Fostering the development of fraction magnitude understanding at the beginning of secondary education - behavioral effects and neural correlates

理解数字符号所代表的大小信息是数字领域数学发展的重要一步。然而，研究表明，许多学生在理解符号分数所代表的大小方面存在困难。到目前为止，我们还不清楚我们如何从理论上描述分数量级理解的发展，以及如何通过教学最好地促进这种发展。在这项干预研究中，我们旨在促进德国六年级学生(大约12岁)分数量级理解的发展。我们的研究使我们能够在现有理论的基础上对我们预期的学习效果进行实证测试。使用跨学科的方法，我们将能够不仅在行为上而且在神经层面上描述学习。之前的神经科学研究已经首次深入了解了成年人碎片处理的神经关联。在这个项目中，我们将调查在校学生是否表现出与成人相同的激活模式。此外，我们将首次能够描述由于学习分数而引起的大脑激活的变化。通过这样做，这个项目对神经科学和教育交叉的新兴研究领域做出了贡献。我们将使用一个实验组和两个控制组的前测后设计。为了在有控制的方式下实施干预，我们使用了一个基于计算机的学习环境，该环境依赖于认知心理学和数学教育理论对外部视觉表征的使用。学习环境特别注重将分数的符号表示和视觉表示联系起来。我们将使用磁共振成像来描绘学习效果的神经关联。由于其高空间分辨率，该方法可以识别相关的大脑结构。该项目的结果将为理论上有良好基础的教学方法的有效性提供经验支持。研究结果还将更全面地加深我们对数值学习的神经关联的理解。我们的目标是通过整合数学教育和神经科学的专业知识，最大限度地提高跨学科方法的外部有效性。

Understanding the magnitude information represented by number symbols is an important step of mathematical development in the domain of numbers. However, research shows that many school students struggle with understanding magnitudes represented by symbolic fractions. It is to date unclear how we can theoretically describe the development of fraction magnitude understanding, and how we can foster best this development through instruction.In this intervention study, we aim at fostering the development of fraction magnitude understanding in German sixth-graders (about 12 years of age). Our study allows us to test empirically the learning effects that we expect based on current theories. Using an interdisciplinary approach, we will be able to describe learning not only on the behavioural but also on the neural level. Previous neuroscience research has gained first insights into the neural correlates of fraction processing in adults. In this project we will investigate whether school students show the same activation patterns as adults do. Furthermore, we will be able to describe for the first time the changes in brain activation arising from learning of fractions. In doing so, this project contributes to the emerging field of research at the intersection between neuroscience and education.We will use a pre-post test design with one experimental and two control groups. To implement the intervention in a controlled manner, we use a computer-based learning environment, which relies on cognitive psychology and mathematics education theories on the use of external visual representations. The learning environment focuses particularly on linking symbolic and visual representations of fractions. We will use magnetic resonance imaging to map the neural correlates of the learning effects. Due to its high spatial resolution, this method allows identifying the relevant brain structures.The results from this project will provide empirical support for the effectiveness of a theoretically well grounded teaching approach. The results will also enhance our understanding of the neural correlates of numerical learning more generally. We aim at maximizing the external validity of an interdisciplinary approach by integrating expertise from mathematics education and neuroscience.