Understanding the development of non-linear processes such as economic or population growth is an important prerequisite for informed decisions in those areas. In the function-learning paradigm, people's understanding of the function rule that underlies the to-be predicted process is typically measured by means of extrapolation accuracy. Here we argue, however, that even though accurate extrapolation necessitates rule-learning, the reverse does not necessarily hold: Inaccurate extrapolation does not exclude rule-learning. Experiment 1 shows that more than one third of participants who would be classified as “exemplar-based learners” based on their extrapolation accuracy were able to identify the correct function shape and slope in a rule-selection paradigm, demonstrating accurate understanding of the function rule. Experiment 2 shows that higher proportions of rule learning than ruleapplication in the function-learning paradigm is not due to (i) higher a priori probabilities to guess the correct rule in the rule-selection paradigm; nor is it due to (ii) a lack of simultaneous access to all function values in the function-learning paradigm. We conclude that rule application is not tantamount to rule-learning, and that assessing rule xlearning via extrapolation accuracy underestimates the proportion of rule learners in function-learning experiments.

了解经济或人口增长等非线性过程的发展是在这些领域做出明智决策的重要先决条件。在函数学习范式中，人们对作为待预测过程基础的函数规则的理解通常通过外推精度来衡量。然而，在这里我们认为，即使准确的外推需要规则学习，反过来也不一定成立：不准确的外推并不排除规则学习。实验 1 表明，超过三分之一的根据外推精度被归类为“基于范例的学习者”的参与者能够在规则选择范例中识别正确的函数形状和斜率，表明对函数规则的准确理解. 实验 2 表明，在函数学习范式中，规则学习的比例高于规则应用的比例并不是因为（i）在规则选择范式中猜测正确规则的先验概率更高；也不是因为 (ii) 无法同时访问功能学习范式中的所有功能值。我们得出结论，规则应用并不等同于规则学习，并且通过外推精度评估规则 xlearning 低估了功能学习实验中规则学习者的比例。