<p>I do, too. The biggest problem with rubrics is that you can, for example, write an over-the-top publication-quality paper and then lose a bunch of points for not being able to find 5 pictures and add appropriate captions (no matter how unnecessary they may be). I think this process stifles creativity and encourages the development of a safe, bureaucratic checklist-type mindset.</p>
<p>For subjects such as math, it can even be much worse. Both my sons were math naturals in high school, inventing their own shortcuts and alternate ways of solving problems. A rubric which gave points for “show all your steps” would have been a nightmare when unorthodox approaches were used.</p>
<p>If you are the best in your school in a given subject year after year, there is a high probability that you will get an A in the next class in that subject. After, say, 4 weeks in that new class, you should have a pretty good idea of whether or not the subject matter or the instructor’s grading system has thrown you any curve balls. If it’s business as usual, it’s safe to say that the A is once again a foregone conclusion (as long as you do the work).</p>
<p>Alternately, if the instructor tells the class that at least 40% of them will receive A’s and you’re interested in the subject, good at it, near the top of your class and willing and eager to do the work on time, I would consider the A a foregone conclusion.</p>
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<p>I think in most classes the students quickly figure out who the very best students are. In my case, I used to have friendly competitions with select classmates; we would show each other our grades and declare “ha! beat you!” or “That’s just one battle - I’ll get you next time!”</p>
<p>But there are other ways, too.</p>
<p>The intro programming class at Brown is taught by a legend in the CS field and he tells the class on the first day that he “likes to give out A’s.” So 40-50% of the class is likely to get an A. But along the way, there are also special competitions, where 2-5 students get recognition for the best project design or the fastest algorithm or something similar plus a trivial number of bonus points. Well, it’s pretty hard in a school like Brown to be one of the top 5 in a class of 175 students and the extra points are irrelevant for anyone good enough to win such a competition. So why do it? Because when you have a group of elite students together, be it in an AP class, a college honors program or a top-50 school, proving yourself among your peers is still important.</p>
<p>If they show all of their unorthodox steps, then that should certainly be acceptable. However, it can be a problem if the teacher is not familiar with the unorthodox method or does not understand it.</p>
There is no approach so unorthodox that you should not be able to show all the steps you used. If your “shortcut” is doing it in your head, then it’s not acceptable if I want to see all your steps.</p>
<p>^The teacher should be pretty much able to figure out any method a student uses at this level of instruction. If she doesn’t see it directly, then surely asking the student for clarification would be better than just docking them points.</p>
<p>A math teacher would require all steps so that she can see where creativity worked and where mistakes were made (computation, understanding). She would require it of everyone all the time so that she wouldn’t have to fight over it regularly when a problem is marked wrong . . . and the student protests. She could simply note where the error is on the test.</p>
<p>As far as rubrics, as someone who has administrated university programs, I hate them (though I don’t forbid them). They are rarely detailed enough to be meaningful and often are used by lazy teachers to avoid specific comments for particular students on individual assignments. They really don’t standardize very well because a teacher can fudge whatever she wants out of the rubric and students aren’t really able to compare results enough to notice discrepancies.</p>
<p>Clearly you have no direct experience dealing with highly-gifted right-brained thinkers. Both my sons would “see” answers in their heads and take intuitive leaps rather than use step-by-step methods to solve all manner of problems. </p>
<p>Note Linda Silverman’s comment on right-brained visual-spatial learners: “They arrive at correct solutions without taking steps, so ‘show your work’ may be impossible for them.”</p>
<p>My sons should have been penalized because they could get the right answer 10 times out of 10 using an alternative method that neither the teacher or I might not immediately understand?</p>
<p>Even when they could show their work, the steps might not immediately make sense to an elementary school teacher. Consider this problem:
multiply 87x93</p>
<p>answer:
90x90 = 8100
3x3 = 9
900 - 9 =8091</p>
<p>The mental math solution is algebraic rather than arithmetic, a^2 - b^2. My first son used to do such problems in his head at age 5 because, for him, the greater chore was the manual dexterity involved in doing it the long way on paper.</p>
<p>You may note that the math problem above is a special case; however, my sons would frequently apply special cases, thus solving similar-looking problems in different ways, based on what was most efficient.</p>
<p>^Amazingly enough, you were able to write down the steps, and even more amazingly I was able to understand them. Ergo you did not support your argument with that example. Care to try another one?</p>
<p>I’ve had several discussions with college professors who had trouble getting their kid’s elementary or high school teacher to understand that an answer given in a slightly different algebraic form was the equivalent of the answer given in the teacher’s guide. So the fact that you can understand this particular process is irrelevant, because many teachers cannot. Plus it was an easy problem and I threw in a big hint about algebraic which my son at the time is unlikely to have mentioned – there are extensions to the same methodology which are much harder to follow.</p>
<p>problem: multiply 85x85</p>
<p>8x9 = 72
add the digits 25 to end
answer: 7225</p>
<p>I can see both sides of the math debate. I’m impressed with LI son’s algebraic thinking, but sort of think he should have to explain it. That said, my kid was similar. Here’s an example I remember from a 2nd grade worksheet. He was asked to come up with coins that would make up a certain sum. His method was to look at the number, say $1.15. He’d immediately know what the coins were, his method then was just to check that they did indeed add up to the correct number, but he did not go through any math process that he was aware of. A less intuitive kid might first subtract four quarters, then a dime and then the nickel. He’d just see what the answer had to be. </p>
<p>My younger son was just the opposite. He had to show all his work, because he could not remember short cuts or standard methods to save his life. He’d do things on tests like figure out the Pythagorean theorem from scratch. Needless to say he lost a lot of time on tests, but his pre-calc teacher actually was quite impressed and wrote a lovely letter of recommendation. Nothing like an LD combined with giftedness to give weird results!</p>
<p>All that said, I mostly like rubrics. I also like tests to be against standards not some artificial curve. If you give a spelling test, you shouldn’t put words on it that the students weren’t told to study just so some of them can get C’s. That’s essentially what happens in a lot of colleges that believe in curves.</p>
<p>I was able to follow the simple one but as the problem gets harder, the solution gets more complicated and hard to follow. This coming from a guy with an Engineering degree. I can only imagine for an elementary or even a HS teacher.</p>
<p>My D had a similar experience with her 3rd grade teacher when they’re learning about rectangles, squares and parallelograms. On their test, my daughter marked the square as a rectangle and marked the rectangle as a parallelogram. Of course, the teacher marked them wrong. Well, my daughter asked me to print an article to show the teacher that explains “all squares are rectangle but not all rectangles are squares” and “all squares/rectangles are parallelogram but not all parallelogram are squares/rectangle”.</p>
<p>“If you give a spelling test, you shouldn’t put words on it that the students weren’t told to study just so some of them can get C’s. That’s essentially what happens in a lot of colleges that believe in curves.”</p>
<p>My first reaction was going to be to say that that isn’t at all how difficult college tests are written, until I realized that your example was perfect.</p>
<p>For an elementary school child, asking them to spell a word they have never seen is unfair. For a college level student, it could very well be a perfect application of using word origin, and meaning to apply the rules they know to an unfamiliar situation.</p>
<p>THAT is the essence of how difficult test should be written. C level work means that you studied what was presented and can do the examples shown. A level work means that you truly understand the work and can take the principles and apply them, along with other techniques you know, and solve the problem.</p>
<p>^^ Two lessons there - one for the teacher who should learn not to write ambiguous questions around clever children, and two, one for the parent to tell the child that although their answer was clever, one should also not try to be so clever around people who have the ability to make your life miserable because they were shown up by an 8 year-old.</p>
<p>EQ lessons are sometimes just as important as the IQ lessons.</p>
And that’s exactly what I did. I didn’t do it right away but talked to D after she did it again to a test that the teacher is expecting an “equilateral triangle” as the answer but my D put “isosceles triangle”.</p>
<p>MrMom62, #114, the thing is that the children aren’t taking their approaches to be “clever,” this is just how they naturally approach the problems. I think it’s a tall order to ask an elementary school child to figure out what an adult (the teacher) understands or does not understand. The only good feature I see is that it adds a layer of complexity to what would otherwise be humdrum assignments: solve the problem, and then decide how to present it so that the teacher “gets” it. Resolve if necessary.</p>
<p>I don’t see this as an IQ vs. EQ problem. It would be, if the students were showing off with their approach. It seems to me to be much more a cognitive problem–to understand how much the teacher will be able to understand. Quite tricky. And hard to convey to a child without patronizing the teacher pretty severely.</p>
<p>Consider yourself lucky with the “clever” child. My kids and I are too insecure(?) to be clever. I know I would be paralyzed with fear/self-doubt if I had to choose among square, rectangle, and parallelogram. </p>
<p>Does the teacher want me to pick all three, am I missing something, is it a trick question… I’m in a line of work where I take test on an annual basis and I am always second guessing myself on poorly written question.</p>
And the child should still be called to task to explain his answers. Because it’s not 130682 that’s important, but the process. It wouldn’t mean much if I were to say that I have a great math theorem and the proof is in my head but I can’t write it down. </p>
<p>If the child is indeed at a level well exceeding that of his classmates, then he needs to be put in a gifted instruction group so he can develop accordingly. I just hate the “my child is too smart to be bothered doing what you ask for” attitude. Why not just pull him from the math class altogether, since it’s a total waste of his time which could be better spent on other pursuits?</p>
<p>Richard Feynman used to challenge people who were whizzes with the abacus to contests involving multiplication, division, and in one really memorable case, even a cube root. Feynman used basically the same approach that Lorem Ipsum’s son is using.</p>
<p>This is not a case of having the proof of a theorem in one’s head, and not writing it down.</p>
<p>This is a case of writing down an analysis that is obvious to someone who “gets” it, and confusing to someone who doesn’t.</p>
<p>An adult should be able to gauge the audience and pitch a presentation accordingly. An elementary school student faces a real challenge to figure out what the adults in his/er life “get,” out of the set of things that seem obvious.</p>
<p>I am sure that students who followed a more conventional line of thought got full credit for writing down no more than Lorem Ipsum’s son did.</p>
<p>As a final twist, the preferred approach on the state math tests as part of NCLB, by 4th or 5th grade, is a minor variant on Lorem Ipsum’s son’s method.</p>