If you estimate something will cost/take/whatever 10 times what you’ve got then you know its a waste of time to consider it further. Or at the very least your next next iteration of calculation doesn’t need to be perfect in every detail, just a bit better than first. Rinse, lather, repeat.
Also, when you do the “right” complex way of doing/calculating/engineering something its nice to have that orginal “estimate” to compare it to. The problem with the detailed way of calculating something is that its much more likely you’ll screw something up and because of all the details you won’t catch it. If they don’t match terribly well then you have a big hint something quite possibly got screwed up big time somewhere.
I’d imagine there are plenty of real world cases where failure to do one of these two things caused some epic disasters.
I think that if that question had just said, “There are 40 trees in the sample area,” or if there had been 40 trees in the sample area (or better yet 10 trees without having each tree represent 4 trees) it would have been a totally legit question. It was the weird pictograph used in the sample area that made it seem totally artificial to me.
That particular test was administered on paper, so students would have been able to use their pencil and a scrap of paper. Rulers are only allowed in math at grades 3 and 4, and all other grades get calculators for math and science. The rulers for grades 3 and 4 are provided by the test administrator as well as the calculators.
I don’t think anyone vets the nominees for committee participation for their ideological views toward assessment in general. That seems like maybe reversing the cause-and-effect. What I can tell you, from my own personal observations of some of these meetings (where I’ve been tasked with recording notes), I would guess that the dipshits wouldn’t or couldn’t really dig into the work required of them. It’s very… thinky. Some of the teachers I’ve met have been truly impressive in terms of intellect, passion for their calling, extensive experience, and deep, deep knowledge of how to be an educator. You want the smartypants thinky types who do exactly what y’all are doing in this thread: tearing apart each and every item, looking for flaws and reasons it could be a bullshit item. Some committee of math teachers (probably several at different points) spent a whole lot of time with that palmetto problem trying to determine if the item fairly and accurately assessed the benchmark it assesses. It made it to the test after a grueling two-year journey through various committees, so it must not be *complete *crap. I am not an educator, so I don’t really have an opinion on that item in particular, in terms of how well it assesses the benchmark. I would be interested in taking a look at the psychometic data that were collected when that item was in use, just to see if the SDMB assessment that the item is bullshit bears out from the data, but that would require a bunch of digging and I’m not even sure I could come up with it anyway. (It could be that only 60% of students answered that correctly. That’s considered on the low end of a “good” item. 100% correctly answering would mean the item is too easy, and 0% would mean the item is unacceptably flawed.) Also to keep in mind: there may have been several other items on the same test (or on a different form) that were completely different, yet assessed the same benchmark.
You know, you might actually be bringing up editorial issues (did we word that item clearly) that would be of great interest to me. If that were still a live item, I’d really be digging into your comments, but that item has been chucked. Still, be aware that I’m absorbing your comments as another thing to keep in mind when I’m reading these things for clarity and correctness. I find I agree with you about the pictograph and we are often getting ride of extraneous art and graphics with some of the items. If the student doesn’t need the art to answer the question, it’s usually more clear to omit it altogether. It may have been determined that the item was made more challenging by throwing in that weird pictograph to sort of throw off students. Maybe there were already a couple of easy estimation items in the hopper and this one needed to have a bit more cognitive complexity to it.
The key tells you that each triangle is worth 4 palms; it’s a very easy concept and only one of the answers is in the right ballpark. There’s no trickery and concepts like this are used all the time in real life.
You’re partly responding to something I didn’t say: I never said the problem involved trickery. And you’re partly wrong: there’s no time in real life when you’d be confronted with a pictograph like this and need to make an estimation based on it, unless you were dealing with someone really incompetent.
I think Dogzilla is probably right, that the testmakers wanted to have a very difficult estimation problem on the test, so they took the graphic and turned the picture of trees into a pictograph in order to add an extra step to the problem (a step where a lot of students would flub, not paying attention to the pictograph’s key). I understand the desire to have a very difficult question on the test, since you want very few students to max out on the test, getting every question right.
My problem with the question is that it increases the difficulty through an unrealistic scenario.
Dogzilla, I do appreciate your comments here and in other threads on testing. I tend to regard you as a worthy adversary ;).
Yeah, that’s a crap question, and I say that as someone who got it right. It doesn’t even say that the map and square are to scale which is something you never assume on a written test unless they tell you it’s the case. Near as I can tell, that question tests you on how well you can use your pencil as a makeshift ruler. (And they said this test didn’t show case real world problem-solving skills!)
I think we are wandering off topic. We are focusing on one question out of 60. I was talking about a school board member that didn’t understand any of the questions. That means he is significantly more innumerate than the dumbest kid that passed the test and a lot of the kids that failed it.
I don’t expect school board members to be accountants, but they do need to understand the budgets they are approving or rejecting and that takes a lot more than simple arithmetic. People like this can end up wasting millions of dollars of taxpayers money every year.
The problem isn’t just that people like this are elected to the school board. They are also elected to the State and Federal legislatures and frankly sometimes to the presidency. Do you really want someone who can’t pass the FCAT making decisions about Social Security?
I used my little finger… it was about as wide as the little square, and a mark on my nail lined up more or less with the height of the square. Then I just measured how many pinkie-squares I could fit.
You don’t need a ruler to measure something within a certain amount of accuracy.
Somewhere along the line I learned that if I don’t push down on the paper, my pinkie is pretty close to a centimetre wide. That proved to be very useful in a few school projects and stuff where I needed a quick measurement in order to get a part or something. I also know that if my hand is held loosely open (not fingers stuck together, but not splayed either) the width of my palm is about 4 inches. Good enough to measure a sheet of aluminum with.
Well, I can think of one example: microbiology. Estimating the amount of bacterial growth after a certain amount of time (say, to determine exposure to a harmful bacteria after a failed cleaning in a hospital) requires a count and measure of growth colonies in a petri dish. Sometimes these colonies are irregular either in size or shape.
If you are given information like “there is a bacterial concentration of X per cubic centimetre” and you have some big and some small blobs, you may need to be able to estimate the area of all the blobs combined and determine that you have Y amount of bacteria.
If your standards for “passing” such a test are simply that you cannot have more than Z bacteria, being able to do such an estimate will tell you that you can a) take your time or b) emergency notify the hospital that patients and staff may have been exposed to a harmful bacteria and precautions should be taken until more information is obtained (as a random simplified example)
The problem with “when do you have to use this in real life? Let kids who want to do math/other hard stuff if they want and don’t force us all to do it” is that
kids won’t do the hard stuff on their own. At least most won’t… because it’s hard.
kids don’t know how to evaluate what they might want to do in the future and whether they might ever need to be able to use some fundamental math or science bit of knowledge.
The purpose of general education is to provide a general education… not to provide training for the very specific task career that we settle on/choose/are forced into as adults. We need to teach a broad foundation to children because we need a broad range of workers, and the only way kids become those workers one day is if they learn the basics when they are young.
If we only taught what school administrators knew, we’d have a hell of a lot of school administrators and no engineers, doctors, metal workers, heck even garbage men. And that’s just silly, isn’t it?
The big thing that everyone seems to be forgetting is that the FCAT is not really about about the knowledge, sure basic concepts are required to figure out most of the questions but you really only need to know the vague direction to look to solve them. The truth is that the FCAT is built to lie, cheat, and steal away the answers from the kids taking it. It largely consists of long story problems and complex graphs full of useless and unrelated data to confuse and slow down the test takers.
Basic test taking strategies are far more important than the actual knowledge when taking tests like this, and that’s the fundamental flaw with the FCAT. With 60 multiple choice questions randomly answered you should statistically get 15 or so right. However most questions have at least one out there and obviously impossible answer, randomly guessing between those three will yield about 20 correct answers.
If you read between the lines and maybe do a little of the basic math footwork you might be able to get rid of another answer or two further increasing your odds. That’s still assuming of course that you still don’t know how to properly solve the problem, if you know even just a handful your odds go up even further. In short if you are a calm and levelheaded student who reads the questions carefully and have a few ounces of logic in your head than the difficulty of the problems themselves is not a major concern.
But it’s a stupid key, as no one in their right mind would represent data that way. When you have real life data points that are randomly arranged like that, you would be counting each one; e.g., bacteria colonies on a grid of a petri dish. There is no reason in the world to represent the tree like that. Either put a triangle in for every tree, arrange the triangles in an orderly grid, or just state how many trees are in that area. I got the answer right, but the question sucked. Or maybe it was a test of botany and Palmetto trees actually grow in clumps of 4?
I actually support standardized tests, but when I see stuff like this it make crazy.
You didn’t look at the test or read the previous posts very carefully. Only half the questions are multiple choice. The other half are actually coming up with the correct answer.
I was speaking about the FCAT in general, most years I’ve taken the math it’s been primarily multiple choice especially for the lower grades. 60 was just the number being thrown around so I used it. I think that the actual tests are a little bit longer IIRC.
7 out of 7, and I’m in my mid-40s with a degree in music. I pinky-squared the palmettos too.
I don’t mind standardized exams but exams primarily measure the ability to take that type of exam. Applicability to real life is often secondary, sadly.
