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Purpose – The aim of this chapter is to analyze the measurement error due to partial observability of circumstances, given the current methodologies used to capture the inequality of opportunity.

Methodology – We limit our analysis to the case in which IOp is measured by using an inequality index and evaluated according to the ex ante and the ex post approaches proposed by Checchi and Peragine (2010). Both approaches rely on the use of two hypothetical distributions obtained by standardizing and smoothing processes so that in one of them all inequalities are due to effort and in the other they are all caused by individuals circumstances. The impact of a change in the observability of circumstances has been analyzed directly in the first case (ex ante approach) and indirectly in the second (ex post approach). Hence, in the latter results are obtained by using a decomposable inequality index, while in the first case the result holds for any Lorenz consistent inequality index.

Findings – We have shown that, in both cases, we can only identify a lower bound of opportunity inequality, and the results obtained when measuring IOp with the two approaches are biased in the same direction.

Originality – The idea that inequality of opportunity, as it is generally measured, is only a lower bound of the real inequality of opportunity has already been hinted in Peragine (2004a), Fleurbaey (2008, Chap. 9), and Ferreira and Gignoux (2011). We attempt to bring this intuition to complete fruition in this chapter by providing clear and distinct demonstrations of this result for both the ex ante and the ex post approach for measuring IOp.

In this chapter the potential to use water-based Trombe walls to provide heated water for building applications during the summer months is investigated. Design Builder software is used to model a simple single-story building with a south-facing Trombe wall. The effects of using different thermal storage mediums within the Trombe wall on building heating loads during the winter and building cooling loads during the summer are modeled. The amount of thermal energy stored and temperature of water within the thermal storage medium during hot weather conditions were also simulated. On a sunny day on Toronto, Canada, the average temperature of the water in a Trombe wall integrated into a single-story building can reach ∼57°C, which is high enough to provide for the main hot water usages in buildings. Furthermore, the amount of water heated is three times greater than that required in an average household in Canada. The results from this work suggest that water-based Trombe walls have great potential to enhance the flexibility and utility of Trombe walls by providing heated water for building applications during summer months, without compromising performance during winter months.

The quality of students' relationships with their teachers plays a significant role in their success in school. Social and emotional learning (SEL) curriculums show great promise for supporting student development. However, quality implementation requires that teachers recognize and understand how their behavior and interactions with students impact the development of these skills. The Prosocial Classroom Model proposes that teacher social and emotional competencies (SECs) play a critical role in creating and maintaining a classroom where everyone feels safe, connected, and engaged in learning. In this chapter, we extend the understanding of SEC to include leadership styles as defined by evolutionary motivational systems theory. We argue that a critical dimension of effective SEL instruction and teacher SEC is effective leadership that skillfully applies an understanding of the social and emotional dimensions of classroom interactions that promote motivation, engagement, and learning. Implications for educational theory, policy and practice, and research are discussed.