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

这项研究项目通过课程和教学干预的发展来研究关于计算思维学习的猜想。这一干预措施为一项名为代数项目的成功努力增加了一个计算环境，并专注于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，这项工作试图找到一种补救办法，以弥补这样一个事实，即许多表现不佳的学生对他们在数学课程中学到的符号缺乏足够的背景理解。这项研究试图证明，使用各种类型的计算思维可以增加概念理解、视觉推理和表象逻辑。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。在这一干预中，学生们将以小组形式相互协作，并与近距离同行的导师和导师合作，检查以数学和计算逻辑为基础的共享经验。通过他们的持续合作和讨论，学生将为他们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，学生们还将学习使用Python脚本和函数来帮助他们进行分析。这项研究性研究将使用一种特定类型的基于Python的微世界，它将激活-图标表示与由代数项目开发的经验式数学课程方法相结合。代数项目的课程方法使用了一个五步合作模式来在课堂上进行数学探究。第一步是让学生体验一次共同的活动。接下来，学生们通过用图画表示事件，然后通过日常语言，然后通过商定的日常语言条理，最后通过使用标志性的和传统的符号表示和方程式来检验这种体验。这项研究将扩展代数项目的课程和教学方法，为学生提供激活的、图标的和图解的数学结构，他们可以在计算环境中虚拟地操作这些结构，他们可以使用这些结构来进一步检查所涉及的数学特征和逻辑结构。这个研究小组在城市背景下对非常少数的学生进行了这种方法的试验，其先前的工作结果发现，参与研究的学生对核心数学概念，即基于视觉推理和表征逻辑的方程和函数，有了更好的概念性理解。此外，指标表明所有权和参与度有所改善。研究小组还没有检查学生在多大程度上发展了计算思维的核心要素，这项研究将解决这个问题，并扩大所涉及的数学和计算材料的内容。这个项目得到了CS for All：Research and RPPS计划的支持。这个奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.