Heuristics and biases in mental arithmetic: revisiting and reversing operational momentum

ABSTRACT

Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3−0) but reverse OM with non-zero problems (e.g., 2+1, 4−1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving.

KEYWORDS:

• Heuristics
• mental arithmetic
• mental number line
• operational momentum
• problem-solving

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Please note that our participants were Hebrew-speaking healthy adults. They read arithmetic problems from left to right; hence, the first operand is their anchor and reading direction for text is an irrelevant concern here (see also Fischer & Shaki, 2016, who found typical left-to-right spatial-numerical associations in this population whenever the task does not require left/right responses).

² Both the main effect of starting condition and the steeper increase of line lengths with magnitudes in the line compared to the dot starting condition reflect perceptual anchoring – as opposed to the conceptual anchoring we are discussing here.

Additional information

Funding

MHF was funded by DFG [grant FI 1915/2-1] “Manumerical cognition”.