Visualizations while Solving Modelling Problems 2

实证研究结果的有效性绘图指令，以促进学生的建模能力在几何领域的混合，并指出，绘图特定的战略知识（战略知识绘图，SKD）起着重要的作用。第一阶段资助（“ViMo 1”）的结果证实，声明性SKD（即，关于好的绘图的特性的知识）是产生具有高水平精度的绘图和找到建模问题的解决方案的必要但不充分的先决条件。因此，后续项目“ViMo 2”的总体目标是研究手术SKD（即，如何在建模过程中构建和使用绘图的知识）在几何领域的学生有效使用绘图和建模表现中起作用。除了程序性SKD，我们还考虑了陈述性SKD以及认知、元认知和动机因素。在后续项目的框架内，可以预期在以下领域的理论，经验和实践相关的调查结果：第一，该项目将提供战略培训的潜力，以促进数学建模能力在几何领域的调查结果。第二，该项目将有助于研究自我生成的图纸。与第一阶段的资金相比，眼动的记录和分析有望在策略执行层面上对绘画教学背后的机制有更多的了解。使用EMME（眼动建模示例）也有望深入了解这种创新形式的数学和科学学习教学的潜力。第三，本项目将有助于学习策略的研究。我们希望证实和扩展Borkowski等人的假设关系。S（2000）的理论模型，区分SKD的声明性和程序性部分。第四，在实际应用方面，本研究所开发的学习环境可应用于数学教学。

Empirical findings on the effectiveness of drawing instructions to promote students’ modelling competencies in the field of geometry are mixed and indicate that drawing-specific strategy knowledge (strategic knowledge about drawing, SKD) plays an important role. Results from the first phase of funding ("ViMo 1") have confirmed that declarative SKD (i.e., knowledge about the characteristics of a good drawing) is a necessary but not sufficient precondition for producing drawings with a high level of accuracy and for finding a solution to a modeling problem. The overarching goal of the follow-up project "ViMo 2" is therefore to investigate what role procedural SKD (i.e., knowledge of how to construct and use a drawing in the modeling process) plays in the effective use of drawings and in modeling performance by students in the field of geometry. In addition to procedural SKD, we are also taking into account declarative SKD as well as cognitive, metacognitive, and motivational factors. Within the framework of the follow-up project, theoretical, empirical, and practice-relevant findings can be expected in the following areas: First, the project will provide findings on the potential of strategy training for promoting mathematical modelling competencies in the field of geometry. Second, the project will contribute to research on self-generated drawings. Compared with the first phase of funding, the recording and analysis of eye movements promises additional insights into the mechanisms behind instruction in drawing at the level of strategy execution. The use of EMME (Eye Movement Modeling Examples) also promises insights into the potential of this innovative form of instruction for mathematics and science learning. Third, the project will contribute to learning strategy research. We expect to confirm and expand relationships postulated in Borkowski et al.’s (2000) theoretical model by distinguishing between declarative and procedural parts of SKD. Forth, regarding practical implications, the learning environment that we are developing in the project can be used in mathematics instruction.