Natural differentiation

an approach to cope with heterogeneity

Günter Krauthausen

pp. 325-341

in: Gabriele Kaiser, Helen Forgasz, Mellony Graven, Alain Kuzniak, Elaine Simmt, Binyan Xu (eds), Invited lectures from the 13th international congress on mathematical education, Berlin, Springer, 2018

Abstrakt

Teachers in their classes always have to cope with heterogeneity, and that by no means is a new problem. In Germany e.g. plenty of (mostly pedagogical) publications from the midst 1970s until today offer brilliant advice for several kinds of differentiation. How then can it be that after forty years, heterogeneity and differentiation are still called a ›mega issue‹? Could it be that those traditional kinds of differentiation are admittedly to be considered or necessary, but not sufficient—and if: why? This paper will discuss questions like these aiming to bring together crucial issues for (primary) math education in heterogeneous classes, like standards for mathematical practice, standards for mathematical content, social learning with and from each other, and heterogeneity. Main theoretical concepts are substantial learning environments (Wittmann in Educational Studies in Mathematics 15(1):25–36, 1984; Wittmann in Educational Studies in Mathematics 48(1):1–20, 2001a; Wittmann in Proceedings of the Ninth International Congress on Mathematical Education. Kluwer Academic Publishers, Norwell, MA, 2004) and natural differentiation (Wittmann and Müller in Grundkonzeption des Zahlenbuchs. Klett, Stuttgart, 2012; Krauthausen and Scherer in Ideas for natural differentiation in primary mathematics classrooms. Vol. 1: The substantial environment number triangles. Wydawnictwo Uniwersytetu Rzeszowskiego, Rzeszòw, 2010a; Krauthausen and Scherer in Motivation via natural differentiation in mathematics. Wydawnictwo Universytetu Rzeszowskiego, Rzeszów, pp. 11–37, 2010b; Krauthausen and Scherer in Natürliche Differenzierung im Mathematikunterricht – Konzepte und Praxisbeispiele aus der Grundschule. Kallmeyer, Seelze, 2014).