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

TL;DR

This paper analyzes self-assessment confidence methods for secondary school math students, proposing improved scoring functions, and examines their varied effects on student learning across different schools and ability levels.

Contribution

It introduces new scoring functions that incentivize truthful confidence reporting and analyzes their impact on teaching effectiveness and student self-assessment skills.

Findings

Certain scoring methods promote truthful confidence reporting.

Effects of SAC vary significantly across schools and ability groups.

Incorporating SAC can improve student self-awareness but has mixed educational benefits.

Abstract

We first consider the method of scoring students' self-assessment of confidence (SAC) used by Foster in [1], and find that with it reporting their true confidence is not the optimal strategy for students. We then identify all continuously differentiable scoring functions that both drive the student towards the optimal strategy of truthful reporting of confidence and satisfy an additional axiom ensuring motivation also to give correct answers to the questions asked. We discuss the relative merits of some of them, and favour splitting marks between a signed mark for correctness or not and a second mark for SAC based on the apparent Shannon information on whether the answer is correct, as the latter also imparts a useful life skill, namely avoiding being overconfident. We then turn to do further Bayesian analysis of the public dataset associated with [1], showing that the effects of incorporating SAC into teaching vary both by school and by quartile of ability in class. Finally we speculate on the potential reasons for this and discuss how future research could identify and avoid some of the causes.