Zig-zagging in geometrical reasoning in technological collaborative environments: a Mathematical Working Space-framed study concerning cognition and affect

This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic model such as that outlined in the Mathematical Working Spaces (MWS) framework, in order to describe the interplay between cognition and affect in the transitions from instrumental to discursive geneses in geometrical reasoning. The results based on empirical data from a teaching experiment at a middle school show that the use of dynamic geometry software favours students’ attitudinal and volitional dimensions and helps them to maintain productive affective pathways, affording greater intellectual independence in mathematical work and interaction with the context that impact learning opportunities in geometric proofs. The reflective and heuristic dimensions of teacher mediation in students’ learning is crucial in the transition from instrumental to discursive genesis and working stability in the Instrumental-Discursive plane of MWS.

Mapping variation in children’s mathematical reasoning: the case of ‘what else belongs?’

Explaining appears to dominate primary teachers’ understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop mathematical reasoning. The task used in this study of children’s reasoning is a number commonality problem. We analysed written and verbal samples of reasoning gathered from children in grades 3 and 4 from three primary schools in Australia and one elementary school in Canada to map the variation in their reasoning. We found that comparing and contrasting was a critical aspect of forming conjectures when generalising in this context, an action not specified in frameworks for generalising in early algebra. The variance in children’s reasoning elicited through this task also illuminated the difference between explaining and justifying.

Primary teachers notice the impact of language on children’s mathematical reasoning

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children’s mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise mathematical reasoning in children’s actions and words. As part of a larger study, we explored whether observation of educators conducting mathematics lessons can develop teachers’ sensitivity in noticing children’s reasoning and consideration of how to support reasoning. In the Mathematical Reasoning Professional Learning Research Program, demonstration lessons were conducted in Australian and Canadian primary classrooms. Data sources included post-lesson group discussions. Observation of demonstration lessons and engagement in post-lesson discussions proved to be effective vehicles for developing a professional eye for noticing children’s individual and whole-class reasoning. In particular, the teachers noticed that children struggled to employ mathematical language to communicate their reasoning and viewed limitations in language as a major barrier to increasing the use of mathematical reasoning in their classrooms. Given the focus of teachers’ noticing of the limitations in some types of mathematical language, it seems that targeted support is required for teachers to facilitate classroom discourse for reasoning.

Motivated reasoning in the prediction of sports outcomes and the belief in the “hot hand”

The present paper explores the role of motivation to observe a certain outcome in people's predictions, causal attributions, and beliefs about a streak of binary outcomes (basketball scoring shots). In two studies we found that positive streaks (points scored by the participants' favourite team) lead participants to predict the streak's continuation (belief in the hot hand), but negative streaks lead to predictions of its end (gambler's fallacy). More importantly, these wishful predictions are supported by strategic attributions and beliefs about how and why a streak might unfold. Results suggest that the effect of motivation on predictions is mediated by a serial path via causal attributions to the teams at play and belief in the hot hand.

Moral reasoning in sport: validation of the Portuguese version of the RSBH value-judgement inventory in adolescents

The purpose of this study was to examine the validity and reliability of the Portuguese version of the Rudd Stoll Beller Hahm Value-judgement Inventory (RSBHVI) in a sample of adolescents. The RSBHVI, which measures moral and social reasoning, was translated using a back translation method. A sample of 238 10th to 12th grade high school students (age mean value 16.93 years, s = 1.34) completed the Portuguese versions of RSBH, and the Task and Ego-orientation Questionnaire. Partial support for the original structure of the moral reasoning scale, but not the social reasoning scale, was found. Females, and non-athletes and individual sport athletes scored significantly higher than males and team sport athletes in moral reasoning, respectively. Moral reasoning was negatively correlated with ego-orientation (r = −30; p <. 001) and uncorrelated with task-orientation (r = .10, p > .05). Participants who were low-ego scored higher in moral reasoning than those who were high-ego. It is suggested that decreasing levels of ego-orientation may be necessary to improve athletes’ moral reasoning.

Reasoning in science through representation

In this chapter we argue that our analysis of student reasoning through constructing representations points to a range of informal and formal reasoning processes. This suggests the need for researchers and teachers to shift from an exclusive focus on formal syllogistic reasoning as the main or only reasoning resource for science learning. First we review the literature to identify how informal reasoning is described, and relates to reasoning through representation, then examine one case of reasoning during a representational challenge, to argue that reasoning should be thought of as deliberative thinking that involves choices, leading to a justifiable claim. Two case studies from RILS units are then used to identify how reasoning through representation can occur at a number of points during a representational challenge, and finally to develop an indicative taxonomy of the different purposes of reasoning as part of the processes of science.

Professional learning in mathematical reasoning: reflections of a primary teacher

Reasoning is an important aspect in the understanding and learning of mathematics. This paper reports on a case study presenting one Australian primary teacher’s reflections regarding the role played by a professional learning program in her developing understanding of mathematical reasoning. Examination of the transcripts of two interviews identified changes in her perceptions of mathematical reasoning by mapping interview responses against the Mathematical Reasoning Framework (Herbert et al., 2015). This change indicates that a well planned program of professional learning based on a demsonstration is efficacious in developing teachers’ understanding of mathematical reasoning.

Making use of students’ research journals as instruments for detecting students’ reasoning in co-constructing scientific concepts in a German and Australian primary school

This chapter describes two cases, one from Germany and the other from Australia in which science journals were used in classrooms that adopted an inquiry-based approach to teaching science. We are interested in the following research questions:1. In what ways do teachers use journals to promote student learning of science?2. What evidence of reasoning is present in the cases in respect of the use of learning journals?3. When and in which form is feedback given in journals?

Prediction of Length of Hospital Stay in Preterm Infants - A Case-Based Reasoning View

The length of stay of preterm infants in a neonatology service has become an issue of a growing concern, namely considering, on the one hand, the mothers and infants health conditions and, on the other hand, the scarce healthcare facilities own resources. Thus, a pro-active strategy for problem solving has to be put in place, either to improve the quality-of-service provided or to reduce the inherent financial costs. Therefore, this work will focus on the development of a diagnosis decision support system in terms of a formal agenda built on a Logic Programming approach to knowledge representation and reasoning, complemented with a case-based problem solving methodology to computing, that caters for the handling of incomplete, unknown, or even contradictory in-formation. The proposed model has been quite accurate in predicting the length of stay (overall accuracy of 84.9%) and by reducing the computational time with values around 21.3%.

A case-based reasoning view of thrombophilia risk

Thrombophilia stands for a genetic or an acquired tendency to hypercoagulable states that increase the risk of venous and arterial thromboses. Indeed, venous thromboembolism is often a chronic illness, mainly in deep venous thrombosis and pulmonary embolism, requiring lifelong prevention strategies. Therefore, it is crucial to identify the cause of the disease, the most appropriate treatment, the length of treatment or prevent a thrombotic recurrence. Thus, this work will focus on the development of a diagnosis decision support system in terms of a formal agenda built on a logic programming approach to knowledge representation and reasoning, complemented with a case-based approach to computing. The proposed model has been quite accurate in the assessment of thrombophilia predisposition risk, since the overall accuracy is higher than 90% and sensitivity ranging in the interval [86.5%, 88.1%]. The main strength of the proposed solution is the ability to deal explicitly with incomplete, unknown, or even self-contradictory information.

Healthcare Computer Reasoning Addressing Chronically Ill Societies Using IoT: Deep Learning AI to the Rescue of Home-Based Healthcare

The authors present a proposal to develop intelligent assisted living environments for home based healthcare. These environments unite the chronical patient clinical history sematic representation with the ability of monitoring the living conditions and events recurring to a fully managed Semantic Web of Things (SWoT). Several levels of acquired knowledge and the case based reasoning that is possible by knowledge representation of the health-disease history and acquisition of the scientific evidence will deliver, through various voice based natural interfaces, the adequate support systems for disease auto management but prominently by activating the less differentiated caregiver for any specific need. With these capabilities at hand, home based healthcare providing becomes a viable possibility reducing the institutionalization needs. The resulting integrated healthcare framework will provide significant savings while improving the generality of health and satisfaction indicators.

Strategies to Promote Research and Logical Reasoning in the Teaching of Mathematics in the Schools

The purpose of this paper is to raise a debate on the urgent need for teachers to generate innovative situations in the teaching-learning process, in the field of Mathematics, as a way for students to develop logical reasoning and research skills applicable to everyday situations. It includes some statistical data and possible reasons for the poor performance and dissatisfaction of students towards Mathematics. Since teachers are called to offer meaningful and functional learning experiences to students, in order to promote the pleasure of learning, teacher training should include experiences that can be put into practice by teachers in the education centers. This paper includes a work proposal for Mathematics Teaching to generate discussion, curiosity and logical reasoning in students, together with the Mathematical problem solving study.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Developing a supportive culture for teaching and learning : a university, faculty and school perspective

In the early 1990's the University of Salford was typical of most pre-1992 Universities in that whilst students provided much of it's income, little attention was paid to pedagogy. As Warren Piper (1994) observed, University teachers were professional in their subject areas but generally did not seek to acquire a pedagogy of HE. This was the case in Alsford. Courses were efficiently run but only a minority of staff were engaged in actively considering learning and teaching issues. Instead staff time was spent on research and commercial activity.----- In the mid-1990's the teaching environment began to change significantly. As well as Dearing, the advent of QAA and teaching quality reviews, Salford was already experiencing changes in the characteristics of its student body. Wideing access was on our agenda before it was so predominant nationally. With increasing numbers and heterogeneity of students as well as these external factors, new challenges were facing the University and teaching domain.----- This paper describes how a culture which values teaching, learning and pedagogic inquiry is being created in the university. It then focuses on parts of this process specific to the Faculty of Business and Informatics, namely the Faculty's Learning and Teaching Research Network and the establishment of the Centre for Construction Education in the School of Construction and Property Management.----- The Faculty of Business and Informatics' Learning and Teaching Research Network aims to raise the profile, quality and volume of pedagogic research across the five schools in the faculty. The initiative is targeted at all academics regardless of previous research experience. We hope to grow and nurture research potential where it exists and to acknowledge and use the existing expertise of subject-based researchers in collaborative ventures. We work on the principle that people are deliged to share what they know but need appreciation and feedback for doing so. A further ain is to surface and celebrate the significant amount of tacit knowledge in the area of pedagogy evidenced by the strength of student and employer feedback in many areas of the faculty's teaching.----- The Faculty embraces generic and core management expertise but also includes applied management disciplines in information systems and construction and property management where internationally leading research activities and networked centres of excellence have been established. Drawing from this experience, and within the context of the Faculty network, a Centre for Construction Education is being established with key international external partners to develop a sustainable business model of an enterprising pedagogic centre that can undertake useful research to underpin teaching in the Faculty whilst offering sustainable business services to allow it to benefit from pump-priming grant funding.----- Internal and external networking are important elements in our plans and ongoing work. Key to this are our links with the LTSN subject centres (BEST and CEBE) and the LTSN generic centre. The paper discusses networking as a concept and gives examples of practices which have proved useful in this context.----- The academic influences on our approach are also examined. Dixon’s (2000) work examining how a range of companies succeed through internal knowledge sharing has provided a range of transferable practices. We also examine the notion of dialogue in this context, defined by Ballantyne (1999) as ‘The interactive human process of reasoning together which comes into being through interactions based on spontaneity or need and is enabled by trust’ Social constructionist principles of Practical Authorship (Shotter, 1993, Pavlica, Holman and Thorpe, 1998)) have also proved useful in developing our perspective on learning and knowledge creation within our community of practice.