Mathematics through Programming in the Elementary Grades

小学数学通过编程

• 批准号: 1934161
• 负责人: E. Paul Goldenberg
• 金额: $ 249.68万
• 依托单位: Education Development Center
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1934161&HistoricalAwards=false
• 关键词: Mathematics; through; Programming; Elementary; Grades

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.

这个为期3年的项目与3-5年级的儿童和他们的老师一起工作，调查了通过适当的编程语言表达和探索数学可能会使儿童更容易充分参与并享受和学习数学的想法。孩子们需要他们的自然语言来谈论使用数学的上下文-不仅仅是单词问题-以及他们解决问题时的推理。多年来，他们学习第二种语言，即表达算术和代数语句所需的数学符号。两者都是需要的，但都不是表达过程的最佳选择-显示计算的执行方式（想想如何解释37 x 43的乘法或3/4 + 1/2的加法），或者以可以用不同的起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。在早期的一项针对二年级学生的探索性工作中，研究小组调查了一种儿童友好但非常丰富的编程语言（Snap！）作为第三语言。当孩子们有机会向机器解释一个过程时--也就是说，通过将这个过程描述为一个小程序，他们会发展出更清晰、更简洁的方式来用他们的自然语言解释这个过程。将这个过程表达为一个小程序不仅可以帮助孩子们进行实验和归纳，而且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，正确或不正确，一个可运行的代码可以让孩子们得到他们的工作立即反馈，并帮助他们的数学学习之前很久的职业或大学。建立程序，阐明方法和概括都是计算思维（CT）的关键要素，这越来越成为国家，州和学校的优先事项，因为它现在对于职业和现代大学学习都是如此必要。该项目将调查扩展到3-5年级，在这些年级的更高级数学中寻找新的机会，并寻求更清晰的数据，以了解对数学学习和CT的影响。 本项目由STEM + Computing（STEM+C）项目资助，旨在研究和开发STEM学习中计算和计算思维的整合。项目的目标是了解与小学生常规数学学习相结合的编程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。这一早期设计和开发研究探讨了将编程融入数学课程以延长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）研究一种将编程融入初等数学并建立基本CT思想的模型;（2）开发编程微世界和其他教学资源（例如，印刷材料和教师指南），以支持教师和学生;（3）在48个教室试用这些材料，测试其可行性和可用性;（4）探讨这些模块如何影响学生的学习，并确定有助于或妨碍学习的设计特点;（5）说明在更广泛使用方面面临的挑战，并确定潜在的解决办法;及（6）为不同类别的学生提供更多学习这些范畴的机会。设计实验方法将用于开发，测试和完善微观世界和模块。将使用教师访谈以及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验研究-该奖项反映了NSF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。

项目成果

Programming as a language for young children to express and explore mathematics in school

编程作为幼儿在学校表达和探索数学的语言

• DOI: 10.1111/bjet.13080
• 发表时间: 2021
• 期刊: British Journal of Educational Technology
• 影响因子: 6.6
• 作者: Goldenberg, E. Paul;Carter, Cynthia J.
• 通讯作者: Carter, Cynthia J.

Programming as Language and Manipulative for Second-Grade Mathematics

编程作为二年级数学的语言和操作

• DOI: 10.1007/s40751-020-00083-3
• 发表时间: 2021
• 期刊: Digital Experiences in Mathematics Education
• 作者: Goldenberg, E. Paul;Carter, Cynthia J.;Mark, June;Reed, Kristen;Spencer, Deborah;Coleman, Kate
• 通讯作者: Coleman, Kate

Using Programming to Express Mathematical Ideas

使用编程来表达数学思想

• DOI: 10.5951/mtlt.2022.0354
• 发表时间: 2023
• 期刊: Mathematics Teacher: Learning and Teaching PK-12
• 作者: Spencer, Deborah;Mark, June;Reed, Kristen;Goldenberg, Paul;Coleman, Kate;Chiappinelli, Kathryn;Kolar, Zachary
• 通讯作者: Kolar, Zachary