In this article, I study, from the point of view of the analytic philosophy of mind, the compatibility of students’ ideas studies (SIS) with radical constructivism (RC). I demonstrate that RC is based on a psychology of narrow mental states; that is, the idea that the mental content of an individual can be fully characterised without any reference external to her or him. I show that this fact imposes some severe restrictions to SIS to be incorporated into RC. In particular, I argue that only qualitative studies can comply with the requirement of narrowness. Nevertheless, I propose that quantitative works can be employed as sources of types in order to study token actual students. I use this type-token dichotomy to put forward an outline of a theory of the relation between school contents and mental contents. In this view, token mental contents regarding a given topic can be defined, and probed, only by resorting to typical school contents.

Key words: mental model, educational research, psychological state, causal power, second order model.

The author examines work practices and their effects in the post-industrial culture on public understanding and identification with the arts and sciences within a holistic frame of transdisciplinarity. He sees the possibility of cultural change arising from an informed public debate and from adaptations within the ecology of information, which might yield new ideas and forms of practice. The book elaborates a second-order perspective for cultural work that challenges contemporary forms of political power and social control within the framework of construction, production, and distribution. Based on Heinz von Foerster’s socio-epistemological second-order model of learning, the book promotes a more anticipatory dynamism based on reflexive inquiries into the construction of longer-term impact, sustainable environment awareness, democratic debate, and improved qualities of individual and social interaction. Relevance: The book refers to von Foerster’s second-order cybernetics.

Context: This paper outlines how radical constructivist theory has led to a particular methodological technique, developing second-order models of student thinking, that has helped mathematics educators to be more effective teachers of their students. Problem: The paper addresses the problem of how radical constructivist theory has been used to explain and engender more viable adaptations to the complexities of teaching and learning. Method: The paper presents empirical data from teaching experiments that illustrate the process of second-order model building. Results: The result of the paper is an illustration of how second-order models are developed and how this process, as it progresses, supports teachers to be more effective. Implications: This paper has the implication that radical constructivism has the potential to impact practice.

Key words: Second-order model, radical constructivism, teaching, mathematics education