The importance for students to know “why”

I really enjoyed my fist year in college, however, there was something that made me feel bad about myself, that I was not good enough. All of my classes had something in common; every professor assumed that the students are familiar with the concepts of the corresponding class. Even if sometimes I was already familiar with them I always was wondering “Why are we supposed to know that?”.

Spring of 2017, I took a class about Differential Equations. The first four weeks we had an introduction to Linear Algebra since we would need it later.

Eventually, two or three weeks before finals, we were doing Laplace Transform. I was sure I’ve had heard that name before and I was excited to get started.

My professor started with the definition:

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I was like “huh, so that’s Laplace transform”.

I remember him evaluating some Laplace transforms, starting with L{1}.
I asked one of my classmates “Did I miss any lecture or is it the first day we’re doing Laplace?”. It was indeed the first time we’re doing Laplace transforms.

I was waiting to understand what was going on there, and why we were doing Laplace transform anyway, my professor kept continuing on examples.

I couldn’t keep it inside me anymore. I raised my hand, he asked me if he missed anything again “No, actually I have a question this time… Why are we doing Laplace transform?” – I asked.

He laughed and told me that it is a good question, “Laplace transform is going to be later a useful tool to solve Differential Equations with real coefficients ” he eventually answered.

I was thinking at the moment ” Why he didn’t tell us anything at the beginning of the class, how are we supposed to know why we are doing what we are doing?”.

Unfortunately, I cannot interrupt every single lecture to ask “why” or “where are we going to need it”. I guess it is every professors’ responsibility to let students know at the beginning of the lecture if needed. Sometimes even if I am a math major and understand usually everything that we are doing in my math classes, but the answer to the question why it’s not always obvious.