There are wide variations in cognitive ability for students with Down Syndrome, but understanding an individual's strengths and information intake difficulties can really optimize learning.
Because of malformations of the ear passages, auditory processing disorders are extremely common among children / adults with Down Syndrome. In fact, 70% of individuals with DS have at least unilateral hearing problems, and discrimination problems may be even higher, because of the difficulty in testing. Auditory discrimination problems greatly complicate student's acquisition of language and learning to read, and they can cause daily confusion with mishearing and trouble discerning background noise. Memory for listened information can also be quite impaired, meaning that in general, visual or procedural routes of learning will be preferred. Usually the first order of business is to assess hearing and seeing with qualified experts, and be prepared to reassess as children are better able to cooperate with more specific testing.
For many people with DS, limitation in auditory verbal memory is the biggest obstacle to learning. Once a child is able to read, this can be compensated for a great deal, although parents and teachers need to remember to support instruction rigorously with visual examples and text. Mathematics can be a particularly difficult subject to tackle, but progress can be made by written instructions, visual examples, and accommodations at various steps to reduce the overall working memory demands of mathematical problem solving.
Visual problems are also known to trouble many individuals with Down syndrome (estimates as high as 40-50%, for instance due to cataracts or "lazy eye"), and it is likely that most individuals with DS are having to overcome double-deficits (though both partial) in hearing and seeing as they try to take in new information. Care about how auditory information is presented (slowly, chunk words into short bits, support with text or visual examples) and how visual information is presented (large font, adequate spacing / reduced visual crowding) can also increase the likelihood of accurate information being learned well.
Early on, receptive language tends to be strong than expressive language, although expressive language does improve and that gap may narrow. DS are also well known for their social and empathetic strengths, although parents and teachers sometimes note this is "overused" to compensate for weaknesses.
Check out Dr. Fidler's excellent review below, and Riverbend webpages for more resources. fMRI studies are unfortunately still fairly simplistic for DS, but hopefully more work will be done to elucidate processing difficulties and differences. The Stanford study below did find that parietal function was relatively preserved.
Children with Down Syndrome
Riverbend Down Syndrome Parent Support Group
Hearing and Vision Loss Associated with Down Syndrome
Neuroanatomy of Down Syndrome
Primary Care of Infants and Children with Down Syndrome
Hearing Impairment in Down Syndrome