The vagueness is seen as a feature, not a bug. The kid is supposed to read between the lines and find out what the problems are really about.
That's straight how my teachers would explain it to us, and you see that line of thinking in the "problem solving" bits where the text is intentionally made harder to decrypt.
Reading skills and shared background assessments are baked into most math tests, even if that's not the focus of it.
> The vagueness is seen as a feature, not a bug. The kid is supposed to read between the lines and find out what the problems are really about.
Pity the poor child who is capable of thinking both inductively and reductively. Such lax testing standards reminds me of the story of the WWII cryptographer in Cryptonomicon who is asked to work out how long a ship would take to travel down the river, comes up with a new theory of fluid dynamics, and flunks the test.
Practically I think that just means that the kids end up getting taught vast quantities of "exam technique" rather than content.
I taught myself the essence of calculus when I was 14 or 15 - there were holes in my knowledge but it took I'd estimate 5 years for regular education to catch up to the intuition I built then (on a houseboat on the Thames even, sounds romantic except for the fumes)
I was homeschooled through 6th grade, entering regular school, it was striking just how "slow" everything seemed.
Conversely, I struggled immensely for a year and a half, once my 3 year lead on material ran out.
The difference in quality and speed in something you're self-motivated to do and are doing at your own pace, versus something you're being told to do at someone else's pace, even with the same person in both cases, is quite astounding.
Or maybe that's the viewpoint of someone with ADD, and most people can keep steady progress _and_ lead balanced lives. I'll never really know.
Yes. Kids moving countries hit that wall at full speed, and have to learn the exam system and quirks on top of the actual content.
The interesting aspect to me was how they need to take a step back and look at it as a set of made up conventions, when they might have just absorbed it as universal truth otherwise.
Depends on the kid. Don't you think?
For some the repetition is the only chance they get to find a pattern.
I think where "traditional" education truly sucks tho (unless you are blessed with a gifted teacher), is giving you an overwiew of how the pieces fit together and what is behind each of them.
I think vagueness is kindof ok in math/physics questions - if you think about it there's usually and interpretation that makes more sense, but I doubt most of them are made that way on purpose.
Where I really hate to see it is humanities e.g. psychology tests/surveys - if after reading a question I immediately think of 3 different interpretations I just think it's a bad test. And if I spend any more time thinking about it I get almost nowhere.
> there's usually an interpretation that makes more sense
Yes, I see it as "background" part, or "common sense" perhaps.
I's funny when for instance you have grocery questions about little Jimmy having 3 bags with 4 buns in each, so how many sausages does he need to make hotdogs with all the buns ?
That's cute and straightforward as long as you know what a hotdog is, which is common sense for the question writer.
I don't think that's something that needs to be (or can be) changed, as long as school and exams are seen as a formative step, and not a single chance you'll have to make a decent living. Kids in the later group will have a hard time either way.
> That's cute and straightforward as long as you know what a hotdog is, which is common sense for the question writer.
Even if you don’t know what a hotdog is, it’s indicated you use sausages and buns to make them. The most straightforward method of doing that would lead to the correct answer.
There may be kids that figure that’s too simple and assume they need two or three sausages per bun, but those will be the minority.
Most sandwiches are made with two pieces of bread. Buns happen to be two-pieces-in-one, which isn't disclosed in the question. Somebody who has passing familiarity with sandwiches but not hotdogs or buns specifically might think it takes two buns to make one hot dog.
Thankfully I think most questions usually aren't like this. Cultural loading in questions is a popular excuse for discrepancies in testing outcomes but those discrepancies have a nasty tendency to persist even when tests are redesigned. Usually there's something else going on which causes the outcome discrepancies, particularly bad parenting.
This has been a huge contention point of Common Core and why so many kids had such huge problems with the overall test. Hard questions that seem/potentially-are vague, but are hard questions first.
Personally, I'm a big fan of what Gates was attempting to do, but I have teachers in my family who couldn't get rid of Common Core from their schools fast enough. Debates with them were never good and me, not being an operator, wouldn't dare tell them how to do their jobs.
But, I understand difficult, standardized testing isn't a good answer, but really how do you get a whole nation to up-skill?
De-centralize and de-nationalize schooling. It's clear the feds have no idea how to make the education system work. Let the states have ~50 different curricula, or individual schools to have ~hundreds or ~thousands of different curricula. Even if they're bad on average, some of them will probably figure out how to make an actually good US school by sheer luck. Once we have that, the others have a model to copy.
> Once we have that, the others have a model to copy.
That is a bold expectation. Some schools will have an incentive to just have as much pupils pass the exam by lowering the bar, other will be incentivized to just teach the bare minimum, others won't have enough money if the model of excellence is expensive (and it probably will be).
And the model that applies to, say, a child who grew up with college-educated parents won't necessarily apply to the child from a blue collar family.
That is just to say that this is a hard problem. My intuition is that the only way to achieve the best education (excluding the case of hypergifted people) seems to be by throwing money at it through personalized education and tutoring and solving the child's other life problems, i.e. the wealthy kid model, but obviously that's not realistic when it comes to mass education. But maybe mass education (at the level we seem to expect from it) isn't realistic.
Or maybe we should reduce the number of subjects taught in school to math, language and physical education.
The problem with trying to make a good school is that strong students pretty much teach themselves and their performance far exceeds any effects from good teaching methods. If any school starts to show decent results then word gets around and it becomes a magnet school. Magnet schools attract wealthy and high-performing students, which totally swamp the effects of the teaching method you're trying to study.
Good teachers unfettered by standardized course plans, when dealing with brilliant students, keep pace with and support those students. If this attracts even more brilliant students, all the better! Then the brilliant students will also support and motivate each other leading to even better outcomes. This is an ideal situation unless you're one of those Harrison Bergeron people who wants to cap high achievers so they don't leave the dummies in the dust.
We really should be prioritizing the brightest students, because their brilliance has the best payoff for all of society. Better to have 100 students who are genuine math wizards and are prepared to continue building on what they know than to have 10000 students who sort of learn basic calculus then forget all of it, with those previous 100 lost in the noise and never given the resources to reach their potential.
On the contrary, standardized course plans are actually the most effective way to provide truly reliable instruction at all levels in a mass lecture/group education format. One key reason why those 100 math wizards don't all become PhD's is that math instruction at both school and university level leads to the proliferation of random gaps in learning where some content just wasn't reinforced effectively. Since math instruction generally builds on previously-learned math, once you accumulate enough of these gaps you hit a wall, and will need remedial instruction (often sought via autonomous self-teaching, of course) to make any progress. The dynamic is structurally the same between the "dummies" and the "math whizs", all that changes is the level at which the problem arises.
Focusing on a standardized course plan that the student is able to learn, memorize and ultimately repeat effortlessly makes it easy to ensure that absolutely everything was reinforced properly.
Congrats: what you’re asking for is exactly how things work now! The feds do not set currricula, each state does independently. Common Core is an opt-in, state-led initiative, which was based on the idea of examining the latest research and practices in education across the country, and adjusting curricula to match.
I haven’t been in public school in 15 years but there was 2 public school districts, a public-private magnet school associated with the State University and a Private Catholic school with radically different curriculum in my hometown. Even between the two high schools in the same district there was different courses and funding because of the property taxes funding specific schools and one school was on the nice side of town.
As far as I understand, most public schools are decentralized, at least the State level, if not further. Are you claiming that is not the case currently?
Except that as soon as someone says 'hey X works, here's the data to prove it's all the rent seekers who have gotten happy with the alternatives will fight against its adoption. When I was younger I used to buy into the 'laboratories of democracy' concept, now I think it's more like 'meth labs of bureaucracy.'
Schools and teachers have ways to make sure improvements don't happen. These include - same pay regardless of performance, not hiring or firing based on performance, and teachers don't want to learn or do anything differently, especially if it's even slightly harder than what they already do. They're not really professionals that improve or have any career growth besides management and accumulating number of years experience. Schools don't care either, nor do governments bother to incentivize them to care.
Except in, say, China, where none of that applies and education works great.
> Schools and teachers have ways to make sure improvements don't happen. These include - same pay regardless of performance, not hiring or firing based on performance, and teachers don't want to learn or do anything differently, especially if it's even slightly harder than what they already do
You can just say unions, no need to beat around the bush. Anyway, I don't really agree. Of course some teachers are stuck in the mud, but other teachers are eager to try new things and improve outcomes. If unfettered by standardization they would be eagerly experimenting with new approaches to teaching their subjects. And if school funding weren't reliant on teachers "teaching the test", then schools would find ways to reward these teachers because it makes the administration look good to have passionate and proactive teachers.
There are problems of course, but they end up with higher levels of education despite that. If a country was serious about education, they could just make it work. I guess having to balance too many competing interests weakens it. We don't want extreme lifetime poverty for school dropouts either, which might be part of what's needed to motivate success.
> Even if they're bad on average, some of them will probably figure out how to make an actually good US school by sheer luck. Once we have that, the others have a model to copy.
How could anyone know that, if each school has its own curriculum and exams? If you got 4 gold stars out of 5 on your reading comprehension and I got three palm leaves out of 4 at literature interpretation, which one of us is getting a better education?
> De-centralize and de-nationalize schooling. It's clear the feds have no idea how to make the education system work. Let the states have ~50 different curricula, or individual schools to have ~hundreds or ~thousands of different curricula. Even if they're bad on average, some of them will probably figure out how to make an actually good US school by sheer luck. Once we have that, the others have a model to copy.
Sadly, we already know what works, individualized/custom attention that exposes the kid to a lot of fields. A worse way to put it, more money == better education. And this is largely true even if specifically wrong.
But once you try to scale that up, everything falls apart.
Which is a big problem I have with these sort of tests. A problem that exists in most I.Q.-like assessments. Rather than evaluating how well the student is able to use their brain it's instead filtering those who were coached to think the same way as the test writers. That creates homogenity which is why I believe there are cultural divides in test results.
Like the Cold War era stories where spies use seemingly innocuous or nonsensical code phrases to identify each other. "The sparrow flies at midnight. Calculate the velocity it would need to reach Berlin in 7 days."
I always found that "feature" annoying because students who knew the material well could fail questions testing its mastery due to imprecise instructions. (My personal pet peeve is not making it clear whether "or" is inclusive or exclusive.)
I can't think of a situation in which "or" would ever be used in an exclusive sense unless it was explicitly called out as an XOR or included "but not both".
That's straight how my teachers would explain it to us, and you see that line of thinking in the "problem solving" bits where the text is intentionally made harder to decrypt.
Reading skills and shared background assessments are baked into most math tests, even if that's not the focus of it.