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Whereas most scientists are highly critical of constructivism and relativism in the context of scientific knowledge acquisition, the dominant school of chemical education researchers appears to support a variety of such positions. By reference to the views of Herron, Spencer, and Bodner, I claim that these authors are philosophically confused, and that they are presenting a damaging and anti-scientific message to other unsuspecting educators. Part of the problem, as I argue, is a failure to distinguish between pedagogical constructivism regarding students' understanding of science, and constructivism about the way that scientific knowledge is acquired by expert scientists.

Constructivism was first popularised by Bruner (1960). The underlying theme in Bruner’s theoretical framework is that learning is an active process in which learners construct new ideas or concepts based upon their prior knowledge. This chapter describes how constructivism can be realised in instruction through a lesson design involving a carefully crafted task on the topic of Gradient of Function Curves at a point. The task affords opportunities to activate and differentiate students’ prior knowledge to generate, explore, critique and refine methods for problem solving. The lesson design allows teachers to first understand what students know about a new concept based on students’ representation and solution methods (RSMs) collected from the group work before the teacher teaches the canonical concept during lesson consolidation. The task, coupled with skillful facilitation and lesson consolidation built upon students’ RSMs, can help students develop a deep understanding of the targeted concept. Implications of such constructivist learning design on teachers’ classroom practice are also discussed.

This chapter discusses how a lesson closure, which should be present in every Mathematics lesson, can be carried out effectively to promote offline metacognition. According to the theory of constructivism, learning is achieved through making connection between the new concept and a learner’s prior knowledge, or schema. Lesson closure is crucial to provide a time and space for students to consolidate their learning and acquire the mathematical concepts. We will introduce a strategy to close a lesson in which the teacher uses students’ reflection of their learning to create a visual representation, known as a closure diagram. This activity provides a structure that allows students to either integrate the knowledge into their schema or identify gaps in their learning. Both situations involve students regulating their thinking, which is metacognitive in nature. Variations of the closure strategy for different purposes will also be discussed and illustrated with artefacts from classroom lessons.

We present a laboratory developed in the mathematics activities during the lessons of the research project Mathematical High School at the University of Salerno. We consider a continuous location optimization problem, where an optimal location is found in a continuum on a plane, using a topological approach involving the Voronoi diagram and the Delaunay triangulation to find the equilibrium point.

The history of hydropolitics does not support the claim that the next war shall be about water. The chapter considers a set of variables, including scarcity, geography, relative power, domestic politics, and international water law, to explain the onset of conflict and initiation of cooperation over transboundary waters. Strategies and tactics for promoting cooperation, and eventually an agreement, between riparians are also discussed. After reading this chapter, you will understand that while political disputes over water do take place (and may become most volatile in otherwise unstable regions) they rarely become violent. You will be equipped with evidence showing that for the same reasons that conflict may arise over a shared-water body, cooperation may also come about. You will gain knowledge of several elements that facilitate both conflict and cooperation over transboundary waters. Finally, you will learn about different tactics used to facilitate cooperation and negotiation over transboundary waters, and understand that the intricacies of conflict and cooperation are of highest importance in otherwise precarious regions where a water dispute may aggravate the already tense political environment.

In this article we analyse the problem of downward causation in emergent systems. Our thesis, based on constructivist epistemological remarks, is that downward causation in synchronic emergence cannot be characterized by a direct causal role of the whole on the parts, as these levels belong to two different epistemological domains, but by the way the components are related: that is by their organization. According to these remarks downward causation, considered as relatedness, can be re-expressed as the non-coincidence of the operations of analysis and synthesis performed by the observer on the system.

Partisans of the constructivist approach to mathematics education, such as Brousseau or Chevallard, developed an accurate theoretical framework in which didactical systems are viewed in a systemic perspective. What they somewhat fail to draw, however, is a sharp distinction between role variables – concerning the roles played in the didactical interaction by the individual elements of the system (Student-Teacher-Knowledge) – and contextual variables – concerning the action on the learning process of the system as a whole.

Our research in progress on 2nd graders' word problem solving strategies applies the previous dichotomy to class management strategies adopted by teachers. Partial evidence collected so far points to the tentative conclusion according to which, contextual variables being equal, differences in teaching styles and methods may deeply reshape the role component of didactical systems. If we take into careful account this distinction, we can shed additional light into some hitherto unexplained phenomena observed in the literature.

In this article we analyse the problem of emergence in its diachronic dimension. In other words, we intend to deal with the generation of novelties in natural processes. Our approach aims at integrating some insights coming from Whitehead's Philosophy of the Process with the epistemological framework developed by the "autopoietic" tradition. Our thesis is that the emergence of new entities and rules of interaction (new "fields of relatedness") requires the development of discontinuous models of change. From this standpoint natural evolution can be conceived as a succession of emergences - each one realizing a novel "extended" present, described by distinct models - rather than as a single and continuous dynamics. This theoretical and epistemological framework is particularly suitable to the investigation of the origin of life, an emblematic example of this kind of processes.