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We first consider the method of scoring students' self-assessment ofconfidence (SAC) used by Foster in [1], and find that with it reporting theirtrue confidence is not the optimal strategy for students. We then identify allcontinuously differentiable scoring functions that both drive the studenttowards the optimal strategy of truthful reporting of confidence and satisfy anadditional axiom ensuring motivation also to give correct answers to thequestions asked. We discuss the relative merits of some of them, and favoursplitting marks between a signed mark for correctness or not and a second markfor SAC based on the apparent Shannon information on whether the answer iscorrect, as the latter also imparts a useful life skill, namely avoiding beingoverconfident.  We then turn to do further Bayesian analysis of the public dataset associatedwith [1], showing that the effects of incorporating SAC into teaching vary bothby school and by quartile of ability in class. Finally we speculate on thepotential reasons for this and discuss how future research could identify andavoid some of the causes.

Methods of self-assessment of confidence for secondary school maths students, and the benefits or otherwise of using such methods