Integrating Sonification into Calculus Instruction

数学科学(21)发声是使用非语音音频来传达信息。一种广为人知的成功的发声应用是盖革计数器，它通过可听到的咔哒声的节奏来表示辐射的强度。发声正在寻找跨多个学科的新应用，并提供了另一种交流、演示和发现数学的方式。发声不仅限于音高，还包括声音的其他属性，包括音量、音色和节奏。这个概念验证项目的主要目标是将发声整合到一个学期的微积分课程中。它建立在微积分改革的基础上，强调数学的多种表示法，包括数字、图形、分析和口头或书面表示法。因此，四项规则正在扩展为五项规则。该项目的次要目标包括教学生如何解释发音，确定数学发音的设计原则，并让数学、数学教育和计算机科学的学生参与发音的本科生研究。智力价值：发声为在多媒体环境中长大的学生提供了一种重要的新方法。许多学生很难成功地完成微积分，并使用发音与四规则加强了概念的理解。该项目正在开发资源，用于在实验室环境下对发音进行教学解释，然后在课堂上进行测试。广泛的影响：该项目向数学界展示了在微积分教学中使用发声。因为函数的性质是数学的核心，所以这些教材在整个数学课程中都很有用(例如，微积分预科、代数、统计学、文科专业的数学，以及职前教师的数学)。该项目还为数学和计算机科学专业的本科生提供了可接触的问题，并为那些因为不是视觉学习者或视力受损而不能使用图形的学生提供了一个新的数学交流和发现的渠道。手册和随附的声音文件和软件可在Web和CD上找到。

Mathematical Sciences (21)Sonification is use of non-speech audio to convey information. One widely known and successful application of sonification is the Geiger counter, which represents the intensity of radiation by the tempo of the audible clicks. Sonification is finding new applications across several disciplines and offers another way to communicate, demonstrate, and discover mathematics. Sonifications are not limited to pitch, but include other properties of sound including volume, timbre, and tempo.The primary goal of this proof-of-concept project is to integrate sonification into a one-semester calculus class. It builds on calculus reform efforts that emphasize multiple representations of mathematics including numerical, graphical, analytical, and oral or written representations. Thus the Rule of Four is being expanded to the Rule of Five. Secondary goals of the project include teaching students how to interpret sonifications, identifying design principles for mathematical sonifications, and engaging mathematics, mathematics education, and computer science students in undergraduate research in sonification.Intellectual Merit: Sonification offers an important new method for engaging students who grew up in a multimedia environment. Many students have difficulty completing calculus successfully, and using sonification with the Rule of Four enhances conceptual understanding. The project is developing resources for use in teaching interpretation of sonifications in a laboratory setting and then testing them in classrooms.Broader Impacts: This project is exposing the mathematics community to the use of sonifications in the teaching of calculus. Because properties of functions are central to mathematics, the instructional materials are useful across the mathematics curriculum (e.g., precalculus, algebra, statistics, mathematics for liberal arts majors, and mathematics for preservice teachers.) The project also offers mathematics and computer science majors accessible problems for undergraduate research, and provides students who cannot use graphics because they are not visual learners or are visually impaired a new channel for mathematics communications and discovery. The manuals and accompanying sound files and software are available on the Web and CD.