Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Reading Squadron: Crossing borders in literacy experiences for preservice teachers.

Teaching literacy requires accurate and current knowledge in the field (Commonwealth of Australia, 2005). There have been persistent inquiries into what constitutes specialist knowledge and skills for teaching students to be literate. Preservice teacher education is fundamental to literacy development, which includes the approaches universities employ to prepare graduates for teaching literacy. Indeed, preservice teacher programs and literacy education also elicit insatiable media coverage. There is a continued push to improve literacy outcomes for school students across the nation and prepare the literacy knowledge and skills of Australian teachers. This study mainly focuses on 10 final-year preservice teachers attending a regional university campus who volunteered for further experiences to teach students to read traditional texts. These preservice teachers completed three university literacy units before commencing with practical applications. A literacy program, titled Reading Squadron, was developed in partnership between a local primary school and the university. Primary students were identified by the school as requiring literacy support. Preservice teachers attended a whole day training session run by school staff at the university and then visited the school for two one-hour sessions each week over a six-week period. Each preservice teacher was assigned two students and worked with each student for half an hour twice a week. The aim of this small-scale qualitative study was to investigate the perceptions of the preservice teachers and school staff as a result of their involvement in the Reading Squadron program. The preservice teachers completed a questionnaire to determine their views of the program and ascertain how it assisted their development. Further data were gathered from the preservice teachers through individual face-to-face interviews. Three school staff involved in the program also completed a questionnaire to determine the value of the program. Results indicated that the preservice teachers made links between theory and practice, and felt they gained knowledge about teaching reading. Three preservice teachers noted it was difficult to work around timetable commitments but gained from the experience and suggested embedding such experiences into university literacy units. Data gathered from school staff indicated that six-weeks was not sufficient time to measure improvements in the school students, however, they were supportive of such a program, particularly for its continuation. Collaborations between schools and universities can provide opportunities for preservice teachers to use theoretical knowledge gained from core university subjects with application to assist primary students’ literacy development in schools. Teachers in this study were supportive of the Reading Squadron program, however, more data needed to be collected to understand the literacy improvement of students. Longitudinal studies are required to ascertain specific knowledge and skills gained by preservice teachers to teach reading and how these programs enhance students’ literacy levels.

Fusing curricula : science, technology and ICT

Curriculum demands continue to increase on school education systems with teachers at the forefront of implementing syllabus requirements. Education is reported frequently as a solution to most societal problems and, as a result of the world’s information explosion, teachers are expected to cover more and more within teaching programs. How can teachers combine subjects in order to capitalise on the competing educational agendas within school timeframes? Fusing curricula requires the bonding of standards from two or more syllabuses. Both technology and ICT complement the learning of science. This study analyses selected examples of preservice teachers’ overviews for fusing science, technology and ICT. These program overviews focused on primary students and the achievement of two standards (one from science and one from either technology or ICT). These primary preservice teachers’ fused-curricula overviews included scientific concepts and related technology and/or ICT skills and knowledge. Findings indicated a range of innovative curriculum plans for teaching primary science through technology and ICT, demonstrating that these subjects can form cohesive links towards achieving the respective learning standards. Teachers can work more astutely by fusing curricula; however further professional development may be required to advance thinking about these processes. Bonding subjects through their learning standards can extend beyond previous integration or thematic work where standards may not have been assessed. Education systems need to articulate through syllabus documents how effective fusing of curricula can be achieved. It appears that education is a key avenue for addressing societal needs, problems and issues. Education is promoted as a universal solution, which has resulted in curriculum overload (Dare, Durand, Moeller, & Washington, 1997; Vinson, 2001). Societal and curriculum demands have placed added pressure on teachers with many extenuating education issues increasing teachers’ workloads (Mobilise for Public Education, 2002). For example, as Australia has weather conducive for outdoor activities, social problems and issues arise that are reported through the media calling for action; consequently schools have been involved in swimming programs, road and bicycle safety programs, and a wide range of activities that had been considered a parental responsibility in the past. Teachers are expected to plan, implement and assess these extra-curricula activities within their already overcrowded timetables. At the same stage, key learning areas (KLAs) such as science and technology are mandatory requirements within all Australian education systems. These systems have syllabuses outlining levels of content and the anticipated learning outcomes (also known as standards, essential learnings, and frameworks). Time allocated for teaching science in obviously an issue. In 2001, it was estimated that on average the time spent in teaching science in Australian Primary Schools was almost an hour per week (Goodrum, Hackling, & Rennie, 2001). More recently, a study undertaken in the U.S. reported a similar finding. More than 80% of the teachers in K-5 classrooms spent less than an hour teaching science (Dorph, Goldstein, Lee, et al., 2007). More importantly, 16% did not spend teaching science in their classrooms. Teachers need to learn to work smarter by optimising the use of their in-class time. Integration is proposed as one of the ways to address the issue of curriculum overload (Venville & Dawson, 2005; Vogler, 2003). Even though there may be a lack of definition for integration (Hurley, 2001), curriculum integration aims at covering key concepts in two or more subject areas within the same lesson (Buxton & Whatley, 2002). This implies covering the curriculum in less time than if the subjects were taught separately; therefore teachers should have more time to cover other educational issues. Expectedly, the reality can be decidedly different (e.g., Brophy & Alleman, 1991; Venville & Dawson, 2005). Nevertheless, teachers report that students expand their knowledge and skills as a result of subject integration (James, Lamb, Householder, & Bailey, 2000). There seems to be considerable value for integrating science with other KLAs besides aiming to address teaching workloads. Over two decades ago, Cohen and Staley (1982) claimed that integration can bring a subject into the primary curriculum that may be otherwise left out. Integrating science education aims to develop a more holistic perspective. Indeed, life is not neat components of stand-alone subjects; life integrates subject content in numerous ways, and curriculum integration can assist students to make these real-life connections (Burnett & Wichman, 1997). Science integration can provide the scope for real-life learning and the possibility of targeting students’ learning styles more effectively by providing more than one perspective (Hudson & Hudson, 2001). To illustrate, technology is essential to science education (Blueford & Rosenbloom, 2003; Board of Studies, 1999; Penick, 2002), and constructing technology immediately evokes a social purpose for such construction (Marker, 1992). For example, building a model windmill requires science and technology (Zubrowski, 2002) but has a key focus on sustainability and the social sciences. Science has the potential to be integrated with all KLAs (e.g., Cohen & Staley, 1982; Dobbs, 1995; James et al., 2000). Yet, “integration” appears to be a confusing term. Integration has an educational meaning focused on special education students being assimilated into mainstream classrooms. The word integration was used in the late seventies and generally focused around thematic approaches for teaching. For instance, a science theme about flight only has to have a student drawing a picture of plane to show integration; it did not connect the anticipated outcomes from science and art. The term “fusing curricula” presents a seamless bonding between two subjects; hence standards (or outcomes) need to be linked from both subjects. This also goes beyond just embedding one subject within another. Embedding implies that one subject is dominant, while fusing curricula proposes an equal mix of learning within both subject areas. Primary education in Queensland has eight KLAs, each with its established content and each with a proposed structure for levels of learning. Primary teachers attempt to cover these syllabus requirements across the eight KLAs in less than five hours a day, and between many of the extra-curricula activities occurring throughout a school year (e.g., Easter activities, Education Week, concerts, excursions, performances). In Australia, education systems have developed standards for all KLAs (e.g., Education Queensland, NSW Department of Education and Training, Victorian Education) usually designated by a code. In the late 1990’s (in Queensland), “core learning outcomes” for strands across all KLA’s. For example, LL2.1 for the Queensland Education science syllabus means Life and Living at Level 2 standard number 1. Thus, a teacher’s planning requires the inclusion of standards as indicated by the presiding syllabus. More recently, the core learning outcomes were replaced by “essential learnings”. They specify “what students should be taught and what is important for students to have opportunities to know, understand and be able to do” (Queensland Studies Authority, 2009, para. 1). Fusing science education with other KLAs may facilitate more efficient use of time and resources; however this type of planning needs to combine standards from two syllabuses. To further assist in facilitating sound pedagogical practices, there are models proposed for learning science, technology and other KLAs such as Bloom’s Taxonomy (Bloom, 1956), Productive Pedagogies (Education Queensland, 2004), de Bono’s Six Hats (de Bono, 1985), and Gardner’s Multiple Intelligences (Gardner, 1999) that imply, warrant, or necessitate fused curricula. Bybee’s 5 Es, for example, has five levels of learning (engage, explore, explain, elaborate, and evaluate; Bybee, 1997) can have the potential for fusing science and ICT standards.

Lego robotics : an authentic problem solving tool?

With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the students were able to effectively relate their problem solving strategies to real-world contexts. The qualitative study involved 23 Grade 6 students participating in robotics activities. The study included data collected from researcher observations of student problem solving discussions, collected software programs, and data from a student completed questionnaire. Results from the study indicated that the robotic activities assisted students to reflect on the problem-solving decisions they made. The study also highlighted that the students were able to relate their problem solving strategies to real-world contexts. The study demonstrated that while LEGO robotics can be considered useful problem solving tools in the classroom, careful teacher scaffolding needs to be implemented in regards to correlating LEGO with authentic problem solving. Further research in regards to how teachers can best embed real-world contexts into effective robotics lessons is recommended.

LEGO robotics : an authentic problem solving tool?

With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the students were able to effectively relate their problem solving strategies to real-world contexts. The qualitative study involved 23 Grade 6 students participating in robotics activities at a Brisbane primary school. The study included data collected from researcher observations of student problem solving discussions, collected software programs, and data from a student completed questionnaire. Results from the study indicated that the robotic activities assisted students to reflect on the problem solving decisions they made. The study also highlighted that the students were able to relate their problem solving strategies to real-world contexts. The study demonstrated that while LEGO robotics can be considered useful problem solving tools in the classroom, careful teacher scaffolding needs to be implemented in regards to correlating LEGO with authentic problem solving. Further research in regards to how teachers can best embed realworld contexts into effective robotics lessons is recommended.

A model for curricula integration using the Australian curriculum

Targeting students’ learning is at the centre of education. In addition, education is promoted as a solution on various issues; consequently educators seek ways for teachers to address societal needs, students’ learning needs, and the overcrowded curriculum. There are definition debates and issues around integrating curricula. However, the rationale for primary students undertaking curricula integrated learning can provide motivation for primary teachers to devise and implement curricula integrated lessons in the classroom. More exploration is required to present models for the practical implementation of curricula integration. This paper provides practical ideas for curricula integration that focus on combining achievement standards from the Australian Curriculum: Science and other key learning areas.

Analysing children’s drawings : applied imagination

This article centres on a research project in which freehand drawings provided a richly creative and colourful data source of children’s imagined, ideal learning environments. Issues concerning the analysis of the visual data are discussed, in particular how imaginative content was analysed and how the analytical process was dependent on an accompanying, secondary data source comprising brief, explanatory written texts.

Examining preservice teachers’ applied learning experiences in the Teacher Education Done Differently (TEDD) project

Reviews have criticised universities for not embedding sufficient praxis for preparing preservice teachers for the profession. The Teacher Education Done Differently (TEDD) project explored praxis development for preservice teachers within existing university coursework. This mixed-method investigation involved an analysis of multiple case studies with preservice teacher involvement in university programs, namely: Ed Start for practicum I (n=26), III (n=23), and IV (n=12); Move It Use It (Health and Physical Education program; n=38), Studies of Society and its Environment (SOSE, n=24), and Science in Schools (n=38). The project included preservice teachers teaching primary students at the campus site in gifted education (the B-GR8 program, n=22). The percentage range for preservice teacher agreement of their praxis development leading up to practicum I, III, and IV was between 91-100% with a high mean score range (4.26-5.00). Other university units had similar findings except for SOSE (i.e., percentage range: 10-86%; M range: 2.33-4.00; SD range: 0.55-1.32). Qualitative data presented an understanding of the praxis development leading to the conclusion that additional applied learning experiences as lead-up days for field experiences and as avenues for exploring the teaching of specific subject areas presented opportunities for enhancing praxis.

Learning and teaching reflection : developing capacities for lifelong learning

Reflection is an essential part of being an effective learner and working as a productive teacher. It enables the learner or teacher to deliberate about the factors that lead to successful learning and teaching for them and/or their students, in a particular place and for a specific purpose, so they can make reasoned and effective choices. This chapter introduces important frameworks that cover a century of thinking around reflection in education, and illustrates how preservice teachers can use these ideas across three phases. First, becoming a reflective learner as a university student to enhance learning and assessment outcomes; second, becoming a reflective teacher to improve classroom teaching and learning outcomes; and third, developing the reflective capacities of primary students so they can enhance their skills for lifelong learning.

Negotiating teacher identities : dialogic reflections on classroom interaction in a transnational context

This study investigates the development of teacher identity in a transnational context through an analysis of the voices of sixteen preservice teachers from Hong Kong who engage in interaction with primary students in an Australian classroom. The context for this research is the school-based experience undertaken by these preservice English as a second language teachers as part of their short language immersion (SLIM) program in Brisbane, Australia. Such SLIM programs are a genre of study abroad programs which have been gaining in popularity within teacher education in Australia, attended by preservice and inservice teachers from China, Hong Kong, Korea, and other Asian countries. This research is conducted at a time when the imperative to globalise higher education provision is a strategic factor in the educational policies of both Australia and Hong Kong. In Australia, international educational services now constitute the country’s third largest export with more than 400,000 students coming to Australia to study annually. In order to maintain Australia’s current global position as the third most popular Englishspeaking study destination, the government is now focusing on sustainability and the quality of the study experience being offered to international students (Bradley Review, 2008). In Hong Kong, the government sponsors both preservice and inservice English as a second language (ESL) teachers to undertake SLIM programs in Australia and other English-speaking countries, as part of their policy of promoting high levels of English proficiency in Hong Kong classrooms. Transnational teacher education is an important issue to which this study contributes insights into the affordances and constraints of a school-based experience in the transnational context. Second language teacher education has been defined as interventions designed to develop participants’ professional knowledge. In this study, it is argued that participation in a different community of practice helps to foreground tacit theories of second language pedagogy, making them visible and open to review. Questions of pedagogy are also seen as questions of teacher identity, constituting the way that one is in the classroom. I take up a sociocultural and poststructural framework, drawing on the work of James Gee and Mikhail Bakhtin, to theorise the construction of teacher identity as emerging through dialogic relations and socially situated discursive practices. From this perspective, this study investigates whether these teachers engage with different ways of representing themselves through appropriating, adapting or rejecting Discourses prevailing in the Australian classroom. Research suggests that reflecting on dilemmas encountered as lived experiences can extend professional understandings. In this study, the participants engage in a process of dialogic reflection on their intercultural classroom interactions, examining with their peers and their lecturer/researcher selected moments of dissonance that they have faced in the unfamiliar context of an Australian primary classroom. It is argued that the recursive and multivoiced nature of this process of reflection on practice allows participants opportunities to negotiate new understandings of second language teacher identity. Dialogic learning, based on the theories of Bakhtin and Vygotsky, provides the theoretic framing not only for the process of reflection instantiated in this study, but also features in the analysis of the participants’ second language classroom practices. The research design uses a combined discourse analytic and ethnographic approach as a logic-of-inquiry to explore the dialogic relationships which these second language teachers negotiate with their students and their peers in the transnational context. In this way, through discourse analysis of their classroom talk and reflective dialogues, assisted by the analytic tools of speech genres and discourse formats, I explore the participants’ ways of doing and being second language teachers. Thus, this analysis traces the process of ideological becoming of these beginner teachers as shifts in their understandings of teacher and student identities. This study also demonstrates the potential for a nontraditional stimulated recall interview to provide dialogic scaffolding for beginner teachers to reflect productively on their practice.

Curricula Integration

Targeting students’ learning is at the centre of education. In addition, education is promoted as a solution for addressing various issues; consequently educators seek ways in which teachers can meet societal needs and students’ learning needs, and address the overcrowded curriculum. There are debates on the defi nition of curricula integration and its place in education. However, ationalising the value of primary students undertaking curricula-integrated learning can provide motivation for primary teachers to devise and implement curricula-integrated lessons in the classroom. The Applied Learning Experiences highlighted in this chapter provide practical ideas for curricula integration that focus on combining achievement standards from the Australian Curriculum.

Thinking as if you are another : drama, persuasive language and pretexts

Using Shaun Tan’s picture book Rules of Summer (2013) as a pretext, this practical session will explore how primary teachers can engage middle and upper primary students in drama-based activities that support student learning and assessment outcomes in both English and The Arts (with a particular emphasis on drama and media arts). The session will explore notions of persuasive text (written and oral), points of view, devised storytelling and embodied learning.

Reflexive writers : re-thinking writing development and assessment in schools

Writing is a complex and highly individual activity, which is approached in different ways by different writers. Writers reflexively mediate subjective and objective conditions in specific and nuanced ways to produce a product in time and place. This paper uses a critical realist theory of reflexivity to argue that the teaching and assessment of writing must account for the different ways that students manage and make decisions in their writing. Data from linguistically and culturally diverse primary students in Australia are used to illustrate how four distinct reflexive modalities constitute the ways in which students approach writing. The paper offers a new approach to assessing writing for and of learning that considers writers as reflexive and agentic in different ways. It posits the importance of making visible and explicit the context and reflexive decision-making as writers shape a product for a purpose and audience.

Writers as performers : developing reflexive and creative writing identities

Writing is a complex and learned activity in that it requires us to shape our thoughts into words and texts that are appropriate for the purpose, audience and medium of a variety of communicative forms. Writers must constantly make decisions about how to represent their subject matter and themselves through language. In this way, writing can be conceptualised as a performance whereby writers shape and represent their identities as they mediate social structures and personal considerations. In this paper I use theories of reflexivity and discourse to analyse interviews and writing samples of culturally and linguistically diverse Australian primary students for evidence of particular kinds of writing identities. Findings indicate a clear influence of particular teaching strategies and contexts on the writing identities of students. I argue that making students aware of their writing choices, the influences on, and the potential impact of those choices on themselves, their text and their audience, is a new imperative in the teaching of writing.

Introducing the practice of statistics: are we environmentally friendly?

The practice of statistics is the focus of the world in which professional statisticians live. To understand meaningfully what this practice is about, students need to engage in it themselves. Acknowledging the limitations of a genuine classroom setting, this study attempted to expose four classes of year 5 students (n=91) to an authentic experience of the practice of statistics. Setting an overall context of people’s habits that are considered environmentally friendly, the students sampled their class and set criteria for being environmentally friendly based on questions from the Australian Bureau of Statistics CensusAtSchool site. They then analysed the data and made decisions, acknowledging their degree of certainty, about three populations based on their criteria: their class, year 5 students in their school and year 5 students in Australia. The next step was to collect a random sample the size of their class from an Australian Bureau of Statistics ‘population’, analyse it and again make a decision about Australian year 5 students. At the end, they suggested what further research they might do. The analysis of students’ responses gives insight into primary students’ capacity to appreciate and understand decision making, and to participate in the practice of statistics, a topic that has received very little attention in the literature. Based on the total possible score of 23 from student workbook entries, 80 % of students achieved at least a score of 11.