Center for Research and Interdisciplinarity, Paris Descartes University, Paris, France.
IDEA Lab, Faculty of Psychology and Educational Sciences, University of Geneva, Geneva, Switzerland.
Psychon Bull Rev. 2019 Oct;26(5):1738-1746. doi: 10.3758/s13423-019-01628-3.
Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical problems involving these entities? We argue that such daily-life knowledge interferes with arithmetic word problem solving, to the extent that experts can be led to failure in problems involving trivial mathematical notions. We created problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14 - 2 = 12. A first experiment studied how university-educated adults dealt with seemingly simple arithmetic problems evoking knowledge that was either congruent or incongruent with the problems' solving procedure. Results showed that in the latter case, the proportion of participants incorrectly deeming the problems "unsolvable" increased significantly, as did response times for correct answers. A second experiment showed that expert mathematicians were also subject to this bias. These results demonstrate that irrelevant non-mathematical knowledge interferes with the identification of basic, single-step solutions to arithmetic word problems, even among experts who have supposedly mastered abstract, context-independent reasoning.
我们对于苹果、汽车或蓝精灵的了解是否会妨碍我们解决涉及这些实体的数学问题的能力?我们认为,这种日常生活知识会干扰算术应用题的解决,以至于专家在涉及琐碎数学概念的问题上也可能失败。我们创建了一些问题,唤起了我们非数学的、一般知识的不同方面。它们可以通过一个涉及小数量的减法来解决,例如 14-2=12。第一个实验研究了受过大学教育的成年人如何处理看似简单的算术问题,这些问题唤起的知识与问题的解决过程要么一致,要么不一致。结果表明,在后一种情况下,参与者错误地认为问题“无法解决”的比例显著增加,正确答案的反应时间也增加了。第二个实验表明,专家数学家也受到这种偏见的影响。这些结果表明,无关的非数学知识会干扰对算术应用题基本的、单步解决方案的识别,即使是那些据称已经掌握了抽象、独立于上下文推理的专家也会受到这种影响。