This goes back to something Elon Musk mentions in one of his talks; reasoning from first principles vs. reasoning from analogy. On the face of it, accepting pre-determined knowledge is a necessity, but I don't think you should accept something blindly, but integrate into the axiomatic knowledge you already have. This is why I always focus on concepts and foundations through the vehicle of practical applications. Understanding in our schools and universities seems to be an after thought in many cases. I can't count the students I've met just looking to 'check the boxes' so to speak. I was one of them for a while as well.
Why is this? Ultimately, it is because of a lack of purpose and vision. Why are you learning the material? Why is it important? Are you going to blindly accept the equation, or are you going to pester Mr. Davidson until you understand the underlying mathematical assumptions? These are important questions. And I think the best vehicle for that in this day and age is Big Data.
Big Data can teach us so much about the world when well analyzed. This field is so exciting because it is at the heart of everything we will do. Every major industry from molecular biology and genetic engineering to google and fantasy football will use big data to understand and solve new problems.
Why is it so useful? Because analyzing and reducing data helps us to understand the root causes of phenomena and apply that understanding to anticipate future problems.