Question 1 - Study design for measuring the growth of the ability to do metacognitive monitoring.
I think there are two approaches to studying how the brain develops over time -- one approach might be a longitudinal study that tracks performance on a set of activities over time, tracked with a single-event study that brings in populations at various age groups. One idea that might be worth investigating in addition is whether this growth is gradual over time or if it is punctuated by some specific internal milestone. So it would be worthwhile to try out various frequencies within the longitudinal study to see if you can find any evidence for a concentrated period where the child suddenly leaps forward in their abilities.
At any rate, to assess metacognitive monitoring and control, I think you'd want to collect data for how different ages seem to fare at the memorization task, including asking them to give you a FoK and JoL assessment as they go. You could watch how an individual's calibration curve changes over time, and compare that against a standard age group curve to see if your intervention in testing them also changed the result.
Playing 'memory' at home also seems like a way to increase the accuracy of one's FoK, and maybe JoL. Asking if the child plays memory or has played it frequently might be a way to increase understanding of how children develop these skills as part of the study design.
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