Many believe that Islam has banned critical thinking and introduced a kind of stagnation in the field. So, I want to answer the common question "Does Islam permit critical thinking?"
People state, "Most Muslim schools focus on rote memorization of religious texts and discourage independent thinking". There are two different things; critical thinking and rational or independent thinking. There are categories where the mind should play its role and where it should not poke its nose. The clear and apparent meanings of the Glorious Qur'aan and the Hadith, which are called "Mansusaat" or 'Nusoos-e-Qatiyah' in Islamic terms, have no place for criticism. Here, rational thinking to find out the depth is not only permissible but also encouraged in Islam. The principle beliefs, obligatory practices are from this category where the human mind is allowed to explore the reasons and the facts of the matters, but it is not allowed to criticize since the mind has its own limitation as other human faculties have.
For instance, what the hearing faculty can do the smelling faculty cannot, and what the eyes can see the others cannot. As we see a plane flying in the sky, looks very little, if we use only our eyes and not mind, it will be that the plane is small like a bird. But here, we use our mind and say 'no' since the plane is at a certain height that is why we see it small otherwise it is huge. As in this example, there comes one point where the boundary of eye's action ends and the boundary of mind's action begins. Likewise, there is one point where certainly the human mind fails. This is a common idea every sane believes in.
But ahead of this, there is difference between Muslims and others. Muslims believe in 'Wahy', which can be translated as 'revelation' which is by Allah almighty to his messengers and prophets through different ways. The action of 'Wahy' begins from where the action of human mind comes to an end. The 'Wahy' tells us specially about the things which generally a mere human mind cannot find out. The existence of Allah, His attributes, the hell, the paradise, Day of Judgment etc are known only by 'Wahy'. Since, these matters are out of the reach of human mind so the human beings are asked just to believe in. The issue of 'wahy' is based on a principle that every action of human being is poised with error, it is only Allah and His Messengers who are free from human mistakes. That is why there is no possibility of error and criticism in their matters. The human body is temporal and mundane so the parts of the body are also mortal. They cannot have the feeling of things which belongs to another permanent and eternal world. This even we observe in our day-to-day life that if a villager is told about the facts of astronomy he nearly denies all the same.
Besides, Islam allows critical thinking in other matters. The four major schools of thought in Islamic Fiqh i.e. Hanafi, Shaf'ee, Maliki, Hanbli are the clear proof of the claim. The scholars, having deep knowledge of the Glorious Qur'aan, Hadith and Islamic sciences, discussed the matters, which were not explicitly mentioned in the Qur'aan and Hadith, and they perform Ijtihad. In this course, they many times contradicted each other and had different opinions about same issue. But, after all, there opposition was barely not an opposition to play down the other but sincere and concrete opposition based on proofs and evidences. That is why today nearly all of the Ummah follows any of the four schools and none of them deny the other, each of them believes that all are on right path.
Likewise, in Islam 'Amr bil Maroof' (enjoining the right) and 'Nahy anil Munkar' (forbidding from wrong) are the basic rules of a social life, which Allah almighty has counted in one of the characteristics of this Ummah as He states:
"You are the best community that has been raised up for mankind. You enjoin right conduct and forbid indecency; and you believe in Allah." (Surah Ale-Imran, 3:110)
This is emphasized by other verses and holy Hadiths, as for example a Hadith says:
"If any of you sees an evil done he/she should stop it by his hand, if he/she cannot he/she should protest against it, if cannot then at least he/she should repulse it by heart, and this is the weakest from of faith." (Sahih Muslim, V 1 p 51)
As another Hadith assets "The best form of Jihad is to utter the truth before an oppressor ruler". You might know the story of a common person who stood before Hazrat Umar Farooq while he was delivering a sermon and said if you will go wrong we will rectify you by our swords, in reply Hazrat Umar thanked Allah that his caliphate enjoys persons determined for truth and justice. Here, one thing should be kept in mind that, though Islam has allowed criticizing, it sternly prohibits backbiting and hurting others.
"O ye who believe! Let not a folk deride a folk who may be better than they (are), nor let women (deride) women who may be better than they are; neither defame one another, nor insult one another by (insulting) nicknames. Bad is the name of lewdness after faith. And whoso turneth not in repentance, such are evil doers. O ye who believe! Shun much suspicion; for lo! some suspicion is a crime. And spy not, neither backbite one another. Would one of you love to eat the flesh of his dead brother? Ye abhor that (so abhor the other)! And keep your duty (to Allah). Lo! Allah is Relenting, Merciful." (Surah Al-Hujrat, 49: 12, 13)
So, this means that criticism should not be for the sake of criticism, and on personal basis but it should be with a good intention, i.e. 'Islaah' based on social etiquettes.
All these things prove that Islam has never discouraged independent thinking and criticizing, it has allowed human mind to function in areas where it can work. Not only this that Islam has allowed independent thinking, but it is The Glorious Qur'aan which has set the tradition of thinking in the creation of Allah and asked its followers to reflect on the natural phenomena. For example the Glorious Qur'aan praises people who think:
"Lo! In the creation of the heavens and the earth and (in) the difference of night and day are tokens (of His sovereignty) for men of understanding. Such as remember Allah, standing, sitting, and reclining, and consider the creation of the heavens and the earth, (and say): Our Lord! Thou created not this in vain. Glory be to Thee! Preserve us from the doom of Fire" (Surah Ale-Imran, 3: 190, 191)
Before Islam, nearly every religion, which existed then, adopted creatures as God. This concept stopped them to think in the reality of the creatures of the heaven and earth. When Islam came it concentrated the human belief only in Allah and regarded the entire universe as the servant of the human beings. Thus, Islam opened the door of independent thinking in Muslims and it led them to a grand era of science.
It is not correct to write: "they (students) are not allowed to learn about modern scientific ideas such as evolution, secular histories of other nations, or anything which would conflict with the religious tenants of Islam." There is a vast difference between believing and learning. Islam has fully allowed Muslims to learn scientific education but not to believe in the matters that contradict with established Islamic beliefs. Because, the science is ever-growing and ever-changing. For example, the scientific facts of Newton in 17th century known as 'Gravitation Laws' were so widely believed that those who denied were called as insane. But, later in 20th century Einstein came and the entire theory of Newton turned up side down. So, as a Muslim, one should think whether one is going to change one's beliefs which are told by All-Knowing Allah to the notions that have no concrete ground.
Some one wrote "Some of the religious schools (madrasas) merely propagandize militant Islamic beliefs and indoctrinate little boys into becoming warriors for the next Jihad." I do not know any madrasa, specially in India, where so called 'militant Islamic beliefs' are 'propagandized', and I do not even understand what this 'militant Islamic beliefs' mean. Likewise, the one who made this statement should point out in which madrasa little boys are indoctrinated to become 'warriors for Jihad'. I will be highly thankful to the one who wrote this to provide me correct information. Otherwise, let me very plainly say that the above statement is a lie and some people became habitual to believe in wide spread lies. They have closed their sights and hearing and blocked their minds and now believe blindly in what's being spread by some anti-Islamic elements.
Allah knows the best!