The Classroom as a Potential Space-teaching Negotiation through Paradox

In this article, we describe and analyze a way of teaching negotiation which recognizes and accepts paradoxes, such as caring and frustrating the students at the same time and helping them being more autonomous while manipulating them. In this analysis, the classroom is considered tantamount to a transitional space (Winnicott). This way of teaching is not the easiest one for the professor and for the students, as it is shown. But it helps the students to really listen to others, to sincerely try to understand the rational of others, and finally be more creative in the options they propose, all skills and capacities necessary to better negotiate.Creativity; Negotiation; Paradox; Teaching; Transitional Space; Winnicott

Carnap: an Open Framework for Formal Reasoning in the Browser

This paper presents an overview of Carnap, a free and open framework for the development of formal reasoning applications. Carnap’s design emphasizes flexibility, extensibility, and rapid prototyping. Carnap-based applications are written in Haskell, but can be compiled to JavaScript to run in standard web browsers. This combination of features makes Carnap ideally suited for educational applications, where ease-of-use is crucial for students and adaptability to different teaching strategies and classroom needs is crucial for instructors. The paper describes Carnap’s implementation, along with its current and projected pedagogical applications

Processing mathematics through digital technologies: A reorganisation of student thinking?

This article reports on aspects of an ongoing study examining the use of digital media in mathematics education. In particular, it is concerned with how understanding evolves when mathematical tasks are engaged through digital pedagogical media in primary school settings. While there has been a growing body of research into software and other digital media that enhances geometric, algebraic, and statistical thinking in secondary schools, research of these aspects in primary school mathematics is still limited, and emerging intermittently. The affordances of digital technology that allow dynamic, visual interaction with mathematical tasks, the rapid manipulation of large amounts of data, and instant feedback to input, have already been identified as ways mathematical ideas can be engaged in alternative ways. How might these, and other opportunities digital media afford, transform the learning experience and the ways mathematical ideas are understood? Using an interpretive methodology, the researcher examined how mathematical thinking can be seen as a function of the pedagogical media through which the mathematics is encountered. The article gives an account of how working in a spreadsheet environment framed learners' patterns of social interaction, and how this interaction, in conjunction with other influences, mediated the understanding of mathematical ideas, through framing the students' learning pathways and facilitating risk taking

Affordances of spreadsheets in mathematical investigation: Potentialities for learning

This article, is concerned with the ways learning is shaped when mathematics problems are investigated in spreadsheet environments. It considers how the opportunities and constraints the digital media affords influenced the decisions the students made, and the direction of their enquiry pathway. How might the leraning trajectory unfold, and the learning process and mathematical understanding emerge? Will the spreadsheet, as the pedagogical medium, evoke learning in a distinctive manner? The article reports on an aspect of an ongoing study involving students as they engage mathematical investigative tasks through digital media, the spreadsheet in particular. In considers the affordances of this learning environment for primary-aged students

Helping Students Master Concepts in Mechanics by Graphing with Spreadsheets

An example of a curricular activity to help students master concepts in mechanics is presented. Students measure positions and times of movements using calculators, and construct graphs using spreadsheets. Students learn to connect concepts in mechanics and reinforce them following a spiral approach of increasing complexity. Comments from students about the activity are also presented