Gaining flexibility in dealing with arithmetic situations: a qualitative analysis of second graders’ development during an intervention

Abstract

The influence of language and situation structure on the difficulty of word problems has been investigated intensively in the field of mathematics education. However, instructional approaches to overcoming students’ difficulties are still not widely available. This paper describes an intervention to develop second graders’ skills in handling additive word problems flexibly. During ten small-group sessions of 40 min, two strategies to restructure the situation described in a word problem were introduced: (1) changing the direction of mathematical relations and (2) changing semantic structures. The introduction of these strategies was supported using macro-scaffolding. The development of students’ flexibility in dealing with arithmetic situations during the intervention was analyzed in a longitudinal case study focusing on four students, who were preselected from a larger sample based on their language skills. We examined audio data and student work by applying qualitative content analysis. Students’ development in handling word problems flexibly was compared with the intended learning trajectory in the intervention. The results provide insights into potential key processes when gaining flexibility, and yield information on the necessary adaptations of the learning trajectory.