Abstract This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties.

中文翻译：

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理解对数概念的基本思维方式

摘要 本研究探讨了两名本科预科生在完成指数函数和对数函数的概念性探索课程时对对数概念的理解。学生们参加了连续的个人教学实验，重点是 Sparky——一种每周都会增加一倍高度的动画神秘仙人掌。指数课程的重点是培养学生对生长因子和元组（例如，倍增）周期的概念，作为有意义地概念化对数和对数属性的基础理解。本文描述了学生在指数和对数增长的介绍性课程中获得的有效概念，