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ideasrule
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buffordboy23 said:Using their critical thinking skills and knowledge of trigonometry, the former student realizes that they can accurately measure the baseline from some position to the tree and the angle from this position to the top of the tree and compute the height of the tree to good accuracy. Thus, the question is answered and learning trigonometry has proved useful to the student. There are many more examples that can convey the value of advanced mathematics, but it requires competency on the part of the teacher to show this to students, and unfortunately, this does not generally happen in our classrooms.
I don't agree that providing real-world examples are likely to improve students' interest. In your example, learning the trigonometry needed to calculate the tree's height is only interesting if the student is actually faced with the problem, takes out a measuring tape to measure the baseline, constructs a device to measure angles, and calculates the tree's height using the collected data. That would be interesting because the answer is a meaningful physical quantity of a real object, not a useless number that happens to be on the answer sheet.
I can't speak for other people, but I absolutely hated the "problem solving" questions in math class, many of which were similar to buffordboy's tree example. I considered them pathetic attempts at demonstrating the simplistic math we used was useful. At the same time, I often used math to calculate physical quantities, like the speed of a falling raindrop or the altitude of the Sun, because actually collecting the data was fun, not because the math was interesting. If a homework question asked me to calculate the speed of a raindrop based on somebody else's data, I would have considered that question as boring as the others.