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<p>An indication of lazy teaching.</p>
<p>If someone can write a computer program to generate math placement test problems like [url=<a href=“http://math.berkeley.edu/courses/choosing/placement-exam]this[/url”>http://math.berkeley.edu/courses/choosing/placement-exam]this[/url</a>], it should not be too hard for a teacher to vary the test enough to ensure that old tests would only be useful as practice problems.</p>
<p>ptontiger - Did you mean analytic geometry? I say that because true Euclidean geometry is more or less free of algebraics and can be grasped by “regular” first graders. I think the reason many students are put off by modern maths is due to the mushing together of two or more schools of mathematical thought, and the clarity in the rationale of the original conventions is lost, especially by the time the amalgam reaches kids in the tertiary literature of Glencoe-type compendium books. For example: arcsin “exponents”.</p>
<p>Yes, thank you Polarbear. I mean analytic and Cartesian geometry. While this type of geometry may be difficult for some, I still believe that given the effort and time (instead of wasting those on video games and TV), most students can grasp most concepts. Now some may be difficult (I don’t understand what you mean by arcsin “exponents”) but still within reach. </p>
<p>One reason why children in other nations learn faster, better, and at a younger age is because they are free of the educational distractions we have. It’s hard to be distracted by a video game or TV when you don’t even have those things! Our children spend too much time playing Skyrim and too little on their studies. This is a reflection of our society.</p>
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Berkeley’s test generator simply draws questions from a small test bank. I’d estimate about 50% overlap between any two exams I generated. A teacher doing that would probably still be considered lazy in your book.</p>
<p>It’s not that easy to write fundamentally different exams. When I went to high school, we had state standards for how we were to be tested. Every exam needed to contain “transfer questions” that required the use familiar knowledge/techniques in unfamiliar ways. Every old “practice exam” that’s circulating the hallways would eliminate an entire category of possible transfer questions.</p>
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I’m assuming PolarBear is referring to the practice of writing sin^-1{x} to mean the arcsin{x} or the inverse function of the sin{x} rather than to mean 1/sin{x} as the exponent (-1) is used to mean elsewhere. It gets confusing when the same exact sort of notation means different things in different places, especially when sin^2{x} actually DOES mean “the square of the sin{x}”.</p>
<p>Non-math types feel free to skip on by this post :)</p>
<p>Oh, then this convention is easily fixed. Mathematicians simply write arcsin to designate the inverse function of the sine and sin^-1 to mean 1/sin or csc. There is some ambiguity in mathematics, but you get the same in English - albeit a lot more of it. “i before e except after c”… oh, except for the case of sleigh… or neighbor… and yet we don’t “dumb down” English in our high schools.</p>
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<p>Every university I’ve ever attended has made previous tests available either as handouts in the dark ages or on a web site. I see no reason why it would not work in high school.</p>
<p>Who says we haven’t dumbed down English in our high schools. Have you seen a NYS Regents Examination for English in recent years? It’s a disgrace. And far too many NYS public schools teach to the test. </p>
<p>Math? Yes, the Regents exams for Algebra I and Geometry don not require the same level of understanding as 30 years ago, but they are significantly more challenging than the English exam.</p>
<p>At least you’ve got the Regents exam. Here in Illinois, there are no standardized tests tied to high school graduation, so each high school defines for itself what acceptable performance is for graduation. The result, in many districts, is that people are getting diplomas with dramatic deficiencies in basic knowledge and skills.</p>
<p>A young lady graduated two years ago from our local high school. Somehow she got hired by the local library as a library assistant, and for some unfathomable reason they have her writing the library press releases. The poor thing cannot write a grammatical English sentence. I’m not exaggerating: she cannot write a grammatical English sentence. And no, her first language is not something other than English.</p>
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<p>It is likely that at least some knowledge of the old exams is floating around the hallways; having a public exam file puts all students on a level playing field and prevents the instructor from recycling identical exams. Keeping exams “secret” and recycling them without any changes just increases the temptation to cheat, because cheating would be more effective (remember the radiology exam scandal?).</p>
<p>There are only so many classes of problems available for a given high school math topic, so it is not unreasonable if the real exam has problems similar to, but not identical to, problems found on practice exams and homework assignments.</p>
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<p>This isn’t a recent phenomenon or one restricted to NYS. As a freelance college academic tutor and undergrad, I saw unbelievably horrid demonstrations of English writing skills from native-born Americans at every college/university I’ve visited…including a few Ivies. </p>
<p>From what I’ve seen, it is far too much to ask many incoming freshman/undergrads to write coherently enough to be understood…much less demonstrate impeccable grammar and polished English writing skills. One classmate who was overconfident ended up wondering why her paper was returned ungraded with a note for her to rewrite it. When her friend showed it to me, I noticed it was so incoherent, confused, and logically inconsistent that I told him to tell her she’d be better off starting over from scratch. </p>
<p>This was further confirmed by several international grad student friends at an Ivy who were shocked at how many incoming freshmen had serious issues with writing proficiency when they TAed Freshman writing, literature, history, poli-sci, or any course requiring decent writing skills. </p>
<p>They all said that if any high school demonstrated the atrociously poor levels of writing they saw as TAs at that Ivy back in their home countries, those students wouldn’t even be allowed to take their country’s university…much less matriculate at one.</p>
<p>I’m going to catch hell for this thought… </p>
<p>Maybe a a bigger question than “is math too hard” is: “does everyone really need 12 years of school?”</p>
<p>Not everyone is cut out for college. From the NYT article:
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<p>Would it be more less job-limiting for non-academically inclined students to graduate gracefully after the 11th grade with a diploma, than for them to drop out and have no credential at all. College-track students could continue on and graduate with a 12-year diploma.</p>
<p>Do plumbers and auto mechanics really need to know how to factor polynomials? Would they be economically better off entering the work force one year earlier?</p>
<p>I think a better way to state it is we teach math incorrectly. The scope and sequence is messed up from the very beginning. I home-schooled in kindergarten (age 5). She had no problem adding and subtracting numbers as long as your arm, and was bored with that, so we went on to multiplication, and then touched on division. She also had worksheets in logic…I put her back in public school in 1st grade (had too). She aced the math portion of her sat. We don’t expose kids to complex mathematical concepts and open their little minds early enough.</p>
<p>cromette–one example doesn’t prove that the system is wrong though. Kids develop at different rates and a LOT of kids in kindergarten could not do complex math problems even if you exposed them to the problems. Their brains are just not ready to deal with them yet. It doesn’t mean they are doomed to being poor math students, just that their bodies have developed in different areas. Same goes for reading, some kids are reading before kindergarten, some not until 2nd grade or later. There is just way too much variation in ability at that age. What IS needed is that we go back to tracking kids so those that ARE ready are not held back by those that are not.</p>
<p>SteveMA, totally agree that kids develop at different rates and that results may vary. Lol. My point is - how will we KNOW what a kid can grasp if we are not even giving them the opportunity to move past what most have mastered? I have helped in kindergarten and 1st grade classes where the ENTIRE class has near mastery of the simple skills they are exposed to, and I just don’t think we take it to the next level as we should. I think we’re stunting their growth. This new culture of not moving kids along to save the feelings of someone who needs to go a little slower stunts us all.</p>
<p>I think we don’t realize how much they can learn and how young. Exposing them to a lot of things doesn’t hurt.</p>
<p>This debate reminds me of the Rede Lecture, delivered by C P Snow in 1959:</p>
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<p>I wonder what Lord Snow would have to say about our understanding of math?;)</p>
<p>That was pretty interesting (I looked up The Two Cultures) on Wikipedia.</p>
<p>I was at a shooting range recently and saw an eight-year-old kid empty a clip from a 9mm into a target like he was playing with a set of legos. His father is an engineer and into hunting, fishing, camping and survival. His mother has a liberal arts backround from one of the British Commonwealth countries. I’d guess that this kid has better survival skills than most adults in the US. I also think that he’s going to be a pretty well-educated kid overall in ten years.</p>
<p>You opine this because he is picking up on his fathers hobbies?
What if he wants to play the violin and paint?</p>
<p>I’ve observed him spending a lot of time running around in the forest. I also see him doing things like wood carving. His sisters are more into the arts and crafts stuff so I’d guess that those things are available in their home if he’s interested. They homeschool their kids so there’s plenty of time for them to do what they want to.</p>
<p>This is something that I haven’t run into in my corner of New England. I’m sure that it happens as there are a lot of rural areas in Northern New England but I live in a suburban environment where there’s probably a lot less of this. There are all kinds of skills and knowledge that can be useful besides arts and sciences. Being able to fix a toilet, sink, flat tire or alternator are useful too.</p>