A national-level dataset (n = 7770) at grade 1 of primary school is re-analyzed to study preconditions in proficiency in mathematical concepts, operations and mathematical abstractions and thinking. The focus is on those pupils whose preconditions are so low that they are below the first measurable level of proficiency in the common framework with reference to mathematics (CFM). At the beginning of school, these pupils may not be familiar with, e.g., the concepts of numbers 1–10, they may not be aware of the consecutive nature of numbers, and they have no or very limited understanding of the basic concepts of length, mass, volume, and time. A somewhat surprising finding is that the key factor explaining the absolute low proficiency in mathematics appeared to be a low proficiency in listening comprehension. This variable alone explains 41% of the probability of belonging to the group of pupils who are not able to show proficiency enough to reach the lowest level in any of the criteria. It is understandable that, if language skills are underdeveloped in general, a child is not expected to master the specific mathematical vocabulary either and, hence, the low score in a test of preconceptions in mathematics too. Other variables predicting the absolute low level or preconditions of mathematics are the decision on intensified or special support, status of Finnish or Swedish as second language, and negative attitudes toward mathematics.