Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: Cifarelli and Sevim discuss the development of individual students’ abstract conceptual structures while problem solving, using constructs for analysis that are consistent with von Glasersfeld’s radical constructivism: re-presentation and reflective abstraction. This commentary discusses the on-going contributions of reflective abstraction to individual and collective learning.

Open peer commentary on the article “From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research” by Jérôme Proulx & Jean-François Maheux. Upshot: The target article succeeds in conceptualizing mathematical problem-solving as a form of organism-environment coupling. So conceived, it is a suitable subject for both enactive and ecological descriptions, and is open to embodied, dynamical explanations that have no need for cognitivist models. In other words, Proulx and Maheux have shown how to get across the “cognitive gap.”

Purpose: This study aims to address the possibility of integrating some elements of the “radical constructivist” approach to management accounting teaching. It answers the following two questions: to what extent should management accounting educators construct a “radical constructivist” foundation to guide active learning? Then, in which ways can management accounting educators use qualitative methods to facilitate “radical constructivist” education? Design/methodology/approach – The study uses a teaching cycle that implements innovative learning elements, e.g. learning from ordinary people, designed following the principles of “radical constructivism”, to engage students with “externalities” at the centre of their knowledge construction. It adopts an ethnographic approach comprising interviews and participant observation for the data collection, followed by the application of qualitative content and narrative analysis of the data. Findings: The study findings and reflections illustrate that the majority of students respond positively to radical constructivist learning if the educators can develop an innovative problem-solving and authentic environment that is close to their real lives. The radical constructivist teaching cycle discussed in this study has challenged the mindsets of the management accounting students as it altered the traditional objectivist academic learning approaches that students were familiar with. Its use of qualitative methods facilitated active learning. Student feedback was sought as part of the qualitative design, which provided a constructive mechanism for the students and educators to learn and unlearn from their mistakes. This process enriched the understanding of learners (students) and educators of successful engagement in radical constructivist management accounting education and provides a base upon which to design future teaching cycles. Originality/value – The paper provides proof of the ability of accounting educators, as change agents, to apply radical constructivist epistemology combined with multiple qualitative research methods by creating new constructive learning structures and cultures associated with innovative deep-learning tasks in management accounting education.

Key words: radical constructivism, deep learning, , qualitative methodology, teaching cycle, management accounting education.

The primary goal of this theory is to foster problem solving and conceptual development. It is intended for ill-defined or ill-structured domains.

Excerpt: I believe that input from a wide community of constructivist scholars and teachers will profoundly improve biology education by developing future biologists and biology teachers who have a much better understanding of scientific investigation through their own development and use of investigative software, laboratory, and field activities. This community of teachers and scholars should have biologists of many varieties, researchers in science education and educational technology, computer scientists, and philosophers of science. Based on my commitment to transforming the nature and quality of science education, I believe that exploratory environments on microcomputers will empower many co-learners (teachers and students) primarily by conflating these two previously polar roles. Computer exploratoriums are not a panacea (in particular, this approach alone can do little to change who per se it is that does science), but they can provide an environment in which students can have ample opportunity to develop their confidence and competence in problem posing, long-term inference making, and contextualized problem solving through experiential and collaborative learning. ||

Objectives: The purpose of this literature review was to explore the use of distinct assumptions of constructivism when studying the impact of problem-based learning (PBL) on learners in undergraduate nursing programs. Design: Content analysis research technique. Data sources: The literature review included information retrieved from sources selected via electronic databases, such as EBSCOhost, ProQuest, Sage Publications, SLACK Incorporation, Springhouse Corporation, and Digital Dissertations. Review methods: The literature review was conducted utilizing key terms and phrases associated with problem-based learning in undergraduate nursing education. Out of the 100 reviewed abstracts, only 15 studies met the inclusion criteria for the review. Four constructivist assumptions based the review process allowing for analysis and evaluation of the findings, followed by identification of issues and recommendations for the discipline and its research practice in the field of PBL. Results: This literature review provided evidence that the nursing discipline is employing PBL in its programs, yet with limited data supporting conceptions of the constructivist perspective underlying this pedagogical approach. Three major issues were assessed and formed the basis for subsequent recommendations: (a) limited use of a theoretical framework and absence of constructivism in most of the studies, (b) incompatibility between research measures and research outcomes, and (c) brief exposure to PBL during which the change was measured. Conclusion: Educators have made the right choice in employing PBL as a pedagogical practice, yet the need to base implementation on constructivism is mandatory if the aim is a better preparation of graduates for practice. Undeniably there is limited convincing evidence regarding integration of constructivism in nursing education. Research that assesses the impact of PBL on learners’ problem-solving and communication skills, self-direction, and motivation is paramount.

Key words: constructivism, constructive assumptions, problem-based learning, undergraduate nursing education

Open peer commentary on the article “From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research” by Jérôme Proulx & Jean-François Maheux. Upshot: Proulx and Maheux’s view of problem-posing|solving compels insights about roles and lived experiences of teachers. Living and reporting co-emergence of teaching activity and mathematical activity are discussed.

In a recent book titled Beyond Constructivism: A Models & Modeling Perspective on Mathematics Problem Solving, Learning & Teaching (Lesh & Doerr, 2003a), the concluding chapter describes a number of specific ways that a models and modeling perspective moves significantly beyond the implications that can be drawn from constructivist theories in the context of issues that are priorities to address for teachers, curriculum developers, or program designers. In that chapter (Lesh & Doerr, 2003b), the following topics were treated as cross-cutting themes: (a) the nature of reality, (b) the nature of mathematical knowledge, (c) the nature of the development of children’s knowledge, (d) the mechanisms that drive that development, (e) the relationship of context and generalizability, (f) problem solving, and (g) teachers’ knowledge and the kinds of teaching and learning situations that contribute to the development of children’s knowledge. In this article, we organize our comments directly around the preceding topics and describe how a models and modeling perspective provides alternative ways of thinking about mathematics teaching and learning that enable teachers, researchers and others to produce useful and sharable conceptual tools that have powerful implications in the context of decision-making issues that are of priority to practitioners.

In recent years the Artificial Intelligence research group at the University of New Mexico have considered several areas of problem solving in interesting and complex domains. These areas have ranged from the low level explorations of a robot tasked to explore, map, and use a new environment to the development of very sophisticated control algorithms for the optimal use of particle beam accelerators. Although the results of our research have been reflected in computer-based problem solvers, such as the robot discovering and mapping out its world, these computational tasks are in many ways similar to expert human performance in similar tasks. In fact, in many important ways our computer-based approach mimics human expert performance in such domains. This paper describes three of these task domains as well as the software algorithms that have achieved competent performances therein. We conclude this paper with some comments on how software models of a domain can elucidate aspects of intellectual performance within that context. Furthermore, we demonstrate how exploratory problem solving along with model refinement algorithms can support a constructivist epistemology.

Key words: artificial intelligence, constructivist epistemology, human complex problem solving, model refinement, diagnostic reasoning, intelligent control.

The question ‘What is intelligence?” can be approached with at least two attitudes: (a) to assume ‘intelligence’ denotes a distinct property or attribute of some organisms; (b) to assume there is a class of behaviour of organisms in general, that an observer calls ‘intelligent behaviour’, making connotative reference to the relations that take place between the participating systems. We take the second approach and pose the biological question ‘What is intelligent behaviour as a phenomenon proper to living systems and how is it generated?’. The notions of problem-solving or goal-oriented behaviour, being observerdependent descriptions, are shown to be irrelevant in this view, since intelligent behaviour results from a kind of interactions between organisms within a particular context. Living systems are autopoietic entities with a plastic structure which allows them to interact with each other in a recursive manner, generating a form of ontogenic structural coupling called consensual domain, or to interact with its environment, generating another form of ontogenic structural coupling called ontogenic adaptation. The processes that generate intelligent behaviour are those that participate in the establishment of any domain of ontogenic structural coupling and those that participate in the operation of the involved organisms within such a domain. Although one can refer to intelligence as a phenomenon, because it is a configuration of relations between processes occurring during structural coupling, it is not directly observable and thus it cannot be measured. All that can be observed are instances of consensuality or of ontogenic adaptation in the form of intelligent behaviour. The IQ Test can, at most, estimate a subdomain of the domain of consensuality between the observer and the subject. No biological basis can be found for racial, social or educational discrimination, based on intelligence since the word ‘intelligence’ does not refer to a discrete individual attribute or property.