FUNCTIONALISM
Functionalists are called functionalists because they always ask, "What function does (the education system or the family etc) perform for society?"
Functionalists share similar assumptions about how society works. For example,
They assume that for a social institution to exist it must perform some positive function for society, or otherwise it wouldn't exist. For example, schools exist to socialize us into a set of common core values, such as turning up on time for school (and later work); to value achievement (for example exam success and later success at work) and so on.
They also see the values promoted by these institutions as acting in all our interests. For example, it is in all our interests that we are socialized to obey authority and turn up on time for school, because if we did not learn these values, society would break down. Therefore there is consensus (agreement) in society about these values. Just think what society would be like if the bus driver turned up at school whenever they liked and ignored what the boss had to say at work? Society would be very inefficient and chaotic.
MARXISM
Marxists believe that a powerful group called the ruling class are able to dominate society and society's institutions like the education system. For Marxists', the ruling class are those that own industry and big business generally. They believe that they have the power to make sure that their interests are dominant. For example, Marxist believe that schools socialize children to be obedient workers for their industries by installing in children punctuality and obedience, so they will obey their bosses without question when they leave school. Unlike functionalists though, they see this as not being in our interests, but in the interests of the ruling class. They therefore believe that there is not consensus (agreement) but conflicting interests in society.
SUMMARY
In short
Functionalists see society working in a harmonious way, with everyone working towards common goals (we all want an abundance of goods such as mobile phones etc) and we are in general agreement about how to reach those goals (I give orders and you obey or we will never get anything done - you obey me because I did better at school than you and have earned my authority).
Marxists see conflicting interests in society. For example there is conflict at work with the boss wanting you to work more and more hours for less wages, while we want the opposite. The boss however has the power to impose their will on you (they will sack you if you do not toe the line).
BIBLIOGRAPHY
Use the index at the back of your textbook to look up the words and Marxism and Functionalism. Make a table of their views. For example
Education
Social Class