What makes us 'choke' under stress? Well, that depends. For athletes it seems choking involves being too 'self-aware' of performance. It's not really that worries are taking too much away from thinking. When you're in athletic flow, at least the idea goes, you shouldn't be thinking. Choking is conquered in athletics by learning to forget that you're being watched. Golfers that choke don't do so because of being overloaded in working memory. They manage perfectly well if given additional concentration tasks to perform while they put.
Performing complicated calculations is another story though. In this sad figure, see how the mightiest subjects with working memory were also the most likely to choke. Choking during activities like this is is caused by competition for attention and working memory. Maybe the highest working memory folks are already working to near capacity. Unlike golfers, you can make these guys choke on their math problems by having them do another concentration task at the same time.
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