SBIR Phase I: Telling Mathematical Stories: A Combination of Research and Technology

Cappo这个小企业创新研究第一阶段项目的重点是将当前研究与最新技术结合到多媒体环境中的能力，使早期学习者能够获得对数字感的概念理解，为他们学习更正式的数学做好准备。目前的研究已经确定了这个项目的四个中心：现实问题、模型、自己的作品和声学。现实问题是那些在孩子的日常经历中实际发生的数学情况，因此对他或她有意义。模型是任何数量的表征，允许孩子们应用他们自己对数学的理解。这些可能包括他们自己发明的和非正式的策略，使用数轴或空白数轴，或其他模型，如头串，算术架等。自己的作品是指儿童对数学情境的建构或用他们自己的方式对它们的描述。声学指的是研究儿童如何通过声音、节奏和运动来学习，以及这如何影响他们对数字作为结构表征的理解。根据目前对早期学习的研究，所有这些都对儿童发展数学理解的方式产生影响。此外，众所周知，这种理解是通过不同的抽象层次逐步发展的，例如：通过使用发明的或正常的策略将具体问题数学化，到使用模型，然后到形式化或抽象数学。该项目旨在研究创造一个积极和现实的学习环境的可行性，在这个环境中，学生能够建立在理解水平的基础上。技术的新进步，包括使用视频（学生可以操纵和“编辑”来描绘数学）、图形（用作构建模型或数学情况的表示）、声音（用于语音描述或加强学习中的声学含义）和文本工具，都可以放大研究中定义的小学生的学习潜力。主要目标是充分利用这些技术的优势，同时保持对小学生友好的界面。学校市场需要一种结合高度视觉和逼真的视频和声音以及有趣的数学问题的K-2数学课程。一个超越练习和实践的项目，整合了新的学习研究，特别是上面提到的那些方面，可以对小学的数学教学和数字感的发展产生很大的影响。此外，拟议的产品可以想象跨越到国内市场。

9560768 Cappo This Small Business Innovation Research Phase I project focuses on the ability to conjoin current research with the latest technology into a multimedia environment that allows early learners to gain the conceptual understanding of number sense that will prepare them for more formal mathematics. Current research has defined four foci which are at the center of this project: realistic problems, models, own productions, and acoustics. Realistic problems are those mathematical situations that actually occur in a child's daily experience and so hold meaning for him or her. Models are any number of representations that allow children to apply their own understanding of mathematics. These may include their own invented and informal strategies, use of the number line or blank number line, or other models such as the bead string, arithmetic rack, etc. Own productions refers to children's constructions of mathematical situations or descriptions of them in their own terms. Acoustics refers to studies of how children learn through sound, rhythm, and movement and how this affects their understanding of numbers as structural representations. According to current research on early learning, all of these have an affect on the way in which children develop their understanding of mathematics. In addition, it is known that this understanding progresses gradually through varying levels of abstraction, such as the following: mathematizing concrete problems through the use of invented or normal strategies, to the use of models, and then to formal or abstract mathematics. This project intends to study the feasibility of creating an active and realistic learning environment in which students are able to build upon the levels of understanding. New advancements in technology, including the use of video (which students can manipulate and 'edit' to portray mathematics), graphics (to use as constructed models or representations of mathematical situations), sound (for vocal descriptions or as r einforcement of acoustic implications in learning), and text tools can all amplify the learning potential of primary grade students as defined through the research. A major objective is to exploit these technologies to their fullest advantage while maintaining an interface that is friendly to the primary student. A K-2 Math program which incorporates highly visual and realistic video and sound with intriguing mathematics problems is needed in the school market. A program that goes beyond drill and practice and integrates new research on learning, especially those aspects identified above, could make a great impact on mathematics instruction and the development of number sense in the primary years. Also, the proposed product could conceivably cross over to the Home Market.