This study presents a measurement model of the concept of coherence in Teacher Professional Development (TPD), and explores the specific contribution of this variable on mathematics student achievement, drawing data from the 2012 round of the Programme for International Student Assessment (PISA). By coherence I mean the extent to which TPD activities are actively managed to be consistent with the improvement goals of schools. Thus, the concept is conceived in the context of the improvement of school capacity (Newmann, King and Youngs, 2000) and, therefore, assumed as a logical step for effective TPD (Darling-Hammond et al., 2009). In particular, it represents one of the key components of the quality of such activities (Desimone, 2009) and, as such, it has been found to be associated to better school outcomes at the national level in the US (Garet et al., 2001). Coherence in TPD is usually measured using teachers’ perception about recent experiences of in-service training (Newman et al., 2001; Penuel et al., 2007), however a number of studies have also described the concept in terms of how districts become able to organise a coherent system of teacher learning activities for schools' improvement (Elmore and Burney, 1997).

The study of the coherence in TPD activities is important both for teachers and policy makers as it represents “the logical chain” by which the learning needs of the staff connect with the educational goals of the system . In particular, the quality of teachers' performance could be boosted by this feature, given that coherent TPD is likely to develop teachers’ skills according to what is specifically required in the school context in which they work. As a consequence, students' achievement might benefit as teachers become more skilled to synthesise their acquired knowledge according to the particular characteristics of their students.

Despite its importance, it is striking that very little is known about the process through which school goals and teacher learning might converge into such activities, which largely resides under the realm of headteachers’ management (Youngs and King, 2002). Certainly, specific tasks undertaken daily by leaders determine this feature of the quality of TPD, so even the most carefully designed strategy depends on that role. However, no study has directly examined self-reports from headteachers about what they actually do to affect the coherence of TPD. Furthermore, it is worth noting that this construct has been so far only studied in the US context, so the question remains in relation to its pertinence to assess the quality of TPD in other countries. As national contrasts in the organisation of schools and the provision of TPD might affect this dimension, further research is necessary to estimate whether benefits can be also observed in other countries.

At this juncture, data gathered in PISA 2012 provide an interesting opportunity to examine this construct as a number of actions implemented by headteachers aimed to make of TPD a coherent practice within their schools have been collected from 65 countries. Given that these data have not yet been analysed in detail nor in relation to the influence of TPD on national educational outcomes, relevant insights could be obtained by means of describing the extent to which such actions are undertaken. It is expected to be revealing to explore how coherent TPD is across the four countries of interest of this study (the US, UK, Japan and Finland). In particular, does a coherent approach to TPD in schools relate to student achievement?

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