Out-of-Field Mathematics Teachers’ Beliefs and Practices: an Examination of Change and Tensions Using Zone Theory

Abstract

This paper describes an empirical study examining action research papers submitted by a group (n=81) of out-of-field mathematics teachers as part of a professional development programme in Ireland. Utilising document analysis, the papers were qualitatively analysed for evidence of teachers' beliefs and practices with respect to the teaching and learning of mathematics. In particular, demonstration of directtransmission and constructivist beliefs and practices was explored. The authors draw on Valsiner's zone theory in conceptualizing the 'teacher-as-learner' in this out-offield context and it provided a means for analyzing teachers' development in terms of their beliefs and practices. Findings indicate a prevalence of direct transmission or traditional teaching practices prior to the out-of-field teachers' action research, with some inconsistency with professed constructivist beliefs. There was evidence of a majority shift towards constructivist beliefs and practices post action research for a myriad of reasons, including increased pedagogical confidence in mathematics and the successful experience of constructivist approaches. Findings also highlight the role of reflective self-study in facilitating the creation of productive tensions, as well as the importance of the teachers' interpretation of their zone of free movement in resolving complex issues and enabling out-of-field teachers' development of constructivist beliefs and practices.

Impact of a national professional development programme for out-of-field teachers of mathematics in Ireland

“…First, to partially counter the possibility that teachers may have overreported the effects of participation in the programme, we followed Desimone's (2009) recommendation to interpret teachers' self-reports of behavioural change in the context of the epistemological and pedagogical beliefs elicited via other survey items. Second, our claims are supported by previous studies, conducted by Lane andFaulkner (2021), that involved different cohorts of PDMT participants and different data sources and analysis methods. Both of these studies collected data on self-reported beliefs and classroom practices before and after teachers experienced specific components of the PDMT programme (action research for the former study; pedagogy workshops for the latter study); and both studies found evidence of a reported shift away from a traditional, teacher-led style to more student-centred, inquiry-based pedagogies that emphasise development of mathematical understanding.…”

“…Desimone (2009) notes that it is rare for a single study to investigate all four elements of this model; in particular, there are significant methodological difficulties in designing evaluations that measure the specific effects of professional development on student achievement. Our own research has concentrated on analysing the critical features of the PDMT programme (Step 1 in Desimone's model; see Goos et al 2020) and its effect on the teachers who participated in the programme (Steps 2 and 3; see Lane and Ní Ríordáin 2020;Ní Ríordáin, Paolucci, and O'Dwyer 2017;O'Meara and Faulkner 2021). In this paper, we further examine the impact of the PDMT on teachers' beliefs and pedagogical approaches as key elements in Desimone's (2009) model of teacher change.…”

An Evaluation of The Preservice-Teacher Training for Children’s Literature and Mathematics Integration

“…Hence, pre-service teachers may have had more positive beliefs in terms of mathematics teaching self-efficacy beliefs. Studies also enlightened those pre-service and in-service teachers' understanding and beliefs regarding training may be changed, their self-efficacy towards mathematics increases, they are more motivated to use innovative approaches for mathematics lessons and their anxiety about teaching mathematics decreases when effectively designed educational content is provided (Ginsburg & Uscianowski, 2017;Jao, 2018;Jett, 2018;Lane & Ríordáin, 2020;Rogers et al, 2015). From this point of view, these kinds of training may be suggested for teacher education to integrate mathematics and children's literature.…”

“…Therefore, it is of upmost importance to understand the pre-service and in-service teachers' beliefs as intentions' function to ensure their professional development (Qhobela & Moru, 2014). It is also known that teachers' beliefs about teaching might be changed through professionally designed training (Lane & Ríordáin, 2020). Besides, pre-service and in-service teachers encounter similar difficulties in terms of barriers to this integration Can et al, 2020;Prendergast et al, 2019), and the development of practitioner competencies regarding integration has become increasingly popular in recent years (Edelman et al, 2019).…”

Non-specialist secondary mathematics teachers learning in study groups by engaging with activities of algebra

“…Explicating the characteristics and impacts of study groups as an approach to teacher learning will be helpful to mathematics educators, researchers, and policymakers as they design PD activities and/or conduct research (Borko & Potari, 2020;Darling-Hammond et al, 2017). More importantly, teaching 'outof-field' is a present obstacle in mathematics education in many countries, and the development of PD programs aimed at upskilling non-specialist teachers is a growing field (see Lane & Ní Ríordáin, 2020). The findings presented in this study contribute to our understanding of supporting non-specialist mathematics teachers' knowledge needed to teach the subject and plausibly improving teacher and teaching quality (du Plessis, 2015;Faulkner et al, 2019).…”