"Of course I will...": The combined effect of certainty and level of expectancies on persistence and performance

The importance of performance expectancies for the prediction of regulation of behavior and actual performance has long been established. Building on theories from the field of social cognition, we suggest that the level of performance expectancies, as well as the certainty of the expectancy, have a joint influence on an individual’s beliefs and behavior. In two studies (one cross sectional using a sample of secondary school students and one longitudinal using a sample of university students) we found that expectancies more strongly predicted persistence, and subsequent performance, the more certain the expectancy was. This pattern was found even if prior performance was controlled, as in Study 2. The data give an indication that it may be useful to include certainty as an additional variable in expectancy models.

How task experience influences students' performance expectancies: The role of certainty

The importance of performance expectancies for predicting behavior has long been highlighted in research on expectancy-value models. These models do not take into account that expectancies may vary in terms of their certainty. The study tested the following predictions: task experience leads to a higher certainty of expectancies; certainty and mean expectancies are empirically distinguishable; and expectancies held with high certainty are more accurate for predicting performance. 273 Grade 8 students reported their performance expectancy and the certainty of expectation with regard to a mathematics examination immediately before and after the examination. Actual grades on the examination were also assessed. The results supported the predictions: there was an increase in certainty between the two times of measurement; expectancies and certainty were unrelated at both times of measurement; and for students initially reporting higher certainty, the accuracy of the performance expectancy (i.e., the relation between expectancy and performance) was higher than for students reporting lower certainty. Given lower certainty, the accuracy increased after the students had experience with the examination. The data indicate that it may be useful to include certainty as an additional variable in expectancy-value models.

Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).