Developing Numerical Understanding in Early Mathematics Subtraction.

In the realm of subtraction tasks, decomposition strategies are often considered more effective than methods based on counting. However, despite employing decomposition, many students still encounter difficulties in solving these tasks. This study investigates how students perceive number relations in a three-digit subtraction problem, focusing on the nature of these perceptions. Data were collected through interviews with 55 second-grade students who used decomposition to solve 306 − 295. The analysis, grounded in the variation theory of learning, sought to uncover the number relations students identified and how this influenced their success or failure. The results indicated that students who recognized both intra-number and inter-number relations were more likely to solve the problem correctly, while those who failed to make these connections were unsuccessful. These insights are critical for understanding the key elements students must grasp to effectively solve subtraction problems.