Department of Psychology, Ariel University, Ariel, Israel.
Department of Psychology, Potsdam University, Potsdam, Germany.
Psychol Res. 2024 Nov 27;89(1):27. doi: 10.1007/s00426-024-02035-7.
Mental arithmetic is widely studied, both with symbolic digits and with non-symbolic dot patterns that require operand estimation. Several studies reported surprising biases in adults' performance with both formats while their direction (over/underestimation in addition/subtraction) remains controversial (operational momentum effect or OM; Prado & Knops, Prado and Knops, Psychonomic Bulletin & Review, in Press., 2024). Theoretical accounts of OM make opposing predictions, thus enabling a decisive test: Using symbolic stimuli and responses, we enabled accurate operand encoding and result reporting, thus leaving mental calculation as only source of bias. Importantly, we manipulated operand order through calculation instructions (e.g., "29 + 19" vs. "add 19 to 29") to assess the crucial role of first operand size as cognitive anchor. With both auditory (Experiment 1, N = 30) and visual presentation (Experiment 2, N = 30), we observed reverse OM, i.e., overestimations in subtraction and underestimations in addition. Importantly, this instance of operation-based anchoring was independent of a second anchoring effect related to operand order: A large operand is a stronger anchor when mentioned first. Our discovery of both operation-based and order-based anchoring extends the well-known anchoring effect into mental arithmetic and eliminates several competing theories about the origin of OM.
心算在符号数字和需要操作数估计的非符号点模式方面都得到了广泛的研究。几项研究报告称，成年人在这两种格式下的表现都存在令人惊讶的偏差，但其方向（加法或减法的高估或低估）仍存在争议（操作动量效应或 OM；Prado & Knops，2024 年，心理学报与评论，待发表）。OM 的理论解释做出了相反的预测，因此可以进行决定性的测试：我们使用符号刺激和反应，使操作数的准确编码和结果报告成为可能，从而使心算成为唯一的偏差来源。重要的是，我们通过计算指令（例如，“29+19”与“add 19 to 29”）来操纵操作数的顺序，以评估第一个操作数大小作为认知锚的关键作用。在听觉（实验 1，N=30）和视觉呈现（实验 2，N=30）中，我们观察到相反的 OM，即减法高估和加法低估。重要的是，这种基于操作的锚定与与操作数顺序相关的第二个锚定效应无关：当首先提到大操作数时，它是一个更强的锚。我们对基于操作和基于顺序的锚定的发现将著名的锚定效应扩展到心算中，并消除了关于 OM 起源的几个竞争理论。
