Empirical Research: Emerging Research: Learning with Multiple Graphical Representations in a Complex, Real-world domain: Intelligent Software Tutors for Fractions

认知科学和教育心理学文献提供了充分的证据表明，明智地结合学习内容的多种表征(MRS)的教学材料和活动可以具有显著的学习益处。这些文献的大部分都集中在文本和图形的组合学习上，只有一部分集中在多个图形表示的学习上。为了从多个表示中受益，学生必须将关键信息连接到不同的表示中。学生在这方面通常必须得到支持(Ainsworth，2006)。这个项目研究了MRS在分数领域的使用，这对中学生来说是一个非常具有挑战性的数学领域，在其中广泛使用图形表示法(例如，饼图、数字线、分数条、集合模型等)。这项研究集中于教学设计者在创建涉及MRS的课程时面临的三个一般性(和开放的)问题：第一，当学习材料被使用多种表征时，学习者应该多频繁地在表征之间切换？第二，什么样的活动能最有效地帮助学生在不同的表征之间建立联系？第三，学生的比例是多少？应该花时间在表征之间建立联系，相对于以单一表征为中心的活动？来自卡内基梅隆大学和弗莱堡大学(德国)的研究人员在一种成熟的教育技术：智能辅导系统的背景下研究了这些问题。这些类型的软件导师已经被证明在一些科学研究中改善了学生的数学学习。卡内基梅隆大学实验室开发的一套创作工具使这些导师的开发比过去更具成本效益，也更容易为教育研究人员所接受。在为期三年的资助期间，该项目将(1)创建基于网络的智能家教，作为分数学习的补充活动；这些家教支持学生使用分数的交互式图形表示，并在这些表示之间建立联系的活动，以及(2)在匹兹堡中学进行对照实验，以调查上述三个研究问题。它将产生关于如何最好地使用分数表示来支持稳健学习的新知识。本研究有可能对中低年级的分数教学产生更有效的指导作用，从而促进以后的数学学习。拟议的软件辅导将在数学辅导网站(http://webmathtutor.org).)上免费提供

The cognitive science and educational psychology literatures provide ample evidence that instructional materials and activities that judiciously combine multiple representations of learning content (MRs) can have significant learning benefits. Much of this literature has focused on learning with a combination of text and figures; only some of it has focused on learning with multiple graphical representations. In order to benefit from multiple representations, students must connect key information across the different representations. Students typically must be supported in doing so (Ainsworth, 2006).This project studies the use of MRs in the domain of fractions, a very challenging area of mathematics for middle-school students in which graphical representations are used extensively (e.g., pie charts, number lines, fraction strips, set models, etc.) The research focuses on three general (and open) questions that instructional designers face when creating a curriculum that involves the use of MRs: First, when multiple representations of learning materials are used, how frequently should learners switch between representations? Second, what kinds of activities are most effective in helping students make connections between different representations? Third, what fraction of the students? time should be devoted to making connections between representations, relative to activities centered on a single representation?Researchers from Carnegie Mellon University and the University of Freiburg (Germany) investigate these questions in the context of an established educational technology: intelligent tutoring systems. These types of software tutors have been shown to improve students' mathematics learning in a number of scientific studies. A set of authoring tools created in a lab at Carnegie Mellon make the development of these tutors more cost effective and more accessible to education researchers than it used to be. During a three-year grant period, the project will (1) create web-based intelligent tutors as supplemental activities for fractions learning; these tutors support activities in which students work with interactive graphical representations of fractions, and make connections between the representations, and (2) conduct controlled experiments in Pittsburgh middle schools to investigate the three research questions outlined above.The proposed research will result in principles for learning with MRs. It will produce new knowledge about how fraction representations can best be used to support robust learning. The proposed research has the potential to produce more effective fractions instruction in the lower and middle grades, and thereby facilitate later mathematics learning. The proposed software tutors will be made freely available on the Mathtutor website (http://webmathtutor.org).