The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

Numeracy and statistical reasoning on entering university

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on mathematics anxiety. Gnaldi (2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning, basic numeracy skills, mathematics background and attitudes towards statistics. This work reports on some key relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Numeracy counts in the statistical reasoning equation

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on maths anxiety. Gnaldi (Gnaldi 2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning ability, basic numeracy skills and attitudes towards statistics. This work reports on the relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Exploring an innovative educational approach to facilitating student nurses' clinical-reasoning skills in North Sulawesi Province, Indonesia

This study examined the effect of an educational intervention utilizing principles of cognitive apprenticeship on students’ ability to apply clinical reasoning skills within the context of a purpose-built clinical vignette. A quasi-experimental, non-equivalent control-group design was used to evaluate the effect of the educational intervention on students’ accuracy, inaccuracy and self-confidence in clinical reasoning. This study makes an important contribution to nursing education by providing evidence to understand how best to facilitate nursing students’ development of clinical reasoning.

A preference-based semantics for CTD reasoning

In [8] the authors developed a logical system based on the definition of a new non-classical connective ⊗ capturing the notion of reparative obligation. The system proved to be appropriate for handling well-known contrary-to-duty paradoxes but no model-theoretic semantics was presented. In this paper we fill the gap and define a suitable possible-world semantics for the system for which we can prove soundness and completeness. The semantics is a preference-based non-normal one extending and generalizing semantics for classical modal logics.

Reasoning about natural language phrases for semantic goal driven exploration

This paper presents a symbolic navigation system that uses spatial language descriptions to inform goal-directed exploration in unfamiliar office environments. An abstract map is created from a collection of natural language phrases describing the spatial layout of the environment. The spatial representation in the abstract map is controlled by a constraint based interpretation of each natural language phrase. In goal-directed exploration of an unseen office environment, the robot links the information in the abstract map to observed symbolic information and its grounded world representation. This paper demonstrates the ability of the system, in both simulated and real-world trials, to efficiently find target rooms in environments that it has never been to previously. In three unexplored environments, it is shown that on average the system travels only 8.42% further than the optimal path when using only natural language phrases to complete navigation tasks.

Student understandings of numeracy problems: Semantic alignment and analogical reasoning

Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all curriculum areas are responsible for numeracy. This general capability approach confuses what numeracy should look like, especially when compared to the structure of numeracy as defined on standardised national tests. In seeking to define numeracy, schools tend to look at past NAPLAN papers, and in doing so, we do not find examples drawn from the various aspects of school curriculum. What we find are more traditional forms of mathematical worded problems.

Populational reasoning

This section focuses on systems of reasoning that imagine youth as a unified whole, one that can be researched, talked about, planned for, and managed. Even research that focuses on individuals or specific contexts depends on and reproduces ideas of youth as an identifiable population. This section interrogates the rules and scaffolding of discourses that construct the social spaces in which we problematize and study youth in society. This introduction will set the agenda by addressing four elements of this process: the first addresses the rise of some of the crucial elements of contemporary governance, the instrument and practices through which the notion of the population was able to take shape. The second examines the rise of the personage of “the child,” and how new forms of governance not only utilized this new identity for the purposes of ongoing social management, but also organized its differentiation into a growing array of new social and administrative categories. The third specifically addresses “youth,” examining its various predecessors as targets for moral concern, as well as some of the recent cultural triggers for its formation. Finally, there is an assessment of the contemporary governance of populations of youth, based as it is around its twin existence as a governmental object, a target for an almost endless array of social, educational, legal, and psychological concerns and interventions, but also as an identity, a set of practices of the self.

Building teachers' pedagogy practices in reasoning, to improve students' dispositions towards mathematics

Drawing on participatory action research, this study identifies the pedagogies necessary to advance reasoning, which is one of the proficiencies from the Australian Curriculum Mathematics, and explores how reasoning leads to greater productive disposition. With the current emphasis on STEM in schools, this research is timely. This thesis makes an original and substantive contribution to the understanding of why and how teachers can most effectively advance student proficiency in reasoning through targeted instructional strategies and style of instruction. The study explores the ways in which teacher practices, when focused on reasoning, enhance the disposition of students towards greater mathematical proficiency.

Reasoning about discontinuance of information system use

While many studies have explored conditions and consequences of information systems adoption and use, few have focused on the final stages of the information system lifecycle. In this paper, I develop a theoretical and an initial empirical contribution to understanding individuals’ intentions to discontinue the use of an information system. This understanding is important because it yields implications about maintenance, retirement, and users’ switching decisions, which ultimately can affect work performance, system effectiveness, and return on technology investments. In this paper, I offer a new conceptualization of factors determining users’ intentions to discontinue the use of information systems. I then report on a preliminary empirical test of the model using data from a field study of information system users in a promotional planning routine in a large retail organization. Results from the empirical analysis provide first empirical support for the theoretical model. I discuss the work’s implications for theory on information systems continuance and dual-factor logic in information system use. I also provide suggestions for managers dealing with cessation of information systems and broader work routine change in organizations due to information system end-of-life decisions.

Clinical reasoning: The relative contribution of identification, interpretation and hypothesis errors to misdiagnosis

The aim of this study was to identify and describe the types of errors in clinical reasoning that contribute to poor diagnostic performance at different levels of medical training and experience. Three cohorts of subjects, second- and fourth- (final) year medical students and a group of general practitioners, completed a set of clinical reasoning problems. The responses of those whose scores fell below the 25th centile were analysed to establish the stage of the clinical reasoning process - identification of relevant information, interpretation or hypothesis generation - at which most errors occurred and whether this was dependent on problem difficulty and level of medical experience. Results indicate that hypothesis errors decrease as expertise increases but that identification and interpretation errors increase. This may be due to inappropriate use of pattern recognition or to failure of the knowledge base. Furthermore, although hypothesis errors increased in line with problem difficulty, identification and interpretation errors decreased. A possible explanation is that as problem difficulty increases, subjects at all levels of expertise are less able to differentiate between relevant and irrelevant clinical features and so give equal consideration to all information contained within a case. It is concluded that the development of clinical reasoning in medical students throughout the course of their pre-clinical and clinical education may be enhanced by both an analysis of the clinical reasoning process and a specific focus on each of the stages at which errors commonly occur.

The association between student characteristics and the development of clinical reasoning in a graduate-entry, PBL medical programme

This study sought to assess the extent to which the entry characteristics of students in a graduate-entry medical programme predict the subsequent development of clinical reasoning ability. Subjects comprised 290 students voluntarily recruited from three successive cohorts of the University of Queensland's MBBS Programme. Clinical reasoning was measured once a year over a period of three years using two methods, a set of 10 Clinical Reasoning Problems (CRPs) and the Diagnostic Thinking Inventory (DTI). Data on gender, age at entry into the programme, nature of primary degree, scores on selection criteria (written examination plus interview) and academic performance in the first two years of the programme were recorded for each student, and their association with clinical reasoning skill analysed using univariate and multivariate analysis. Univariate analysis indicated significant associations between CRP score, gender and primary degree with a significant but small association between DTI and interview score. Stage of progression through the programme was also an important predictor of performance on both indicators. Subsequent multivariate analysis suggested that female gender is a positive predictor of CRP score independently of the nature of a subject's primary degree and stage of progression through the programme, although these latter two variables are interdependent. Positive predictors of clinical reasoning skill are stage of progression through the MBBS programme, female gender and interview score. Although the nature of a student's primary degree is important in the early years of the programme, evidence suggests that by graduation differences between students' clinical reasoning skill due to this factor have been resolved.

The clinical reasoning characteristics of diagnostic experts

The aim of this study was to identify and describe the clinical reasoning characteristics of diagnostic experts. A group of 21 experienced general practitioners were asked to complete the Diagnostic Thinking Inventory (DTI) and a set of 10 clinical reasoning problems (CRPs) to evaluate their clinical reasoning. Both the DTI and the CRPs were scored, and the CRP response patterns of each GP examined in terms of the number and type of errors contained in them. Analysis of these data showed that six GPs were able to reach the correct diagnosis using significantly less clinical information than their colleagues. These GPs also made significantly fewer interpretation errors but scored lower on both the DTI and the CRPs. Additionally, this analysis showed that more than 20% of misdiagnoses occurred despite no errors being made in the identification and interpretation of relevant clinical information. These results indicate that these six GPs diagnose efficiently, effectively and accurately using relatively few clinical data and can therefore be classified as diagnostic experts. They also indicate that a major cause of misdiagnoses is failure to properly integrate clinical data. We suggest that increased emphasis on this step in the reasoning process should prove beneficial to the development of clinical reasoning skill in undergraduate medical students.

Assessing clinical reasoning: A method to monitor its development in a PBL curriculum

The aim of this study was to develop and trial a method to monitor the evolution of clinical reasoning in a PBL curriculum that is suitable for use in a large medical school. Termed Clinical Reasoning Problems (CRPs), it is based on the notion that clinical reasoning is dependent on the identification and correct interpretation of certain critical clinical features. Each problem consists of a clinical scenario comprising presentation, history and physical examination. Based on this information, subjects are asked to nominate the two most likely diagnoses and to list the clinical features that they considered in formulating their diagnoses, indicating whether these features supported or opposed the nominated diagnoses. Students at different levels of medical training completed a set of 10 CRPs as well as the Diagnostic Thinking Inventory, a self-reporting questionnaire designed to assess reasoning style. Responses were scored against those of a reference group of general practitioners. Results indicate that the CRPs are an easily administered, reliable and valid assessment of clinical reasoning, able to successfully monitor its development throughout medical training. Consequently, they can be employed to assess clinical reasoning skill in individual students and to evaluate the success of undergraduate medical schools in providing effective tuition in clinical reasoning.