Strategies informed by various ways of experiencing number relations in subtraction tasks

The aim of this paper is to develop greater understanding of how the way students experience a task is related to which, and how, number relations are discerned. We study how 42 Grade 1 students solved a word problem in a number range that was new to them: 32-25 = _. The variation theory of learning has informed our analysis, opening for thorough analyses of what constitutes differences in the students' acts in solving the arithmetic word problem and how they experience the task. Observations of their strategies and ways of reasoning revealed that how the students discern the semantic structure and number relations relates to their ways of encountering the task and consequently their success in solving it. The study offers a complementary approach to understanding arithmetic skills that contribute knowledge as to why some students develop powerful ways of solving arithmetic tasks while others get stuck in cumbersome strategies.