Understanding the ‘auxiliary task’ conceptually – Discrete versus continuous cardinal objects

Abstract

For conceptually understanding the ,Auxiliary Task’, learners have to understand the compensation process. Yet, since the strategy is highly complex compared to other mental calculation strategies, an important question is how the conceptual understanding of the strategy can be fostered and for this purpose, ordinal as well as cardinal learning environments were developed and evaluated in a design-based-study (which is part of the mixed-methods MaG-Project). Prior analyzes showed that especially the cardinal learning environment leads to more thorough conceptual discourses. In this paper, qualitative insights into the use of specific forms of cardinal representation – discrete versus continuous – and its interpretations by four 11-year-old German primary school learners’ will be given.