Today in geometry we had the "when am I ever going to use this" talk. It happens every year, in every section of every course, to every teacher, ever. It is my belief that the answer and approach to this question can make or break a class for some students. It was my moment to get them hooked or lose them.
I'm always honest with my students when it comes to this question: in reality, most of them will probably never solve these types of problems exactly as they appear in the world outside of high school and college. When I think back over what I learned in high school, maybe 15% is used on a regular basis? Maybe that estimate is off a bit and you think it should be higher or lower, I don't know. Even my college coursework, I use very little of it, and I teach this stuff. I think my students feel a sense of ease when I express this to them because I'm not sugar coating anything and coming up with ridiculous scenarios of how this can be used. In reality, I could come up with perfectly viable situations in where they might need the Pythagorean Theorem or Hero's Formula but they always have a response ready for me to counter act it. This doesn't bother me; I get it.
I do tell them that the real-world-ness is not the important part of education. The point of education is to learn for the sake of learning, and if that's not enough for them, the point of math is to be able to problem solve. I know that my students have not been challenged mentally before, and if they have it has not been overly strenuous or very often. I know that if I ask them to write me a paragraph on what it means to graph y=3x+5 they will give me a step-by-step procedure but little to no meaning (as I was explaining this to them most nodded their heads in agreement). I don't want step-by-step procedures from my students, and I don't want to teach that. I want them to see the connections within the mathematics. I want them to be able to problem solve. After they leave my class, I don't want them to ever look at a problem and give up without ever trying because 'it looks too hard.' My job, as an educator, is to show them that all of this math stuff can be used somewhere, and somewhere else, and somewhere else, and if you manipulate it a little bit, somewhere else. I want to give them challenging problems that they start, and struggle with, and from the solutions we can learn new things. On the last day of the semester, if I give them a super challenging problem, I want them to remember what we did in the first week of class and be able to recognize that it might work in this new scenario, even though we've never explicitly done it that way before. I want them to think critically, think through the problems, try new solutions, verify their work, and most of all not be afraid to do it.
So, to answer the question of 'when am I ever going to use this in my life,' I usually respond with the above explanation, attached with a "I don't know, and you don't either." My students don't know when/if they'll ever encounter any of this geometry stuff outside of school or in another class. But, if they do, I want them to be prepared and confident in their ability to use it. After all of this and possibly some more conversation, my students are on board. They get it. They've never had a teacher tell them they may never use this stuff, but they appreciate the honesty and can understand the logic behind my purpose.
Students like to be challenged, even if they complain through the entire process. When they see the solution at the end, or better yet when they get their on their own, there is a sense of pride. This whole 'real-world' argument that they present could be a defense mechanism to get out of doing the work, but more importantly it's because they have a desire to see some usefulness in the material. Students need relevance, but not necessarily always in a real-world context. If we as teachers can hook them, follow and encourage their thought process, and make them thirsty for more, we're on a path to success, and they are too.
I'm sure I'll have this conversation with my students again throughout the year, it always happens more than once, and I have no issue with that. I will do my best to keep them engaged and challenge their thinking, and most of all blow their minds, with math and all that it can do. If they leave my room at the end of the year and feel no different about math or are not any more confident in their problem solving ability than the day they walked in, then I have some serious reflecting to do. I think so far I've got them hooked. I believe they trust me to not lead them astray. That's the first step and now its time, in the words of a fellow colleague, to change lives.
I said a lot of things...