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<p>In English maybe, but in Spanish a pre-primary school student won’t have a clue what you’re saying if you told him/her “Creo que lo sepas.”</p>
<p>(which means “I believe that you know it” and uses the subjunctive, which is why the kid won’t understand until he has formarlly learned it)</p>
<p>But I guess that problem doesn’t really exist for English, considering that the subjunctive is so rarely used while in Spanish it’s used almost as much as the indicative.</p>
<p>The English subjunctive is used frequently enough, especially in its popular form, “was”. (It hasn’t been lost, only modified.) </p>
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<p>Remember, correlation != causation</p>
<p>I would hypothesise that he would learn it even if he had never been formally taught it – it’s just that the principles of subordinate clause inflections would take more time to acquire. </p>
<p>It seems like it’s just begging for a Spanish version of the Wug test. :)</p>
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<p>Which IMO makes for a badly-worded question.</p>
<p>True galoisien. I always thought that we were just using the subjunctive form incorrectly or forgoing it completely when we say “was.” </p>
<p>Oh, and correction to my example: “No creo que lo sepas.”</p>
<p>Heh, do you add “no” because it’s the Spanish version of the French ne-expletif? (Which is becoming mostly literary in the French language itself…)</p>
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<p>Nah, some prescriptivists just don’t like change. 
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<p>Note that many supposed “losses” in language trends aren’t really true losses – they are replaced in other ways. If a language needs to express a fine distinction in an area, it will create a means. Note that for example, English doesn’t really have a true future tense – nor do most (if not all, IIRC) of the Germanic languages. We use an auxiliary periphrastic form “will”.</p>
<p>The use of subjunctives outside hypotheses like “if I was a wealthy girl…” (or “were,” if one feels that much of a need to be a pedant towards Gwen Stefani) is way less utilised in English than in other IE languages, but a periphrastic equivalent can be achieved by modal auxiliaries like “should” or “may.” Basically this follows a larger historical trend in English to be less synthetic and more analytic – that is, use more free morphemes and less inflection. (You must also pardon me as I’m not sure how familiar you’re with linguistics; if you don’t get these terms, do ask me to clarify them – don’t follow their literal senses!) </p>
<p>Where in the 13th century or even the 17th century we might have used the subjunctive for many of our subordinate clauses, we today prefer, “The principal said we should clean up…” or have the subjectivity stored in the infinitive following specific verbs (“he said to clean up”), rather than a sentence like, “He demands we clean [subjunct.] up”.</p>
<p>Hi, galoisien, do you think visually? You’ve got quite an interest in linguistics.</p>
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<p>Are you always this dense or are you trying to demonstrate your absolute lack of understanding of the format of international standardized tests? May I suggest you do make a modest effort in learning about them? </p>
<p>Or, as an alternative, you might follow a less serious path and watch the Monthy Python sketch on arguments and contradictions. It’s eerily similar to some of the exchanges in this thread.</p>
<p>[YouTube</a> - Argument Clinic](<a href=“http://www.youtube.com/watch?v=T_e8ETqWjdI]YouTube”>http://www.youtube.com/watch?v=T_e8ETqWjdI)</p>
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<p>xiggi: No, the point that you didn’t address is that at least until you hit Riemannian manifolds and n-dimension packing problems, mathematics tests should not be sight-dependent, nor should a problem be dependent on a diagram. Having a diagram can help a lot of course, but it shouldn’t be absolutely critical to solving the problem.</p>
<p>Believe me, I’ve bashed America’s education system myself, and there was a time not too long ago when I was ranting on how Singapore mathematics was better than the atrocious mathematics education I was receiving in my sophomore/junior year of high school. I have made the same overgeneralisations in the past. I’ve come to realise the situation and root causes are actually very complex, and far from, “Oh, our politicians simply don’t have the will,” etc. </p>
<p>Besides, your argument seemed to assume a curious sort of relativism in mathematics, which is far from what we want to aim for. It doesn’t matter if 90% of countries are okay with a particular type of question with ambiguous wording – it does not change the fact that the problem could be worded better. Math isn’t democracy.</p>
<p>Galoisien, there is no need to introduce such a pedantic level of mathematical erudition in a debate about a math test that targets 15 to 17 years old students. After all, this is not about Weill, Nicolas Bourbaki, or Georges Papy --to please your francophile references-- … it’s all about tests of simple arithmetic and geometry that, just like the SAT, most 8th graders should solve. </p>
<p>And yes those tests combine reasoning, reading comprehension, logic, and visual interpretation.</p>
<p>And, by the way, the “fact” that the problem could have been written better is not a fact. As Daniel Patrick Moynihan said: “Everyone is entitled to his own opinion, but not his own facts.” Even an erroneous one like yours in this case.</p>
<p>tokenadult: Ehh I don’t really subscribe to the whole “thinking visually / verbally / mathematically” kind of thing (though I do believe in the overall idea of multiple intelligences). To me the nature of each individual’s thought is far more complex and deserves more than to be put into convenient Aristotelian-esque classifications (but that’s just my opinion). </p>
<p>I had a rather long debate with a friend over Wittgenstein a while ago (a year ago, actually) over the nature of words and pictures. One thing I realised that a distinction between different “styles” of thinking can be sometimes superficial. Symbolic thought is so intimately connected with both language and visual depiction that I wonder if it’s really meaningful to distinguish the two (in terms of thinking – I agree it’s useful to distinguish their different expressions).</p>
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<p><em>sigh</em> </p>
<p>You don’t get me.</p>
<p>It’s precisely because it’s a test for 15-17 year-old students that the problems should not <em>rely</em> on a diagram to tell its story. Good problems can be solved without an accompanying diagram from the problem-setter (though it may be less convenient).</p>
<p>Please do not take me for a pedant. I’m not actually a francophile (I just study French) – my love actually lies in cosmopolitan cultures like one would find in Iraq (before the war, anyway) or Algeria.</p>
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<p>Any problem that can be interpreted ambiguously without a diagram is a badly-worded problem and is “problematic.” It is also an issue that is relatively easy to correct. This is prima facie self-evident.</p>
<p>Why do we have such precise definitions of what it means to have complementary/supplementary angles, to be perpendicular, parallel, have vertices and so forth? It’s so we can describe mathematical situations in words with little ambiguity, which is critical for proofs if you’re not submitting a purely visual proof.</p>
<p>Mathematics should test spatial interpretation, not visual interpretation. The former is quite reasonable. The second is unnecessarily exclusive.</p>
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<p>A: I told you once.
M: No you haven’t.
A: Yes I have.
M: When?
A: Just now.
M: No you didn’t.
A: Yes I did.
M: You didn’t
A: I did!
M: You didn’t!
A: I’m telling you I did!
M: You did not!!
A: Oh, I’m sorry, just one moment. Is this a five minute argument or the full half hour?
M: Oh, just the five minutes.
A: Ah, thank you. Anyway, I did.
M: You most certainly did not.
A: Look, let’s get this thing clear; I quite definitely told you.
M: No you did not.
A: Yes I did.
M: No you didn’t.
A: Yes I did.
M: No you didn’t.
A: Yes I did.
M: No you didn’t.
A: Yes I did.
M: You didn’t.
A: Did.
M: Oh look, this isn’t an argument.
A: Yes it is.
M: No it isn’t. It’s just contradiction.
A: No it isn’t.
M: It is!
A: It is not.
M: Look, you just contradicted me.
A: I did not.
M: Oh you did!!
A: No, no, no.
M: You did just then.
A: Nonsense!</p>
<p>How ironic, considering you’ve spent most of this thread directly evading the point and insulting those who disagree with you.</p>
<p>How hard is it to correct a problem’s wording to be unambiguous without a diagram? What’s with your constantly defending otherwise?</p>
<p>Galoisien, what “point” was there to evade? The inexistant point you have been trying to make without any success? Your point of contention is that the question was poorly written. </p>
<p>You claim that there exist some ambiguity in the TEXT when there is none. </p>
<p>The question was **extremely **clear in that a student should **add **the length of a tape wrapping a box to the 25 centimeters. </p>
<p>Fwiw, the reason there was a need for a diagram is that the diagram DID show how the ribbon was placed. This was necessary to avoid anyone attempting to solve the problem by wrapping the ribbon in a different manner such as diagonally.</p>
<p>Again, anyone with a modicum of knowledge of the design of tests should know that. Sorry!</p>
<p>Non-existent, you mean. Whatever.</p>
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<p>Yes, extremely clear. <em>rolleyes</em> This is truly cultural fossilism as its best, as only culture dictates why I can’t wrap the bow in a manner the text didn’t rule out. There exist at least multiple solutions according to the TEXT, and yet the problem only accounts for one. Hardly extremely clear. </p>
<p>Btw, I’m currently using lynx (a commandline browser), so I can’t see any image at the moment. Your abuse of me (and your smug attitude against the sightless, for that matter) has been entirely unfair. </p>
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<p>You have to describe the bloody picture more clearly.</p>
<p>The key issue I was first wondering of was lengthwise versus breadthwise.</p>
<p>Did the verbal problem even specify “ONLY AS IN THE DIAGRAM PROVIDED” – how are we supposed to know that isn’t only one of the possibilities? </p>
<p>Any math-thinking person would realise right away that the verbal problem immediately suggests the presence of multiple solutions.</p>
<p>Also, as I have been in both the American and Singaporean systems, please stop thinking that malcomprehension of this problem would be an issue specific to America. The Singapore PSLE (a primary school exam!) would have better standards than this.</p>
<p>Look, Evariste, the image has been one click away. Here’s the same link that was made available in the original post. </p>
<p><a href=“http://www.education.umd.edu/news/timssarticleholliday.pdf[/url]”>http://www.education.umd.edu/news/timssarticleholliday.pdf</a></p>
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<p>Feel free to continue this debate without me.</p>
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<p>Never mind a bloated pdf … </p>
<p>Anyway, look – the problem has several interpretations:</p>
<p>Only along the length of the box: 2(12 + 3) + 25 == 55 </p>
<p>Only along the breadth: 2(8+3) + 25 = 47</p>
<p>Both: 25 + 2(8+3) + 2 (12+3) = 77 </p>
<p>But already you can see the key flaws of this problem. Firstly the problem (as I have heard it so far, since lynx usually doesn’t load images) doesn’t say ONLY according to the diagram. Secondly, the problem doesn’t qualify that there will be alternative solutions that aren’t in the answer set (47 and 55 – and imagine if they were present as alternate options! From which interpretation would a blind student choose!). Thirdly, it’s plainly absurd to tie across both the length and the width with one ribbon without some major acrobatics that will require way more than 77 cm.</p>
<p>Creative and intelligent students (especially since many of tricky problems require creativity and constant realisations of all approaches to a problem) could easily be tripped up by this problem.</p>
<p>I also love your posting of one-liners. Your posting of Argument Clinic is (as I have observed) ironic.</p>
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<p>This is just so funny - this whole “relevance” issue… Isn’t math supposed to be about the ability to think abstractly?</p>
<p>Also, I remember all those 4th grade math problems we used to have to solve about a pool that was being filled from two pipes that pumped water at a different rate… It was not in the US, so no one complained that 4th graders do not pump water into pools, and most of us could solve those just fine…</p>