This paper brings together research on slope from mathematics education and research on line of best fit from statistics education by considering what knowledge of slope students transfer to a novel task involving determining the placement of an informal line of best fit. This study focuses on two students who transitioned from placing inaccurate to accurate lines of best fit during a task-based interview. The analysis focuses on describing shifts in slope reasoning that accompanied the change to accurately placed lines, and investigates factors that may have influenced the shift in reasoning. The results have implications for the teaching of both slope and the line of best fit.

中文翻译：

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最佳拟合的斜率和线：知识转移案例研究

本文通过考虑斜率学生的哪些知识转移到涉及确定非正式最佳拟合线的位置的新任务，将数学教育中的斜率研究和统计教育中的最佳拟合线研究结合起来。这项研究的重点是两名学生，他们在基于任务的面试中从放置不准确的线过渡到最适合的准确线。分析的重点是描述随着精确放置线的变化而发生的斜率推理的变化，并调查可能影响推理变化的因素。结果对斜率和最佳拟合线的教学都有影响。