The first point that made me stop was that mathematics does not always develop because of practical needs. Many mathematical ideas were created to solve real or scientific problems, but some also came from logic or mathematical problems themselves. It reminds me the invention of complex numbers and non-Euclidean geometry. It means sometimes, math tools are not all necessarily designed for economical demands, mathematical development can also help us discover new things about the world.
The second point that made me stop was the difference between simply teaching historical facts and using history to guide how math class should be planned. Before this reading, I thought the history of math could be an interesting addition to my classes, mainly through stories about mathematicians, discoveries, and interesting old methods. Now I see that history can also help students understand what questions originally led to a mathematical idea and why the idea was needed. This can give teachers another way to introduce a topic instead of starting directly from definitions and formulas.
Your point about not always starting a topic with definitions and formulas stood out to me. Starting with the original question or problem could make students wonder about it first, and then the formula might have more meaning when it comes later.
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