Chen Yalin, Campbell Jamie I D
Department of Psychology, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK, Canada, S7N 5A5.
Psychon Bull Rev. 2018 Apr;25(2):739-753. doi: 10.3758/s13423-017-1328-2.
We review recent empirical findings and arguments proffered as evidence that educated adults solve elementary addition problems (3 + 2, 4 + 1) using so-called compacted procedures (e.g., unconscious, automatic counting); a conclusion that could have significant pedagogical implications. We begin with the large-sample experiment reported by Uittenhove, Thevenot and Barrouillet (2016, Cognition, 146, 289-303), which tested 90 adults on the 81 single-digit addition problems from 1 + 1 to 9 + 9. They identified the 12 very-small addition problems with different operands both ≤ 4 (e.g., 4 + 3) as a distinct subgroup of problems solved by unconscious, automatic counting: These items yielded a near-perfectly linear increase in answer response time (RT) yoked to the sum of the operands. Using the data reported in the article, however, we show that there are clear violations of the sum-counting model's predictions among the very-small addition problems, and that there is no real RT boundary associated with addends ≤4. Furthermore, we show that a well-known associative retrieval model of addition facts-the network interference theory (Campbell, 1995)-predicts the results observed for these problems with high precision. We also review the other types of evidence adduced for the compacted procedure theory of simple addition and conclude that these findings are unconvincing in their own right and only distantly consistent with automatic counting. We conclude that the cumulative evidence for fast compacted procedures for adults' simple addition does not justify revision of the long-standing assumption that direct memory retrieval is ultimately the most efficient process of simple addition for nonzero problems, let alone sufficient to recommend significant changes to basic addition pedagogy.
我们回顾了近期的实证研究结果及相关论据，这些研究结果和论据被视作证据，用以表明受过教育的成年人在解决简单加法问题（如3 + 2、4 + 1）时会使用所谓的紧凑程序（例如无意识的自动计数）；这一结论可能具有重大的教学意义。我们首先来看由于伊滕霍夫、特韦诺和巴鲁耶（2016年，《认知》，第146卷，第289 - 303页）所报告的大样本实验，该实验让90名成年人解答从1 + 1到9 + 9的81道一位数加法问题。他们将12道两个操作数均≤4（例如4 + 3）的非常小的加法问题确定为一个独特的子问题组，这些问题是通过无意识的自动计数来解决的：对于这些题目，答案反应时间（RT）与操作数之和呈现近乎完美的线性增长。然而，通过使用该文章中所报告的数据，我们表明在这些非常小的加法问题中明显存在对和计数模型预测的违背，并且不存在与加数≤4相关的实际反应时间界限。此外，我们表明加法事实的一个著名的联想检索模型——网络干扰理论（坎贝尔，1995年）——能够高精度地预测这些问题所观察到的结果。我们还回顾了为简单加法的紧凑程序理论所提出的其他类型证据，并得出结论，这些研究结果本身并不令人信服，且与自动计数仅有微弱的一致性。我们的结论是，关于成年人简单加法快速紧凑程序的累积证据并不足以证明需要修正长期以来的假设，即对于非零问题，直接记忆检索最终是简单加法最有效的过程，更不用说足以建议对基本加法教学法进行重大改变了。
