Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Tyrosine monitoring in children with early and continuously treated phenylketonuria: Results of an international practice survey

Investigations into the biochemical markers associated with executive function (EF) impairment in children with early and continuously treated phenylketonuria (ECT-PKU) remain largely phenylalanine-only focused, despite experimental data showing that a high phenylalanine:tyrosine (phe:tyr) ratio is more strongly associated with EF deficit than phe alone. A high phe:tyr ratio is hypothesized to lead to a reduction in dopamine synthesis within the brain, which in turn results in the development of EF impairment. This paper provides a snapshot of current practice in the monitoring and/or treatment of tyrosine levels in children with PKU, across 12 countries from Australasia, North America and Europe. Tyrosine monitoring in this population has increased over the last 5 years, with over 80% of clinics surveyed reporting routine monitoring of tyrosine levels in infancy alongside phe levels. Twenty-five percent of clinics surveyed reported actively treating/managing tyrosine levels (with supplemental tyrosine above that contained in PKU formulas) to ensure tyrosine levels remain within normal ranges. Anecdotally, supplemental tyrosine has been reported to ameliorate symptoms of both attention deficit hyperactivity disorder and depression in this population. EF assessment of children with ECT-PKU was likewise highly variable, with 50% of clinics surveyed reporting routine assessments of intellectual function. However when function was assessed, test instruments chosen tended towards global measures of IQ prior to school entry, rather than specific assessment of EF development. Further investigation of the role of tyrosine and its relationship with phe and EF development is needed to establish whether routine tyrosine monitoring and increased supplementation is recommended.

Do strategy choices matter for nascent firms? Effectuation in the early stages of venture creation

This paper explores empirically effects of Effectuation on nascent firms’ performance. Three potential outcomes for nascent firms using different levels of effectuation and causation are investigated. Innovation, a measure of venture sophistication was introduced as a moderator. We examine a longitudinal random sample of 625 nascent firms collected over two years in Australia and provide support for our hypotheses. Results show that in situation of high uncertainty, nascent firms using effectuation are more likely to reach operational stage than their counterpart using causation.

High-challenge teaching for senior English as an Additional Language (EAL) learners in times of change

This paper will present a brief overview of the recent shifts within English and EAL/D (English as an additional language/dialect) curriculum documents and their focus on critical literacy, using the Queensland context as a case in point. The English syllabus landscape in Queensland has continued to morph in recent years. From 2002 to 2009, teachers of senior English and English as an Additional Language (EAL/D) have witnessed no less than four separate syllabus documents that impact on their daily work. The Australian Curriculum, when finally implemented, will also require teachers to navigate and grapple with its particular obligations and affordances. The combined effect of the shifts and tensions between recent policy documents has led to confusion about exactly how to cater for EAL/D learners in mainstream English. We discuss the possible effects of this on teachers as the agents of policy implementation and argue that in spite of such contradictions, EAL/D teachers can productively use syllabus frameworks to craft pedagogy to cater for their EAL/D learners’ language and literacy needs. Following this, we present aspects of the teaching practice of four teachers of senior EAL/D, who provide intellectually-engaging, critical literacy pedagogy that takes into account the language proficiency level of their learners, within the required curriculum. Such practice provides teachers with valuable pedagogic possibilities to meet EAL/D learners’ needs within continually varying policy terrain.

The ‘good’ parent in relation to early childhood literacy : symbolic terrain and lived practice

In this paper we consider the place of early childhood literacy in the discursive construction of the identity( ies) of ‘proper’ parents. Our analysis crosses between representations of parenting in texts produced by commercial and government/public institutional interests and the self-representations of individual parents in interviews with the researchers. The argument is made that there are commonalities and disjunctures in represented and lived parenting identities as they relate to early literacy. In commercial texts that advertise educational and other products, parents are largely absent from representations and the parent’s position is one of consumer on behalf of the child. In government-sanctioned texts, parents are very much present and are positioned as both learners about and important facilitators of early learning when they ‘interact’ with their children around language and books. The problem for which both, in their different ways, offer a solution is the ‘‘not-yet-ready’’ child precipitated into the evaluative environment of school without the initial competence seen as necessary to avoid falling behind right from the start. Both kinds of producers promise a smooth induction of children into mainstream literacy and learning practices if the ‘good parent’ plays her/his part. Finally, we use two parent cases to illustrate how parents’ lived practice involves multiple discursive practices and identities as they manage young children’s literacy and learning in family contexts in which they also need to negotiate relations with their partners and with paid and domestic work.

Nascent entrepreneurship and the developing individual : early entrepreneurial competence in adolescence and venture creation success during the career

What predicts a person's venture creation success over the course of the career, such as making progress in the venture creation process and multiple successful venture creations? Applying a life span approach of human development, this study examined the effect of early entrepreneurial competence in adolescence, which was gathered retrospectively by means of the Life History Calendar method. Human and social capitals during the founding process were investigated as mediators between adolescent competence and performance. Findings were derived from regression analyses on the basis of prospective and retrospective data from two independent samples (N = 88 nascent founders; N = 148 founders). We found that early entrepreneurial competence in adolescence had a positive effect on making progress in the venture creation process. Nascent founders' current human and social capital also had a direct effect, but it did not mediate the effect of early competences. Finally, the data revealed that early entrepreneurial competence in adolescence positively predicted habitual entrepreneurship (multiple successful venture creations) exhibited over a longer period of the individual career (specifically, 18 years). In line with the results from prospective longitudinal studies on early precursors of entrepreneurship, our findings underscore the long neglected importance of adolescent development in the explanation of entrepreneurial performance during the subsequent working life.

The association between playgroup participation, learning competence and social-emotional wellbeing for children aged 4-5 years in Australia

Data from Growing Up in Australia: The Longitudinal Study of Australian Children is used to examine the associations between playgroup participation and the outcomes for children aged 4 to 5 years. Controlling for a range of socio-economic and family characteristics, playgroup participation across the ages of 0-3 years was used to predict learning competence and social-emotional functioning outcomes at age 4-5 years. For learning competence, both boys and girls from disadvantaged families scored 3-4% higher if they attended playgroup when aged 0-1 and 2-3 years compared to boys and girls from disadvantaged families who did not attend playgroup. For social and emotional functioning, girls from disadvantaged families who attended playgroup when they were aged 0-1 and 2-3 years scored nearly 5% higher than those who did not attend. Demographic characteristics also showed that disadvantaged families were the families least likely to access these services. Despite data limitations, this study provides evidence that continued participation in playgroups is associated with better outcomes for children from disadvantaged families.

Determinants of skin self-examination (SSE) in men aged 50 years or older

Background: Queensland men aged 50 years and older are at high risk for melanoma. Early detection via skin self examination (SSE) (particularly whole-body SSE) followed by presentation to a doctor with suspicious lesions, may decrease morbidity and mortality from melanoma. Prevalence of whole-body SSE (wbSSE) is lower in Queensland older men compared to other population subgroups. With the exception of the present study no previous research has investigated the determinants of wbSSE in older men, or interventions to increase the behaviour in this population. Furthermore, although past SSE intervention studies for other populations have cited health behaviour models in the development of interventions, no study has tested these models in full. The Skin Awareness Study: A recent randomised trial, called the Skin Awareness Study, tested the impact of a video-delivered intervention compared to written materials alone on wbSSE in men aged 50 years or older (n=930). Men were recruited from the general population and interviewed over the telephone at baseline and 13 months. The proportion of men who reported wbSSE rose from 10% to 31% in the control group, and from 11% to 36% in the intervention group. Current research: The current research was a secondary analysis of data collected for the Skin Awareness Study. The objectives were as follows: • To describe how men who did not take up any SSE during the study period differed from those who did take up examining their skin. • To determine whether the intervention program was successful in affecting the constructs of the Health Belief Model it was aimed at (self-efficacy, perceived threat, and outcome expectations); and whether this in turn influenced wbSSE. • To determine whether the Health Action Process Approach (HAPA) was a better predictor of wbSSE behaviour compared to the Health Belief Model (HBM). Methods: For objective 1, men who did not report any past SSE at baseline (n=308) were categorised as having ‘taken up SSE’ (reported SSE at study end) or ‘resisted SSE’ (reported no SSE at study end). Bivariate logistic regression, followed by multivariable regression, investigated the association between participant characteristics measured at baseline and resisting SSE. For objective 2 proxy measures of self-efficacy, perceived threat, and outcome expectations were selected. To determine whether these mediated the effect of the intervention on the outcome, a mediator analysis was performed with all participants who completed interviews at both time points (n=830) following the Baron and Kenny approach, modified for use with structural equation modelling (SEM). For objective 3, control group participants only were included (n=410). Proxy measures of all HBM and HAPA constructs were selected and SEM was used to build up models and test the significance of each hypothesised pathway. A likelihood ratio test compared the HAPA to the HBM. Results: Amongst men who did not report any SSE at baseline, 27% did not take up any SSE by the end of the study. In multivariable analyses, resisting SSE was associated with having more freckly skin (p=0.027); being unsure about the statement ‘if I saw something suspicious on my skin, I’d go to the doctor straight away’ (p=0.028); not intending to perform SSE (p=0.015), having lower SSE self-efficacy (p<0.001), and having no recommendation for SSE from a doctor (p=0.002). In the mediator analysis none of the tested variables mediated the relationship between the intervention and wbSSE. In regards to health behaviour models, the HBM did not predict wbSSE well overall. Only the construct of self-efficacy was a significant predictor of future wbSSE (p=0.001), while neither perceived threat (p=0.584) nor outcome expectations (p=0.220) were. By contrast, when the HAPA constructs were added, all three HBM variables predicted intention to perform SSE, which in turn predicted future behaviour (p=0.015). The HAPA construct of volitional self-efficacy was also associated with wbSSE (p=0.046). The HAPA was a significantly better model compared to the HBM (p<0.001). Limitations: Items selected to measure HBM and HAPA model constructs for objectives 2 and 3 may not have accurately reflected each construct. Conclusions: This research added to the evidence base on how best to target interventions to older men; and on the appropriateness of particular health behaviour models to guide interventions. Findings indicate that to overcome resistance those men with more negative pre-existing attitudes to SSE (not intending to do it, lower initial self-efficacy) may need to be targeted with more intensive interventions in the future. Involving general practitioners in recommending SSE to their patients in this population, alongside disseminating an intervention, may increase its success. Comparison of the HBM and HAPA showed that while two of the three HBM variables examined did not directly predict future wbSSE, all three were associated with intention to self-examine skin. This suggests that in this population, intervening on these variables may increase intention to examine skin, but not necessarily the behaviour itself. Future interventions could potentially focus on increasing both the motivational variables of perceived threat and outcome expectations as well as a combination of both action and volitional self-efficacy; with the aim of increasing intention as well as its translation to taking up and maintaining regular wbSSE.

Neuropsychological development in children with early and continuously treated phenylketonuria : association with biochemical markers

PKU is a genetically inherited inborn error of metabolism caused by a deficiency of the enzyme phenylalanine hydroxylase. The failure of this enzyme causes incomplete metabolism of protein ingested in the diet, specifically the conversion of one amino acid, phenylalanine, to tyrosine, which is a precursor to the neurotransmitter dopamine. Rising levels of phenylalanine is toxic to the developing brain, disrupting the formation of white matter tracts. The impact of tyrosine deficiency is not as well understood, but is hypothesized to lead to a low dopamine environment for the developing brain. Detection in the newborn period and continuous treatment (a low protein phe-restricted diet supplemented with phenylalanine-free protein formulas) has resulted in children with early and continuously treated PKU now developing normal I.Q. However, deficits in executive function (EF) are common, leading to a rate of Attention Deficit Hyperactivity Disorder (ADHD) up to five times the norm. EF worsens with exposure to higher phenylalanine levels, however recent research has demonstrated that a high phenylalanine to tyrosine ratio (phenylalanine:tyrosine ratio), which is hypothesised to lead to poorer dopamine function, has a more negative impact on EF than phenylalanine levels alone. Research and treatment of PKU is currently phenylalanine-focused, with little investigation of the impact of tyrosine on neuropsychological development. There is no current consensus as to the veracity of tyrosine monitoring or treatment in this population. Further, the research agenda in this population has demonstrated a primary focus on EF impairment alone, even though there may be additional neuropsychological skills compromised (e.g., mood, visuospatial deficits). The aim of this PhD research was to identify residual neuropsychological deficits in a cohort of children with early and continuously treated phenylketonuria, at two time points in development (early childhood and early adolescence), separated by eight years. In addition, this research sought to determine which biochemical markers were associated with neuropsychological impairments. A clinical practice survey was also undertaken to ascertain the current level of monitoring/treatment of tyrosine in this population. Thirteen children with early and continuously treated PKU were tested at mean age 5.9 years and again at mean age 13.95 years on several neuropsychological measures. Four children with hyperphenylalaninemia (a milder version of PKU) were also tested at both time points and provide a comparison group in analyses. Associations between neuropsychological function and biochemical markers were analysed. A between groups analysis in adolescence was also conducted (children with PKU compared to their siblings) on parent report measures of EF and mood. Minor EF impairments were evident in the PKU group by age 6 years and these persisted into adolescence. Life-long exposure to high phenylalanine:tyrosine ratio and/or low tyrosine independent of phenylalanine were significantly associated with EF impairments at both time points. Over half the children with PKU showed severe impairment on a visuospatial task, and this was associated only with concurrent levels of tyrosine in adolescence. Children with PKU also showed a statistically significant decline in a language comprehension task from 6 years to adolescence (going from normal to subnormal), this deficit was associated with lifetime levels of phenylalanine. In comparison, the four children with hyperphenylalaninemia demonstrated normal function at both time points, across all measures. No statistically significant differences were detected between children with PKU and their siblings on the parent report of EF and mood. However, depressive symptoms were significantly correlated with: EF; long term high phe:tyr exposure; and low tyrosine levels independent of phenylalanine. The practice survey of metabolic clinics from 12 countries indicated a high level of variability in terms of monitoring/treatment of tyrosine in this population. Whilst over 80% of clinics surveyed routinely monitored tyrosine levels in their child patients, 25% reported treatment strategies to increase tyrosine (and thereby lower the phenylalanine:tyrosine ratio) under a variety of patient presentation conditions. Overall, these studies have shown that EF impairments associated with PKU provide support for the dopamine-deficiency model. A language comprehension task showed a different trajectory, serving a timely reminder that non-EF functions also remain vulnerable in this population; and that normal function in childhood does not guarantee normal function by adolescence. Mood impairments were associated with EF impairments as well as long term measures of phenylalanine:tyrosine and/or tyrosine. The implications of this research for enhanced clinical guidelines are discussed given varied current practice.

Symbolic number : the integration of magnitude and spatial representations in children aged 6 to 8 years

The process of learning symbolic Arabic digits in early childhood requires that magnitude and spatial information integrates with the concept of symbolic digits. Previous research has separately investigated the development of automatic access to magnitude and spatial information from symbolic digits. However, developmental trajectories of symbolic number knowledge cannot be fully understood when considering components in isolation. In view of this, we have synthesized the existing lines of research and tested the use of both magnitude and spatial information with the same sample of British children in Years 1, 2 and 3 (6-8 years of age). The physical judgment task of the numerical Stroop paradigm (NSP) demonstrated that automatic access to magnitude was present from Year 1 and the distance effect signaled that a refined processing of numerical information had developed. Additionally, a parity judgment task showed that the onset of the Spatial-Numerical Association of Response Codes (SNARC) effect occurs in Year 2. These findings uncover the developmental timeline of how magnitude and spatial representations integrate with symbolic number knowledge during early learning of Arabic digits and resolve inconsistencies between previous developmental and experimental research lines.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Event-related brain potentials dissociate the developmental time-course of automatic numerical magnitude analysis and cognitive control functions during the first three years of primary school

In this study we set out to dissociate the developmental time course of automatic symbolic number processing and cognitive control functions in grade 1-3 British primary school children. Event-related potential (ERP) and behavioral data were collected in a physical size discrimination numerical Stroop task. Task-irrelevant numerical information was processed automatically already in grade 1. Weakening interference and strengthening facilitation indicated the parallel development of general cognitive control and automatic number processing. Relationships among ERP and behavioral effects suggest that control functions play a larger role in younger children and that automaticity of number processing increases from grade 1 to 3.

Keeping friends safe : a prospective study examining early adolescent's confidence and support networks

There is a continued need to consider ways to prevent early adolescent engagement in a variety of harmful risk-taking behaviours for example, violence, road-related risks and alcohol use. The current prospective study examined adolescents’ reports of intervening to try and stop friends’ engagement in such behaviours among 207 early adolescents (mean age = 13.51 years, 50.1% females). Findings showed that intervening behaviour after three months was predicted by the confidence to intervene which in turn was predicted by student and teacher support although not parental support. The findings suggest that the benefits of positive relationship experiences might extend to the safety of early adolescent friendship groups particularly through the development of confidence to try and stop friends’ risky and dangerous behaviours. Findings from the study support the important role of the school in creating a culture of positive adolescent behaviour whereby young people take social responsibility.

Identification of early-stage colorectal cancer patients at risk of relapse post-resection by immunobead reverse transcription-PCR analysis of peritoneal lavage fluid for malignant cells

Purpose: Colorectal cancer patients diagnosed with stage I or II disease are not routinely offered adjuvant chemotherapy following resection of the primary tumor. However, up to 10% of stage I and 30% of stage II patients relapse within 5 years of surgery from recurrent or metastatic disease. The aim of this study was to determine if tumor-associated markers could detect disseminated malignant cells and so identify a subgroup of patients with early-stage colorectal cancer that were at risk of relapse. Experimental Design: We recruited consecutive patients undergoing curative resection for early-stage colorectal cancer. Immunobead reverse transcription-PCR of five tumor-associated markers (carcinoembryonic antigen, laminin γ2, ephrin B4, matrilysin, and cytokeratin 20) was used to detect the presence of colon tumor cells in peripheral blood and within the peritoneal cavity of colon cancer patients perioperatively. Clinicopathologic variables were tested for their effect on survival outcomes in univariate analyses using the Kaplan-Meier method. A multivariate Cox proportional hazards regression analysis was done to determine whether detection of tumor cells was an independent prognostic marker for disease relapse. Results: Overall, 41 of 125 (32.8%) early-stage patients were positive for disseminated tumor cells. Patients who were marker positive for disseminated cells in post-resection lavage samples showed a significantly poorer prognosis (hazard ratio, 6.2; 95% confidence interval, 1.9-19.6; P = 0.002), and this was independent of other risk factors. Conclusion: The markers used in this study identified a subgroup of early-stage patients at increased risk of relapse post-resection for primary colorectal cancer. This method may be considered as a new diagnostic tool to improve the staging and management of colorectal cancer. © 2006 American Association for Cancer Research.

Young, inexperienced and on the road : do novice drivers comply with road rules?

The graduated driver licensing (GDL) program in Queensland, Australia, was considerably enhanced in July 2007. This paper explores the compliance of young Learner and Provisional (intermediate) drivers with current GDL requirements and general road rules. Unsupervised driving, Learner logbook accuracy, and experiences of punishment avoidance were explored, along with speeding as a Provisional driver. Participants (609 females; M = 17.43 years) self-reported sociodemographic characteristics, driving behaviours and licensing experiences as Learners. A subset of participants (238 females, 105 males) completed another survey six months later exploring their Provisional behaviours and experiences. While the majority of the participants reported compliance with both the GDL requirements and general road rules such as stopping at red lights on their Learner licence; a considerable proportion reported speeding. Furthermore, they reported becoming less compliant during the Provisional phase, particularly with speed limits. Self-reported speeding was predicted by younger age at licensure, being in a relationship, driving unsupervised, submitting inaccurate Learner logbooks, and speeding as a Learner. Enforcement and education countermeasures should focus upon curtailing noncompliance, targeting speeding in particular. Novice drivers should be encouraged to comply with all road rules, including speed limits, and safe driving behaviours should be developed and reinforced during the Learner and early Provisional periods. Novice drivers have been found to model their parents’ driving, and parents are pivotal in regulating novice driving. It is vital young novice drivers and parents alike are encouraged to comply with all road rules, including GDL requirements.