Inquiry pedagogy to promote emerging proportional reasoning in primary students

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for proportional reasoning in later years. In this paper, excerpts from a classroom case study of a fourth-grade classroom (students aged 9) are presented as they address an inquiry problem that required proportional reasoning. As the inquiry unfolded, students' additive strategies were progressively seen to shift to proportional thinking to enable them to answer the question that guided their inquiry. In wrestling with the challenges they encountered, their emerging proportional reasoning was supported by the inquiry model used to provide a structure, a classroom culture of inquiry and argumentation, and the proportionality embedded in the problem context

‘Even though it might take me a while, in the end, I understand it’: a longitudinal case study of interactions between a conceptual change strategy and student motivation, interest and confidence

Although there have been many investigations of the social, motivational, and emotional aspects of conceptual change, there have been few studies investigating the intersection of these factors with cognitive aspects in the regular classroom. Using a conceptual change approach, this case study reports experiences of a student of low to average prior attainment who achieved high levels of conceptual gains in five science topics over a two-year period. Her experience in the cognitive, social and affective domains was probed through analysis of interviews, student artefacts, video recordings of classroom learning, pre/post-tests and questionnaire results. For this student, peripheral or incidental persuasion of belonging to a supportive small group initially led to greater engagement with the construction of understanding through production of multiple student-generated representations, resulting in improved self-confidence and high levels of conceptual change. Evidence of transfer from performance to mastery approach goals, adoption of positive activating emotions and increased interest in science were observed. This study highlights that adoption of a multidimensional conceptual change approach with judicious organisation of small groups to support construction of verbal, pictorial and written representations of understanding may bring about changes in motivational stance, self-confidence and emotions to maximise conceptual change

The communicative functions of metaphors between explanation and persuasion

In the literature, the pragmatic dimension of metaphors has been clearly acknowledged. Metaphors are regarded as having different possible uses, and in particular, they are commonly viewed as instruments for pursuing persuasion. However, an analysis of the specific conversational purposes that they can be aimed at achieving in a dialogue and their adequacy thereto is still missing. In this paper, we will address this issue focusing on the distinction between the explanatory and persuasive goal. The difference between explanation and persuasion is often blurred and controversial from a theoretical point of view. Building on the analysis of explanation in different theories and fields of study, we show how it can be conceived as characterized by a cognitive and a pragmatic dimension, where the transference of understanding is used pragmatically for different dialogical goals. This theoretical proposal will be applied to examples drawn from the medical context, to show how a pragmatic approach to explanation can account for the complexity of the cases that can be found in actual dialogical contexts

Preservice Elementary Science Teachers' Argumentation Competence: Impact of a Training Programme

The recent literature has shown the importance of Preservice Elementary Science Teachers (PESTs) having a deep understanding of argumentation, as this factor may affect the nature of the class activities that are taught and what students learn. A lack of understanding of this factor may represent an obstacle in the development of science education programmes in line with the development of scientific competences. This paper presents the results of the design and implementation of a training programme of 6 sessions (12 hours of class participation plus 8 hours of personal homework) on argumentation. The programme was carried out by 57 Spanish PESTs from Malaga, Spain. The training programme incorporates the innovative use of certain strategies to improve competence in argumentation, such as teaching PESTs to identify the elements of arguments in order to design assessment rubrics or by including peer assessment during evaluation with and without rubrics. The results obtained on implementing the training programme were evaluated based on the development of PESTs’ argumentation competence using Toulmin’s argumentative model. Data collection methods involved two tasks carried out at the beginning and the end of the programme, i.e., pre-test and post-test, respectively. The conclusion of the study is that students made significant progress in their argumentation competence on completing the course. In addition, PESTs who followed the training programme achieved statistically better results at the end than those in the control group (n = 41), who followed a traditional teaching programme. A 6-month transfer task showed a slight improvement for the PESTs of the experimental group in relation to the control group in their ability to transfer argumentation to practice, especially to the extent to which they mentioned argumentation in their practice portfolios.This work is part of the “I+D Excelencia” project “Development and evaluation of scientific competences through context based and modelling teaching approaches” case studies (EDU2013-41952-P), funded by the Spanish Ministry of Economy and Finance through its 2013 research call

Modelling GDPR-Compliant Explanations for Trustworthy AI

Through the General Data Protection Regulation (GDPR), the European Union has set out its vision for Automated Decision- Making (ADM) and AI, which must be reliable and human-centred. In particular we are interested on the Right to Explanation, that requires industry to produce explanations of ADM. The High-Level Expert Group on Artificial Intelligence (AI-HLEG), set up to support the implementation of this vision, has produced guidelines discussing the types of explanations that are appropriate for user-centred (interactive) Explanatory Tools. In this paper we propose our version of Explanatory Narratives (EN), based on user-centred concepts drawn from ISO 9241, as a model for user-centred explanations aligned with the GDPR and the AI-HLEG guidelines. Through the use of ENs we convert the problem of generating explanations for ADM into the identification of an appropriate path over an Explanatory Space, allowing explainees to interactively explore it and produce the explanation best suited to their needs. To this end we list suitable exploration heuristics, we study the properties and structure of explanations, and discuss the proposed model identifying its weaknesses and strengths