Extending the Theoretical Framework of Numeracy to Engineers

工科学生通常能够将数学应用到他们的学科中，但可能缺乏对数学“所说”的概念性洞察力。一个常见的例子涉及学生解决问题的能力，这些问题涉及将给定的场景转换为相应的数学表示法。一般说来，算术是将数学转换成不同的表示形式或陈述数学所说的内容的能力。工程学中的许多概念对学生来说很难理解，或者建立在对世界如何运作的误解上。当工程概念依赖于高级数学时，数学误解加剧了这种误解。数学误解已经被研究过了，特别是在儿童早期，但从来没有在像导数这样的高级数学计算的镜头下，它们直接应用于工程概念。计算领域的最终目标是防止计算错误概念(例如，理解导数代表什么)与工程错误概念(例如，热量和温度之间的差异)相结合。因此，这项工作将正式定义最常见的算术误解，并为教育工作者提供一种在他们的学生中识别这些误解的方法。通过了解误解的根源是什么，就可以采取措施，使其不再阻碍理解其他学科特定的概念。当前计算领域的一个主要限制是缺乏对工程学和基于微积分的计算的洞察。具体地说，工程教育缺乏与工程计算相关的正式理论框架。这个项目的一个目标是对工程领域中与数学误解相关的文献进行全面的回顾。从文献总结中学到的东西将指导德尔福对专家的研究。德尔福的研究将在工程计算的核心能力构成方面获得专家的共识。Delphi调查的提示将受到文献搜索的影响，Delphi研究将为如何扩大工程计算的文献搜索提供见解。由此产生的框架将允许研究人员在与计算有关的相关工作之间建立联系，并为建立对工程计算错误概念的理解奠定基础。一旦工程计算的理论框架和词典正式形成，将开发一份概念清单来衡量和评估计算能力。这份概念清单将确定个人计算技能的优势和劣势，以指导如何提高这些技能的策略。开发这一概念清单的过程将模仿开发其他概念清单的过程，如热力和运输概念清单。最终，工程计算概念清单的创建将开辟工程教育研究的新领域。

Engineering students typically are capable of the procedural aspects of applying math to their discipline, but may lack conceptual insight into what the math "says". A common example involves students' abilities to solve problems that involve translating a given scenario into its corresponding mathematical representation. In general, numeracy is the ability to translate math into different representations or state what the math says. Many concepts in engineering are difficult for students to understand or are built upon misconceptions regarding how the world works. Mathematical misconceptions compound this misunderstanding when the engineering concept relies upon high-level math. Mathematical misconceptions have been studied, particularly for early childhood, but never under the lens of numeracy for high-level math like derivatives, which have direct application to engineering concepts. The ultimate goal of the numeracy field is to prevent numeracy misconceptions (e.g., understanding what derivatives represent) from compounding engineering misconceptions (e.g. the difference between heat and temperature). As such, this work will formally define the most common numeracy misconceptions and provide a means for educators to identify these misconceptions among their students. By knowing what the root misconception is, steps can be taken so it no longer hinders understanding other discipline-specific concepts.A major limitation in the current field of numeracy is a lack of insight into engineering and calculus-based numeracy. Specifically, engineering education lacks a formal theoretical framework related to engineering numeracy. One objective of this project is to conduct a comprehensive review of the literature associated with mathematical misconceptions in engineering fields. What is learned from summarizing the literature will guide a Delphi Study of experts. The Delphi Study will obtain consensus from experts on what constitute the core competencies of engineering numeracy. Prompts to the Delphi surveys will be influenced by the literature search, and the Delphi Study will provide insight on how to expand the literature search on engineering numeracy. The resulting framework will allow researchers to make connections between related works associated with numeracy in addition to laying the foundation for building understanding of engineering numeracy misconceptions. Once the theoretical framework and lexicon are formalized for engineering numeracy, a concept inventory will be developed to measure and assess numeracy. This concept inventory will identify strengths and weaknesses of an individual's numeracy skills to guide strategies on how to improve those skills. The process of developing this concept inventory will mimic the process used in developing other concept inventories like the Thermal and Transport Concept Inventory. Ultimately, creation of an engineering numeracy concept inventory will open up new areas of research in engineering education.