Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thank you for your good question, which reflects your love and care about the blessed month of Ramadan. Ramadan is a beloved month for all Muslims, for, in addition to being full of abundant blessings, it is also unique in being the month in which the Glorious Qur'an was revealed to the Prophet (peace and blessings be upon him).
In the first place, it should be noted that a Muslim cares a lot about his prayer and he lets nothing distract him from concentrating in it, so as to get its full reward and feel its sweetness.
Responding to the question in point, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states the following:
Those who carry mushafs while praying behind the Imam are violating the rules of prayer and Sunnah. It can be excused only in the case of a person who has been instructed to do so by the Imam in order to correct him in case if he makes mistakes—if there is no other hafiz in the gathering to perform the duty.
If anyone else holds the mushaf while praying behind the Imam, he is violating the rules of Salah and the way of Sunnah. There is no precedent for it in the Qur'an or the Sunnah. By doing such a thing one is guilty of breaking a number of rules:
1. He is engaged in activities extraneous to Salah.
2. He is taking his eyes away from the place of sujud (prostration) where he should be looking
3. It is also taking his attention away from listening to the Imam, which is what we have been ordered to do in Salah while praying behind the Imam.
4. He is introducing an innovation or bid`ah in worship without any precedent.
Excerpted, with slight modifications, from: www.muslims.ca