论文标题
在物理学中使用数学：5。功能依赖性
Using math in physics: 5. Functional dependence
论文作者
论文摘要
当学生学习在物理学中使用数学时，他们需要学习的最重要的想法之一是方程不仅是计算工具。它们代表了一起变化的物理变量之间的关系（COVARY）。一个变量或参数的变化与另一个变量的变化有多少相关联取决于它们在方程式中的显示方式：它们的功能依赖性。在入门数学课上很少教导这种关系，而尚未学会将概念思想与数学符号融合的学生可能看不到这个想法的相关性和力量。我们需要明确教授功能依赖，作为我们帮助学生在科学领域有效使用数学的努力的一部分。
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary). How much a change in one variable or parameter is associated with a change in another depends on how they appear in the equation: their functional dependence. Understanding this sort of relationship is rarely taught in introductory mathematics classes, and students who have not yet learned to blend conceptual ideas with mathematical symbols may not see the relevance and power of this idea. We need to explicitly teach functional dependence as part of our effort to help students to learn to use math productively in science.
