Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

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.

Culture-fair assessment : challenging Indigenous students through effortful mathematics teaching

This paper reports on a mathematics education research project centred on teachers’ pedagogical practices and capacity to assess Indigenous Australian students in a culture-fair manner. The project has been funded by the Australian Research Council Linkage program and is being conducted in seven Catholic and Independent primary schools in north Queensland. Our Industry Partners are Catholic Education and the Association of Independent Schools, Queensland. The study aims to provide greater understanding about how to build more equitable assessment practices to address the issue of underperforming Aboriginal and Torres Strait Islander (ATSI) students in regional and remote Australia. The goal is to identify ways forward by attending to culture-fair assessment practice. The research is exploring the attitudes, beliefs and responses of Indigenous students to assessment in the context of mathematics learning with particular focus on teacher knowledge in these educational settings in relation to the design of assessment tasks that are authentic and engaging for these students in an accountability context. This approach highlights how teachers need to distinguish the ‘funds of knowledge’ (González, Moll, Floyd Tenery, Rivera, Rendón, Gonzales & Amanti, 2008) that Indigenous students draw on and how teachers need to be culturally responsive in their pedagogy to open up curriculum and assessment practice to allow for different ways of knowing and being

Curriculum alignment: Exploring student perception of learning achievement measures

The importance of constructively aligned curriculum is well understood in higher education. Based on the principles of constructive alignment, this research considers whether student perception of learning achievement measures can be used to gain insights into how course activities and pedagogy are assisting or hindering students in accomplishing course learning goals. Students in a Marketing Principles course were asked to complete a voluntary survey rating their own progress on the intended learning goals for the course. Student perceptions of learning achievement were correlated with actual student learning, as measured by grade, suggesting that student perceptions of learning achievement measures are suitable for higher educators. Student perception of learning achievement measures provide an alternate means to understand whether students are learning what was intended, which is particularly useful for educators faced with large classes and associated restrictions on assessment. Further, these measures enable educators to simultaneously gather evidence to document the impact of teaching innovations on student learning. Further implications for faculty and future research are offered.

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

The Australian story : catalysts and inhibitors in the achievement of new women professors

Women are substantially under-represented in the professoriate in Australia with a ratio of one female professor to every three male professors. This gender imbalance has been an ongoing concern with various affirmative action programs implemented in universities but to limited effect. Hence, there is a need to investigate the catalysts for and inhibitors to women’s ascent to the professoriate. This investigation focussed on women appointed to the professoriate between 2005, when a research quality assessment was first proposed, and 2008. Henceforth, these women are referred to as “New Women Professors”. The catalysts and inhibitors in these women’s careers were investigated through an electronic survey and focus group interviews. The survey was administered to new women professors (n=255) and new men professors (n=240) to enable a comparison of responses. However, only women participated in focus group discussions (n=21). An analysis of the survey and interview data revealed that the most critical catalysts for women’s advancement to the professoriate were equal employment opportunities and mentoring. Equal opportunity initiatives provided women with access to traditionally male-dominated forums. Mentoring gave women an insider perspective on the complexity of academia and the politics of the academy. The key inhibitors to women’s career advancement were negative discrimination, the culture of the boys’ club, the tension between personal and professional life, and isolation. Negative discrimination and the boys’ club are problematic because they favour men and marginalise women. The tension between personal and professional life is a particular concern for women who bear children and typically assume the major role in a family for child rearing. Isolation was a concern for both women and men with isolation appearing to increase after ascent to the professoriate. Knowledge of the significant catalysts and inhibitors provides a pragmatic way to orient universities towards redressing the gender balance in the professoriate.

Towards a classification of criterion referenced assessment models in mathematics courses : student and academic perspectives

We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

Direct instruction in mathematics : issues for schools with high Indigenous enrolments : a literature review

Direct instruction, an approach that is becoming familiar to Queensland schools that have high Aboriginal and Torres Strait Islander populations, has been gaining substantial political and popular support in the United States of America [USA], England and Australia. Recent examples include the No Child Left Behind policy in the USA, the British National Numeracy Strategy and in Australia, Effective Third Wave Intervention Strategies. Direct instruction, stems directly from the model created in the 1960s under a Project Follow Through grant. It has been defined as a comprehensive system of education involving all aspects of instruction. Now in its third decade of influencing curriculum, instruction and research, direct instruction is also into its third decade of controversy because of its focus on explicit and highly directed instruction for learning. Characteristics of direct instruction are critiqued and discussed to identify implications for teaching and learning for Indigenous students.

Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

Indigenous mathematics : creating an equitable learning environment

This chapter examines how a change in school leadership can successfully address competencies in complex situations and thus create a positive learning environment in which Indigenous students can excel in their learning rather than accept a culture that inhibits school improvement. Mathematics has long been an area that has failed to assist Indigenous students in improving their learning outcomes, as it is a Eurocentric subject (Rothbaum, Weisz, Pott, Miyake & Morelli, 2000, De Plevitz, 2007) and does not contextualize pedagogy with Indigenous culture and perspectives (Matthews, Cooper & Baturo, 2007). The chapter explores the work of a team of Indigenous and non-Indigenous academics from the YuMi Deadly Centre who are turning the tide on improving Indigenous mathematical outcomes in schools and in communities with high numbers of Aboriginal and Torres Strait Islander students.

Recognising Torres Strait Islander women’s knowledges in their children’s mathematics education

This paper discusses women’s involvement in their children’s mathematics education. It does, where possible, focus Torres Strait Islander women who share the aspirations of Aborginal communities around Australia. That is, they are keen for their children to receive an education that provides them with opportunities for their present and future lives. They are also keen to have their cultures’ child learning practices recognised and respected within mainstream education. This recognition has some way to go with the language of instruction in schools written to English conventions, decontextualised and disconnected to the students’ culture, Community and home language.