Abstract
One of the main goals of research in (mathematics) education is the generation of knowledge on processes of teaching and learning. The approaches of many research projects in German-speaking countries that contributed to achieving this goal during recent decades are diverse. Many of these projects are characterized by narrowly focusing on distinctive phenomena within learning and teaching mathematics, by taking a multi-step approach that develops theory in a series of consecutive studies (often one area of interest is pursued over many years) and by a mixed-method research strategy that integrates different methodological practices. This chapter provides exemplary insight into these kinds of research in mathematics education in German-speaking countries over the last few decades. After a brief glimpse into the beginnings, we deliver four examples that illustrate the features of these kinds of research and also describe the perspectives of researchers by way of short interview excerpts.
Highlights
As early as the 1980s, mathematics education in Germany was already actively using and developing research strategies focusing on distinctive phenomena of mathemat- T
Since it is hardly possible to report comprehensively on this strand of research found throughout mathematics education research in German-speaking countries, we present four more recent examples of projects that illustrate how these features
Speaking, many researches profited from collaborations that led to new approaches, interesting findings, the advancement of empirical research in mathematics and science education, and the development and fruitful integration of theories that had previously not been considered to be interconnected
Summary
As early as the 1980s, mathematics education in Germany was already actively using and developing research strategies focusing on distinctive phenomena of mathemat-. Ursula Viet’s investigation of the cognitive development of fifth- and sixth-grade students in arithmetic and geometry (Viet et al 1982) can serve as an example of such research: Viet and colleagues (1982) emphasized that, while in empirical research on mathematics subject case studies and interventions with pre-post designs dominated, their project aimed to study long-term learning processes Their focus was not on mathematics achievement in general, but on the development of knowledge in focused areas such as “counting and calculating in (non-decimal) place-value-systems” or “geometric mappings in situations with axial symmetry”. In a multi-step design, the project investigated the learning trajectories and learning obstacles of students while working within a “programmed instruction”-environment, i.e., standardized teaching material that excluded teachers and social interaction Their analysis of clinical interviews and of errors in students’ solutions produced knowledge that is specific for the areas under investigation, such as the prevalence and effectiveness of different strategies in calculating in place-value systems. Their statements have been slightly revised and abridged but are intended to maintain their spontaneous and subjective character
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