组之间未发现显着差异。两组学生从学期开始到学期末的数学感知价值和对数学成功的期望都保持稳定。从理论上讲,一个学期可能不足以影响在十二年或更长的时间里所形成的态度的改变。;在实验组中进行的非正式课后态度调查显示,对所用的教学方法有很高的反应。学生们认为,强调概念理解和小组互动可以提高课堂的有效性。进一步研究的建议包括:(1)复制研究内容,包括对概念理解的更实际评估,解决问题的能力和自信心的测试,以及对数学的态度和信念; (2)对学生特征进行定性研究,这些特征可能解释了对发展数学课程的不同反应; (3)纵向研究,以确定实验方法在为学生准备后续的大学水平数学课程方面的有效性。

著录项

  • 作者

    Simpson, Nancy Jane.;

  • 作者单位

    Texas A&M University.;

  • 授予单位 Texas A&M University.;
  • 学科 Mathematics education.
  • 学位 Ph.D.
  • 年度 1992
  • 页码 124 p.
  • 总页数 124
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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