Developing adaptivity in grade 3 and 7. Results from a Danish pilot study.

Flexibility, understood as students’ ability to employ a range of arithmetic strategies, and adaptivity, understood as their ability to select the most efficient strategy for a given problem, are both associated with overall mathematics achievement. Since 2001, Danish curricular documents (Klare mål) have emphasized flexibility and adaptivity as central learning goals in mathematics. Nevertheless, previous research suggests that Danish students’ actual levels of flexibility and adaptivity remain limited, pointing to challenges in translating curricular intentions into instructional practice.
The overarching aim of this project is to examine how instructional designs targeting flexibility and adaptivity in arithmetic can contribute to students’ broader mathematics achievement. In this pilot study, we investigate whether a short, design based instructional intervention focused on flexible strategy use in multi digit arithmetic can enhance students’ flexibility and adaptivity, and how the intervention is enacted by teachers in classroom practice.
Approximately 800 Grade 3 students (39 classes) and 700 Grade 7 students (36 classes) from 14 schools participated in a 10 lesson intervention centered on flexible strategy use in multi digit addition and subtraction, and, for Grade 7, also multiplication. The intervention was designed around three recurring lesson components: (1) whole class number talks to elicit and discuss multiple strategies, (2) compare and contrast activities (pair work) focusing on strategic efficiency, and (3) short number sense games and activities (individual or small group work). Students completed pre and post tests assessing their strategy preferences using an adapted version of the Tri Phase Flexibility Assessment. Half of the students completed the post test immediately after the intervention, while the other half completed it after a two month delay.
To examine both outcomes and enactment, the study combines quantitative effectiveness analyses with classroom observations. Intervention effects will be estimated using multilevel mixed effects regression models controlling for pre test scores, prior achievement, and socioeconomic status, with random effects for classes and schools to account for the nested design. Planned moderator analyses will explore variation related to student, teacher, and classroom characteristics. To evaluate implementation fidelity and instructional interpretation, we observed five Grade 3 and five Grade 7 lessons, focusing on how teachers interpreted and enacted the core design principles of flexibility and adaptivity.
Initial results concerning the effects of the intervention on students’ flexibility and adaptivity in arithmetic was presented. In addition, we discuss between class differences, and future perspectives in next phase of the project (RCT) for development of flexibility and adaptivity in different classroom environments (teacher effect).