Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.

Personalizing the design of computer-based instruction to enhance learning

This paper reports two studies designed to investigate the effect on learning outcomes of matching individuals' preferred cognitive styles to computer-based instructional (CBI) material. Study 1 considered the styles individually as Verbalizer, Imager, Wholist and Analytic. Study 2 considered the bi-dimensional nature of cognitive styles in order to assess the full ramification of cognitive styles on learning: Analytic/Imager, Analytic/ Verbalizer, Wholist/Imager and the Wholist/Verbalizer. The mix of images and text, the nature of the text material, use of advance organizers and proximity of information to facilitate meaningful connections between various pieces of information were some of the considerations in the design of the CBI material. In a quasi-experimental format, students' cognitive styles were analysed by Cognitive Style Analysis (CSA) software. On the basis of the CSA result, the system defaulted students to either matched or mismatched CBI material by alternating between the two formats. The instructional material had a learning and a test phase. Learning outcome was tested on recall, labelling, explanation and problem-solving tasks. Comparison of the matched and mismatched instruction did not indicate significant difference between the groups, but the consistently better performance by the matched group suggests potential for further investigations where the limitations cited in this paper are eliminated. The result did indicate a significant difference between the four cognitive styles with the Wholist/Verbalizer group performing better then all other cognitive styles. Analysing the difference between cognitive styles on individual test tasks indicated significant difference on recall, labelling and explanation, suggesting that certain test tasks may suit certain cognitive styles.

Cognitive skills required in contemporary workplaces

This paper discusses some of the changes occurring in contemporary workplace practices, and the implications these have for the types of knowledge and skills required to work in such environments. Increasingly, workers need to be multi-skilled to function effectively in contemporary work environments. The nature of multi-skilling is explained in terms of cross-skilling, up-skilling and higher-order thinking skills, and the relevance of multi-skilling in today's workplaces is examined. Finally, the paper explores some factors affecting the acquisition of these desired skills in light of current work practices.

Cognitive load and mental rotation : structuring orthographic projection for learning and problem solving

Cognitive load theory was used to generate a series of three experiments to investigate the effects of various worked example formats on learning orthographic projection. Experiments 1 and 2 investigated the benefits of presenting problems, conventional worked examples incorporating the final 2-D and 3-D representations only, and modified worked examples with several intermediate stages of rotation between the 2-D and 3-D representations. Modified worked examples proved superior to conventional worked examples without intermediate stages while conventional worked examples were, in turn, superior to problems. Experiment 3 investigated the consequences of varying the number and location of intermediate stages in the rotation trajectory and found three stages to be superior to one. A single intermediate stage was superior when nearer the 2-D than the 3-D end of the trajectory. It was concluded that (a) orthographic projection is learned best using worked examples with several intermediate stages and that (b) a linear relation between angle of rotation and problem difficulty did not hold for orthographic projection material. Cognitive load theory could be used to suggest the ideal location of the intermediate stages.

Communicating assessment criteria is not sufficient for influencing students' approaches to assessment tasks – perspectives from a differential equations class

This report presents the findings of an exploratory study into the perceptions held by students regarding the use of criterion-referenced assessment in an undergraduate differential equations class. Students in the class were largely unaware of the concept of criterion referencing and of the various interpretations that this concept has among mathematics educators. Our primary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. Quantitative data and qualitative 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, the manner in which they actually approached the assessment activity was not altered as a result of the use of explicitly communicated grading criteria.

Motivational Interviewing changes the treatment trajectory of group Cognitive-Behavioural Therapy for anxiety

Anxiety disorders have been viewed as manifestations of broad underlying predisposing personality constructs such as neuroticism combined with more specific individual differences of unhelpful information processing styles. Given the high prevalence of anxiety and the significant impairment that it causes, there is an important need to continue to explore successful treatments for this disorder. Research indicates that there is still room for significantly improving attrition rates and treatment adherence. Traditionally Motivational Interviewing (MI) has been used to facilitate health behaviour change. Recently MI has been applied to psychotherapy and has been shown to improve the outcome of CBT. However, these studies have been limited to only considering pre- and post-treatment measures and neglected to consider when changes occur along the course of therapy. This leaves the unanswered question of what is the impact of pre-treatment MI on the treatment trajectory of therapy. This study provides preliminary research into answering this question by tracking changes on a weekly basis along the course of group CBT. Prior to group CBT, 40 individuals with a principal anxiety disorder diagnosis were randomly assigned to receive either 3 individual sessions of MI or placed on a waitlist control group. All participants then received the same dosage of 10 weekly 2 hour sessions of group CBT. Tracking treatment outcome trajectory over the course of CBT, the pre-treatment MI group, compared to the control group, experienced a greater improvement early on in the course of therapy in their symptom distress, interpersonal relationships and quality of life. This early advantage over the control group was then maintained throughout therapy. These results not only demonstrate the value of adding MI to CBT, but also highlight the immediacy of MI effects. Further research is needed to determine the robustness of these effects to inform clinical implications of how to best apply MI to improve treatment adherence to CBT for anxiety disorders.

Similarity metrics within a point of view

In vector space based approaches to natural language processing, similarity is commonly measured by taking the angle between two vectors representing words or documents in a semantic space. This is natural from a mathematical point of view, as the angle between unit vectors is, up to constant scaling, the only unitarily invariant metric on the unit sphere. However, similarity judgement tasks reveal that human subjects fail to produce data which satisfies the symmetry and triangle inequality requirements for a metric space. A possible conclusion, reached in particular by Tversky et al., is that some of the most basic assumptions of geometric models are unwarranted in the case of psychological similarity, a result which would impose strong limits on the validity and applicability vector space based (and hence also quantum inspired) approaches to the modelling of cognitive processes. This paper proposes a resolution to this fundamental criticism of of the applicability of vector space models of cognition. We argue that pairs of words imply a context which in turn induces a point of view, allowing a subject to estimate semantic similarity. Context is here introduced as a point of view vector (POVV) and the expected similarity is derived as a measure over the POVV's. Different pairs of words will invoke different contexts and different POVV's. Hence the triangle inequality ceases to be a valid constraint on the angles. We test the proposal on a few triples of words and outline further research.

Driving performance impairments due to hypovigilance on monotonous roads

Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Highway design reduces the driving task mainly to a lane-keeping manoeuvre. Such a task is monotonous, providing little stimulation and this contributes to crashes due to inattention. Research has shown that driver's hypovigilance can be assessed with EEG measurements and that driving performance is impaired during prolonged monotonous driving tasks. This paper aims to show that two dimensions of monotony - namely road design and road side variability - decrease vigilance and impair driving performance. This is the first study correlating hypovigilance and driver performance in varied monotonous conditions, particularly on a short time scale (a few seconds). We induced vigilance decrement as assessed with an EEG during a monotonous driving simulator experiment. Road monotony was varied through both road design and road side variability. The driver's decrease in vigilance occurred due to both road design and road scenery monotony and almost independently of the driver's sensation seeking level. Such impairment was also correlated to observable measurements from the driver, the car and the environment. During periods of hypovigilance, the driving performance impairment affected lane positioning, time to lane crossing, blink frequency, heart rate variability and non-specific electrodermal response rates. This work lays the foundation for the development of an in-vehicle device preventing hypovigilance crashes on monotonous roads.

Legal ethics in a post-Westphalian world : building the international rule of law and otehr tasks

The emergence of strong sovereign states after the Treaty of Westphalia turned two of the most cosmopolitan professions (law and arms) into two of the least cosmopolitan. Sovereign states determined the content of the law within their borders – including which, if any, ecclesiastical law was to be applied; what form of economic regulation was adopted; and what, if any, international law applied. Similarly, states sought to ensure that all military force was at their disposal in national armies. The erosion of sovereignty in a post-Westphalian world may significantly reverse these processes. The erosion of sovereignty is likely to have profound consequences for the legal profession and the ethics of how, and for what ends, it is practised. Lawyers have played a major role in the civilization of sovereign states through the articulation and institutionalisation of key governance values – starting with the rule of law. An increasingly global profession must take on similar tasks. The same could be said of the military. This essay will review the concept of an international rule of law and its relationship to domestic conceptions and outline the task of building the international rule of law and the role that lawyers can and should play in it.

Primary students' performance on map tasks : the role of context

This study investigated the longitudinal performance of 583 students on six map items that were represented in various graphic forms. Specifically, this study compared the performance of 7-9-year-olds (across Grades 2 and 3) from metropolitan and non-metropolitan locations. The results of the study revealed significant performance differences in favour of metropolitan students on two of six map tasks. Implications include the need for teachers in non-metropolitan locations to ensure that their students do not overly fixate on landmarks represented on maps but rather consider the arrangement of all elements encompassed within the graphic.

Co-constructing self-efficacy narratives : a study of four mature age university students

This thesis reports on a study in which research participants, four mature aged females starting an undergraduate degree at a regional Australian university, collaborated with the researcher in co-constructing a self-efficacy narrative. For the purpose of the study, self-efficacy was conceptualized as a means by which an individual initiates action to engage in a task or set of tasks, applies effort to perform the task or set of tasks, and persists in the face of obstacles encountered in order to achieve successful completion of the task or set of tasks. Qualitative interviews were conducted with the participants, initially investigating their respective life histories for an understanding of how they made the decision to embark on their respective academic program. Additional data were generated from a written exercise, prompting participants to furnish specific examples of self-efficacy. These data were incorporated into the individual's self-efficacy narrative, produced as the outcome of the "narrative analysis". Another aspect of the study entailed "analysis of narrative" in which analytic procedures were used to identify themes common to the self-efficacy narratives. Five main themes were identified: (a) participants' experience of schooling . for several participants their formative experience of school was not always positive, and yet their narratives demonstrated their agency in persevering and taking on university-level studies as mature aged persons; (b) recognition of family as an early influence . these influences were described as being both positive, in the sense of being supportive and encouraging, as well as posing obstacles that participants had to overcome in order to pursue their goals; (c) availability of supportive persons – the support of particular persons was acknowledged as a factor that enabled participants to persist in their respective endeavours; (d) luck or chance factors were recognised as placing participants at the right place at the right time, from which circumstances they applied considerable effort in order to convert the opportunity into a successful outcome; and (e) self-efficacy was identified as a major theme found in the narratives. The study included an evaluation of the research process by participants. A number of themes were identified in respect of the manner in which the research process was experienced as a helpful process. Participants commented that: (a) the research process was helpful in clarifying their respective career goals; (b) they appreciated opportunities provided by the research process to view their life from a different perspective and to better understand what motivated them, and what their preferred learning styles were; (c) their past successes in a range of different spheres were made more evident to them as they were guided in self-reflection, and their self-efficacious behaviour was affirmed; and (d) the opportunities provided by their participation in the research process to identify strengths of which they had not been consciously aware, to find confirmation of strengths they knew they possessed, and in some instances to rectify misconceptions they had held about aspects of their personality. The study made three important contributions to knowledge. Firstly, it provided a detailed explication of a qualitative narrative method in exploring self-efficacy, with the potential for application to other issues in educational, counselling and psychotherapy research. Secondly, it consolidated and illustrated social cognitive theory by proposing a dynamic model of self-efficacy, drawing on constructivist and interpretivist paradigms and extending extant theory and models. Finally, the study made a contribution to the debate concerning the nexus of qualitative research and counselling by providing guidelines for ethical practice in both endeavours for the practitioner-researcher.

The psychosocial factors influencing aggressive driving behaviour

Many drivers in highly motorised countries believe that aggressive driving is increasing. While the prevalence of the behaviour is difficult to reliably identify, the consequences of on-road aggression can be severe, with extreme cases resulting in property damage, injury and even death. This research program was undertaken to explore the nature of aggressive driving from within the framework of relevant psychological theory in order to enhance our understanding of the behaviour and to inform the development of relevant interventions. To guide the research a provisional ‘working’ definition of aggressive driving was proposed encapsulating the recurrent characteristics of the behaviour cited in the literature. The definition was: “aggressive driving is any on-road behaviour adopted by a driver that is intended to cause physical or psychological harm to another road user and is associated with feelings of frustration, anger or threat”. Two main theoretical perspectives informed the program of research. The first was Shinar’s (1998) frustration-aggression model, which identifies both the person-related and situational characteristics that contribute to aggressive driving, as well as proposing that aggressive behaviours can serve either an ‘instrumental’ or ‘hostile’ function. The second main perspective was Anderson and Bushman’s (2002) General Aggression Model. In contrast to Shinar’s model, the General Aggression Model reflects a broader perspective on human aggression that facilitates a more comprehensive examination of the emotional and cognitive aspects of aggressive behaviour. Study One (n = 48) examined aggressive driving behaviour from the perspective of young drivers as an at-risk group and involved conducting six focus groups, with eight participants in each. Qualitative analyses identified multiple situational and person-related factors that contribute to on-road aggression. Consistent with human aggression theory, examination of self-reported experiences of aggressive driving identified key psychological elements and processes that are experienced during on-road aggression. Participants cited several emotions experienced during an on-road incident: annoyance, frustration, anger, threat and excitement. Findings also suggest that off-road generated stress may transfer to the on-road environment, at times having severe consequences including crash involvement. Young drivers also appeared quick to experience negative attributions about the other driver, some having additional thoughts of taking action. Additionally, the results showed little difference between males and females in the severity of behavioural responses they were prepared to adopt, although females appeared more likely to displace their negative emotions. Following the self-reported on-road incident, evidence was also found of a post-event influence, with females being more likely to experience ongoing emotional effects after the event. This finding was evidenced by ruminating thoughts or distraction from tasks. However, the impact of such a post-event influence on later behaviours or interpersonal interactions appears to be minimal. Study Two involved the quantitative analysis of n = 926 surveys completed by a wide age range of drivers from across Queensland. The study aimed to explore the relationships between the theoretical components of aggressive driving that were identified in the literature review, and refined based on the findings of Study One. Regression analyses were used to examine participant emotional, cognitive and behavioural responses to two differing on-road scenarios whilst exploring the proposed theoretical framework. A number of socio-demographic, state and trait person-related variables such as age, pre-study emotions, trait aggression and problem-solving style were found to predict the likelihood of a negative emotional response such as frustration, anger, perceived threat, negative attributions and the likelihood of adopting either an instrumental or hostile behaviour in response to Scenarios One and Two. Complex relationships were found to exist between the variables, however, they were interpretable based on the literature review findings. Factor analysis revealed evidence supporting Shinar’s (1998) dichotomous description of on-road aggressive behaviours as being instrumental or hostile. The second stage of Study Two used logistic regression to examine the factors that predicted the potentially hostile aggressive drivers (n = 88) within the sample. These drivers were those who indicated a preparedness to engage in direct acts of interpersonal aggression on the road. Young, male drivers 17–24 years of age were more likely to be classified as potentially hostile aggressive drivers. Young drivers (17–24 years) also scored significantly higher than other drivers on all subscales of the Aggression Questionnaire (Buss & Perry, 1992) and on the ‘negative problem orientation’ and ‘impulsive careless style’ subscales of the Social Problem Solving Inventory – Revised (D’Zurilla, Nezu & Maydeu-Olivares, 2002). The potentially hostile aggressive drivers were also significantly more likely to engage in speeding and drink/drug driving behaviour. With regard to the emotional, cognitive and behavioural variables examined, the potentially hostile aggressive driver group also scored significantly higher than the ‘other driver’ group on most variables examined in the proposed theoretical framework. The variables contained in the framework of aggressive driving reliably distinguished potentially hostile aggressive drivers from other drivers (Nagalkerke R2 = .39). Study Three used a case study approach to conduct an in-depth examination of the psychosocial characteristics of n = 10 (9 males and 1 female) self-confessed hostile aggressive drivers. The self-confessed hostile aggressive drivers were aged 24–55 years of age. A large proportion of these drivers reported a Year 10 education or better and average–above average incomes. As a group, the drivers reported committing a number of speeding and unlicensed driving offences in the past three years and extensive histories of violations outside of this period. Considerable evidence was also found of exposure to a range of developmental risk factors for aggression that may have contributed to the driver’s on-road expression of aggression. These drivers scored significantly higher on the Aggression Questionnaire subscales and Social Problem Solving Inventory Revised subscales, ‘negative problem orientation’ and ‘impulsive/careless style’, than the general sample of drivers included in Study Two. The hostile aggressive driver also scored significantly higher on the Barrett Impulsivity Scale – 11 (Patton, Stanford & Barratt, 1995) measure of impulsivity than a male ‘inmate’, or female ‘general psychiatric’ comparison group. Using the Carlson Psychological Survey (Carlson, 1982), the self-confessed hostile aggressive drivers scored equal or higher scores than the comparison group of incarcerated individuals on the subscale measures of chemical abuse, thought disturbance, anti-social tendencies and self-depreciation. Using the Carlson Psychological Survey personality profiles, seven participants were profiled ‘markedly anti-social’, two were profiled ‘negative-explosive’ and one was profiled as ‘self-centred’. Qualitative analysis of the ten case study self-reports of on-road hostile aggression revealed a similar range of on-road situational factors to those identified in the literature review and Study One. Six of the case studies reported off-road generated stress that they believed contributed to the episodes of aggressive driving they recalled. Intense ‘anger’ or ‘rage’ were most frequently used to describe the emotions experienced in response to the perceived provocation. Less frequently ‘excitement’ and ‘fear’ were cited as relevant emotions. Notably, five of the case studies experienced difficulty articulating their emotions, suggesting emotional difficulties. Consistent with Study Two, these drivers reported negative attributions and most had thoughts of aggressive actions they would like to take. Similarly, these drivers adopted both instrumental and hostile aggressive behaviours during the self-reported incident. Nine participants showed little or no remorse for their behaviour and these drivers also appeared to exhibit low levels of personal insight. Interestingly, few incidents were brought to the attention of the authorities. Further, examination of the person-related characteristics of these drivers indicated that they may be more likely to have come from difficult or dysfunctional backgrounds and to have a history of anti-social behaviours on and off the road. The research program has several key theoretical implications. While many of the findings supported Shinar’s (1998) frustration-aggression model, two key areas of difference emerged. Firstly, aggressive driving behaviour does not always appear to be frustration driven, but can also be driven by feelings of excitation (consistent with the tenets of the General Aggression Model). Secondly, while the findings supported a distinction being made between instrumental and hostile aggressive behaviours, the characteristics of these two types of behaviours require more examination. For example, Shinar (1998) proposes that a driver will adopt an instrumental aggressive behaviour when their progress is impeded if it allows them to achieve their immediate goals (e.g. reaching their destination as quickly as possible); whereas they will engage in hostile aggressive behaviour if their path to their goal is blocked. However, the current results question this assertion, since many of the hostile aggressive drivers studied appeared prepared to engage in hostile acts irrespective of whether their goal was blocked or not. In fact, their behaviour appeared to be characterised by a preparedness to abandon their immediate goals (even if for a short period of time) in order to express their aggression. The use of the General Aggression Model enabled an examination of the three components of the ‘present internal state’ comprising emotions, cognitions and arousal and how these influence the likelihood of a person responding aggressively to an on-road situation. This provided a detailed insight into both the cognitive and emotional aspects of aggressive driving that have important implications for the design of relevant countermeasures. For example, the findings highlighted the potential value of utilising Cognitive Behavioural Therapy with aggressive drivers, particularly the more hostile offenders. Similarly, educational efforts need to be mindful of the way that person-related factors appear to influence one’s perception of another driver’s behaviour as aggressive or benign. Those drivers with a predisposition for aggression were more likely to perceive aggression or ‘wrong doing’ in an ambiguous on-road situation and respond with instrumental and/or hostile behaviour, highlighting the importance of perceptual processes in aggressive driving behaviour.

Investigating the development of the internal and external service tasks of non-executive directors: the case of the Netherlands (1997-2005)

During the last decade, globalisation and liberalisation of financial markets, changing societal expectations and corporate governance scandals have increased the attention for the fiduciary duties of non-executive directors. In this context, recent corporate governance reform initiatives have emphasised the control task and independence of non-executive directors. However, little attention has been paid to their impact on the external and internal service tasks of non-executive directors. Therefore, this paper investigates how the service tasks of non-executive directors have evolved in the Netherlands. Data on corporate governance at the top-100 listed companies in the Netherlands between 1997 and 2005 show that the emphasis on non-executive directors' external service task has shifted to their internal service task, i.e. from non-executive directors acting as boundary spanners to non-executive directors providing advice and counselling to executive directors. This shift in board responsibilities affects non-executive directors' ability to generate network benefits through board relationships and has implications for non-executive directors' functional requirements.