Mathematics through Programming in the Elementary Grades

这个为期3年的项目与3-5年级的孩子和他们的老师一起工作，研究了通过适当的编程语言表达和探索数学的想法，这可能会让孩子们更容易充分参与，享受和学习数学。孩子们需要他们的自然语言来谈论使用数学的环境——远远不仅仅是文字问题——以及他们在解决问题时的推理。随着时间的推移，他们学会了第二种语言，即表达算术和代数语句所需的数学符号。两者都是必需的，但都不是表达过程的最佳选择——显示计算的执行方式（想想解释如何乘37 × 43或加3/4 + 1/2），或者以一种可以用不同的初始值重复的方式编码解决单词问题的方法。为此，需要第三种语言。在对二年级学生进行的早期探索性工作中，研究小组调查了使用儿童友好但非常丰富的编程语言（Snap!）作为第三种语言。当孩子们有机会向机器解释一个过程时——也就是说，通过把这个过程描述成一个小程序，他们会用自己的自然语言发展出更清晰、更简洁的方式来解释这个过程。将这个过程表达成一个小程序不仅可以帮助孩子们进行实验和归纳，还可以为他们的思维提供一个“可运行”的符号。不像写在纸上，只是坐在那里，正确或错误，一段可运行的代码让孩子们得到即时的反馈，并帮助他们在职业或大学之前很久就学习数学。构建程序、阐明方法和概括是计算思维（CT）的所有关键要素，它日益成为国家、州和学校的优先事项，因为它现在对职业和现代大学学习都是如此必要。该项目将调查范围扩大到3-5年级，在这些年级的高等数学中寻找新的机会，并寻求更清晰的数据，以了解数学学习和CT的影响。本项目由STEM+ Computing （STEM+C）项目资助，该项目支持研究和开发，以了解STEM学习中计算和计算思维的整合。该项目的目标是了解编程结合小学生的常规数学学习如何影响数学和计算思维，并确定它是否以及在什么条件下增强思维。这项早期设计和开发研究探讨了将编程融入数学课程以扩大学生在小学数学课堂学习机会的材料的前景，以及实施这些材料的可行性。该项目将(1)研究一个将编程融入初等数学并建立基本CT思想的模型；(2)开发3-5年级的编程微世界和其他教学资源（如印刷材料和教师指南），以支持教师和学生；(3)在48个教室进行试点，测试材料的可行性和可用性；(4)探索模块如何影响学生的学习，并找出有助于或干扰学习的设计特征；(5)描述更广泛使用的挑战并确定潜在的解决方案；(6)为广泛的学生提供在这些领域学习的更多机会。设计实验方法将用于开发、测试和完善微世界和模块。将使用教师访谈和课堂和学生观察工具来收集数据，并将采用混合方法进行试点研究，将体验综合模块的学生与同一学校类似教室的对照组进行比较。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。

Working with children and their teachers in grades 3-5, this 3-year project investigates the idea that expressing and exploring mathematics through an appropriate programming language may make it easier for children to engage fully and enjoy and learn that mathematics. Children need their natural language to talk about the contexts in which mathematics gets used - far more than just word problems - and also their reasoning when solving problems. Over the years, they learn a second language, that is, the mathematical symbols needed for expressing arithmetic and algebraic statements. Both are needed, but neither is optimal for expressing a process - showing the way a calculation is performed (think of explaining how to multiply 37 x 43 or add 3/4 + 1/2), or encoding the method for solving a word problem in a way that can be repeated with different starting values. For that, a third language is needed. In an earlier exploratory work conducted with second grade students, the research team investigated the use of a child-friendly but very rich programming language (Snap!) as the third language. When children are provided with an opportunity to explain a process to a machine - that is, by describing the process as a small program, they develop clearer and more concise ways to explain the process in their natural language. Expressing the process as a small program helps children not only experiment and generalize but gives them a "runnable" notation for their thinking. Unlike writing on paper, which just sits there, correct or incorrect, a runnable piece of code lets children get immediate feedback on their work and helps their mathematical learning long before career or college. Building the program, articulating the methods, and generalizing are all key elements of computational thinking (CT), which is increasingly a national, state, and school priority, because it is now so necessary both for careers and for modern college study. This project extends the investigation to grades 3-5, seeking new opportunities in the more advanced mathematics of those grades and seeking clearer data on the effects on both mathematical learning and CT. This project is funded by the STEM + Computing (STEM+C) program that supports research and development to understand the integration of computing and computational thinking in STEM learning.The goal of the project is to understand how programming, integrated with elementary students' regular mathematics study, influences mathematical and computational thinking, and to determine whether, and under what conditions, it enhances thinking. This early-stage design and development study explores both the promise of materials that integrate programming into the mathematics curriculum to extend students' learning opportunities in the elementary math classroom, and the feasibility of the implementation of these materials. The project will (1) investigate a model that integrates programming into elementary mathematics and builds foundational CT ideas; (2) develop programming microworlds and other instructional resources (e.g., print materials and teacher guides) for grades 3-5 to support teachers and students; (3) pilot the materials in 48 classrooms, testing for feasibility and usability; (4) explore how the modules influence student learning and identify design features that help or interfere with learning; (5) describe challenges to broader use and identify potential solutions; and (6) provide greater opportunities for a wide range of students to learn in these domains. A design experiment methodology will be used to develop, test, and refine the microworlds and modules. Teacher interviews and classroom and student observation tools will be used to collect data, and a pilot study will be conducted using a mixed-methods approach that will compare the computational and mathematical thinking of students who experience the integrated modules with a comparison group in similar classrooms in the same school.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.