A cultural bias towards paper?
Until the early 1990s, most studies came to the conclusion that people read more slowly, less accurately, and less comprehensively on screens than on paper. At first, lack of user experience with screens was held responsible. Later, the phenomenon could be attributed to display quality. 
Since then, the quality of computer monitors and displays has improved considerably. Recent studies therefore tend to lead to inconsistent results or do not find any differences between the media. Nevertheless, there still is a certain preference for paper. In a study from 2013, scientists compared eye movement, brain activity, reading speed and reading comprehension while reading on paper, on an e-reader (e-ink) and a tablet computer. Interestingly, all participants said beforehand that they would rather read on paper. The study itself did not provide any evidence for the assumption that digital media are more strenuous. On the contrary, older participants read faster and with less effort on the tablet computer because the backlight provides better contrast for older eyes. Why then the preference for paper? The authors point to "a general cultural attitude" against reading on screens. 
But on a completely different level, there seems to be a difference between reading on paper and on screen. And this time it's the fluency with which we read on modern screens that is viewed critically.  It is argued that reading on screen is way too easy now. Sometimes we tend to remember information better when it was harder to process the information. Thus, it was shown that modest "disfluency" actually improves retention performance, because the information is processed more precisely and people engage on a deeper level with its content.  And this effect can be seen not only in reading comprehension: It is less effective for learning when students take notes in lectures on the laptop instead of writing them down by hand. The high road into the brain still seems to lead along the right (or left) hand. 
Abstract and concrete thinking
And yet another effect has recently been discovered: Anyone who reads on tablet computers and laptops tends to focus on specific details rather than to process information abstractly. For example, in a study, 66 % of print readers answered questions correctly that required an abstract understanding, whereas only 48 % of digital readers answered the questions correctly. Questions for specific content were answered correctly by 73 % of digital readers, while only 58 % of print respondents answered them correctly.
If this result should be confirmed in further studies, digital media influence HOW we process information. This could have long-term consequences. Because abstract thinking not only shows us the "big picture" but also longer-term consequences. Abstract thinking is also associated with empathy and creativity. However, it is not per se superior to concrete thinking. Both ways of processing information are necessary for optimal cognitive performance.
How about computers at school?
In some (Asian) countries, computers or tablets are already firmly integrated into school teaching. According to an OECD study from 2015, the results are not very surprising given the findings described here are: learning performance did not improve per se with digital media. Rather, it was crucial how digital media were used in the classroom.  As is often the case, it is pointless to give people a new tool and to expect that the benefits will come naturally. One must also enable them to reap the benefits.
- Noyes, J. M., & Garland, K. J. (2008). Computer-vs. paper-based tasks: Are they equivalent?. Ergonomics, 51(9), 1352-1375.
- Kretzschmar, F, Pleimling, D, Hosemann, J, Füssel, S, Bornkessel-Schlesewsky, I and Schlesewsky, M (2013). Subjective Impressions Do Not Mirror Online Reading Effort: Concurrent EEG-eyetracking Evidence From the Reading of Books and Digital Media. PLOS ONE 8(2): e56178.DOI: http://dx.doi.org/10.1371/journal.pone.0056178 (accessed 5 June 2015).
- Benartzi, S., & Lehrer, J. (2015). The smarter screen: Surprising ways to influence and improve online behavior. Portfolio.
- Connor Diemand-Yauman, Daniel M. Oppenheimer, and Erikka B. Vaughan. Fortune favors the Bold and (the Italicized). Effects of Disfluency on Educational Outcomes. Cognition 118.1 (2011): 111-115.
- Mueller, P. A., & Oppenheimer, D. M. (2014). The pen is mightier than the keyboard advantages of longhand over laptop note taking. Psychological science, 0956797614524581.
- Kaufman, Geoff; Flanagan, Mary(2016). High-Low Split: Divergent Cognitive Construal Levels Triggered by Digital and Non-digital Platforms. #chi4good, CHI 2016, San Jose, CA, USA
- Sadegh, Marvin (2015). Pisa-Studie - Computer machen den Unterricht nicht automatisch besser. Die Zeit, http://www.zeit.de/gesellschaft/schule/2015-09/pisa-computer-internet-international