Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts

Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively unexplored in the domain of teaching and learning of mathematics, and has not been examined with respect to students' major field of study. In this study, we examined the performance of 95 senior undergraduate mathematics and education majors in symbolic and verbal tasks about the contraposition equivalence rule . The selection of two different groups of participants allowed for the examination of the hypothesis that students' major may influence the relation between their performance in tasks about contraposition and the context (symbolic/verbal) wherein this is placed. The selection of contraposition equivalence rule also addressed a gap in the body of research on undergraduate students' understanding of proof by contraposition . The analysis was based on written responses of all participants to specially developed tasks and on semi-structured interviews with 11 subjects. The findings showed different variations in the performance of each of the two groups in the two contexts. while education majors performed significantly better in the verbal than in the symbolic tasks, mathematics majors' performance showed only modest variations. The results call for both major- and context- specific considerations of students' understanding of logical principles, and reveal the complexity of the system of factors that influence students' logical thinking.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42655/1/10649_2004_Article_5150044.pd

Changing classroom culture, curricula, and instruction for proof and proving: how amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions?

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways—student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few—they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students’ learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students’ preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are

Validation of Solutions of Construction Problems in Dynamic Geometry Environments

This paper discusses issues concerning the validation of solutions of construction problems in Dynamic Geometry Environments (DGEs) as compared to classic paper-and-pencil Euclidean geometry settings. We begin by comparing the validation criteria usually associated with solutions of construction problems in the two geometry worlds – the ‘drag test’ in DGEs and the use of only straightedge and compass in classic Euclidean geometry. We then demonstrate that the drag test criterion may permit constructions created using measurement tools to be considered valid; however, these constructions prove inconsistent with classical geometry. This inconsistency raises the question of whether dragging is an adequate test of validity, and the issue of measurement versus straightedge-and-compass. Without claiming that the inconsistency between what counts as valid solution of a construction problem in the two geometry worlds is necessarily problematic, we examine what would constitute the analogue of the straightedge-and-compass criterion in the domain of DGEs. Discovery of this analogue would enrich our understanding of DGEs with a mathematical idea that has been the distinguishing feature of Euclidean geometry since its genesis. To advance our goal, we introduce the compatibility criterion , a new but not necessarily superior criterion to the drag test criterion of validation of solutions of construction problems in DGEs. The discussion of the two criteria anatomizes the complexity characteristic of the relationship between DGEs and the paper-and-pencil Euclidean geometry environment, advances our understanding of the notion of geometrical constructions in DGEs, and raises the issue of validation practice maintaining the pace of ever-changing software.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42932/1/10758_2004_Article_6999.pd

Approaching Proof in the Classroom Through the Logic of Inquiry

The paper analyses a basic gap, highlighted by most of the literature concerning the teaching of proofs, namely, the distance between students' argumentative and proving processes. The analysis is developed from both epistemological and cognitive standpoints: it critiques the Toulmin model of reasoning and introduces a new model, the Logic of Inquiry of Hintikka, more suitable for bridging this gap. An example of didactical activity within Dynamic Geometry Environments is sketched in order to present a concrete illustration of this approach and to show the pedagogical effectiveness of the model

Changing outcomes following pelvic exenteration for locally advanced and recurrent rectal cancer

Background Pelvic exenteration for locally advanced rectal cancer (LARC) and locally recurrent rectal cancer (LRRC) is technically challenging but increasingly performed in specialist centres. The aim of this study was to compare outcomes of exenteration over time. Methods This was a multicentre retrospective study of patients who underwent exenteration for LARC and LRRC between 2004 and 2015. Surgical outcomes, including rate of bone resection, flap reconstruction, margin status and transfusion rates, were examined. Outcomes between higher- and lower-volume centres were also evaluated. Results Some 2472 patients underwent pelvic exenteration for LARC and LRRC across 26 institutions. For LARC, rates of bone resection or flap reconstruction increased from 2004 to 2015, from 3.5 to 12.8 per cent, and from 12.0 to 29.4 per cent respectively. Fewer units of intraoperative blood were transfused over this interval (median 4 to 2 units; P = 0.040). Subgroup analysis showed that bone resection and flap reconstruction rates increased in lower- and higher-volume centres. R0 resection rates significantly increased in low-volume centres but not in high-volume centres over time (low-volume: from 62.5 to 80.0 per cent, P = 0.001; high-volume: from 83.5 to 88.4 per cent, P = 0.660). For LRRC, no significant trends over time were observed for bone resection or flap reconstruction rates. The median number of units of intraoperative blood transfused decreased from 5 to 2.5 units (P < 0.001). R0 resection rates did not increase in either low-volume (from 51.7 to 60.4 per cent; P = 0.610) or higher-volume (from 48.6 to 65.5 per cent; P = 0.100) centres. No significant differences in length of hospital stay, 30-day complication, reintervention or mortality rates were observed over time. Conclusion Radical resection, bone resection and flap reconstruction rates were performed more frequently over time, while transfusion requirements decreased

Outcomes of obstructed abdominal wall hernia: results from the UK national small bowel obstruction audit

Background: Abdominal wall hernia is a common surgical condition. Patients may present in an emergency with bowel obstruction, incarceration or strangulation. Small bowel obstruction (SBO) is a serious surgical condition associated with significant morbidity. The aim of this study was to describe current management and outcomes of patients with obstructed hernia in the UK as identified in the National Audit of Small Bowel Obstruction (NASBO). Methods: NASBO collated data on adults treated for SBO at 131 UK hospitals between January and March 2017. Those with obstruction due to abdominal wall hernia were included in this study. Demographics, co-morbidity, imaging, operative treatment, and in-hospital outcomes were recorded. Modelling for factors associated with mortality and complications was undertaken using Cox proportional hazards and multivariable regression modelling. Results: NASBO included 2341 patients, of whom 415 (17·7 per cent) had SBO due to hernia. Surgery was performed in 312 (75·2 per cent) of the 415 patients; small bowel resection was required in 198 (63·5 per cent) of these operations. Non-operative management was reported in 35 (54 per cent) of 65 patients with a parastomal hernia and in 34 (32·1 per cent) of 106 patients with an incisional hernia. The in-hospital mortality rate was 9·4 per cent (39 of 415), and was highest in patients with a groin hernia (11·1 per cent, 17 of 153). Complications were common, including lower respiratory tract infection in 16·3 per cent of patients with a groin hernia. Increased age was associated with an increased risk of death (hazard ratio 1·05, 95 per cent c.i. 1·01 to 1·10; P = 0·009) and complications (odds ratio 1·05, 95 per cent c.i. 1·02 to 1·09; P = 0·001). Conclusion: NASBO has highlighted poor outcomes for patients with SBO due to hernia, highlighting the need for quality improvement initiatives in this group

Contemporary Management of Locally Advanced and Recurrent Rectal Cancer: Views from the PelvEx Collaborative

Pelvic exenteration is a complex operation performed for locally advanced and recurrent pelvic cancers. The goal of surgery is to achieve clear margins, therefore identifying adjacent or involved organs, bone, muscle, nerves and/or vascular structures that may need resection. While these extensive resections are potentially curative, they can be associated with substantial morbidity. Recently, there has been a move to centralize care to specialized units, as this facilitates better multi-disciplinary care input. Advancements in pelvic oncology and surgical innovation have redefined the boundaries of pelvic exenterative surgery. Combined with improved neoadjuvant therapies, advances in diagnostics, and better reconstructive techniques have provided quicker recovery and better quality of life outcomes, with improved survival This article provides highlights of the current management of advanced pelvic cancers in terms of surgical strategy and potential future developments

Elective cancer surgery in COVID-19-free surgical pathways during the SARS-CoV-2 pandemic: An international, multicenter, comparative cohort study

PURPOSE As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19–free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19–free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19–free surgical pathways. Patients who underwent surgery within COVID-19–free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19–free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score–matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19–free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION Within available resources, dedicated COVID-19–free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Elective Cancer Surgery in COVID-19-Free Surgical Pathways During the SARS-CoV-2 Pandemic: An International, Multicenter, Comparative Cohort Study.

PURPOSE: As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19-free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS: This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19-free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS: Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19-free surgical pathways. Patients who underwent surgery within COVID-19-free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19-free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score-matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19-free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION: Within available resources, dedicated COVID-19-free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks