Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

The differential recognition of children’s cultural practices in middle primary literacy classrooms

This paper argues that teachers’ recognition of children’s cultural practices is an important positive step in helping socio-economically disadvantaged children engage with school literacies. Based on twenty-one longitudinal case studies of children’s literacy development over a three-year period, the authors demonstrate that when children’s knowledges and practices assembled in home and community spheres are treated as valuable material for school learning, children are more likely to invest in the work of acquiring school literacies. However they show also that whilst some children benefit greatly from being allowed to draw on their knowledge of popular culture, sports and the outdoors, other children’s interests may be ignored or excluded. Some differences in teachers’ valuing of home and community cultures appeared to relate to gender dimensions.

Inquiry teaching in primary science : a phenomenographic study

In spite of having a long history in education, inquiry teaching (the teaching in ways that foster inquiry based learning in students) in science education is still a highly problematic issue. However, before teacher educators can hope to effectively influence teacher implementation of inquiry teaching in the science classroom, educators need to understand teachers’ current conceptions of inquiry teaching. This study describes the qualitatively different ways in which 20 primary school teachers experienced inquiry teaching in science education. A phenomenographic approach was adopted and data sourced from interviews of these teachers. The three categories of experiences that emerged from this study were; Student Centred Experiences (Category 1), Teacher Generated Problems (Category 2), and Student Generated Questions (Category 3). In Category 1 teachers structure their teaching around students sensory experiences, expecting that students will see, hear, feel and do interesting things that will focus their attention, have them asking science questions, and improve their engagement in learning. In Category 2 teachers structure their teaching around a given problem they have designed and that the students are required to solve. In Category 3 teachers structure their teaching around helping students to ask and answer their own questions about phenomena. These categories describe a hierarchy with the Student Generated Questions Category as the most inclusive. These categories were contrasted with contemporary educational theory, and it was found that when given the chance to voice their own conceptions without such comparison teachers speak of inquiry teaching in only one of the three categories mentioned. These results also help inform our theoretical understanding of teacher conceptions of inquiry teaching. Knowing what teachers actually experience as inquiry teaching, as opposed to understand theoretically, is a valuable contribution to the literature. This knowledge provides a valuable contribution to educational theory, which helps policy, curriculum development, and the practicing primary school teachers to more fully understand and implement the best educative practices in their daily work. Having teachers experience the qualitatively different ways of experiencing inquiry teaching uncovered in this study is expected to help teachers to move towards a more student-centred, authentic inquiry outcome for their students and themselves. Going beyond this to challenge teacher epistemological beliefs regarding the source of knowledge may also assist them in developing more informed notions of the nature of science and of scientific inquiry during professional development opportunities. The development of scientific literacy in students, a high priority for governments worldwide, will only to benefit from these initiatives.

Early years teachers’ attitudes towards mathematics

Worldwide, there is considerable attention to providing a supportive mathematics learning environment for young children because attitude formation and achievement in these early years of schooling have a lifelong impact. Key influences on young children during these early years are their teachers. Practising early years teachers‟ attitudes towards mathematics influence the teaching methods they employ, which in turn, affects young students‟ attitudes towards mathematics, and ultimately, their achievement. However, little is known about practising early years teachers‟ attitudes to mathematics or how these attitudes form, which is the focus of this study. The research questions were: 1. What attitudes do practising early years teachers hold towards mathematics? 2. How did the teachers‟ mathematics attitudes form? This study adopted an explanatory case study design (Yin, 2003) to investigate practising early years teachers‟ attitudes towards mathematics and the formation of these attitudes. The research took place in a Brisbane southside school situated in a middle socio-economic area. The site was chosen due to its accessibility to the researcher. The participant group consisted of 20 early years teachers. They each completed the Attitude Towards Mathematics Inventory (ATMI) (Schackow, 2005), which is a 40 item instrument that measures attitudes across the four dimensions of attitude, namely value, enjoyment, self-confidence and motivation. The teachers‟ total ATMI scores were classified according to five quintiles: strongly negative, negative, neutral, positive and strongly positive. The results of the survey revealed that these teachers‟ attitudes ranged across only three categories with one teacher classified as strongly positive, twelve teachers classified as positive and seven teachers classified as neutral. No teachers were identified as having negative or strongly negative attitudes. Subsequent to the surveys, six teachers with a breadth of attitudes were selected from the original cohort to participate in open-ended interviews to investigate the formation of their attitudes. The interview data were analysed according to the four dimensions of attitudes (value, enjoyment, self-confidence, motivation) and three stages of education (primary, secondary, tertiary). Highlighted in the findings is the critical impact of schooling experiences on the formation of student attitudes towards mathematics. Findings suggest that primary school experiences are a critical influence on the attitudes of adults who become early years teachers. These findings also indicate the vital role tertiary institutions play in altering the attitudes of preservice teachers who have had negative schooling experiences. Experiences that teachers indicated contributed to the formation of positive attitudes in their own education were games, group work, hands-on activities, positive feedback and perceived relevance. In contrast, negative experiences that teachers stated influenced their attitudes were insufficient help, rushed teaching, negative feedback and a lack of relevance of the content. These findings together with the literature on teachers‟ attitudes and mathematics education were synthesized in a model titled a Cycle of Early Years Teachers’ Attitudes Towards Mathematics. This model explains positive and negative influences on attitudes towards mathematics and how the attitudes of adults are passed on to children, who then as adults themselves, repeat the cycle by passing on attitudes to a new generation. The model can provide guidance for practising teachers and for preservice and inservice education about ways to foster positive influences to attitude formation in mathematics and inhibit negative influences. Two avenues for future research arise from the findings of this study both relating to attitudes and secondary school experiences. The first question relates to the resilience of attitudes, in particular, how an individual can maintain positive attitudes towards mathematics developed in primary school, despite secondary school experiences that typically have a negative influence on attitude. The second question relates to the relationship between attitudes and achievement, specifically, why secondary students achieve good grades in mathematics despite a lack of enjoyment, which is one of the dimensions of attitude.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

An exploration of young students' ability to generalise function tasks

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focusing on the identifications, prediction and justification of function rules. It reports on students' attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture that there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

Data modelling in the beginning school years

This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling. Some of the core components of data modelling are addressed. A selection of results from the first data modelling activity implemented during the second year (2010; second grade) of a current longitudinal study are reported. Data modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Reported here are children's abilities to identify diverse and complex attributes, sort and classify data in different ways, and create and interpret models to represent their data.

An evaluation of the pattern and structure mathematics awareness program in the early school years

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.

Developing the Pattern and Structure Assessment (PASA) interview to inform early mathematics learning

The Pattern and Structure Mathematical Awareness Program(PASMAP) stems from a 2-year longitudinal study on students’ early mathematical development. The paper outlines the interview assessment the Pattern and Structure Assessment(PASA) designed to describe students’ awareness of mathematical pattern and structure across a range of concepts. An overview of students’ performance across items and descriptions of their structural development are described.

Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Teacher educators mediating curricular reform : anticipating the Australian curriculum

Many education systems are experiencing a re-scaling and consolidation of governance through rolling national agendas of standardisation and centralisation. This paper considers the case of Australia as it moves towards implementing its first national curriculum, to explore how teacher educators plan to retain pedagogical space for debate, diversity and contestation of such systemic curricular reform. This paper reports on an interview study conducted with nine teacher educators across the four curriculum areas included in the first wave of the Australian Curriculum: English, Science, Mathematics and History. The analysis reveals how teacher educators reported professional dilemmas around curricular design, and planned to resolve such dilemmas between the anticipated changes and their preferences for what might have been. While different curricular areas displayed different patterns of professional dilemma, the teacher educators are shown to construe their role as one of active curriculum mediators, who, in recontextualising curricular reforms, will use the opportunity to reinsert both residualised and emergent alternatives in their students’ professional value sets. The study also identifies a new set of dilemmas emerging around the politicisation and standardisation of curriculum, and its impact on the teaching profession and teacher educators.

Teachers' conceptions of how to engage students through inquiry learning : foundations for STEM

The advocacy for inquiry-based learning in contemporary curricula assumes the principle that students learn in their own way by drawing on direct experience fostered by the teacher. That students should be able to discover answers themselves through active engagement with new experiences was central to the thinking of eminent educators such as Pestalozzi, Dewey and Montessori. However, even after many years of research and practice, inquiry learning as a referent for teaching still struggles to find expression in the average teachers' pedagogy. This study drew on interview data from 20 primary teachers. A phenomenographic analysis revealed three conceptions of teaching that support inquiry learning in science in the primary years of schooling: (a) The Experience-centred conception where teachers focused on providing interesting sensory experiences to students; (b) The Problem-centred conception where teachers focused on challenging students with engaging problems; and (c) The Question-centred conception where teachers focused on helping students to ask and answer their own questions. Understanding teachers' conceptions of teaching has implications for both the enactment of inquiry teaching in the classroom as well as the uptake of new teaching behaviours during professional development, with enhanced outcomes for engaging students in STEM.

Move it, use it : university-school collaboration for learning to teach physical education in primary schools

Reports of increasing numbers of obese Australian children and adolescents have raised the alarm to be proactive in reducing this so called epidemic. It has evoked a call for greater emphasis on teaching physical education in schools, as a measure for attaining fitness not only with obese students but for all students. This paper emphasises how preservice teachers need to be a key target for implementing physical education (PE) reform in schools, as many primary teachers will be generalists and may not be confident enough to implement PE effectively. Through a review of existing literature, teaching practices essential for the effective promotion and implementation of PE were identified under six broad categories: personal-professional skills development, addressing system requirements, pedagogical practices, managing student behaviour, providing feedback to students, and reflecting on practice. Subsequently, the development of these practices in preservice teachers is considered in the context of a university-school collaboration where preservice teachers taught physical education to primary school students for one day per week over a four week period. These authentic teaching experiences provided the preservice teachers with vital opportunities to put theory into practice and interact with “real-world” students. Self-evaluative data from 38 of these preservice teachers, in the form of a five-part Likert scale survey and extended response survey, demonstrated that they were able to develop the majority of the essential teaching practices identified by literature. In particular, the preservice teachers developed self efficacy, enthusiasm, and motivation for teaching PE, facets which are often found to be lacking in generalist primary teachers and yet are essential if children’s perceptions and habits regarding physical activity are to be changed.

Reading students’ representations

Students’ text, symbols, and graphics give teachers a glimpse into mathematical thinking associated with investigating the Peas problem.

The development of the graphics-decoding proficiency instrument

The Graphics-Decoding Proficiency (G-DP) instrument was developed as a screening test for the purpose of measuring students’ (aged 8-11 years) capacity to solve graphics-based mathematics tasks. These tasks include number lines, column graphs, maps and pie charts. The instrument was developed within a theoretical framework which highlights the various types of information graphics commonly presented to students in large-scale national and international assessments. The instrument provides researchers, classroom teachers and test designers with an assessment tool which measures students’ graphics decoding proficiency across and within five broad categories of information graphics. The instrument has implications for a number of stakeholders in an era where graphics have become an increasingly important way of representing information.