The teacher asks them to send blessings upon the Prophet 300 times before each lesson
Question

                I attend a class for learning the rules of Tajweed, but the Shaykh asks all those present to (quietly) send blessings upon the Prophet (peace and blessings of Allaah be upon him) 300 times before starting the lesson. He says that sending blessings upon the Prophet will be a means of being close to him on the Day of Resurrection, and he said that the Messenger (peace and blessings of Allaah be upon him) said: “Those of you who send the most blessings upon me will be the closest to me on the Day of Resurrection.” Is it permissible to join in with them in such things? Otherwise is it permissible for me to quietly say some other dhikr such as praying for forgiveness and the like?.
Praise be to Allah.Always 
    sending this number of blessings upon the Prophet  (peace and blessings 
    of Allaah be upon him) before the lesson is not the way of the Prophet  
    (peace and blessings of Allaah be upon him) or of his companions or those 
    who followed them in goodness. Whatever is like that is an innovation 
    (bid’ah) which the Prophet  (peace and blessings of Allaah be upon him) 
    forbade and warned us against when he said: “Beware of newly-invented 
    matters, for every newly-invented matter is an innovation and every 
    innovation is a going astray.” Narrated by al-Tirmidhi (2600), Abu Dawood 
    (3991), and Ibn Maajah (42); classed as saheeh by al-Albaani in Saheeh 
    al-Jaami’ (2549). 
And the 
    Prophet  (peace and blessings of Allaah be upon him) said: “Whoever does 
    a deed that is not in accordance with this matter of ours will have it 
    rejected.” Narrated by Muslim (1817). 
The reason 
    why this action is an innovation is that worship must be something that is 
    prescribed in its nature, the way it is done, the time when it is done, and 
    the number of times it is done. Allaah can only be worshipped in the ways 
    that He has prescribed in His Book or on the lips of the Messenger of Allaah 
     (peace and blessings of Allaah be upon him). 
Dhikr may be 
    prescribed in principle, but people start to specify the way in it is to be 
    done, or the place or time or number, that may bring it under the category 
    of innovation. 
This is 
    indicated by the report narrated by al-Tirmidhi (204) from ‘Amr ibn Salamah 
    who said: We were sitting at the door of ‘Abd-Allaah ibn Mas’ood before Fajr 
    prayer, when he came out. We walked with him to the mosque, then Abu Moosa 
    al-Ash’ari came to us and said: Has Abu ‘Abd al-Rahmaan come out to you yet? 
    We said: No. So he sat with us until he came out, and when he came out we 
    all stood up. Abu Moosa said to him: O Abu ‘Abd al-Rahmaan, just now I saw 
    something in the mosque that I have never seen before, but I do not think it 
    was anything but good. He said: What was it? He said: If you live, you will 
    see it. He said: In the mosque I saw some people sitting in circles waiting 
    for the prayer. In every circle there was a man, and in their hands they had 
    pebbles. He would say: Say Allaahu akbar (Allaah is Most Great) one 
    hundred times, and they would say Allaahu akbar one hundred times. He would 
    say: Say Laa ilaaha ill-Allaah (there is no god but Allaah) one 
    hundred times, and they would say Laa ilaaha ill-Allaah one hundred times. 
    He would say:  Say Subhaan-Allaah (Glory be to Allaah) one hundred 
    times, and they would say Subhaan-Allaah one hundred times. He said: What 
    did you say to them? He said: I did not say anything to them; I was waiting 
    to see what you think and I waited for your command. He said: Why did you 
    not tell them to count their bad deeds and guarantee to them that their good 
    deeds would not be wasted? Then he moved on and we moved on with him until 
    he came to one of those circles, and he stood over them and said: What is 
    this that I see you doing? They said: O Abu ‘Abd al-Rahmaan, these are 
    stones with which we count the takbeers (‘Allaahu akbar’), tahleel (‘Laa 
    ilaaha illa-Allaah’) and tasbeeh (‘Subhaan-Allaah’). He said: Count your bad 
    deeds, for I guarantee to you that none of your good deeds will be lost. Woe 
    to you, O ummah of Muhammad! How quickly you have become doomed! His 
    companions are still alive and his cloak has not worn out, and his vessel is 
    not yet broken. By the One in Whose hand is my soul, you are either 
    following a way that is more guided that the way of Muhammad or you are 
    opening the door to misguidance. They said: By Allaah, O Abu ‘Abd 
    al-Rahmaan, we intended nothing but good. He said: How many of those who 
    intended good did not achieve it. The Messenger of Allaah  (peace and 
    blessings of Allaah be upon him) told us that some people would recite the 
    Qur’aan and it would not go any further than their collarbones. By Allaah, I 
    do not know, perhaps most of them are from among you. Then he turned away 
    from them and ‘Amr ibn Salamah said: I saw most of those circles on the side 
    of the Khawaarij fighting us on the day of al-Nahrawaan. 
Think about 
    this attitude of Abu Moosa and ‘Abd-Allaah ibn Mas’ood, and how they 
    denounced this method which was not done by the Prophet  (peace and 
    blessings of Allaah be upon him) or his companions, although dhikr is 
    basically prescribed, praiseworthy and encouraged. 
The scholars 
    pointed out that doing an act of worship at a specific time or in a specific 
    place, or in a specific manner, that has not been narrated, is regarded as 
    innovation. In that case it is called bid’ah idaafiyyah (an innovation by 
    adding to something that is basically prescribed). It is prescribed in 
    principle but is rejected because of the way in which it is done. 
Al-Shaatibi 
    (may Allaah have mercy on him) said: Bid’ah (innovation) refers to something 
    that is newly invented in matters of religion that appears similar to that 
    which prescribed, by which people intend to go to extremes in worshipping 
    Allaah. 
This 
    includes adhering to certain ways and manners of worship, such as reciting 
    dhikr in unison, or taking the birthday of the Prophet  (peace and 
    blessings of Allaah be upon him) as an Eid, and so on. 
It also 
    includes doing certain acts of worship at certain times for which there is 
    no basis in sharee’ah, such as always fasting on the fifteenth of Sha’baan (yawm 
    al-nusf min Sha’baan) and spending that night in prayer. 
End quote 
    from al-I’tisaam (1/37-39). 
Sending 
    blessings upon the Prophet  (peace and blessings of Allaah be upon him) 
    is one of the best acts of worship and one of the greatest means of drawing 
    closer to Allaah, but always doing that before every Qur’aan class, with 
    this specific number, is something that is not narrated (from the Prophet 
     (peace and blessings of Allaah be upon him)), so it is an innovation, 
    even if the one who does it intends well. How many of those who intended 
    good did not achieve it, as Ibn Mas’ood (may Allaah be pleased with him) 
    said. 
What you 
    must do is advise this teacher and explain that what he is doing is not 
    Sunnah, rather it is bid’ah. If he responds, then praise be to Allaah, but 
    if he does not respond and you can learn how to recite Qur’aan from someone 
    else, then you should shun him as a rebuke to him and so as to prevent 
    innovation entering schools at his hands.   
May Allaah 
    help us and you to love the Sunnah and defend it, and to love the Prophet 
     (peace and blessings of Allaah be upon him) and his companions. 
See also 
    questions no. 20005, 
    21902 and 
    22457.
    And Allaah knows best.