There is a difference between teaching what and when and teaching how and why. A student can advance through elementary, middle, and high school by being told what content to learn, and by when, without having to learn how or why the content being taught works the way it does.
Many teachers address what, when, how, and why when it comes to introducing content to students; however, there’s often a false premise applied which insists that students inherently learn the how and why of what is being taught (by when) since any content must be taught how in order for what to be learned.
For example, a student who is able to multiply two numbers to get a product has learned to multiply, which means to multiply is the what. However, while the student may have learned how to multiply by being shown specific strategies and then practicing with those strategies, the student does not necessarily know how multiplication actually works. This distinction between knowing how to do something and knowing how something works is where we find ourselves exploring the difference between compliance and mastery specific to the context of teaching and learning.
JUST DO IT BECAUSE IT WORKS.
I was taught to multiply and divide in the late 1980s when the primary teaching strategy involved “drill and kill” – memorize math facts, follow steps for long division, repeat to practice. From an observer’s perspective, it looked like I was learning how to multiply and divide. Yet, if I were asked then what I knew about multiplication and division, my response would be limited to those math facts and that series of steps for long division. In reality, I was learning to multiply and divide – not how multiplication and division actually work.
The question then becomes whether I needed to know how everything works - especially at those early grade levels with such straight forward processes involved. If I was able to multiply two numbers and get the correct product, why wouldn’t that be enough for me to figure out later math in later grade levels? Isn’t it more important that I learned how to multiply as minimum of learning at that point in my schooling journey?
What was overlooked in my experience was how, over the years, the concepts behind multiplication and division were necessary for understanding the concepts behind more complex ideas like exponents and logarithms. Instead of developing that conceptual understanding, I ended up having to memorize new steps for new procedures for those increasingly complex concepts. When I would be asked how I knew how to do something correctly, my response would often be “because the teacher told me to do it this way”.
The takeaway for me, in reflecting on these past schooling experiences, is how the indicator for academic success seemed to rely on how well and how often I was able to motivate myself to do what tasks when they were assigned, and less about my capacity for communicating how and why those concepts connected as progressions across grade levels. In fact, there was a phrase I came to hear often from tutors, siblings, teachers, peers - anyone who cared enough to sit with me and try to help me learn new steps for new equations, a phrase which they likely had been told themselves by their teachers, friends, and family: "just do it this way because it works."
NOT ALL LEARNING IS COMPLEX
Occasionally, people simply have to do things they don't necessarily want to do. This is true in childhood as it is in adulthood. Many of the things needing to be done in a given day are