Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction

Mathematics instruction contains two conflicting demands: on the one hand, the demand for economical efficiency and for well-developed motorways and, on the other hand, the demand that pupils should investigate and discover for themselves and have the freedom to pave their own ways. It is argued that tasks with a certain richness and quality offer some steps towards a constructive handling of this dilemma. The author tries to develop some properties of powerful tasks and to sketch the structure and philosophy of one concrete system of powerful tasks for the concept of angle. The main part of this paper presents seven examples of powerful tasks: five from the system of tasks and two with regard to pupils' working with 2-D-graphic systems. The construction of powerful tasks is viewed as a valuable contribution to bringing the theory and practice of mathematics education closer together.     

Recouping and rethinking the effects of summer vacation on reading achievement

Vacations may have detrimental effects on maths and spelling performance, but the findings for reading are less conclusive. The purpose of this study was to analyse the effects of summer vacation on early literacy skills of young children. Participants included rising first and second‐graders, most of whom were at‐risk, struggling readers. No evidence of summer setback was evident for this sample of children; in fact, gains in reading (or, recoupment of any losses) were more common in children performing at lower levels than for those with higher scores at the end of the school year. Our outcomes are different from those reported by other researchers. We explain this with attention to the content of our comparisons, the grade levels investigated and measures used to assess performance, and discuss implications for future research based on our findings.     

Reflections on an Emerging Field: Researching Mathematics Teacher Education

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education conference proceedings. Some regional sources from various parts of the world were also included. We investigated who was writing, from and in what settings, with what theoretical frameworks, and with what sorts of study designs for what core questions. We also examined the range of findings and conclusions produced in these studies. Our analysis presented here focuses on four themes that stood out from our initial investigation of almost 300 published papers, and systematically elaborated through a focused study of a 160 papers across key journals and conference proceedings in the field. From this vantage point, the paper offers a reflection on the current state of the field of mathematics teacher education research. Our aim is to stimulate discussion that can support the development of the field, not make final pronouncements about its nature. The research presented in this paper was done by five mathematics education researchers, the authors listed above, and presented at ICME10 in Copenhagen in July 2004. This Survey Team (Survey Team 3) was nominated by the International Program Committee for the Congress and asked to survey “Professional Development of Mathematics Teachers” and present this in a plenary at the Congress. A copy of the presentation can be viewed at: http://www.wits.ac.za/jadler/presentations.html. An earlier version of this paper will also appear in the ICME10 proceedings.