Neural combinatorial optimization (NCO) aims at designing problem-independent and efficient neural network-based strategies for solving combinatorial problems. The field recently experienced growth by successfully adapting architectures originally designed for machine translation. Even though the results are promising, a large gap still exists between NCO models and classic deterministic solvers, both in terms of accuracy and efficiency. One of the drawbacks of current approaches is the inefficiency of training on multiple problem sizes. Curriculum learning strategies have been shown helpful in increasing performance in the multi-task setting. In this work, we focus on designing a curriculum learning-based training procedure that can help existing architectures achieve competitive performance on a large range of problem sizes simultaneously. We provide a systematic investigation of several training procedures and use the insights gained to motivate application of a psychologically-inspired approach to improve upon the classic curriculum method.