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

本研究计划透过课程与教学干预的发展，研究有关计算思维学习的猜想。这次干预为一个名为“代数计划”的成功项目增加了一个计算环境，重点是让一所以非裔美国人为主的中学的所有学生参与计算思维。在这样做的过程中，这项工作试图为许多表现不佳的学生在数学课程中被教导要操作的符号缺乏足够的上下文理解这一事实制定一种补救措施。本研究旨在证明如何使用各种类型的计算思维可以提高概念理解，视觉推理和表征逻辑。在追求这一结果的过程中，该项目正在寻求确定特定类型的模拟和建模应用程序在多大程度上能够使教师和中学生在分析数学函数时使用视觉推理和空间逻辑。这种干预的学生将在小组中相互协作，并与同伴导师和导师一起研究基于数学和计算逻辑的共享经验。通过持续的合作和讨论，学生们将为他们所面临的各种任务和挑战确定解决方案。除了在这项工作中使用视觉推理和空间逻辑外，学生还将学习使用Python脚本和函数来帮助他们进行分析。这项研究将通过使用一种特定类型的基于python的微世界来进行，该微世界结合了代数学项目开发的交互式符号表示和体验式数学课程方法。代数项目的课程方法采用五步协作模式在课堂上进行数学探究。第一步是让学生体验一个共同的事件。接下来，学生们通过形象地描述事件来检验经验，然后通过日常语言，然后通过商定的日常语言规范，最后通过使用标志性和传统的符号表示和方程。这项研究将扩展代数项目的课程和教学方法，为学生提供可在虚拟计算环境中操作的动态符号和图解数学结构，他们可以使用这些结构进一步检查所涉及的数学特征和逻辑结构。这个研究小组之前在城市环境中对极少数学生进行了这种方法的试验，结果发现，在视觉推理和表征逻辑的基础上，参与研究的学生对核心数学思想，即方程和函数，有了更深入的概念性理解。此外，指标还表明，在所有权和参与度方面有所改善。研究小组还没有研究计算思维的核心要素在多大程度上是由学生开发的，这项研究将解决这个问题，并扩展所涉及的数学和计算材料的内容。该项目由CS for All: Research and RPPs计划支持。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.