Mathematical Thinking Lab, School of Education and School of Neuroscience, Tel Aviv University, Tel Aviv, Israel.
Cogn Res Princ Implic. 2022 Jul 6;7(1):58. doi: 10.1186/s41235-022-00409-2.
Representing the base-10 structure of numbers is a challenging cognitive ability, unique to humans, but it is yet unknown how precisely this is done. Here, we examined whether and how literate adults represent a number's full syntactic structure. In 5 experiments, participants repeated number-word sequences and we systematically varied the order of words within each sequence. Repetition on grammatical sequences (e.g., two hundred ninety-seven) was better than on non-grammatical ones (hundred seven two ninety). We conclude that the participants represented the number's full syntactic structure and used it to merge number words into chunks in short-term memory. Accuracy monotonously improved for sequences with increasingly longer grammatical segments, up to a limit of ~ 4 words per segment, irrespectively of the number of digits, and worsened thereafter. Namely, short chunks improved memorization, whereas oversized chunks disrupted memorization. This chunk size limit suggests that the chunks are not based on predefined structures, whose size limit is not expected to be so low, but are created ad hoc by a generative process, such as the hierarchical syntactic representation hypothesized in Michael McCloskey's number-processing model. Chunking occurred even when it disrupted performance, as in the oversized chunks, and even when external cues for chunking were controlled for or were removed. We conclude that the above generative process operates automatically rather than voluntarily. To date, this is the most detailed account of the core representation of the syntactic structure of numbers-a critical aspect of numerical literacy and of the ability to read and write numbers.
表示以 10 为基数的数字结构是一种具有挑战性的认知能力，这是人类独有的，但目前尚不清楚人类是如何精确做到这一点的。在这里，我们研究了识字成年人是否以及如何表示数字的完整句法结构。在 5 项实验中，参与者重复数字-单词序列，我们系统地改变每个序列中单词的顺序。在语法序列（例如，two hundred ninety-seven）上的重复要好于在非语法序列（hundred seven two ninety）上的重复。我们的结论是，参与者表示了数字的完整句法结构，并将其用于将数字单词合并到短期记忆中的块中。随着语法片段越来越长，序列的准确性单调提高，最长可达每个片段约 4 个单词，而与数字的位数无关，此后则恶化。也就是说，短块提高了记忆，而过大的块则破坏了记忆。这种块大小限制表明，块不是基于预定义的结构创建的，而预定义结构的大小限制预计不会如此低，而是通过生成过程创建的，例如 Michael McCloskey 的数字处理模型中假设的层次句法表示。即使在过大的块中破坏了性能，也会发生块处理，即使控制或去除了块处理的外部线索。我们的结论是，上述生成过程是自动而非自愿的。到目前为止，这是对数字句法结构核心表示的最详细描述，是数字读写能力和数字能力的关键方面。
