Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

My "middle way" media studies

I would argue that the problems that contemporary capitalism gives rise to are not the result of the classic exercise of power and hegemony characteristic of the monopoly phase of capitalism but of the “creative destruction” of such a phase. Schumpeter’s famous phrase is reflective of Lash and Urry’s (1987) notion of “disorganised capitalism” or of Robert Reich’s (2007) claim that large corporations have significantly less power now than three decades ago. The consequence is that there is a need to explore an economic “middle way” in debates about the narrative of the relationship between culture and economy, between the Scylla of total explanatory political economy and the Charybdis of tedium-by-case-study. This involves a Schumpeterian emphasis on entrepreneurial or enterprise economics (Cunningham, Banks, and Potts 2008). Schumpeter, in 1962, in Capitalism, Socialism and Democracy, argued that Marx had “no adequate theory of enterprise” and failed to “distinguish the entrepreneur from the capitalist” (quoted in McCraw 2007: 349). Schumpeter, his most recent biographer, Thomas McCraw, “told of capitalism in the way most people experience it: as consumer desires aroused by endless advertising; as forcible jolts up and down the social pecking order; as goals reached, shattered, altered, then reached once more as people try, try again.” He knew that “creative destruction fosters economic growth but also that it undercuts cherished human values” (p. 6). Schumpeter’s most recent biographer, Thomas McCraw, says that he elucidated what capitalism “really feels like” (as quoted in McCraw 2007: 349, 6).

Equity and quality in the early years of schooling

For most of the latter part of the twentieth century, the issues of quality and equity have been part of the agenda of compulsory schooling in Australia. However it is only more recently that the two have been brought together, which has drawn attention to the quest to create high quality and high equity schooling. The outcomes of this union have been the focus of analyses undertaken using data from the OECD Programme for International Student Assessment (PISA), which show that several features of Nordic secondary schools have produced high quality and high equity schooling. This article concentrates on the early years of school and considers the role of curriculum and syllabus documents in creating high quality and high equity in the early years, including the non-compulsory prior-to-school year. It draws on recent research in education generally to identify issues of significance that are instructive in the quest to produce high quality and high equity schooling in the early years. These issues include equity of access, syllabus design and curriculum, and transition to school; but before they are considered, I discuss the context of moves to create high quality and high equity schooling.

Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Introducing Engineering Education in the Middle School

This paper first describes a new three-year, longitudinal project that is implementing engineering education in three middle schools in Australia (grade levels 7-9). This important domain is untapped in Australia. Hence, as a starting point, we conducted a context analysis to help situate engineering education in a school system. We report on this analysis with respect to findings from one of two literature-based surveys that gathered middle-school student responses in mathematics (n=172) and science (n=166) towards understanding their dispositions for engineering education. ANOVA indicated gender differences for 3 out of 23 items in both mathematics and science. In addition, the majority of students agreed or strongly agreed with 17 of the 23 survey items, however, there were some differences between mathematics and science. We conclude the paper with some recommendations for establishing engineering education in schools, including the development of partnerships among engineering and education faculties, school systems, and industry to develop contemporary engineering resources to support school-level mathematics, science, and technology.

Assessing the impact of streetscape on residential property in lower to middle socio-economic areas

A number of factors have been shown to influence residential property prices in various locations. Studies have identified the importance of location in relation to services, transport and proximity to negative factors such as power lines and cell phone towers. Often the socio-economic status of a residential precinct can determine the overall quality and nature of the streetscapes in that area, with higher value suburbs or locations offering a better visual appearance compared to areas where these factors are not present. However, does the same value for a good streetscape apply in lower socio-economic areas or a buyers more motivated by less aesthetic factors such as size of the house, construction materials or land size. This paper analyses specific streets in a lower to middle socio-economic suburb of Christchurch New Zealand to determine if the location of a house in a street with good streetscape appeal has greater value, investment performance and saleability compared to adjoining streets with less aesthetic appeal.

Problem solving in a middle school robotics design classroom

Little research has been conducted on how students work when they are required to plan, build and evaluate artefacts in technology rich learning environments such as those supported by tools including flow charts, Labview programming and Lego construction. In this study, activity theory was used as an analytic tool to examine the social construction of meaning. There was a focus on the effect of teachers’ goals and the rules they enacted upon student use of the flow chart planning tool, and the tools of the programming language Labview and Lego construction. It was found that the articulation of a teacher’s goals via rules and divisions of labour helped to form distinct communities of learning and influenced the development of different problem solving strategies. The use of the planning tool flow charting was associated with continuity of approach, integration of problem solutions including appreciation of the nexus between construction and programming, and greater educational transformation. Students who flow charted defined problems in a more holistic way and demonstrated more methodical, insightful and integrated approaches to their use of tools. The findings have implications for teaching in design dominated learning environments.

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Levelling expectations across different years in an undergraduate degree to support work-related learning : evidence for a multi-pronged approach.

One of the ways in which university departments and faculties can enhance the quality of learning and assessment is to develop a ‘well thought out criterion‐referenced assessment system’ (Biggs, 2003, p. 271). In designing undergraduate degrees (courses) this entails making decisions about the levelling of expectations across different years through devising objectives and their corresponding criteria and standards: a process of alignment analogous to what happens in unit (subject) design. These decisions about levelling have important repercussions in terms of supporting students’ work‐related learning, especially in relation to their ability to cope with the increasing cognitive and skill demands made on them as they progress through their studies. They also affect the accountability of teacher judgments of students’ responses to assessment tasks, achievement of unit objectives and, ultimately, whether students are awarded their degrees and are sufficiently prepared for the world of work. Research reveals that this decision‐making process is rarely underpinned by an explicit educational rationale (Morgan et al, 2002). The decision to implement criterion referenced assessment in an undergraduate microbiology degree was the impetus for developing such a rationale because of the implications for alignment, and therefore ‘levelling’ of expectations across different years of the degree. This paper provides supporting evidence for a multi‐pronged approach to levelling, through backward mapping of two revised units (foundation and exit year). This approach adheres to the principles of alignment while combining a work‐related approach (via industry input) with the blended disciplinary and learner‐centred approaches proposed by Morgan et al. (2002). It is suggested that this multi‐pronged approach has the potential for making expectations, especially work‐related ones across different year levels of degrees, more explicit to students and future employers.

Analysing preservice teachers' potential for implementing engineering education in the middle school

Engineering is pivotal to any country's development. Yet there are insufficient engineers to take up available positions in many countries, including Australia (Engineers Australia, 2008). Engineering education is limited in Australia at the primary, middle and high school levels. One of the starting points for addressing this shortfall lies in preservice teacher education. This study explores second-year preservice teachers' potential to teach engineering in middle school, following their engagement with engineering concepts in their science curriculum unit and their teaching of engineering activities to Year 7 students. Using a literature-based pretest-posttest survey, items were categorised into four constructs (ie. personal professional attributes, student motivation, pedagogical knowledge and fused curricula). Results indicated that the preservice teachers' responses had not changed for instilling positive attitudes (88%) and accepting advice from colleagues (94%). However, there was statistical significance with 9 of the 25 survey items (p<0.05) after the preservice teachers' involvement in engineering activities. Fusing engineering education with other subjects, such as mathematics and science, is an essential first step in promoting preservice teachers' potential to implement engineering education in the middle school.

Maternal anxiety and attention problems in children at 5 and 14 years

Objective: This study examines the association between maternal anxiety from pregnancy to 5 years and child attention problems at 5 and 14 years. Method: Birth cohort of 3,982 individuals born in Brisbane between 1981 and 1983 are assessed. Self-reported measures of maternal anxiety are assessed at four time points. Maternal reports of child attention problems using Achenbach’s Child Behavior Checklist are assessed at 5 and 14 years. Results: Children of mothers experiencing anxiety during or after pregnancy are at greater risk of experiencing attention problems at 5 and 14 years. After adjusting for maternal age and child’s gender, antenatal anxiety is strongly associated with persistent attention problems (OR = 3.65, 95% CI = 2.19, 6.07). Children with chronically anxious mothers are 5.67 (95% CI = 3.56, 9.03) times more likely to have persistent attention problems. These associations remain consistent after adjusting for potential confounders. Conclusions: Maternal anxiety appears to increase the rate of child attention problems and identifies a need for treatment programs to have a dual focus—the mother and her child. (J. of Att. Dis. 2009; XX(X) 1-XX)

Middle-class histrionics

Review of 'God of Carnage', Queensland Theatre Company, published in The Australian, 11 May 2009.

Tip-over injuries in children under 5 years of age in Queensland 1999-2008

Furniture and appliance related injuries in children under 5 years of age accounts for an estimated 180 emergency presentations annually in Queensland. Injuries occur when children push or pull items over, climb and fall off furniture, or climb and tip the item over. Children under 2 years of age tend to injure themselves by pulling items over onto themselves Children over 2 years of age are more likely to be injured after climbing the item and either falling off or tipping the item over onto themselves. Tip over injuries (where the item falls over and injures the child) in children under 5 years of age account for an estimated 115 emergency presentations annually in Queensland. The item most commonly associated with a tip over injury is a television (with or without the cabinet) Prevention requires better design and selection of furniture with inherent stability coupled with mechanisms to install or fix less stable items

Pram and stroller related injury in Queensland children under 5 years of age

An estimated 200 Queensland children under 5 years of age are injured every year in incidents involving prams or strollers. The majority of injuries are due to falls from or falls with the pram or stroller Nineteen children were identified as having been caught in the pram or stroller mechanism (13 sustained finger injuries). Stairs and escalators were a factor in nearly 10 percent of pram or stroller fall injuries, with children being tipped out of the pram or stroller, or rolling down the stairs in the device. Roll away injuries accounted for eight percent of all pram or stroller fall injuries (some also involving stairs) Roll away injuries could be prevented by a default brake system similar to airport trolleys. Pram or stroller failure was identified in 2% of injuries

Recruiting older adults to health research studies : a systematic review

Objective: To provide a systematic review of papers comparing the effectiveness of different strategies to recruit older adults (aged 50 years and over) to participate in health research studies, to guide successful recruitment in future research. Methods: Four major databases were searched for papers published between 1995 and 2008 with: target group aged 50 years or over; participants allocated to receive one of two or more recruitment strategies; and an outcome measure of response rate or enrolment in study. Results: Twelve papers were included in the review. Conclusion: For postal questionnaires, recruitment strategies used with older adults had comparable outcomes to those used to recruit from the general population. For other types of studies, strategies involving face-to-face contact may be more effective than indirect methods, but this needs to be balanced against feasibility. Overall, little evidence on the topic exists and more rigorous investigation is necessary.