Some key quotes:
A 2012 study led by Karin James, a psychologist at Indiana University, lent support to that view. Children who had not yet learned to read and write were presented with a letter or a shape on an index card and asked to reproduce it in one of three ways: trace the image on a page with a dotted outline, draw it on a blank white sheet, or type it on a computer. They were then placed in a brain scanner and shown the image again.
The researchers found that the initial duplication process mattered a great deal. When children had drawn a letter freehand, they exhibited increased activity in three areas of the brain that are activated in adults when they read and write: the left fusiform gyrus, the inferior frontal gyrus and the posterior parietal cortex.
By contrast, children who typed or traced the letter or shape showed no such effect. The activation was significantly weaker.
In a study that followed children in grades two through five, Virginia Berninger, a psychologist at the University of Washington, demonstrated that printing, cursive writing, and typing on a keyboard are all associated with distinct and separate brain patterns — and each results in a distinct end product. When the children composed text by hand, they not only consistently produced more words more quickly than they did on a keyboard, but expressed more ideas. And brain imaging in the oldest subjects suggested that the connection between writing and idea generation went even further. When these children were asked to come up with ideas for a composition, the ones with better handwriting exhibited greater neural activation in areas associated with working memory — and increased overall activation in the reading and writing networks.
Two psychologists, Pam A. Mueller of Princeton and Daniel M. Oppenheimer of the University of California, Los Angeles, have reported that in both laboratory settings and real-world classrooms, students learn better when they take notes by hand than when they type on a keyboard. Contrary to earlier studies attributing the difference to the distracting effects of computers, the new research suggests that writing by hand allows the student to process a lecture’s contents and reframe it — a process of reflection and manipulation that can lead to better understanding and memory encoding.
This research is in its early stages, obviously, so it's too early to advance any definitive conclusions. However, said findings should make us wary of any curriculum (such as the CCSS) that downplays the importance of handwriting -- and they certainly strengthen my personal resolve to stay "low-tech" with my own kids until they hit the secondary years.
ETA: And here is some more commentary on the benefits of handwriting notes (this time from Scientific American):
A Learning Secret: Don't Take Notes with a Laptop
Technology offers innovative tools that are shaping educational experiences for students, often in positive and dynamic ways. The research by Mueller and Oppenheimer serves as a reminder, however, that even when technology allows us to do more in less time, it does not always foster learning. Learning involves more than the receipt and the regurgitation of information. If we want students to synthesize material, draw inferences, see new connections, evaluate evidence, and apply concepts in novel situations, we need to encourage the deep, effortful cognitive processes that underlie these abilities. When it comes to taking notes, students need fewer gigs, more brain power.