Down Syndrome - Not Just a Control Group
All of these studies are based on the assumption that Down Syndrome is a good control group. In other words, that DS individuals mostly differ cognitively from neurotypicals only by having a lower IQ. That they don't have their own quirks specific to Down Syndrome, which make them differ from others with cognitive disabilities.
This is not true.
Down Syndrome individuals generally have a relative weakness in verbal skills, specifically verbal short term memory (which raises questions about using them as a control for research into the verbal strengths of Williams Syndrome) and a relative strength in social skills (making them a poor control for autistic kids, especially when you pair them on verbal skills, a weakness for both groups). They also tend to have a strength in adaptive behavior, which means they typically have more independence than their IQs would predict.
They also tend to have certain temperament features. Although the stereotype of DS children as sweet and well-behaved doesn't necessarily fit, and every DS individual has their own personality, certain traits are more often present. They tend to show less intense moods, more positive mood and adapt better to change. And one trait can be seen in early childhood that is very unusual - a certain reaction to learning situations. Whereas NT babies will try hard at a task, whether it's too easy for them, just right, or too difficult for them, DS babies only seem to try their best at tasks that are just the right difficulty. Tasks that are too easy or too hard are avoided, by use of social behaviors such as requesting an adult's help or trying to interact with the adult. In fact, very young DS infants often show cognitive skills at similar levels to NT children of the same age, but because they tend not to practice already-learnt skills, they lose those skills are have to relearn them over and over.
All in all, DS individuals have their own quirks, just like other genetic syndromes do. So why do we use DS as a control group when we wouldn't think of using Williams Syndrome or Fragile X Syndrome as a control group?
I'm not saying we should stop using Down Syndrome individuals as a control group for research into other syndromes. But we should always keep in mind that DS has it's own distinctive phenotype, and that may obscur or amplify the differences being studied. I'd especially be concerned about pairing a strength with a weakness, as occurs when Down Syndrome and Williams Syndrome individuals are paired for language tasks, or autistic and Down Syndrome individuals are paired for social tasks. And Down Syndrome shouldn't always be the first choice for a control group. Fragile X Syndrome is another common genetic syndrome that causes cognitive impairment, and for some tasks they may make a better control than Down Syndrome. At the very least, if Williams Syndrome individuals differ from both DS and Fragile X in similar ways on similar measures, we know it's more due to Williams Syndrome than their comparison group.
And for those people actually working with Down Syndrome individuals, trying to help them achieve to the best of their ability, it's important not to just assume that they'll do best with the same techniques used for all cognitively disabled people. Instead, they should look into techniques that address the unique features of Down Syndrome, such as errorless learning for their motivational quirks, or visual communication techniques such as reading or sign language to support their relatively poor verbal skills.
Indeed, it may turn out that there is no such thing as a mind that works just like NTs but learns at a slower rate. Perhaps every child with a cognitive disability has their own unique learning style that is drastically different, and generally less efficient, than the typical NT style. If we understand these learning styles we may get a lot more success in educating these children.