Can approximate mental calculation account for operational momentum in addition and subtraction?

Abstract

The operational momentum (OM) effect describes a cognitive bias whereby we overestimate the results of mental addition problems while underestimating for subtraction. To test whether the OM emerges from psychophysical characteristics of the mental magnitude representation we measured two basic parameters (Weber fraction and numerical estimation accuracy) characterizing the mental magnitude representation and participants' performance in cross-notational addition and subtraction problems. Although participants were able to solve the cross-notational problems, they consistently chose relatively larger results in addition problems than in subtraction problems, thus replicating and extending previous results. Combining the above measures in a psychophysical model allowed us to partially predict the chosen results. Most crucially, however, we were not able to fully model the OM bias on the basis of these psychophysical parameters. Our results speak against the idea that the OM is due to basic characteristics of the mental magnitude representation. In turn, this might be interpreted as evidence for the assumption that the OM effect is better explained by attentional shifts along the mental magnitude representation during mental calculation.

Keywords:

• Mental number line
• Attention
• Operational momentum
• Approximate number system
• Weber fraction

Notes

¹Due to the wrong use of a variable defining the lower boundary of the jittering range in the digits–digits condition, the presented response alternatives were asymmetrically distributed around the correct outcome. The numerical range of response alternatives that were smaller than the actual outcome was larger than the numerical range of those that were larger than the actual outcome. Consequently, on average, participants chose values that were smaller than the actual outcome for both operations (addition and subtraction).