Natural language helps express mathematical thinking and contexts. Conventional mathematical notation (CMN) best suits expressions and equations. Each is essential; each also has limitations, especially for learners. Our research studies how programming can be a advantageous third language that can also help restore mathematical connections that are hidden by topic-centred curricula. Restoring opportunities for surprise and delight reclaims mathematics' creative nature. Studies of children's use of language in mathematics and their programming behaviours guide our iterative design/redesign of mathematical microworlds in which students, ages 7–11, use programming in their regular school lessons as a language for learning mathematics. Though driven by mathematics, not coding, the microworlds develop the programming over time so that it continues to support children's developing mathematical ideas. This paper briefly describes microworlds EDC has tested with well over 400 7-to-8-year-olds in school, and others tested (or about to be tested) with over 200 8-to-11-year-olds. Our challenge was to satisfy schools' topical orientation and fit easily within regular classroom study but use and foreshadow other mathematical learning to remove the siloes. The design/redesign research and evaluation is exploratory, without formal methodology. We are also more formally studying effects on children's learning. That ongoing study is not reported here.

中文翻译：

---

编程作为幼儿在学校表达和探索数学的语言

自然语言有助于表达数学思维和上下文。传统的数学符号 (CMN) 最适合表达式和方程。每一个都是必不可少的；每个也有局限性，尤其是对于学习者而言。我们的研究研究了编程如何成为一种有利的第三语言，它还可以帮助恢复以主题为中心的课程所隐藏的数学联系。恢复惊喜和喜悦的机会，重新获得了数学的创造性本质。对儿童在数学中使用语言及其编程行为的研究指导了我们对数学微世界的迭代设计/重新设计，其中7-11岁的学生在常规课程中将编程用作学习数学的语言. 虽然由数学而非编码驱动，但微观世界会随着时间的推移发展编程，以便继续支持儿童发展数学思想。本文简要介绍了 EDC 在学校对超过 400 名 7 至 8 岁儿童进行测试的微观世界，以及对 200 多名 8 至 11 岁儿童进行的测试（或即将进行测试）。我们的挑战是满足学校的主题定位并轻松适应常规课堂学习，但使用和预示其他数学学习来消除孤岛。设计/重新设计的研究和评估是探索性的，没有正式的方法论。我们也在更正式地研究对儿童学习的影响。正在进行的研究未在此处报告。