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Toward a description of how engineering students think mathematically.

机译：对工科学生如何数学思考的描述。

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摘要

The purpose of this study was to build a descriptive model for how individuals add mathematical structure to a problem setting. Blum and Leiss's (2007) mathematical modeling cycle was adopted as a research framework. Data was collected using task-based clinical interviews with four engineering students enrolled in differential equations. Analysis led to the creation of three theoretical constructs which together describe the process of structurally enriching (Schwarzkopf, 2007) a nonmathematical context: mathematical framing, the pseudo-empirical setting, and intertwining. The students in this study made sense of the modeling tasks by assuming that the solution had a certain mathematical structure (the mathematical framing) and then verifying that choice by making sure all the necessary information was present (comparing the information in the task to the pseudo-empirical setting). This process of matching up the variables and operations in the mathematical framing with the quantities and relationships in the pseudo-empirical setting was called intertwining. To move forward in the modeling task, the students then externalized a mathematical representation and analyzed it.;Validating activity was observed throughout this process and analysis confirmed five distinct types of validating activity: (i) to check alignment of the mathematical representation with the individual's interpretation of the context (checking mathematical representation against the real model); (ii) confirming alignment between the mathematical framing and the individual's interpretation of the context (checking the mathematical representation against the situation model); (iii) to check alignment between the results of analysis and the individual's interpretation of the context (checking the real results against the real model); (iv) to check the analysis itself (checking mathematical results against the mathematical representation); (v) to check agreement between the results of the analysis and the information available from the real world (checking real results against the situation model).;These findings were used to build a theoretical model of the mathematical modeling process which deviates from previous theoretical and research frameworks used to study mathematical modeling.
机译：这项研究的目的是为个人如何为问题设置添加数学结构建立一个描述性模型。 Blum和Leiss（2007）的数学建模周期被用作研究框架。数据是通过基于任务的临床访谈收集的，其中有四名注册了微分方程式的工程专业学生。分析导致创建了三个理论构造，它们共同描述了非数学上下文在结构上丰富化的过程（Schwarzkopf，2007）：数学框架，伪经验设置和交织。本研究的学生通过假设解决方案具有一定的数学结构（数学框架），然后通过确保存在所有必要的信息（将任务中的信息与伪信息进行比较）来验证选择，从而对建模任务有所了解。 -经验设置）。将数学框架中的变量和运算与伪经验设置中的数量和关系进行匹配的过程称为缠绕。为了继续进行建模任务，学生随后将数学表示形式外在化并进行了分析。在整个过程中观察了验证活动，分析确认了五种不同类型的验证活动：（i）检查数学表示形式是否与个人的上下文的解释（对照真实模型检查数学表示形式）； （ii）确认数学框架与个人对上下文的解释之间的一致性（对照情况模型检查数学表示形式）； （iii）检查分析结果与个人对上下文的解释之间的一致性（对照真实模型检查真实结果）； （iv）检查分析本身（对照数学表示法检查数学结果）； （v）检查分析结果与现实世界中可用信息之间的一致性（根据情况模型检查实际结果）;这些发现被用于建立数学建模过程的理论模型，该模型与先前的理论有所不同和用于研究数学建模的研究框架。

著录项

  • 作者

    Czocher, Jennifer A.;

  • 作者单位

    The Ohio State University.;

  • 授予单位 The Ohio State University.;
  • 学科 Mathematics education.;Science education.;Curriculum development.;Higher education.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 409 p.
  • 总页数 409
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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