There are two hypotheses about why individuals have mathematics learning difficulties (MLD). The core deficit hypothesis claims that disorders in number module which was designated for processing quantities either at approximate or exact levels cause learning difficulties in mathematics. The access deficit hypothesis on the other hand posits that the reason behind MLD is not deficits in processing quantities but deficits in connecting quantities to symbols or vice versa. To test these two hypotheses, we designed dot enumeration, symbolic number comparison, and mental number line tasks. Participants were 487 students from 1st to 4th grades selected from 12 different schools in a mid-Anatolian, large metropolitan city in Turkey. Students were given a curriculum based arithmetic achievement test and they were divided into four groups as MLD risk, low achieving, typical achieving, and high achieving based on the achievement test scores. Results showed that there were large significant differences both among groups and grades. The largest difference was observed in canonic dot counting tasks from first through fourth grade. While Arabic number comparison tasks were important at first and second grade, MNL tasks became more important at the third and fourth grade. We conclude that the results provided evidence for both core deficit hypothesis and access deficit hypothesis. Numerical efficiency changes very little from first to fourth grade. Future research should consider testing for unique contributions of exact and approximate number systems and access to symbols as well as mapping their neural correlates.