>Because jesus, if you are, and those tests are consequential to the kids future, that's a pretty damn relevant and reasonable question.
The point of a test isn't to test every single detail of what you were taught, it's to hit a random distribution of topics and examples of what you were taught. This gives a pretty good indicator of how well you learned the subject overall.
Asking "is this going to be on the test" shows that you have no intention of actually learning everything you're taught, which is the point of the class, and instead you're only interested in memorizing the minimum to pass a limited test, which is not the point of the class.
> Asking "is this going to be on the test" shows that you have no intention of actually learning everything you're taught, which is the point of the class, and instead you're only interested in memorizing the minimum to pass a limited test, which is not the point of the class.
I think you have it backwards. The point of the class is to make kids pass tests. The fiction is that it's so that they learn the material. Learning is ancillary to the systems actual purpose. The fact that a lot of people that are part of the system are well meaning and don't realize this doesn't negate the design of the system itself.
I realize that sounds like some sort of crazy conspiracy theory, but keep in mind that "schooling" and "education" are related but separate things. Public schools are a relatively modern invention from around the industrial revolution, and the inventors of the public school system explicitly designed it to create people that were obedient. They weren't even particularly secretive about it -- a lot of the people that helped found what we think of as our modern school system said as much directly.
Not the most elegant page, but here's a good book on the subject from a former school teacher: http://www.johntaylorgatto.com/underground/toc1.htm (I think at one point he even won a teacher of the year award, or something along those lines, so he's not necessarily just some crackpot)
I wrote so many tests in university that were poor reflections of what was taught in the course that I couldn't ever fault someone for optimizing. There's not enough time in the world to study every word that was said in every course in detail. Students have to try to pick out the important stuff and focus on that.
Knowing what a test is going to be like is pretty useful if that test matters at all. Otherwise there is a higher chance that the people who fare well on the test will be those who happened to work more on the topics or skills which come up. I'm happy my lecturer for group theory in university let me know which of the 5+ page proofs of theorems from the course wouldn't need to be known for our exam - it wouldn't have been very good use of my time to fully internalise all of them. However they were interesting and I think it added value that they were in the course.
I think you just have an idealised picture of how tests work. In the best maths exams I have taken, you know all you could within reason about what you need to know and what will be the content of the test, and yet the questions still surprise you and cause you to think in new ways.
Knowing what a test is going to be like is pretty useful if that test matters at all.
Knowing and understanding the subject matter is likely to be pretty useful if the test matters at all. This is why you study and understand the entire course, which is the point of the course. However, being told explicitly which portions you will be tested on goes against this goal.
which of the 5+ page proofs of theorems from the course wouldn't need to be known for our exam - it wouldn't have been very good use of my time to fully internalise all of them
What? If you're doing mathematics correctly, you are ably to derive the proofs on the fly. You don't have to memorize "five pages of proofs". You understand the concept, you understand the mechanics, and you derive the proof as necessary.
I think you just have an idealised picture of how tests work.
I'll refrain from saying what I think about your "picture of how tests work".
Maybe I worded my post badly; I was trying to say that your idea of a good test isn't in line with how tests are designed in my experience of education. If you agree with the sentiment that children should be punished for trying to optimise for exams, then yes I think your picture of how tests work (at the moment, in school especially and somewhat college) is wrong. I see nothing wrong with a well designed test, made to cover a whole course and to be fruitless to optimise for. At least in the UK in school, all STEM type exams are not like that as far as I remember. Humanities exams are much closer in style to this.
I do think GCSE and A-level science exams could be much better designed. At college level though I'm not sure the way you describe is the only good way to do things.
I'll refrain from saying what I think about your idea of how to "do mathematics correctly".
>Because jesus, if you are, and those tests are consequential to the kids future, that's a pretty damn relevant and reasonable question.
The point of a test isn't to test every single detail of what you were taught, it's to hit a random distribution of topics and examples of what you were taught. This gives a pretty good indicator of how well you learned the subject overall.
Asking "is this going to be on the test" shows that you have no intention of actually learning everything you're taught, which is the point of the class, and instead you're only interested in memorizing the minimum to pass a limited test, which is not the point of the class.