<p>I suspect that some of the problem we see here is really the unfortunate flipside of one of the U.S.'s great virtues–personal freedom and value of individuality. Perhaps American students feel more free to think that certain kinds of questions are “stupid” and certain kinds of skills are unnecessary to them. They know, for example, that they will be able to go to college even if they don’t do all that well on standardized tests, which is not the case in all countries. The challenge is to fix this attitude without taking away the freedom and individuality.</p>
<p>Perhaps, we should hold responsible the people who find it acceptable that 2/3 of seniors in high school are unable to solve a 6th grade math problem.</p>
<p>The people? The same people who are too busy negotiating higher wages, smaller workdays, or more benefits for teachers and administrators, and, of course, making sure to use their financial muscle to elect candidates who will support the further erosion of education in our country.</p>
<p>if its THIS math problem, well, its a stupid problem that is unclear and poorly written</p>
<p>sometimes, its the problems that are dumb, not the students</p>
<p>look at some of the textbooks forced upon our teachers and look at NCLB- it didn’t help any</p>
<p>if you want to blame teachers for the erosion of our education system, that is just wrong</p>
<p>its the funding, its the support, its the taking away program after program</p>
<p>but of course don’t put any blame where it matters- to the feds for forcing programs on schools and then not funding them</p>
<p>I find it offensive to blame all teachers for this and pretty shallow thinking</p>
<p>Better than hitting the keyboard with any thinking whatsoever. </p>
<p>Reading comprehension goes a long way to help understand a post … or a stupid problem.</p>
<p>how is it unclear and poorly written? With the diagram in place, there is absolutely nothing even remotely unclear about this problem. And placing the blame for failure anywhere but on themselves is what keeps some students from making any progress.</p>
<p>Eyeopening is the math section of the teacher certification tests.
Perhaps we should have those writing and administering the student tests, first take them and publicly post their scores</p>
<p>
</p>
<p>It’s the Ed Schools:
[Horsefeathers</a> - ON EDUCATION: BY RITA KRAMER](<a href=“http://doctor-horsefeathers.com/archives2/000391.php]Horsefeathers”>http://doctor-horsefeathers.com/archives2/000391.php)</p>
<p>And, it’s the unproven education ideology and pedagogy currently in widespread use:
An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching
<a href=“http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf[/url]”>http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf</a></p>
<p>Let me try to explain in a different way why I think this wording of this question is problematic.</p>
<p>First, note that the question itself involves an ellipsis of material after ‘need’, which can be filled in as follows (reconstituted elliptical material in brackets).</p>
<p>How long a piece of ribbon does he need [to wrap around a box measuring 3X8X12 cm]?</p>
<p>Here, the reconstituted element contains only material from one of the conjoined verb phrases. You would solve the problem for only the amount of ribbon around the box, which is 52cm, and give choice (b).</p>
<p>Now, it is possible to find situtations in which the reconstituted elliptical material <em>must</em> be only taken from one of the conjoined verb phrases. You need to have a biasing context here.</p>
<p>Biasing context: Stu has 16 students in his science class.</p>
<p>Stu wants to take as many students as he can to the local science musem and have 3 left behind to supervise the on-going experiments.</p>
<p>Question: How many students does he need?</p>
<p>Here, you would only look for the number of students he needs to take to the local science museum.</p>
<p>Now, the question given does not have the biasing context, but that doesn’t mean that a student might not provide a biasing context such as </p>
<p>Context: Stu has a certain length of ribbon.</p>
<p>Stu wants to wrap some ribbon around a box (etc. etc.) and have 25 cm left for the bow. How long a piece of ribbon does he need?</p>
<p>The student might interpret this as a question of ‘the (least) amount of ribbon needed to cover the box so that there is 25 cm left for the bow’–you don’t want to use up too much ribbon so that there isn’t enough left for the bow. So you solve for the least amount of ribbon to cover the box as shown.</p>
<p>Note that this isn’t that different from the above with the science class–the amount of students to take so that there are 3 students left to supervise the experiments.</p>
<p>I would also say that stating ‘having 25cm left’ might also cause trouble, because of the word ‘left’. The question wants the total amount of ribbon, including the amount ‘left’. But usually, the stuff that is ‘left’ is typically not part of a total.</p>
<p>Of course, if you do go this route, then you are in trouble. Because then you have to battle trying to figure out the ideology of the test maker. If you go this route, you then wonder why 25 cm is given at all, since this number is not used in the calculation. You may try to say that this is ‘distractor information’–to be ignored. Or you may say that there are two unknowns–the original length of ribbon and the amount around the box and that the problem involves more complex math than you first realized or know how to do. </p>
<p>Or you can go and reread the question again, figure out that the question asks for both the amount for the box and the bow and get it right.</p>
<p>But here, you are battling not a bad math background but a problem of interpretation.</p>
<p>And, as I stated previously, perhaps the wording in other languages does not allow the student to go the route that I did, thus making the problem a bit easier.</p>
<p>So that is why I am curious if 52cm wasn’t the most likely ‘error’. And note that to get this 52cm, you do need to know the basic math involved.</p>
<p>So simply stating that only 32% got this right tells us nothing about why they got it wrong and little about what we need to do to correct the problem.</p>
<p>
</p>
<p>Sorry, but that explanation makes as much sense as the four “subtle” explanations offered by the Holliday tandem. </p>
<p>Fwiw, if you were to focus on the answers, you’ll notice that ONLY an answer of 77 cm would satisfy the original question. For instance, starting with a 52 cm ribbon would only allow to wrap the box and have … none left. The question is VERY clear, “Stu needs TWO things: wrap the ribbon around a box AS SHOWN **and **have 25 cm left for the bow.” </p>
<p>When facing a standardized test question --at least the type of questions written by reputed organizations such as ETS-- a student needs to pay close attention to the ENTIRE set of information and focus on the specific instructions. One of the biggest dangers is idle speculation and erroneous inferences about what MIGHT be asked. The 25 cm for the bow was not a distractor but a main component of the problem. And, fwiw, people who have looked at standardized test for some time know that the use of distractors is extremely rare. The allegations of tests being tricky are usually presented by people who do not understand the process in the first place.</p>
<p>In this case, there is only one way to answer this question. Answering anything but 77cm means that the student was unable to understand the question or was unable to answer correctly. And, for the purpose of the test, in both cases, the conclusion remains the same. Understanding a question correctly is as important as being able to perform elementary school math. </p>
<p>Even if the american student comes out with the same amount of self-esteem.</p>
<p>Hey, xiggi, I originally agreed with you, but your responses to the other posts in this thread are gradually making me think that you’re the one that’s wrong. Just saying.</p>
<p>Xiggi,</p>
<p>You are right. Students should do better and should be able to find the correct interpretation to the problem. However, you miss the basic point of my response.</p>
<ol>
<li><p>I tried to show how the wording of the question lead me down an incorrect garden path that I had to recover from. I suggested that this additional garden path may not have been available in other languages (irrespective of the kind of teaching, test prep etc.). Given that (1) I needed to commit extra cognitive resources to recover from the garden path, resources that take away from solving the main problem (2) that a student working in another language may not have needed to employ these additional resources and (3) committing such resources away from the main problem can lead to greater errors, my hypothesis here is that the difference between US and foreign students may be related to such garden pathing and not necessarily to math education itself. Such a hypothesis is easily testable.</p></li>
<li><p>The quip about self-esteem, while humorous, does nothing to address the overall problem. Let’s say that many students did get 52 cm but failed to add the 25. Or let’s say that many students simply did not know how to find the length of ribbon around the box. You would do something very different in the first case than in the second. But note that saying the cause of the problem is ‘too much self esteem’ is too vague and unhelpful to address the problem–it could apply to just about any problem–from not knowing how to add, not knowing how to find the length of ribbon, or not interpreting the question correctly. </p></li>
<li><p>I find it interesting that the following are OK to present as the cause of poor performance and open to scrutiny and criticism:</p></li>
<li><p>school administrators</p></li>
<li><p>teacher certification (and by extension, teachers themselves).</p></li>
<li><p>teacher unions</p></li>
<li><p>current pedagogy</p></li>
<li><p>textbooks</p></li>
<li><p>current educational standards </p></li>
</ol>
<p>But to suggest that the test itself may be problematic is seen as ‘hilarious’ and merely providing an ‘excuse’. </p>
<p>To suggest that the cause of the problem is “the focus on self-esteem” or “the same people who are too busy negotiating higher wages, smaller workdays, or more benefits for teachers and administrators, and, of course, making sure to use their financial muscle to elect candidates who will support the further erosion of education in our country” is no more enlightening as to providing a solution as “the test is written poorly.”</p>
<p>All aspects should be subject to scrutiny, including the test itself.</p>
<p>Why is the test itself so privileged that it can’t come under scrutiny? Isn’t the test created by those same poorly certified union teachers who use rotten textbooks, promote some misguided and faddish pedagogy, focus too much on self esteem and don’t have high enough standards?</p>
<p>Skrlvr, at this stage, it might be best to agree to disagree on the issue of ambiguity of the question. While I see the question as very clear and comparable to the typical SAT or PSAT question, you believe it to be ambiguous. Unfortunately, there is no way for me to convince you that I am correct, or … vice versa. </p>
<p>However, when I posted the article, I opined that the excuses used to explain the 68% failure of US students were hilarious and pathetic. For good measure, here were the FOUR items questioned by the Holliday tandem. </p>
<p>
</p>
<p>As best as I can see, the “subtle” problems raised by the authors of the article quoted were about conversion of metric standards, experience with wrapping boxes, experience with tying a box, and relevance of the entire exercise. They did not bring up the issue of a confusing problem statement.</p>
<p>And, yes, I found the attempt to excuse the poor performance through those FOUR items hilarious and pathetic. Fwiw, while I do not agree with a conclusion that the question or the test were problematic, I would have accepted more easily a position decrying the ambiguity of the question --as you did. However, that is NOT what the scholars did.</p>
<p>For the record, I am completely in favor of questioning or scrutinizing every question that appears on a PSAT, SAT, or other test. I have done this repeatedly when looking at questions written by companies such as Princeton Review, Kaplan, and even the ACT, which often suffers from poorly designed questions. </p>
<p>PS The issue of self-esteem versus actual results is a subject often discussed when approaching the TIMMS and PISA test. The origin of the discussion stems from a series of question posed to the student. When asked how well US students *thought *they did, most expressed a high level of confidence. Japanese students, for instance, expressed greater doubts about their perfomance. Unfortunately, for the US, the bravado did not change the results of the tests that hardly matched the confidence of the students.</p>
<p>
</p>
<p>No, again, the box did not show how it was wrapped at the bottom. Furthermore, for a while in my life I assumed the standard procedure was to double tie – go over the same length twice (in order to wrap it up in one loop). Maybe I fail at tying gifts. But that should not affect how I do the problem.</p>
<p>There are multiple solutions.</p>
<p>Now 77 cm was the only valid solution out of the five given, but that does not mean it is the only solution. In fact, the process of elimination is a test-taking technique, not necessarily a show of mathematical skill.</p>
<p>Wow, so how did all those kids from other countries figure out what the question was about? DO you really think they are better at wrapping boxes with ribbons? Or maybe they are better at elementary math after all?</p>
<p>I’m a Singaporean.</p>
<p>The international success rate as I recall, wasn’t that much higher (IIRC).</p>
<p>To me, what would be very interesting to know is how many kids attempted the question and got it wrong, as compared to how many shut down and didn’t try it (even if they marked a bubble). No way to really tell, but I wonder about it.</p>
<p>It plays into an American mental block against metrics.</p>
<p>Sadly, seeing metrics in any problem is enough to cause some weak students to hiccup over it and not even try. </p>
<p>Sadly, their logic isn’t there to recognize that the unit of measurement is irrelevant to getting this answer correct.</p>
<p>Sadly, they have an inability to guesstimate the answer (a spin-off of unfamiliarity with metrics) so the calculated answer can be mentally compared to this thought question, “Does my first answer make sense?” Students are trained to ask themselves this in elementary school, but if they are at sea in terms of the measurement system, they have no reality with which to self-monitor their first calculated answer. </p>
<p>Just creating an illustrative example: students might know feet and yards. If so, and their first answer calculates a kitchen tablecloth measurement length of “20 yards,” they know immediately that can’t be right, so go back to recalculate an answer more like “2 yards of fabric.” (Yes I know about width so please don’t split hairs and follow my main point, please ;)</p>
<p>Although some posters identified the box/ribbon as “a simple addition problem,” it’s a bit more than that, not that it should be beyond a h.s. student. It’s a multi-step word problem that includes some addition and some geometry (or algebra, depending how you want to describe the box). </p>
<p>There’s a host of skills required to teach young kids to approach word problems, including asking themselves “what’s the question really asking?” Approaching word problems is early in math lessons. WIth experience, they gain confidence (NOT “self-esteem,” just confidence with word problems, plain and simple.) </p>
<p>I’m just pointing out a few items where, if fundamental early education in math is weak, the weakness continues throughout high school.</p>
<p>Xiggi’s point is that the authors look to straw arguments, such as pop-on bows (too funny) to explain why the American kids might be less successful than kids from other nations. </p>
<p>I happen to agree with Xiggi that the authors’ article full of straw arguments represents the self-same problem they decry, namely, poor Math education in the USA. Problem is, the authors should be solving the educational problem, not personifying it.</p>
<p>Interesting note, the ambiguity of the question is ambiguous, no one here seems to be able to get everyone here to agree on a singular unambiguous interpretation of the problem. And it is possible for students to slip up on questions in English that are perfectly clear in other languages. Take the word love for instance, we only have one commonly used word for love. Now in ancient greek there were several different words, encompassing most needed definitions. Also don’t forget that english is the only language in which slim chance and fat chance mean the same thing, but wise man and wise guy are total opposites, a cliche I know, but still true.</p>
<p>The correct answer would be achieved in the following way:
4x3 + 2x12 + 2x8 + 25 = 77
Now, if we ignore the 25, 52 becomes the answer, so that is 2 possible answers. If instead the student assumes the answer is the sum of two times each of the side lengths + 25, the equation becomes 2x3 + 2x12 + 2x8 + 25 = 71, another possible answer. And in the latter case if the student forgets to add 25 he gets 46. That gives four out of the five answers can be reached by leaving out some information, or none of it. The last answer of 65 can only be reached by ignoring the inclusion of the height of the box. This last answer, is not excusable, but can be reached, by not going to far off course. </p>
<p>This reminds of a story, its veracity is unknown, about a company that was looking to expand operations and needed to decide between two applicants that they thought were roughly comparable. So the hiring manager gives them a test and calls them in the next day. He tells them that they scored equally well on the test, the exact same 9 problems right, and based on their right answers he can’t make a decision. So he tells them that the decision will be made based on the one question they both got wrong, one person wrote, I don’t know, the other wrote, I don’t know either. </p>
<p>While I don’t know if this story is true, it is telling that so much information can be gleaned from the wrong then the right ones. However, all this test tells us is the percentage of students who got the question absolutely right, not why they got it right or wrong in the case of the wrong students. </p>
<p>Also a student not good at arithmetic could easily improve his chances of getting it right through guessing. 8 and 12 are both about ten, 4 times ten is 40, plus an additional 25 is 65, adding numbers that end in 0 and 5 are fairly easy, and multiplication by 10 is very easy. With the fact that there is still some amount over, that narrows the choice down to two answers 71 and 77, which you have far better odds of guessing correctly then if you could chose between all five.</p>
<p>A very good book for all of you who are interested in the issues discussed in this thread to read is </p>
<p>Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States by Liping Ma </p>
<p>[Amazon.com:</a> Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning.): Liping Ma: Books](<a href=“http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0805829091/]Amazon.com:”>http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0805829091/) </p>
<p>It’s a very thought-provoking book, sure to be interesting reading to anyone who cares about good education.</p>
<p>k as a present wrapper, you have from 1/2cm to a 1cm in the criss crossing of the ribbon, or the potential for that as well as the knot at the top, or is that part of the “bow”</p>
<p>anyone that wraps presents knows this is not such a straight forward question, thus 77 is not the “only” answer and in fact, the 77 is an answer that requires no imagination or reality whatsoever</p>
<p>the 77 is just the simple answer imo…knowing my ds, they would wonder, as would I have, what about the bottom…was it criss crossed, thus increasing the lentht needed or was it cut up or was the bottom half empty, with ribbon just taped at the edges, and what about the unseen sides, are we to assume there is ribbon there, or is the ribbon just taped at the edge?</p>
<p>so imagine if you have a box, and turn it over…you could logically have ribbon just taped at the end, so 77 is not the only vaild answer</p>
<p>it could be 51, because how do we know ribbon is on all the sides?</p>
<p>explain to me why 51 would be wrong in this case</p>
<p>we are to assume the ribbon was all around the box, but the question doesn’t say that</p>
<p>“around” seems to be pretty arbitrary</p>
<p>the question says “as is shown below”</p>
<p>well, as shown below does not show all sides of the box, and thus you cannot, nor should you, assume there is ribbon on all sides, including the bottom, of the box</p>
<p>to do so, is reading more into the question then is actually asked and presneted, and making assumptions about the ribbon that have no factual basis, according to the question and to the actual drawing, is coming up with an answer that is faulty, as it is based on incomplete data</p>
<p>I would be more impressed with a kid who wondered about the unseen portions of the box and the bottom, then one who just assumed there was ribbon there</p>
<p>its the thinking outside the box in this case</p>