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.