Imagine if your high school math teacher approached algebra like the typical church approaches faith education.
First of all, class would only meet once or twice a week and there would be no expectation of students doing any learning outside of class.
The teacher's sole approach would be lecture.
Correct answers would be supplied for every problem - no need for students to wrestle through any sort of practice exercises.
Worst of all, the teacher would skip around the math book, pulling out random, disconnected lessons from week to week. Today from chapter 7, next week a single equation from chapter 13, and then back to chapter 2 the following week.
The only thread tying the lessons together would be the fact that they all concern numbers.
It's fair to say that the students sitting under that math teacher would be thoroughly confused and constantly frustrated.
And bored.
Week after week, they would be no closer to comprehending math than when they started.
Along the way they may pick up some math terminology, but they would not grasp workable definitions.
At the end of the semester, the teacher would still be the only one in the room who truly understood math.
(If even he did.)
And when all was said and done, most of the students would drop out of further math classes at the first opportunity - unless maybe they enjoyed hanging out with their friends in the class.
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