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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 Swedish Grade 1. A goal was that at the end of Grade 1, students would solve tasks like 15–7= using part-whole relations of numbers. 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, to investigate long-term effects and whether students used a structural approach when solving tasks in Grade 2. Results show that students in the intervention group increased their learning outcomes the most and to a larger extent solved tasks in higher number ranges using a structural approach.

The use of variation theory as a tool for designing lessons has been widely applied and received a lot of attention e.g. in mathematics education. More limited attention has been given to the use of variation theory as a means to analyze teaching and learning. This theoretical paper addresses the connection between the afforded and experienced variation when analyzing teaching and learning with a variation theory framework. Variation theory is in this case used as a tool for analyzing the relationship between teaching and learning, exploring the enacted, and lived object of learning. The connection between what is afforded in teaching and what students learn, can in this way be described in commensurable terms. With examples from a study about students’ learning of number relations in mathematics in first grade, we highlight this connection by illustrating differences identified in the teachers enactment of the same task, and what the students’ learned.