Cognitive Scaffold

Preparing your thinking workspace

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MENTAL MODEL · M5188

Bat-and-Ball Problem

Bat-and-Ball Problem
Learn & MetacognitionHigh supportCognitive Psychology
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Updated 2026-08-08

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INTRODUCTION

English translation pending.

CORE DEFINITION

A question introduced by Shane Frederick as part of the Cognitive Reflection Test: a bat and a ball cost 1.10 dollars together, and the bat costs 1.00 dollar more than the ball, so how much does the ball cost. The intuitive answer, ten cents, is wrong; the correct answer is five cents. The problem is designed so that an obvious but incorrect response arrives before any computation, and overriding it requires deliberate checking. Performance on the item correlates with measures of reflective thinking and predicts resistance to some decision biases.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Pause protocol: treat a smooth, obvious answer as a signal to verify rather than to proceed. - Arithmetic check: substitute the intuitive answer back into the conditions to see whether it holds. - Round-number suspicion: distrust answers that land exactly on a tidy figure.

anchor

Anchor fast decisions

Familiar phrasing triggers a pattern match, and the matched answer is delivered with the subjective fluency that normally accompanies correctness. Because fluency is used as a cue for truth, the answer feels verified without being checked. Verification requires holding the first answer in mind while running the actual computation, which is effortful and is skipped under time pressure. The item therefore measures whether deliberation is engaged at all, not whether the person can do arithmetic.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Cognitive_reflection_testZH · Explicit
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