Mathematics education is a vibrant field, replete with diverse theoretical views that cultivate varied understandings and interpretations of complex phenomena in mathematical thinking, learning, and teaching. However, the abundance of disparate theories encourages both the multiplication of perspectives and the division of thought into opposing schools. This frequently hinders dialogue across traditions and paradigms, biases theorists, and promotes the creation and growth of narrow, and at times restricting, theories.
Recognizing this challenge, Thorsten Scheiner explores theoretical tensions, conflicts, and paradoxes that impede and enable theoretical innovation. In pursuing diverse, yet mutually reinforcing, set of lines of inquiry, Thorsten Scheiner's research highlights contradictions and interdependencies of critical phenomena in mathematical cognition and teacher cognition that might serve as catalysts for the development of more comprehensive theoretical accounts of the phenomena under consideration. In exploring and encouraging both greater expansion and more interlinking of multiple, at times competing, theoretical positions and approaches, theory and scholarly debate may become more detailed and useful, moving beyond deceptive dualisms and enabling deeper and more accurate understandings for theoreticians, practitioners, and researchers.
Thorsten Scheiner's research contributes to fostering a perspective from which one can appreciate the interaction between seemingly conflicting, yet ultimately interconnected insights. The theoretical perspectives generated in his research demonstrate that it is possible to construct bridges between seemingly dissimilar viewpoints, revealing that some conflicting viewpoints underscore interwoven, rather than contradictory, facets of complex phenomena. In doing so, his research contributes to raising awareness that seemingly unambiguous phenomena and issues in mathematical cognition and teacher cognition are more nuanced than they have heretofore been considered and that existing theoretical conceptualizations and theories that attempt to account for them are in many ways restricting.
Scheiner, T. (2019). If we want to get ahead, we should transcend dualisms and foster paradigm pluralism. In G. Kaiser & N. Presmeg (Eds.), Compendium for early career researchers in mathematics education (pp. 511-532). Cham, Switzerland: Springer. link
The research aims at better accounting of the complex dynamic processes involved when individuals ascribe meaning to the mathematical objects of their thinking. The focus is on three processes that are convoluted in the complex dynamics in mathematical concept formation: contextualizing, complementizing, and complexifying. New interpretative possibilities and theoretical hypotheses are generated that inform research on mathematics cognition and elucidate the three processes, recognizing their epistemological, conceptual, and cognitive significance in mathematics knowing and learning processes.
Scheiner, T., & Pinto, M. M. F. (2019). Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying. Educational Studies in Mathematics, 101(3), 357-372. link
Scheiner, T. (2016). New light on old horizon: constructing mathematical concepts, underlying abstraction processes, and sense making strategies. Educational Studies in Mathematics, 91(2), 165-183. link
SENSE-MAKING IN MATHEMATICS
Individuals have been regarded as active sense-makers in mathematical concept formation, that is, students actively seek comprehensibility of a mathematical concept. Individuals might, in this process, develop conceptions of a mathematical concept that are activated to make sense of how they perceive (or regard) a mathematical concept that comes into being in a certain context. Recent research, however, suggests that individuals also imagine (or envision) a mathematical concept that is yet to become. In those cases, conceptual development is not meant to reflect an actual concept, but to create a potential concept. The aim of this research is to clarify in which respects this act of creation differs from sense-making construed as an act of comprehension.
Scheiner, T. (2017). Conception to concept or concept to conception? From being to becoming. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 145-152). Singapore: PME. pdf
The last few decades have produced a considerable body of literature that conceptualizes, operationalizes, and measures teacher knowledge. The focus of this research is on general orientations and tendencies in conceptualizing mathematics teacher knowledge, and how the field currently conceives of what makes mathematics teacher knowledge specialized. The purpose of this research is to identify serious limitations of these orientations and tendencies and to provide alternative views to each of these orientations and tendencies that foreground topics in what makes mathematics teacher knowledge specialized that have only been partially investigated.
Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. (2019). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 17(1), 153-172. link
The notion of teacher noticing shows great promise for merging various research lines in teacher education. The aim of this research is to go beyond an intuitive model of teacher noticing to better address the complexities of the processes involved, from attending to certain events, to becoming aware of these events in dynamic situations. The research draws on phenomena described in and findings gained from cognitive science and the applied science of human factors to better account of the interdependencies between individual and environment, or, in more detail, the interactions between cognitive and contextual resources, perceptual and cognitive processes, and the actual situation.
Scheiner, T. (2016). Teacher noticing: enlightening or blinding? ZDM Mathematics Education, 48(1), 227-238. link