Because science is a modeling enterprise, a key question for educators is: What kind of repertoire can initiate students into the practice of generating, revising, and critiquing models of the natural world? Based on our 20 years of work with teachers and students, we nominate variability as a set of connected key ideas that bridge mathematics and science and are fundamental for equipping youngsters for the posing and pursuit of questions about science. Accordingly, we describe a sequence for helping young students begin to reason productively about variability. Students first participate in random processes, such as repeated measure of a person's outstretched arms, that generate variable outcomes. Importantly, these processes have readily discernable sources of variability, so that relations between alterations in processes and changes in the collection of outcomes can be easily established and interpreted by young students. Following these initial steps, students invent and critique ways of visualizing and measuring distributions of the outcomes of these processes. Visualization and measure of variability are then employed as conceptual supports for modeling chance variation in components of the processes. Ultimately, students reimagine samples and inference in ways that support reasoning about variability in natural systems.

中文翻译：

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掌握可变性

因为科学是一项建模事业，教育工作者面临的一个关键问题是：什么样的曲目可以引导学生进入生成、修改和批判自然世界模型的实践中？基于我们与教师和学生 20 年的合作，我们将可变性命名为一组连接数学和科学的相互关联的关键思想，并且是装备年轻人提出和追求科学问题的基础。因此，我们描述了一个帮助年轻学生开始对可变性进行有效推理的序列。学生首先参与随机过程，例如重复测量一个人伸出的手臂，这会产生可变的结果。重要的是，这些过程具有易于识别的可变性来源，这样，年轻学生就可以很容易地建立和解释过程变化和结果收集变化之间的关系。按照这些初始步骤，学生发明并批判了可视化和测量这些过程结果的分布的方法。然后，可变性的可视化和测量被用作概念支持，以对过程组件中的机会变化进行建模。最终，学生以支持自然系统可变性推理的方式重新构想样本和推理。然后，可变性的可视化和测量被用作概念支持，以对过程组件中的机会变化进行建模。最终，学生以支持自然系统可变性推理的方式重新构想样本和推理。然后，可变性的可视化和测量被用作概念支持，以对过程组件中的机会变化进行建模。最终，学生以支持自然系统可变性推理的方式重新构想样本和推理。