Assessing orienting of attention to understand the time course of mental calculation

Anchoring bias in mental arithmetic

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.

Spatial attention in mental arithmetic: A literature review and meta-analysis

We review the evidence for the conceptual association between arithmetic and space and quantify the effect size in meta-analyses. We focus on three effects: (a) the operational momentum effect (OME), which has been defined as participants' tendency to overestimate results of addition problems and underestimate results of subtraction problems; (b) the arithmetic cueing effect, in which arithmetic problems serve as spatial cues in target detection or temporal order judgment tasks; and (c) the associations between arithmetic and space observed with eye- and hand-tracking studies. The OME was consistently found in paradigms that provided the participants with numerical response alternatives. The OME shows a large effect size, driven by an underestimation during subtraction while addition was unbiased. In contrast, paradigms in which participants indicated their estimate by transcoding their final estimate to a spatial reference frame revealed no consistent OME. Arithmetic cueing studies show a reliable small to medium effect size, driven by a rightward bias for addition. Finally, eye- and hand-tracking studies point to replicable associations between arithmetic and eye or hand movements. To account for the complexity of the observed pattern, we introduce the Adaptive Pathways in Mental Arithmetic (APiMA) framework. The model accommodates central notions of numerical and arithmetic processing and helps identifying which pathway a given paradigm operates on. It proposes that the divergence between OME and arithmetic cueing studies comes from the predominant use of non-symbolic versus symbolic stimuli, respectively. Overall, our review and findings clearly support an association between arithmetic and spatial processing.

Embodied Processing at Six Linguistic Granularity Levels: A Consensus Paper

Language processing is influenced by sensorimotor experiences. Here, we review behavioral evidence for embodied and grounded influences in language processing across six linguistic levels of granularity. We examine (a) sub-word features, discussing grounded influences on iconicity (systematic associations between word form and meaning); (b) words, discussing boundary conditions and generalizations for the simulation of color, sensory modality, and spatial position; (c) sentences, discussing boundary conditions and applications of action direction simulation; (d) texts, discussing how the teaching of simulation can improve comprehension in beginning readers; (e) conversations, discussing how multi-modal cues improve turn taking and alignment; and (f) text corpora, discussing how distributional semantic models can reveal how grounded and embodied knowledge is encoded in texts. These approaches are converging on a convincing account of the psychology of language, but at the same time, there are important criticisms of the embodied approach and of specific experimental paradigms. The surest way forward requires the adoption of a wide array of scientific methods. By providing complimentary evidence, a combination of multiple methods on various levels of granularity can help us gain a more complete understanding of the role of embodiment and grounding in language processing.