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.

Preparation of macroporous methacrylate monolithic material with convective flow properties for bioseparation : Investigating the kinetics of pore formation and hydrodynamic performance

The preparation of macroporous methacrylate monolithic material with controlled pore structures can be carried out in an unstirred mould through careful and precise control of the polymerisation kinetics and parameters. Contemporary synthesis conditions of methacrylate monolithic polymers are based on existing polymerisation schemes without an in-depth understanding of the dynamics of pore structure and formation. This leads to poor performance in polymer usage thereby affecting final product recovery and purity, retention time, productivity and process economics. The unique porosity of methacrylate monolithic polymer which propels its usage in many industrial applications can be controlled easily during its preparation. Control of the kinetics of the overall process through changes in reaction time, temperature and overall composition such as cross-linker and initiator contents allow the fine tuning of the macroporous structure and provide an understanding of the mechanism of pore formation within the unstirred mould. The significant effect of temperature of the reaction kinetics serves as an effectual means to control and optimise the pore structure and allows the preparation of polymers with different pore size distributions from the same composition of the polymerisation mixture. Increasing the concentration of the cross-linking monomer affects the composition of the final monoliths and also decreases the average pore size as a result of pre-mature formation of highly cross-linked globules with a reduced propensity to coalesce. The choice and concentration of porogen solvent is also imperative. Different porogens and porogen mixtures present different pore structure output. Example, larger pores are obtained in a poor solvent due to early phase separation.

Performance of R-N(R′)-R″ functionalised poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) monolithic sorbent for plasmid DNA adsorption

High-throughput plasmid DNA (pDNA) manufacture is obstructed predominantly by the performance of conventional stationary phases. For this reason, the search for new materials for fast chromatographic separation of pDNA is ongoing. A poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) (GMA-EGDMA) monolithic material was synthesised via a thermal-free radical reaction, functionalised with different amino groups from urea, 2-chloro-N,N-diethylethylamine hydrochloride (DEAE-Cl) and ammonia in order to investigate their plasmid adsorption capacities. Physical characterisation of the monolithic polymer showed a macroporous polymer having a unimodal pore size distribution pivoted at 600 nm. Chromatographic characterisation of the functionalised polymers using pUC19 plasmid isolated from E. coli DH5α-pUC19 showed a maximum plasmid adsorption capacity of 18.73 mg pDNA/mL with a dissociation constant (KD) of 0.11 mg/mL for GMA-EGDMA/DEAE-Cl polymer. Studies on ligand leaching and degradation demonstrated the stability of GMA-EGDMA/DEAE-Cl after the functionalised polymers were contacted with 1.0 M NaOH, which is a model reagent for most 'cleaning in place' (CIP) systems. However, it is the economic advantage of an adsorbent material that makes it so attractive for commercial purification purposes. Economic evaluation of the performance of the functionalised polymers on the grounds of polymer cost (PC)/mg pDNA retained endorsed the suitability of GMA-EGDMA/DEAE-Cl polymer.

Towards the design of a scalable and commercially viable technique for plasmid purification using a methacrylate monolithic stationary phase

A monolithic stationary phase was prepared via free radical co-polymerization of ethylene glycol dimethacrylate (EDMA) and glycidyl methacrylate (GMA) with pore diameter tailored specifically for plasmid binding, retention and elution. The polymer was functionalized. with 2-chloro-N,N-diethylethylamine hydrochloride (DEAE-Cl) for anion-exchange purification of plasmid DNA (pDNA) from clarified lysate obtained from E. coli DH5α-pUC19 culture in a ribonuclease/ protease-free environment. Characterization of the monolithic resin showed a porous material, with 68% of the pores existing in the matrix having diameters above 300 nm. The final product isolated from a single-stage 5 min anion-exchange purification was a pure and homogeneous supercoiled (SC) pDNA with no gDNA, RNA and protein contamination as confirmed by ethidium bromide agarose gel electrophoresis (EtBr-AGE), enzyme restriction analysis and sodium dodecyl sulfate-polyacrylamide gel electrophoresis. This non-toxic technique is cGMP compatible and highly scalable for production of pDNA on a commercial level.

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.