As students we take plenty of courses both at school and at college. However, when we tackle a real-world problem, oftentimes things do not look like what we have seen in any of our courses. Usually the first instinct is to say: *how come they never taught us to do that, instead they crammed us with useless knowledge*? If you ask the instructors, they would say: *We are not training the students but educating them*. If all that the teachers needed to do was to train the students, then very soon the teachers can also train a *machine*. The reason it is called *education* is because the hope is that students will able to synthesize knowledge from the class in a completely different context. However, the question to ask is are students able to abstract out the knowledge and extrapolate?

There are many reasons it is difficult to apply a concept when taken out of context. The students, the instructors, and the education assessment framework, all play a part in making it difficult. In my opinion, the situation is quite drastic in courses with topics heavy in math. There is barely enough time to teach the necessary background in math to understand the concepts. Ultimately students understand only the most basic things by working out numerous examples. That results in memes like the one below (source: https://ahseeit.com/?qa=118512/questions-asked-in-class-homework-and-exam-be-like-meme)

While the last part in the above meme is an exaggeration, this is exactly how one feels as a student. And the instructor is thinking the students need to be able to synthesize what they learned to solve bigger problems. Before moving on, it is also important to look at the homework line above versus what is taught in class. That is what we mean by *extrapolation* which many machine learning algorithms are not easily capable of doing. Although the context is simplistic, the essential idea is precisely what is written above. As humans we truly bring value, ideas, intelligence, and creativity while tacking a problem. This is a skill that is expected in the workplace.

Another critical difference between real-life problems and many textbook problems, especially in math-oriented subjects, is in terms of the **right answer**. As an instructor I do like it when there is one correct answer because it makes everything so easy to grade, and there is very like subjectivity. However, in the real world, there is no one right answer to a problem. Each solution may have its merits and demerits. To give a concrete example, say that we wish to determine the number of copies of a particular textbooks a bookstore must stock. If they stock too many, it is wasted space that could have been used for other books. If they stock too few, that is significant loss in opportunity to sell more. This is a standard classroom problem.

In the classroom, we would typically make a few assumptions such as: we wish to maximize the expected profit; we know the distribution of demand; we are given the cost price, the sale price, and the cost of holding items; we assume away any unforeseen issues like the instructor changing the book. If we make those assumptions, then the problem has a single solution. However, in real life, none of those assumptions are true. Then all of a sudden the students are not sure what to do. One option is to still make those assumptions. Another option is to try various possibilities and among the various alternatives pick one that makes most sense. Now, what if the real life problem is in determining the number of safety gloves a hospital needs to buy and store? None of the assumptions apply but the basic principles do.

In that light, here are some thoughts for students:

## Pay attention in class to things that are important but not tested

In the beginning of the course and in the last class (if not the rest of the course), instructors would talk about the course and how it fits in the curriculum. Also, there are many small things that would be said in class but never tested. These are sometimes where the teacher would say how things would work in real life. Sadly, at least in my experience, most questions in class are about what will be asked in exams.

## Ask questions in class to help with your ability to synthesize

The courses are just not a collection of formulae. The formulae are tools to solve important problems. But the tools need to be combined with other tools to be effective. Usually these tools can be used in a large variety of contexts. Many times these contexts are explained in the word problems. At any rate, it would be useful to ask the instructor questions pertaining to the use of the tools.

## Find out what assumptions are made while solving class problems

As described a few paragraphs above here, the number of textbooks to keep in a bookstore had several assumptions. Many times we may not even know we are making those assumptions. Just understanding the assumptions and how we went from the assumptions to solve the problem greatly improves our ability to know what can be tried as alternative solutions to problem.

Having said that, this is not just the responsibility of the students, but both the *instructors* and *stakeholders* (i.e. companies that employ the students) must also put in the effort to make this happen.