Large language models show an emergent ability to learn a new task from a small number of input-output demonstrations.However, recent work shows that in-context learners largely rely on their pre-trained knowledge, such as the sentiment of the labels, instead of finding new associations in the input.However, the commonly-used few-shot evaluation settings using a random selection of in-context demonstrations can not disentangle models’ ability to learn a new skill from demonstrations, as most of the randomly-selected demonstrations do not present relations informative for prediction beyond exposing the new task distribution.To disentangle models’ in-context learning ability independent of models’ memory, we introduce a Conceptual few-shot learning method selecting the demonstrations sharing a possibly-informative concept with the predicted sample. We extract a set of such concepts from annotated explanations and measure how much can models benefit from presenting these concepts in few-shot demonstrations.We find that smaller models are more sensitive to the presented concepts. While some of the models are able to benefit from concept-presenting demonstrations for each assessed concept, we find that none of the assessed in-context learners can benefit from all presented reasoning concepts consistently, leaving the in-context concept learning an open challenge.