Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe

Relationships between students' conceptions of constructivist learning and their regulation and processing strategies

The present study investigated relationships between students' conceptions of constructivist learning on the one hand, and their regulation and processing strategies on the other hand. Students in a constructivist, problem-based learning curriculum were questioned about their conceptions of knowledge construction and self-regulated learning, as well as their beliefs regarding their own (in)ability to learn and motivation to learn. Two hypothesized models were tested within 98 psychology students, using a structural equation modelling approach: The first model implemented regulation and processing variables of the Inventory of Learning Styles [ILS, Vermunt (Learning styles and regulation of learning in higher education - towards process-oriented instruction in autonomous thinking, 1992)], the second model of the Motivated Strategies for Learning Questionnaire [MSLQ, Pintrich and de Groot (Journal of Educational Psychology, 82, 33-40, 1990)]. Results showed that structural relations exist between conceptions of constructivist learning and regulation and processing strategies. Furthermore, students who express doubt with regard to their own learning capacities are at risk for adopting an inadequate regulation strategy. A three-tiered structure of conceptual, controlling, and operational level appeared valid for the MSLQ variables, but not entirely for those of the ILS

Empowering Qualitative Research Methods in Education with Artificial Intelligence

Artificial Intelligence is one of the fastest growing disciplines, disrupting many sectors. Originally mainly for computer scientists and engineers, it has been expanding its horizons and empowering many other disciplines contributing to the development of many novel applications in many sectors. These include medicine and health care, business and finance, psychology and neuroscience, physics and biology to mention a few. However, one of the disciplines in which artificial intelligence has not been fully explored and exploited yet is education. In this discipline, many research methods are employed by scholars, lecturers and practitioners to investigate the impact of different instructional approaches on learning and to understand the ways skills and knowledge are acquired by learners. One of these is qualitative research, a scientific method grounded in observations that manipulates and analyses non-numerical data. It focuses on seeking answers to why and how a particular observed phenomenon occurs rather than on its occurrences. This study aims to explore and discuss the impact of artificial intelligence on qualitative research methods. In particular, it focuses on how artificial intelligence have empowered qualitative research methods so far, and how it can be used in education for enhancing teaching and learning

Intersubjectivity in Mathematics Teaching: Meaning-Making from Constructivist and/or Sociocultural Perspectives?

In 1996, Stephen Lerman wrote a paper entitled Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm? In this paper he presented two views of “intersubjectivity”, one a sociocultural view, rooted in the work of Vygotsky and the other a radical constructivist view, with particular reference to the work of Ernst von Glasersfeld and Les Steffe. He was very critical of the latter view. I found this paper and subsequent papers and arguments from Steffe and from Steve, hugely interesting and influential on my own work. In this chapter, I take up the two perspectives of intersubjectivity and, through a number of examples, try to show how interactions and associated meanings could be addressed using each perspective as a lens. For me it is important that the perspectives do not point to what “is” but rather offer a way of interpreting what is seen; offering a conjecture relating to the social factors and cultures that influence what we observe. One conclusion is that, though the theories are not interchangeable and their approaches to conceptualising knowledge construction are incommensurable, they say nothing about what is right or wrong. As researchers we have to be extremely transparent in our use of theory, justifying arguments and interpretations rigorously in relation to the perspective we take