Supporting computational thinking for middle school mathematics students through diagrammatic reasoning and representational logic

通过图解推理和表征逻辑支持中学数学学生的计算思维

• 批准号: 2031490
• 负责人: Alan Shaw
• 金额: $ 49.83万
• 依托单位: Kennesaw State University Research and Service Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2031490&HistoricalAwards=false
• 关键词: Supporting; computational; thinking; middle; mathematics

This research project studies conjectures about the learning of computational thinking through the development of a curricular and pedagogical intervention. The intervention adds a computational environment to a successful effort called the Algebra Project, and is focused on engaging all students in a predominantly African American middle school in computational thinking. In so doing, this work seeks to develop a remedy for the fact that many low-performing students lack a sufficient contextual understanding of the symbols that they are taught to manipulate in their mathematics courses. This research seeks to demonstrate how the use of various types of computational thinking can increase conceptual understanding, visual reasoning, and representational logic. In pursuit of this outcome, this project is seeking to determine to what extent a specific type of simulation and modeling application can enable teachers and middle-school students to use visual reasoning and spatial logic when analyzing mathematical functions. Students in this intervention will work collaboratively in small groups among themselves, and with near peer mentors and tutors, to examine shared experiences that are grounded in mathematical and computational logic. Through their ongoing collaboration and discourse, the students will determine solutions for various tasks and challenges that they are presented. In addition to using visual reasoning and spatial logic in this work, students will also learn to use Python scripts and functions to aid them in their analyses.This research study will be carried out by using a specific type of Python-based microworld, that combines enactive-iconic representations with an experiential math curricular approach developed by the Algebra Project. The Algebra Project’s curricular approach uses a 5-step collaborative model for mathematics inquiry in the classroom. The first step begins with the students experiencing a shared event. Next, students examine the experience by representing the event pictorially, then through everyday language, then through an agreed upon regimentation of everyday language, and finally through the use of iconic and conventional symbolic representations and equations. This research will extend the Algebra Project’s curricular and pedagogical approach by providing students with enactive-iconic and diagrammatic mathematical constructions that they can manipulate virtually in a computational environment that they can use to further examine the mathematical features and logical structures involved. The results of the previous work of this research team that piloted this approach with a very small number of students in an urban context, found that the students involved developed a greater conceptual understanding of core mathematical ideas, namely equation and function, grounded in visual reasoning and representational logic. Furthermore, indicators suggested improvements in ownership and engagement. The research team had not yet examined the extent to which core elements of computational thinking were developed by the students, and this research will address that issue, as well as expand the content of the mathematics and computational material involved. This project is supported by the CS for All: Research and RPPs program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该研究项目研究通过开发当前和教学干预措施来学习计算思维的学习。干预措施为称为代数项目的成功努力增加了计算环境，并专注于让所有学生参与主要是非裔美国中学的计算思维。在这样做时，这项工作旨在发展一个事实，即许多表现不佳的学生缺乏对他们在数学课程中操纵的符号的足够的上下文理解。这项研究旨在证明使用各种计算思维的使用如何增加概念理解，视觉推理和代表性逻辑。为了追求这一结果，该项目正在寻求确定特定类型的模拟和建模应用程序可以使教师和中学生在分析数学功能时能够使用视觉推理和空间逻辑。这项干预中的学生将在小组中与近乎同伴的导师和导师进行协作，以研究基于数学和计算逻辑的共同经验。通过持续的合作和话语，学生将确定针对他们提出的各种任务和挑战的解决方案。除了在这项工作中使用视觉推理和空间逻辑外，学生还将学会使用Python脚本和功能来帮助他们进行分析。这项研究将通过使用基于Python的特定类型的基于Python的微世界进行研究，该研究结合了Algebra Project由Algebra Project开发的专家现代方法。代数项目的当前方法使用课堂上数学查询的5步协作模型。第一步始于学生参加共同活动。接下来，学生通过图像刻画，然后通过每天的语言，然后通过商定的每日语言进行制定，最后通过使用标志性和传统的符号表示和方程来检查经验。这项研究将通过为学生提供构成的和诊断性的数学结构来扩展代数项目的课程和教学方法，它们可以在计算环境中几乎可以操纵，它们可以用来进一步检查涉及的数学特征和逻辑结构。该研究团队先前工作的结果通过在城市环境中少数学生试行这种方法的结果发现，参与的学生对核心数学思想（即方程式和功能）有了更大的概念理解，即基于视觉推理和代表性逻辑。此外，指标表明所有权和参与度有所改善。研究团队尚未研究学生开发计算思维的核心要素的程度，这项研究将解决该问题，并扩大涉及的数学和计算材料的内容。该项目得到了CS的支持：研究和RPPS计划。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准来评估值得支持的。

项目成果

Computational Thinking and The Algebra Project: From Voice to Agency

计算思维和代数项目：从声音到代理

• DOI: 10.34024/prometeica.2023.27.15348
• 发表时间: 2023
• 期刊: Prometeica - Revista de Filosofía y Ciencias
• 作者: Shaw, Alan;Lawler, Brian R.;Crombie, William;McKlin, Tom;Richards, Tamika
• 通讯作者: Richards, Tamika

Supporting Orality and Computational Thinking in Mathematics

支持数学中的口语和计算思维

• 发表时间: 2021
• 期刊: Mathematics Education and Society Conference 11
• 作者: Shaw, A.