Facilitating growth in prospective teachers’ knowledge : teaching geometry in primary schools

This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants’ pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.

Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

Re-engaging adolescent students in science : an experienced teachers' classroom

Adolescents are both aware of and have the impetuous to exploit aspects of Science, Technology, Engineering and Mathematics (STEM) within their personal lives. Whether they are surfing, cycling, skateboarding or shopping, STEM concepts impact their lives. However science, mathematics, engineering and technology are still treated in the classroom as separate fragmented entities in the educational environment where most classroom talk is seemingly incomprehensible to the adolescent senses. The aim of this study was to examine the experiences of young adolescents with the aim of transforming school learning at least of science into meaningful experiences that connected with their lives using a self-study approach. Over a 12-month period, the researcher, an experienced secondary-science teacher, designed, implemented and documented a range of pedagogical practices with his Year-7 secondary science class. Data for this case study included video recordings, journals, interviews and surveys of students. By setting an environment empathetic to adolescent needs and understandings, students were able to actively explore phenomena collaboratively through developmentally appropriate experiences. Providing a more contextually relevant environment fostered meta-cognitive practices, encouraged new learning through open dialogue, multi-modal representations and assessments that contributed to building upon, re-affirming, or challenging both the students' prior learning and the teacher’s pedagogical content knowledge. A significant outcome of this study was the transformative experiences of an insider, the teacher as researcher, whose reflections provided an authentic model for reforming pedagogy in STEM classes.

A visual description of early-number counting, addition and subtraction knowledge

Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain of knowledge. This visual language is based upon Piaget’s notion of reflective abstraction (Dubinsky, 1991; Piaget, 1977/2001), and thus captures the epistemological associations that link the problems, concepts and representations of the domain. The constructs of this visual language are introduced and then applied to the early-number domain. The introduction to this visual language may prompt reflection upon its suitability and significance to the description of other domains of knowledge. Through such a process of analysis and description, the visual language may serve as a scaffold for enhancing pedagogical content knowledge and thus ultimately improve learning outcomes.

Education for sustainability : a case study of pre-service primary teachers' knowledge and efficacy

This study investigated the relationships between knowledge and efficacy for teaching sustainability in a sample of 266 pre-service primary teachers at a large, metropolitan university in Australia. A survey gathered information about the participant’s attitudes and self-efficacy for education for sustainability, along with their perceived and actual knowledge of environmental sustainability issues. The participants typically believed they were confident in their abilities to engage with education for sustainability with self-efficacy increasing with increased levels of perceived knowledge. However no relationship was found between perceived knowledge and actual knowledge which suggests that the participants either do not feel constrained by their lack of knowledge, or are perhaps unaware of their actual knowledge of sustainability issues. This lack of relationship may have implications for the development of pedagogical content knowledge with pre-service teachers potentially developing shallow, tokenistic approaches to Education for Sustainability.

The knowledge base of subject-matter experts in teaching : A case study of a professional scientist as a beginning teacher

One method of addressing the shortage of science and mathematics teachers is to train scientists and other science-related professionals to become teachers. Advocates argue that as discipline experts these career changers can relate the subject matter knowledge to various contexts and applications in teaching. In this paper, through interviews and classroom observations with a former scientist and her students, we examine how one career changer used her expertise in microbiology to teach microscopy. These data provided the basis for a description of the teacher’s instruction which was then analysed for components of domain knowledge for teaching. Consistent with the literature, the findings revealed that this career changer needed to develop her pedagogical knowledge. However, an interesting finding was that the teacher’s subject matter as a science teacher differed substantively from her knowledge as a scientist. This finding challenges the assumption that subject matter is readily transferable across professions and provides insight into how to better prepare and support career changers to transition from scientist to science teacher.

Primary students’ spatial visualization and spatial orientation : an evidence base for instruction

This paper reports on the performance of 58 11 to 12-year-olds on a spatial visualization task and a spatial orientation task. The students completed these tasks and explained their thinking during individual interviews. The qualitative data were analysed to inform pedagogical content knowledge for spatial activities. The study revealed that “matching” or “matching and eliminating” were the typical strategies that students employed on these spatial tasks. However, errors in making associations between parts of the same or different shapes were noted. Students also experienced general difficulties with visual memory and language use to explain their thinking. The students’ specific difficulties in spatial visualization related to obscured items, the perspective used, and the placement and orientation of shapes.

An in-depth study of a teacher engaged in an innovative primary science trial professional development project

The implementation of effective science programmes in primary schools is of continuing interest and concern for professional developers. As part of the Australian Academy of Science's approach to creating an awareness of Primary Investigations, a project team trialled a series of satellite television broadcasts of lessons related to two units of the curriculum for Year 3 and 4 children in 48 participating schools. The professional development project entitled Simply Science, included a focused component for the respective classroom teachers, which was also conducted by satellite. This paper reports the involvement of a Year 4 teacher in the project and describes her professional growth. Already an experienced and confident teacher, no quantitative changes in science teaching self efficacy were detected. However, her pedagogical content knowledge and confidence to teach science in the concept areas of matter and energy were enhanced. Changes in the teacher's views about the co-operative learning strategies espoused by Primary Investigations were also evident. Implications for the design of professional development programmes for primary science teachers are discussed.

A model of teacher professional development based on the principles of lesson study

The researcher’s professional role as an Education Officer was the impetus for this study. Designing and implementing professional development activities is a significant component of the researcher’s position description and as a result of reflection and feedback from participants and colleagues, the creation of a more effective model of professional development became the focus for this study. Few studies have examined all three links between the purposes of professional development that is, increasing teacher knowledge, improving teacher practice, and improving student outcomes. This study is significant in that it investigates the nature of the growth of teachers who participated in a model of professional development which was based upon the principles of Lesson Study. The research provides qualitative and empirical data to establish some links between teacher knowledge, teacher practice, and student learning outcomes. Teacher knowledge in this study refers to mathematics content knowledge as well as pedagogical-content knowledge. The outcomes for students include achievement outcomes, attitudinal outcomes, and behavioural outcomes. As the study was conducted at one school-site, existence proof research was the focus of the methodology and data collection. Developing over the 2007 school year, with five teacher-participants and approximately 160 students from Year Levels 6 to 9, the Lesson Study-principled model of professional development provided the teacher-participants with on-site, on-going, and reflective learning based on their classroom environment. The focus area for the professional development was strategising the engagement with and solution of worded mathematics problems. A design experiment was used to develop the professional development as an intervention of prevailing teacher practice for which data were collected prior to and after the period of intervention. A model of teacher change was developed as an underpinning framework for the development of the study, and was useful in making decisions about data collection and analyses. Data sources consisted of questionnaires, pre-tests and post-tests, interviews, and researcher observations and field notes. The data clearly showed that: content knowledge and pedagogical-content knowledge were increased among the teacher-participants; teacher practice changed in a positive manner; and that a majority of students demonstrated improved learning outcomes. The positive changes to teacher practice are described in this study as the demonstrated use of mixed pedagogical practices rather than a polarisation to either traditional pedagogical practices or contemporary pedagogical practices. The improvement in student learning outcomes was most significant as improved achievement outcomes as indicated by the comparison of pre-test and post-test scores. The effectiveness of the Lesson Study-principled model of professional development used in this study was evaluated using Guskey’s (2005) Five Levels of Professional Development Evaluation.

Academic rigour in science assessment tasks

The critical problem of student disengagement and underachievement in the middle years of schooling (Years 4 . 9) has focussed attention on the quality of educational programs in schools, in Australia and elsewhere. The loss of enthusiasm for science in the middle years is particularly problematic given the growing demand for science professionals. Reshaping middle years programs has included an emphasis on integrating Information and Communication Technologies (ICTs) and improving assessment practices to engage students in higher cognitive processes and enhance academic rigour. Understanding the nature of academic rigour and how to embed it in students. science assessment tasks that incorporate the use of ICTs could enable teachers to optimise the quality of the learning environment. However, academic rigour is not clearly described or defined in the literature and there is little empirical evidence upon which researchers and teachers could draw to enhance understandings. This study used a collective case study design to explore teachers' understandings of academic rigour within science assessment tasks. The research design is based on a conceptual framework that is underpinned by socio-cultural theory. Three methods were used to collect data from six middle years teachers and their students. These methods were a survey, focus group discussion with teachers and a group of students and individual semi-structured interviews with teachers. Findings of the case study revealed six criteria of academic rigour, namely, higher order thinking, alignment, building on prior knowledge, scaffolding, knowledge construction and creativity. Results showed that the middle years teachers held rich understandings of academic rigour that led to effective utilisation of ICTs in science assessment tasks. Findings also indicated that teachers could further enhance their understandings of academic rigour in some aspects of each of the criteria. In particular, this study found that academic rigour could have been further optimised by: promoting more thoughtful discourse and interaction to foster higher order thinking; increasing alignment between curriculum, pedagogy, and assessment, and students. prior knowledge; placing greater emphasis on identifying, activating and building on prior knowledge; better differentiating the level of scaffolding provided and applying it more judiciously; fostering creativity throughout tasks; enhancing teachers‟ content knowledge and pedagogical content knowledge, and providing more in-depth coverage of fewer topics to support knowledge construction. Key contributions of this study are a definition and a model which clarify the nature of academic rigour.

Students as decoders of graphics in mathematics

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

Adaptive teachers embracing new ways of learning with robotics in Chinese schools

In July 2010, China announced the “National Plan for Medium and Long-term Education Reform and Development(2010-2020)” (PRC 2010). The Plan calls for an education system that: • promotes an integrated development which harnesses everyone’s talent; • combines learning and thinking; unifies knowledge and practice; • allows teachers to teach according to individuals’ needs; and • reforms education quality evaluation and personnel evaluation systems focusing on performance including character, knowledge, ability and other factors. This paper discusses the design and implementation of a Professional Learning Program (PLP) undertaken by 432 primary, middle and high school teachers in China. The aim of this initiative was to develop adaptive expertise in using technology that facilitated innovative science and technology teaching and learning as envisaged by the Chinese Ministry of Education’s (2010-2020) education reforms. Key principles derived from literature about professional learning and scaffolding of learning informed the design of the PLP. The analysis of data revealed that the participants had made substantial progress towards the development of adaptive expertise. This was manifested not only by advances in the participants’ repertoires of Subject Matter Knowledge and Pedagogical Content Knowledge but also in changes to their levels of confidence and identities as teachers. It was found that through time the participants had coalesced into a professional learning community that readily engaged in the sharing, peer review, reuse and adaption, and collaborative design of innovative science and technology learning and assessment activities.