I love math. I think it is a fantastic subject that really does have many real world applications for people of all professions. I can even make the argument and not feel like it is a cop out that some of the math the students may never use in the real world but the logical and analytical thinking skills they will. So I'm okay teaching my students about factoring knowing they won't ever factor for a living some day.
But some days I just don't know. I'm teaching about circles right now in my geometry class and I firmly believe that I am basically giving them a bunch of formulas and teaching them which situations require which formula. Why? Besides the fact that the curriculum says so what is the point to it all? Why do they need to know how to deal with situations such as the intersection of two secant lines to a circle drawn from a common point? How can we get them the skills they need to do the real world math without boring them and shoving in a lot of state standards that really do have no real use?
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It seems to me that you need to revisit the purpose of mathematics. It is a tool, a basic tool used to help bring understanding to the world. Yes, you are giving them formulas and teaching them to use them appropriately, but you are also teaching them how to utilize mathematical formulas and you are also teaching them critical thinking skills. Bill Cosby once said, "Mathematics is Philosophy." Like all philosophies, it is not for some. However, higher order thinking skills in the field of mathematics is critical to student success.
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