Constructionism and the space of reasons

Constructionism, best known as the framework for action underpinning Seymour Papert’s work with Logo, has stressed the importance of engaging students in creating their own products. Noss and Hoyles have argued that such activity enables students to participate increasingly in a web of connections to further their activity. Ainley and Pratt have elaborated that learning is best facilitated when the student is engaged in a purposeful activity that leads to appreciation of the power of mathematical ideas. Constructionism gives prominence to how the learner’s logical reasoning and emotion-driven reasons for engagement are inseparable. We argue that the dependence of constructionism upon the orienting framework of constructivism fails to provide sufficient theoretical underpinning for these ideas. We therefore propose an alternative orienting framework, in which learning takes place through initiation into the space of reasons, such that a person’s thoughts, actions and feelings are increasingly open to critique and justification. We argue that knowing as responsiveness to reasons encompasses not only the powerful ideas of mathematics and disciplinary knowledge of modes of enquiry but also the extralogical, such as in feelings of the aesthetic, control, excitement, elegance and efficiency. We discuss the implication that mathematics educators deeply consider the learner’s reasons for purposeful activity and design settings in which these reasons can be made public and open to critique

Theory of didactical situations and instrumental genesis for the design of a cabri elem book

The contributions of two theoretical frameworks (Theory of Didactic Situations and Instrumental Genesis) to the design of a sequence of tasks in the Cabri Elem envi-ronment, where task and technology design are closely linked, are shown. Considering the potential for instrumental genesis as a theory of technology design reveals a fundamental difficulty in dealing with representations. It is hence suggested that the role of the artefact be broadened to include environments, tools, and entities

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Stable or improved neurological manifestations during miglustat therapy in patients from the international disease registry for Niemann-Pick disease type C: an observational cohort study

Background: Niemann-Pick disease type C (NP-C) is a rare neurovisceral disease characterised by progressive neurological degeneration, where the rate of neurological disease progression varies depending on age at neurological onset. We report longitudinal data on functional disease progression and safety observations in patients in the international NPC Registry who received continuous treatment with miglustat. Methods: The NPC Registry is a prospective observational cohort of NP-C patients. Enrolled patients who received ≥1 year of continuous miglustat therapy (for ≥90 % of the observation period, with no single treatment interruption >28 days) were included in this analysis. Disability was measured using a scale rating the four domains, ambulation, manipulation, language and swallowing from 0 (normal) to 1 (worst). Neurological disease progression was analysed in all patients based on: 1) annual progression rates between enrolment and last follow up, and; 2) categorical analysis with patients categorised as 'improved/stable' if ≥3/4 domain scores were lower/unchanged, and as 'progressed' if <3 scores were lower/unchanged between enrolment and last follow-up visit. Results: In total, 283 patients were enrolled from 28 centers in 13 European countries, Canada and Australia between September 2009 and October 2013; 92 patients received continuous miglustat therapy. The mean (SD) miglustat exposure during the observation period (enrolment to last follow-up) was 2.0 (0.7) years. Among 84 evaluable patients, 9 (11 %) had early-infantile (<2 years), 27 (32 %) had late-infantile (2 to <6 years), 30 (36 %) had juvenile (6 to <15 years) and 18 (21 %) had adolescent/adult (≥15 years) onset of neurological manifestations. The mean (95%CI) composite disability score among all patients was 0.37 (0.32,0.42) at enrolment and 0.44 (0.38,0.50) at last follow-up visit, and the mean annual progression rate was 0.038 (0.018,0.059). Progression of composite disability scores appeared highest among patients with neurological onset during infancy or childhood and lowest in those with adolescent/adult-onset. Overall, 59/86 evaluable patients (69 %) were categorized as improved/stable and the proportion of improved/stable patients increased with age at neurological onset. Safety findings were consistent with previous data. Conclusions: Disability status was improved/stable in the majority of patients who received continuous miglustat therapy for an average period of 2 years

The duo “pascaline and e-pascaline”: an example of using material and digital artefacts at primary school.

International audienceThe paper presents the design and the analysis of teaching experiments at primary school concerning the introduction and use of a “duo of artefacts”, constituted by the pascaline i.e., the arithmetical machine Zero+1 and its digital version e-pascaline. The idea of ‘duo of artefacts’ represents the innovative component of this research work, because the e-pascaline is constructed in a complementary way with respect to the pascaline. The duo of artefacts is proposed to support student’s conceptualization processes of numbers as sign of a quantity, number sequences and recursive addition. Computation and manipulation of base ten notation are two processes that students often consider separately. This duo enables the design of situations that required those two processes to be connected and to consider their effect on each other. With duo of artefacts, technology allows the development of learning environments in which it is possible to study the articulation between material and virtual manipulatives for mathematical conceptualization