We're looking at Burger and Starbird's text The Five Elements of Effective Thinking, chapter 1: Understand Deeply.
Summary: Advanced ideas are often built on a foundation of other ideas. It's important to understand the fundamentals clearly and deeply. One of the key skills here is stripping away the fluff to get to the core of the idea you're investigating. Don't be satisfied with your current depth of understanding, because you can always go deeper, you can always understand more clearly. Push yourself to increasing your understanding.
Critical Quotes:
"It is at the interface between what you actually know and what you don't yet know that true learning and growth occur." (p. 35)
"Commonly held opinions are frequently just plain false. Often we are persuaded by authority and repetition rather than by evidence and reality." (p. 36)
"Becoming aware of the basis of your opinions or beliefs is an important step toward a better understanding of yourself and your world." (p. 38)
Ben's Thoughts:
Not following this principle is one of the most common errors I see in the classroom. I remember one of my Latin professors in college telling us a story about her high school Latin class studying/translating Caesar's campaign against the Gauls, and one of the questions on the final exam was "Who was Vercingetorix?" and none of the students knew that he was the leader of the Gauls whom Caesar captured and brought back to Rome, which marked the end of his campaign. The students had translated Caesar's journals all year, but they got so lost in the intricacies of translation that they lost sight of the bigger historical picture.
In my own classroom, I see it happen with concepts like differentiation. Students learn the limit definition of the derivative, and then they learn the Power Rule, the Chain Rule, the Quotient Rule, the Product Rule, etc. And I always start differentiation by showing the tangent line problem and visualizing taking a secant line with a diminishing delta "x" (as this sets up the limit definition nicely) until it becomes a tangent, etc. But still, when I ask: "What does it mean to take the derivative of a function?" I get blank stares, because my students failed to deeply understand the basic concept. I probably did the same as a student.
This, to me, is the real difficulty of being a teacher: a good teacher is one who has thought extensively and deeply about the truths and mysteries of her/his subject, and s/he is trying to introduce students to the fundamentals, but students just haven't put in the time to see the beauty of the underlying structure of the subject. And if they don't put in the time, they'll remain forever mired in the quicksand of shallow understanding.
Summary: Advanced ideas are often built on a foundation of other ideas. It's important to understand the fundamentals clearly and deeply. One of the key skills here is stripping away the fluff to get to the core of the idea you're investigating. Don't be satisfied with your current depth of understanding, because you can always go deeper, you can always understand more clearly. Push yourself to increasing your understanding.
Critical Quotes:
"It is at the interface between what you actually know and what you don't yet know that true learning and growth occur." (p. 35)
"Commonly held opinions are frequently just plain false. Often we are persuaded by authority and repetition rather than by evidence and reality." (p. 36)
"Becoming aware of the basis of your opinions or beliefs is an important step toward a better understanding of yourself and your world." (p. 38)
Ben's Thoughts:
Not following this principle is one of the most common errors I see in the classroom. I remember one of my Latin professors in college telling us a story about her high school Latin class studying/translating Caesar's campaign against the Gauls, and one of the questions on the final exam was "Who was Vercingetorix?" and none of the students knew that he was the leader of the Gauls whom Caesar captured and brought back to Rome, which marked the end of his campaign. The students had translated Caesar's journals all year, but they got so lost in the intricacies of translation that they lost sight of the bigger historical picture.
In my own classroom, I see it happen with concepts like differentiation. Students learn the limit definition of the derivative, and then they learn the Power Rule, the Chain Rule, the Quotient Rule, the Product Rule, etc. And I always start differentiation by showing the tangent line problem and visualizing taking a secant line with a diminishing delta "x" (as this sets up the limit definition nicely) until it becomes a tangent, etc. But still, when I ask: "What does it mean to take the derivative of a function?" I get blank stares, because my students failed to deeply understand the basic concept. I probably did the same as a student.
This, to me, is the real difficulty of being a teacher: a good teacher is one who has thought extensively and deeply about the truths and mysteries of her/his subject, and s/he is trying to introduce students to the fundamentals, but students just haven't put in the time to see the beauty of the underlying structure of the subject. And if they don't put in the time, they'll remain forever mired in the quicksand of shallow understanding.
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