Programming as a language for young children to express and explore mathematics in school
Programming as a language for young children to express and explore mathematics in school
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编程作为幼儿在学校表达和探索数学的语言
DOI：
10.1111/bjet.13080
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发表时间：
2021
影响因子：
6.6
通讯作者：
Carter, Cynthia J.
中科院分区：
文献类型：
--
作者：
Goldenberg, E. Paul;Carter, Cynthia J.
自然语言有助于表达数学思维和上下文。常规数学符号（CMN）最适合表达式和方程。每一种都是必不可少的;每一种都有局限性，特别是对学习者来说。我们的研究研究了编程如何成为一种有利的第三语言，也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，恢复了数学的创造性。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观世界的迭代设计/重新设计，其中7-11岁的学生在他们的常规学校课程中使用编程作为学习数学的语言。虽然由数学驱动，而不是编码，微世界随着时间的推移开发编程，以便它继续支持儿童发展数学思想。本文简要介绍了微世界EDC已经测试了400多名7至8岁的学生，以及其他测试（或即将测试）超过200名8至11岁的学生。我们的挑战是满足学校的主题导向，并很容易地适应常规课堂学习，但使用和预示其他数学学习，以消除筒仓。设计/再设计研究和评价是探索性的，没有正式的方法。我们也在更正式地研究对儿童学习的影响。这项正在进行的研究在这里没有报道。实践者注意到已经知道的是积极的学习-做-支持学习。协作学习-一起做-支持学习。课堂话语集中，相关的讨论，而不仅仅是讨论-支持学习。清晰地表达一个人的思想，即使只是对自己，有助于发展这种思维。本文所补充的是我们在课堂数学中使用的共同语言-自然语言用于表达数学情境的含义和背景，以及解释我们的推理;而传统数学符号的形式（书面）语言，我们在数学表达式和等式中使用的符号，两者都是必不可少的，但每一个都提出了需要另一个的障碍。然而，即使是在一起，它们也是不够的，特别是对年轻的学习者。编程，适当的设计和使用，可以是第三语言，既减少障碍，又提供儿童所需要的缺失的表达和创造能力。在常规数学课堂中使用的适当设计需要使关键的数学内容明显，强大和活动的“驱动力”，并且需要将技术“开销”减少到接近于零。跨年级的持续有用性需要发展儿童的语言复杂性和知识;孩子们迅速获得与（自然）语言也为他们学习正式语言的方法提供了指导。对政策和/或实践的影响数学教学可以利用儿童通过实验和关注结果来学习的方法，以及孩子们如何使用他们的语言大脑，甚至是数学。特别是，编程--在由数学内容驱动的微观世界中，旨在最大限度地减少分心和开销，开放探索和发现，以达到专注的目标，并让孩子自我评价--可以清晰地表达思想，进行即时反馈的实验。因为它有助于数学，它还建立了计算思维，并满足了学校日益关注的扩大计算机科学思想的途径。
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 lessonsas 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.Practitioner notesWhat is already knownActive learning—doing—supports learning.Collaborative learning—doingtogether—supports learning.Classroom discourse—focused, relevantdiscussion, not just listening—supports learning.Clear articulation of one's thinking, even just to oneself, helps develop that thinking.What this paper addsThe common languages we use for classroom mathematics—natural language for conveying the meaning and context of mathematical situations and for explaining our reasoning; and the formal (written) language of conventional mathematical notation, the symbols we use in mathematical expressions and equations—are both essential but each presents hurdles that necessitate the other. Yet, even together, they are insufficient especially for young learners.Programming, appropriately designed and used, can be the third language that both reduces barriers and provides the missing expressive and creative capabilities children need.Appropriate design for use in regular mathematics classrooms requires making key mathematical content obvious, strong and the ‘driver’ of the activities, and requires reducing tech ‘overhead’ to near zero.Continued usefulness across the grades requires developing children's sophistication and knowledge with the language; the powerful ways that children rapidly acquire facility with (natural) language provides guidance for ways they can learn a formal language as well.Implications for policy and/or practiceMathematics teaching can take advantage of the ways children learn through experimentation and attention to the results, and of the ways children use their language brain even for mathematics.In particular, programming—in microworlds driven by the mathematical content, designed to minimise distraction and overhead, open to exploration and discoveryen routeto focused aims, and in which childrenself‐evaluate—can allow clear articulation of thought, experimentation with immediate feedback.As it aids the mathematics, it also builds computational thinking and satisfies schools' increasing concerns to broaden access to ideas of computer science.
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