A framework for primary teachers’ perceptions of mathematical reasoning

Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning.

Self-identification of problems in the process of listening to English in pre-service interpreters

Questa tesi ha come oggetto di studio i problemi riscontrati nelle trascrizioni di testi orali in lingua inglese prodotte da 39 studenti della laurea magistrale in Interpretazione. Nel Capitolo 1 viene presentato l’ascolto, che viene definito prima da un punto di vista storico, poi analizzato come processo composto da quattro fasi, come sostiene Michael Rost (2011). Il capitolo si conclude con l’ascolto nell’ambito dell’interpretazione. Nel Capitolo 2 viene analizzato in maniera contrastiva l’apprendimento dell’ascolto nella prima e nella seconda lingua. I primi due capitoli forniscono le basi per comprendere il caso di studio. Il Capitolo 3 concerne la metodologia dello studio. Vengono presentati il metodo di analisi delle trascrizioni, la categorizzazione dei problemi riscontrati e il processo di creazione del sistema di analisi utilizzato. Nel Capitolo 4 vengono presentati i dati ottenuti seguendo il metodo esposto nel Capitolo 3. Si presentano i problemi riscontrati, che vengono suddivisi in categorie in base a ciò che può averli causati. Il Capitolo 5 è dedicato alle conclusioni. Qui vengono suggerite possibili strategie mirate ad aiutare gli studenti di Interpretazione a migliorare le proprie capacità di ascolto in lingua inglese. Esta tesis quiere analizar los problemas encontrados en transcripciones de textos orales en inglés hechas por 39 estudiantes del máster en Interpretación. En el Capítulo 1 se presenta la escucha, que se define primero desde una perspectiva histórica, y luego como un proceso formado por cuatro fases, como argumenta Michael Rost (2011). El capítulo se cierra con la escucha en el ámbito de la interpretación. En el Capítulo 2 se analizan de forma contrastiva el aprendizaje de la escucha en la primera y segunda lengua. Los primeros dos capítulos constituyen la base para comprender el caso de estudio. El Capítulo 3 atañe a la metodología del estudio. Se presentan el método de análisis de las transcripciones, la categorización de los problemas encontrados y el proceso de creación del sistema de análisis que se ha empleado. En el Capítulo 4 se proporcionan los datos obtenidos gracias al método presentado en el Capítulo 3. Se presentan los problemas encontrados, que han sido divididos en categorías según qué puede haberlos ocasionado. El Capítulo 5 está dedicado a las conclusiones. Aquí se sugieren posibles estrategias cuyo objetivo es ayudar a los estudiantes de Interpretación a mejorar sus capacidades de escucha en inglés.

Características del desarrollo de una mirada profesional en estudiantes para profesor de matemáticas en un contexto b-learning

Esta investigación presenta un estudio cuyo objetivo es identificar aspectos que apoyan el desarrollo de la mirada profesional en estudiantes para profesores de matemáticas en un contexto b-learning. Analizamos las producciones de un grupo de estudiantes para profesores de matemáticas de educación secundaria (documentos escritos y participaciones en un debate on-line) cuando analizaban el razonamiento proporcional de estudiantes de educación secundaria. Los resultados indican que la interacción en el debate en línea permitió a algunos estudiantes para profesor mejorar su capacidad de identificar e interpretar aspectos relevantes del pensamiento matemático de los estudiantes de educación secundaria. Estos resultados indican que el desarrollo de “una mirada profesional” del profesor es un proceso complicado pero que la posibilidad de construir un discurso progresivo en línea es un factor importante para su desarrollo.

A Jaworskian analysis of four senior class primary teachers endeavouring to teach mathematics from a constructivist-compatible perspective

A constructivist philosophy underlies the Irish primary mathematics curriculum. As constructivism is a theory of learning its implications for teaching need to be addressed. This study explores the experiences of four senior class primary teachers as they endeavour to teach mathematics from a constructivist-compatible perspective with primary school children in Ireland over a school-year period. Such a perspective implies that children should take ownership of their learning while working in groups on tasks which challenge them at their zone of proximal development. The key question on which the research is based is: to what extent will an exposure to constructivism and its implications for the classroom impact on teaching practices within the senior primary mathematics classroom in both the short and longer term? Although several perspectives on constructivism have evolved (von Glaserfeld (1995), Cobb and Yackel (1996), Ernest (1991,1998)), it is the synthesis of the emergent perspective which becomes pivotal to the Irish primary mathematics curriculum. Tracking the development of four primary teachers in a professional learning initiative involving constructivist-compatible approaches necessitated the use of Borko’s (2004) Phase 1 research methodology to account for the evolution in teachers’ understanding of constructivism. Teachers’ and pupils’ viewpoints were recorded using both audio and video technology. Teachers were interviewed at the beginning and end of the project and also one year on to ascertain how their views had evolved. Pupils were interviewed at the end of the project only. The data were analysed from a Jaworskian perspective i.e. using the categories of her Teaching Triad of management of learning, mathematical challenge and sensitivity to students. Management of learning concerns how the teacher organises her classroom to maximise learning opportunities for pupils. Mathematical challenge is reminiscent of the Vygotskian (1978) construct of the zone of proximal development. Sensitivity to students involves a consciousness on the part of the teacher as to how pupils are progressing with a mathematical task and whether or not to intervene to scaffold their learning. Through this analysis a synthesis of the teachers’ interpretations of constructivist philosophy with concomitant implications for theory, policy and practice emerges. The study identifies strategies for teachers wishing to adopt a constructivist-compatible approach to their work. Like O’Shea (2009) it also highlights the likely difficulties to be experienced by such teachers as they move from utilising teacher-dominated methods of teaching mathematics to ones in which pupils have more ownership over their learning.

Primary teachers’ algebraic thinking: example from lesson study

Previous studies have reported on primary children’s algebraic thinking and generalising in a range of problem settings but there is little evidence of primary teachers’ knowledge of algebraic thinking. In this paper the development in algebraic thinking of one primary teacher who taught a research lesson in a Japanese Lesson Study project involving teachers from three primary schools is presented. The findings suggest the need for professional learning in algebra and reasoning and indicate the value of Lesson Study.

New Zealand primary teachers’ ICT professional development and classroom practices

This research presented fifteen New Zealand primary school teachers’ stories about the impact professional development in using information and communication technologies (ICT) had on their classroom practice. These teachers made changes to their classroom practice in accordance to appreciating the need for change, changes in their pedagogical thinking, their beliefs about teaching and learning, overcoming barriers to, and their skills and confidence in using ICT in the classroom.

Relationships with special needs students: exploring primary teachers' descriptions

Positive teacher-student relationships play an established role in the developmental outcomes of students. Ongoing research suggests that positive teacher-student relationships may be particularly beneficial for students with special educational needs [Baker, J. A. 2006. "Contributions of Teacher-Child Relationships to Positive School Adjustment During Elementary School."Journal of School Psychology 44 (3): 211-229]. However, particular learning and behavioural characteristics are known to pose certain challenges when developing these relationships. For instance, teachers may have difficulty in forming close relationships with students who behave in a hostile way. Likewise, they might feel stressed with students who take longer to learn material [Baker 2006; Yoon, J. S. 2002. "Teacher Characteristics as Predictors of Teacher-Student Relationships: Stress, Negative Affect and Self Efficacy." Social Behaviour and Personality 30: 485-494]. This study conducted a focus group with six mainstream teachers from a primary school in the Western Suburbs of Melbourne to investigate the following questions: (1) How do primary school teachers describe their relationships with special needs students? (2) Are these descriptions substantively different from the way in which relationships with non-special needs students are described? And (3) what, if any, are teachers' reported concerns with inclusive education practice? Thematic analysis provided three primary themes and nine secondary themes, indicating that in the context of inclusive practices, the quality of teacher-student relationships is affected by a combination of psychosocial factors. In concurrence with previous literature, the use of qualitative methodology was considered optimal for exploring teachers' descriptions.

Primary teachers notice the impact of language on children’s mathematical reasoning

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children’s mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise mathematical reasoning in children’s actions and words. As part of a larger study, we explored whether observation of educators conducting mathematics lessons can develop teachers’ sensitivity in noticing children’s reasoning and consideration of how to support reasoning. In the Mathematical Reasoning Professional Learning Research Program, demonstration lessons were conducted in Australian and Canadian primary classrooms. Data sources included post-lesson group discussions. Observation of demonstration lessons and engagement in post-lesson discussions proved to be effective vehicles for developing a professional eye for noticing children’s individual and whole-class reasoning. In particular, the teachers noticed that children struggled to employ mathematical language to communicate their reasoning and viewed limitations in language as a major barrier to increasing the use of mathematical reasoning in their classrooms. Given the focus of teachers’ noticing of the limitations in some types of mathematical language, it seems that targeted support is required for teachers to facilitate classroom discourse for reasoning.

‘Fixing’ student deficit in contexts of diversity: another cautionary tale for pre-service teacher education

This article presents one teacher’s perspective on issues of student difference. ‘Elissa’s’ account begins with her views as a pre-service teacher and continues through to her early career teaching. Elissa’s overwhelming tendency to construct students of difference as deficit alongside her efforts to ‘fix’ these deficits to align with an Anglo-Australian middle class ideal strongly resonate with concerns long expressed in the literature about teacher–student cultural discontinuity; teachers’ ill-preparedness for addressing student diversity; and the failure of universities to support pre-service teachers in this respect. Amid broader climates of unprecedented diversity where equity for marginalised groups is a mandated schooling goal, Elissa’s story is another cautionary tale. It further illuminates the gap between the kinds of teachers currently being produced and the kinds of teachers likely to realise social justice through education. As such it provides further warrant for rethinking how best to support teachers to productively address student diversity.

Preparing high achieving English teachers to work in disadvantaged schools : 'I'll teach Shakespeare when I'm 60'

The recent release of the Gonski Review recognises the decline in Australia’s schooling performances over the last decade, noting in particular a distressing increase in the ‘achievement gap’ affecting students from low SES backgrounds (Gonski, 2012). The report details the need for more quality in teachers throughout the schooling system, particularly within the schools with the greatest academic needs. This paper specifically focuses on a group of high-achieving pre-service English teachers. In their last two years of university study, they participated in a program called Exceptional Teachers for Disadvantaged Schools (ETDS), designed to prepare them to work in disadvantaged or low SES schools. We wanted to capture their experiences of teaching in challenging settings during their practicum, and as they prepared to graduate, we wondered what they now felt about teaching English in low SES schools. Using narrative inquiry, we analysed a range of reflective data to gain insight into such things as their initial motivations for entering the teaching profession and how their preconceived expectations may or may not have shifted after practicum experiences in low SES schools. We encouraged open reflection about how they perceived themselves as English teachers.

Reconciling dilemmas of social justice in literacy lessons : a case study of preservice primary teachers

Literacy is promoted as one factor in overcoming disadvantage. In this paper, we employ Fraser’s (1997 & 2008) framing of social justice in order to analyse the disparate agendas of literacy education for improved outcomes in national policy. We do this to better understand the dilemmas confronting preservice teachers as they prepare to become teachers in complex education contexts. We then examine what 20 preservice primary teachers say about social justice in interview responses to a scripted scenario. Our findings demonstrate that most preservice teachers are trying to demonstrate that they have a well-placed commitment to teaching for social justice, however, most of our respondents are yet to frame productive practices that might work in providing socially just education for the students they will teach. These outcomes raise possibilities for future iterations of preservice teacher courses at the case study site and beyond.

New Frontiers or old certainties: The pre-service teacher internship

Teacher education in Australia has a rich history of evolution from apprenticeships to university education. In this chapter the teacher education internship is examined. More specifically, the chapter outlines the Western Australian Combined Universities Training School (WACUTS) project, with its focus on reducing the gap between theory and practice through a collaborative and reflective approach. The successes and challenges faced in the first six months of implementation are presented