This paper investigates how mathematics teachers describe their ethical decision making related to instructional practices, drawing on frameworks that incorporate both rational and non-rational approaches. We employed a multiple-case study method, selecting three teachers as cases through criterion sampling. Data were collected via four…

The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive…

We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students' understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit…

This paper offers a typology of forms and uses of abduction that can be exploited to better analyze abduction in proving processes. Based on the work of Peirce and Eco, we describe different kinds of abductions that occur in students' mathematical activity and extend Toulmin's model of an argument as a methodological tool to describe students'…

According to theoretical concepts like constructivism, each learner has to build up knowledge on his or her own. The learner creates hypotheses in order to explain "facts". Hypotheses do not guarantee certainty. They have to be verified. In this article, a theoretical framework will be presented which can help to understand and analyse the…