Metacognition is central to children’s cognitive development. However, there is conflicting evidence about children’s ability to accurately monitor their performance and subsequently control their behavior. This is of particular interest for mathematics topics on which children exhibit persistent misconceptions—that is, when children’s knowledge of a topic is inaccurate, yet resistant to change. This study investigated elementary school children’s metacognitive regulation on mathematical equivalence problems (N = 52, ages 6.7–9.8 years), including their ability to accurately monitor their certainty and their ability to control their behavior by making strategic help-seeking decisions. Results revealed that children were exceedingly confident—even when their answers were incorrect—resulting in relatively low accurate monitoring scores. However, their help-seeking decisions were largely strategic—reflecting children’s tendency to not ask for help when feeling confident—resulting in relatively high control scores. Additionally, individual differences in accurate monitoring and in strategic control were positively correlated with children’s comprehensive knowledge of mathematical equivalence, and the correlation with accurate monitoring held up after controlling for baseline accuracy, certainty, and help-seeking. Collectively, these results suggest that children may face unique, but critically important, metacognitive challenges when solving mathematical equivalence problems.

中文翻译：

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关于数学对等问题的元认知监控和帮助决策

元认知对于儿童的认知发展至关重要。但是，关于儿童能否准确监控自己的表现并随后控制其行为的能力，有相互矛盾的证据。对于儿童表现出持续性误解的数学主题，这尤其令人感兴趣，也就是说，当儿童对某个主题的知识不准确，但却难以改变时。这项研究调查了小学儿童对数学等价问题（N = 52岁，年龄在6.7-9.8岁之间），包括他们通过策略性的寻求帮助决策来准确监控其确定性的能力以及控制其行为的能力。结果显示，即使答案不正确，孩子们也会充满信心，从而导致较低的准确监测分数。但是，他们的寻求帮助的决定在很大程度上具有战略意义-反映出孩子自信时倾向于不寻求帮助的倾向-导致控制得分较高。此外，在准确监控和策略控制方面的个体差异与儿童的数学等效全面知识正相关，在控制了基线准确性，确定性和寻求帮助后，与准确监控的相关性得以保持。总的来说，