Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade classes. One goal was that by the end of first grade, students would be able to solve tasks such as subtracting 8 from 15 by using part-whole number relations. In this paper, we report on learning outcomes from task-based interviews with intervention and control groups before, immediately after, and one year after the intervention, in order to investigate long-term effects and whether students used a structural approach when solving tasks in a higher number range in the second grade. In comparison to controls, students in the intervention group showed higher increases in their learning outcomes. Moreover, the intervention group used a structural approach to a larger extent when solving tasks in higher number ranges, whereas students in the control group more commonly used single-unit counting to solve such tasks. These findings have implications both for teaching and for research on students’ development of arithmetic skills.

How could calculating with negative numbers be taught for understanding? What is necessary to be aware of in order to understand? What is critical for learning this? This was the task for a group of teachers who collaboratively used a systematic approach to investigate what it takes to learn to subtract negative numbers in grade seven and eight in a Swedish compulsory school. In this approach, student learning and their understanding of that which was taught was the main concern and in the fore of the teachers' attention. In an iterative process of planning, observing and revising a single lesson, they in depth analysed and inquired the progress of student learning before, in and after the lesson. From an analysis of students' written tests and from a close observation of video recorded lessons the teachers learned about what was critical for students' learning.