Negative quantities in mechanics: a fine-grained math and physics conceptual blend?
Negative quantities in mechanics: a fine-grained math and physics conceptual blend?
复制标题
力学中的负量：细粒度的数学和物理概念混合？
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Brahmia
中科院分区：
文献类型：
--
作者：
S. Brahmia
物理学专家在与物理量相关的负号的各种含义之间流畅地移动。虽然研究学生对负数的理解在数学教育中很常见，但很少有研究关注学生在物理量背景下对负数的解释。在这项研究中，我们调查了学生的推理与加速度，工作和位置相关的负号。消极的数学性质的理论模型指导我们开发的三个开放式的调查项目，管理学生在微积分为基础的物理课程。我们观察到，使用矢量方向作为资源来推理负加速度和负功的学生，在我们调查中探索的三种消极性质中，往往比主要使用基于运动和能量的推理的学生更灵活。我们随后进行了一项二次研究，要求干预组在消极工作的背景下从数学角度解释他们的推理，并观察到这种认识上的推动导致了显着的改善。我们将与物理量相关的生产性推理空间解释为一个紧密的认知混合体，其中物理和数学是不可区分的。这种解释与先前基于可分离的物理世界和数学世界的模型不同。
Physics experts move fluidly between varied meanings of the negative sign associated with physical quantities. Although researching student understanding of negative numbers is common in mathematics education, little research has been published that focusses on students’ interpretation of negativity in the context of physics quantities. In this study, we investigated student reasoning about the negative sign associated with acceleration, work and position. A theoretical model of the mathematical nature of negativity guided our development of three open-ended survey items which were administered to students in introductory calculus-based physics courses. We observed that students who use vector direction as a resource to reason about negative acceleration and negative work tend to be more flexible across the three natures of negativity probed in our survey than students who use predominantly motion and energy-based reasoning. We followed up with a secondary study in which the intervention group was asked to explain their reasoning from a mathematical perspective in the context of negative work, and observed that this epistemic nudge led to significant improvement. We interpret the productive reasoning space associated with physics quantity as a tight cognitive blend in which the physics and the mathematics are indistinguishable. This interpretation departs from prior models based on separable physics worlds and math worlds.