Intrinsic motivation describes the young child.

Many philosophers write as if instrumental value is the only type ofextrinsic value, but that is a mistake. Suppose, for instance, that theresults of a certain medical test indicate that the patient is in goodhealth, and suppose that this patient's having good health isintrinsically good. Then we may well want to say that the results arethemselves (extrinsically) good. But notice that the results are ofcourse not a means to good health; they are simply indicative of it. Orsuppose that making your home available to a struggling artist whileyou spend a year abroad provides him with an opportunity he wouldotherwise not have to create some masterpieces, and suppose that eitherthe process or the product of this creation would be intrinsicallygood. Then we may well want to say that your making your home availableto him is (extrinsically) good because of the opportunity it provideshim, even if he goes on to squander the opportunity and nothing goodcomes of it. Or suppose that someone's appreciating the beauty of theMona Lisa would be intrinsically good. Then we may well wantto say that the painting itself has value in light of this fact, akind of value that some have called “inherent value”(Lewis 1946, p. 391; cf. Frankena 1973, p. 82).(“Inherent value” may not be the most suitableterm to use here, since it may well suggest intrinsic value,whereas the sort of value at issue is supposed to be a type ofextrinsic value. The value attributed to the painting is onethat it is said to have in virtue of its relation to something elsethat would supposedly be intrinsically good if it occurred, namely,the appreciation of its beauty.) Many other instances could be givenof cases in which we are inclined to call something good in virtue ofits relation to something else that is or would be intrinsically good,even though the relation in question is not a means-end relation.

Intrinsic motivation reflects the desire to do something because it is enjoyable.
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[…] extrinsic rewards can light the fire of motivation, intrinsic motivators keep it burning. Good onboarding encourages both, through a combination of challenging tasks, curiosity, and […]

Motivation can be either intrinsic or extrinsic.

The main difference between intrinsic and extrinsic motivation is the goals of the students.
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Source: James A. Middleton, “A Study of Intrinsic Motivation in the Mathematics Classroom: A Personal Constructs Approach,” Journal for Research in Mathematics Education, Vol. 26, No. 3, pages 255-257.

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Disadvantages: On the other hand, extrinsic motivators can often distract students from learning the subject at hand. It can be challenging to devise appropriate rewards and punishments for student behaviors. Often, one needs to escalate the rewards and punishments over time to maintain a certain effect level. Also, extrinsic motivators typically do not work over the long term. Once the rewards or punishments are removed, students lose their motivation.

Carrot And Stick – Intrinsic vs Extrinsic Nature of Motivation

Athletes compete in and practice sport for a variety of reasons. These reasons fall into the two major categories of intrinsic and extrinsic motivation. Athletes who are intrinsically motivated participate in sports for internal reasons, such as enjoyment, whereas athletes who are extrinsically motivated participate in sports for external reasons, such as material rewards.
Extrinsic rewards are central to competitive sports; athletes receive publicity, awards, and money, among other things, and college level athletes obtain scholarships for their talents. Extrinsic rewards, when used correctly, can be beneficial to athletes. However, athletes in highly competitive levels of sport may experience decreases in their intrinsic motivation because of the increasing use of extrinsic rewards offered by the media, coaches, and parents. As a coach, you can help increase or maintain the intrinsic motivation of college athletes even with the presence of extrinsic rewards, such as scholarships.