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Solving mathematics word problems: Problem features affect strategy choice.

机译:解决数学单词问题:问题特征影响策略的选择。

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摘要

Cognitive research has demonstrated that variations in a task can cause changes in strategy use, yet information about strategy use by problem solvers is not usually available to test designers or teachers. For example, some of the word problems presented in algebra courses may be solved instead through a non-algebraic strategy, "plug-in", which involves testing the validity of hypothesized answers.; The model of strategy choice developed in the current research asserts that for a given problem, students will choose a strategy requiring less cognitive "effort" (less of a burden on working memory) than alternative strategies. Working memory load was operationally defined as the maximum amount of information considered simultaneously during problem solving.; The memory load theory was instantiated and tested by varying four problem features in mathematics word problems. These problem features were expected to affect the amount of cognitive effort required to employ one of the strategies (either algebra or plug-in), but to have no effect on the other strategy.; The problem features manipulated were: (1) the number of different types of quantities (units of measurement) in the problem; (2) the number of semantic relationships in the problem; (3) whether or not the problem statement mapped directly onto algebraic equations; and (4) the difficulty of calculations required to employ the plug-in strategy. Strategies were determined from students' written solutions. Verbal protocols were also collected.; The strongest effect was found for the number of different types of quantities in the problem: as the number of different types of quantities increased from one to two, a greater proportion of students used plug-in. The number of semantic relationships and type of mapping did not affect strategy selection. Students avoided using plug-in when calculations were extremely difficult. The results applied to students at all levels of mathematics ability.; The theoretical understanding of students' problem-solving processes gained from this research can aid in design of algebra instruction. Tailoring test problems to elicit particular strategies may help to increase the construct validity of traditional tests in the difficult domain of mathematics word problems.
机译:认知研究表明,任务的变化会导致策略使用的变化,然而问题解决者对策略使用的信息通常无法提供给测试设计师或教师。例如,代数课程中出现的某些单词问题可以改为通过非代数策略“插件”来解决,该策略涉及测试假设答案的有效性。当前研究中开发的策略选择模型断言,对于一个给定的问题,学生将选择比替代策略需要更少的认知“努力”(减轻工作记忆负担)的策略。工作内存负载在操作上被定义为在解决问题期间同时考虑的最大信息量。通过改变数学单词问题中的四个问题特征,实例化并测试了内存负载理论。预期这些问题特征会影响采用一种策略(代数或插件)所需的认知努力量,但对另一种策略没有影响。处理的问题特征为:(1)问题中不同类型的数量(度量单位)的数量; (2)问题中语义关系的数量; (3)问题陈述是否直接映射到代数方程; (4)采用插件策略所需的计算难度。策略是根据学生的书面解决方案确定的。还收集了口头协议。对于问题中不同类型数量的数量,发现了最强烈的效果:随着不同类型数量的数量从一增加到两个,使用插件的学生比例也越来越高。语义关系的数量和映射类型不影响策略选择。当计算极其困难时,学生避免使用插件。该结果适用于学生的所有数学能力水平。从这项研究中获得的对学生解决问题过程的理论理解可以帮助设计代数教学。量身定制测验问题以引出特定策略可能有助于提高传统测验在数学单词问题这一困难领域中的构造效度。

著录项

  • 作者

    Berger, Aliza Esther.;

  • 作者单位

    Columbia University.;

  • 授予单位 Columbia University.;
  • 学科 Education Mathematics.; Education Educational Psychology.; Education Tests and Measurements.
  • 学位 Ph.D.
  • 年度 1995
  • 页码 183 p.
  • 总页数 183
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 教育心理学;教育;
  • 关键词

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