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Comment by danieltillett | Hacker News Reader

The thing I am always amazed by people who developed metrics is they never seem to stop and think how the metric will be gamed and then take action to prevent this. It should be part of the development of any new metric to have a "evil" team work out all the ways the metric can be gamed so this can be blocked.

For example, it should be impossible to "teach the test" other than by teaching broadly the underlying concepts being tested. A well designed test will touch on so many concepts that only a education that is broad will work.

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Why do you assume they don't stop to think about that? People who develop assessments usually think quite rigorously about exactly such problems, assuming they're following proper methods. Is it so surprising to you that this is a very difficult problem?

I would compare this to asking, "Why don't software developers think about bugs?" They do, and they attempt to handle them, but it's almost impossible to solve all such problems in programs (tests) of non-trivial size.

If they did then it would not be possible to “teach the test” other than by teaching the full subject. If there are any shortcuts a teacher can take with the class then the test is a failure.

I used to write tests all the time in my subjects and my tests could not be gamed. I would have half multiple choice questions drawn from every area we covered in the semester and half essay questions where the students had to integrate what they learned into a coherent answer. My students would ask me what they had to learn for the final exam and I would always say everything - if it wasn’t going to be examined there was no point teaching it because the students won’t both learning it :)

Well, then the solution there is to only write trivial programs. Haha.

Though, with enough resources, time, and effort, I think almost any program one would want in practice could be written with a formal proof of correctness. (I won't say every, because that runs up against halting problem / incompleteness things, but I think for almost all that you would actually want)

It's just that there isn't enough demand, and time, for the programs to be proven correct.

If there was a program that we could all stand to wait for a very long time for (maybe even a few generations?), and it was important enough that it be completely free of bugs, that could be done, I think. I'm not sure what it would be that important though. Starship stuff?

20 years ago, a certain chain of fast food restaurants pushed through new metrics to compare different locations by. One of those was which shifts kept drive through average times under 60 seconds.. We got all sorts of recognition and praise.. Nobody noticed that first thing when opening was we ran through 20 or orders through drive through for water (no cost) and closed within 5 seconds. Then intermixed all day between orders, when it was slow.

This is a excellent example of a poor metric resulting from the test developers not thinking about how the metric could be gamed. If they had they could have made sure that they only counted orders over a certain value or even better counted size adjusted orders.

If gaming the metric is a useful behavior, the metric is useless.

Secondary infections in hospitals is a good metric. If you game it, it's still a net win for everybody.

Pass rates in schools is a bad metric. I can improve my metric by getting my lowest students to quit.

Rather than trying to "anti-game" a metric, simply observe if the metric is being gamed. If it is, the metric is a priori bad and should be removed.

> If gaming the metric is a useful behavior, the metric is useless.

That is exactly why you should have a review of how a metric might be gamed, before you accept to use a this metric.

Yes this is 100% true, but the point I was making is if the test writes think first about how the metric can be gamed then they can take action to prevent the gaming including changing the metric and test.

I'm not even sure the voters/parents want the tests to be made harder like that. Then test scores would go down further and schools would have to devote even more time to passing them.

And FWIW, I've looked at the Texas tests and they didn't seem game-able to me. If they were, the "don't teach to the test" rabblerousers would cite them in a heartbeat. But no one seems to follow the logical implication of this argument.

You can make the tests as easy or as hard as you like and still prevent teaching to the test. The pass/fail rate is a function of the effectiveness of the teaching and the difficulty of the exam. If the fail rate is above the politically acceptable rate then make the test easier, just don’t make the test gameable.

I'm sure the teachers would already prefer a quicker way of teaching that also conveys a more general understand and enables the students to pass the test.

But if they already knew this method and could implement it, they would already be doing it.

The problem is the teachers don’t control the test difficulty so they are left with gaming.

There is no quick way of really teaching. Teaching well is a really hard problem that many think is easy. It is not.

You're saying the tests are too difficult? Have you looked at them?

No I am not saying the tests are too difficult, but I am saying that if the failure rate is politically too high then the way to solve this by making the tests easier rather than making the tests gameable.

Of course the best solution is to improve the quality of teaching, but this is a much harder problem.

How do you define "genius" or "satisfactory"?

Education should be taught in a way such that one is exposed to the methodologies by which one should approach problems, rather than solving the problem itself[1]. "Teaching to the test" is awful, I agree. How can one, on a national basis, ensure that every school is affording as equal an opportunity as possible? I'm not being sarcastic - what is the better alternative, the better metric by which we can gauge the performance of both our students and our teachers? I certainly don't think 8th grade math teachers should be penalized for the poor performance of their students if those 7th graders who matriculated into your class on September didn't have a functional understanding of fractions. (Conversely, I think teachers who reached 'tenure'[2] and have clocked out until they've hit that pension-year _should_ be punished). How should those teachers be evaluated? One could suggest "grade the teachers on the improvement of performance of their students compared to their prior years performance" but that brings us back to the same problem -- you have a test. I ask this without snark - how do you test as many concepts at that broad a scope of subject, at that grand a scale (let's start small - 3 districts in NY state chosen at random)? How do you even choose what concepts are important at that broad a level?

[1] This gets into a whole meta-discussion about what the appropriate methodologies are, which I'll leave as an exercise to those doctoral candidates finishing up their dissertations. [2] Tenure as I understand it serves to allow researchers could undergo extensive, perhaps subversive, study to enrich the human body of knowledge while retaining job security. While educators at a grade/secondary school level perform a great service, I fail (heh) to see the purpose it serves at that level.

Well each year should have a syllabus and what the students are expected to know and be able to do (we used to call them rubrics). You just test that the students perform in all the things in the syllabus. The only way to “teach the test” if testing was done like this would be to teach the syllabus which is exactly what the teachers are supposed to be doing anyway.

It's always possible to "teach the standardized test". The only way to avoid it is to make the test subjective and non-standard. But then students who failed will complain that they were treated unfairly.

The key point is that unfair treatment of some students should be considered an unavoidable risk, because the alternative is unfair treatment of all students.

Why don't you Google real Texas or California standardized tests (as opposed to hypothetical badly designed tests) and then list some explicit techniques for "teaching to the test"?

That would be far more convincing than merely claiming teaching to the test is real and can be done in all cases.

Here's an example of the technique for "teaching to the test": the formula you use should include all the numbers in the question. For example, if the question is "find the angle alpha in this right triangle" and gives lengths of the two sides, you know the answer should be some function of these two numbers (and nothing else).

More importantly, non-interactive nature of the test does not allow for follow-up questions. A few follow-up questions on oral exam let the examiner probe a lot deeper in less time, therefore getting a much better picture of student's ability and skill level.

I think a very important part of learning math is learning that it's not magic or memory, it's just mechanical procedure transforming inputs to outputs (and therefore the output must contain the input).

I.e., you aren't just teaching the test, you are also improving understanding.

Now consider a question like "length of alpha, beta=2, gamma=3, a) sqrt(2^2+3^2) b) sqrt(2+3), c) 2^2+3^2, d) 7". Using your heuristic the student can rule out (d) and has a 33% chance of getting the right answer. The test reveals (averaging this over many questions) that they know a little bit, but nothing close to 100%.

The test would reveal that the student knows a little bit about taking the test. The heuristic would still work even if the test was written in Russian and the student did not understand a single word in the question.

Are you suggesting that teachers don’t engage in “teaching to the test” or that they are doing it, but under the mistaken idea that the standardised tests are gameable?

I'm suggesting that I don't think "teaching to the test" (defined as things which increase scores but not understanding) is possible on well designed tests, such as the ones I cited.

I'm sure teachers might do it if they could (shady people teachers are), but don't see any evidence they can.

OK. I certainly agree with you that a good test is not gameable, but the evidence seems to be teachers believe they can game the metric even in CA and TX. This is a problem even if the test is not gameable since the student's time is being wasted.

Edit. I have been meaning to mention that I always enjoy your posts Chris even if I don't always agree with you.

> The only way to avoid it is to make the test subjective and non-standard.

How so? You can make it multiple-choice (objective) difficult, non-algorithmic math problems comprising multiple concepts each and then grade the whole test on a curve.

Impossible to game except to actually teach the students a broad range of math skills and how to problem-solve, while still objective and standard (in the sense that everyone gets the same test and is graded the same).

As a former English as a Foreign Language teacher, I can assure you that there are always ways to game exams in English. Because I had to help some of my students get into university, I took a look at the entrance exams. Even though I am a native English speaker, I found that I could not finish the Todai (top school in Japan) entrance exam for English in the required time. It required reading and understanding very large amounts of text and then answering difficult multiple choice questions at the end. Sometimes the questions were difficult to understand and required that you were really careful about concentrating on the wording.

So instead, I decided to try again (with a different year's test) and instead of reading the material ahead of time, I used the questions to direct my efforts. I would look at all the answers and then scan the text for areas that talked about those things. Having identified those, I then looked at the question and ruled out the answers that didn't seem related. Finally I settled on the answers -- mainly by applying grammar rules mechanically (i.e., a wrong answer would be in the wrong tense compared to the supplied text).

I was able to complete the exam in time and get full marks. I had absolutely no idea what the text said. In fact, I didn't even know what half of the questions asked.

Now for my dilemma as a teacher. If my student gets accepted to Todai, it will basically make their life. You are almost guaranteed to get a good job that will give you the kind of life that most Japanese people are looking for. If I ask the student to try to do the exam properly, by reading the text, they will fail. Even I would fail. I can teach them to pass it in a different way.

What should I do? The test is too difficult. There are always going to be ways to game it and the successful students do. Therefore the test gets more difficult and the students are forced to game it even more. As a teacher, should I tell my student that they can't go to Todai, or should I teach them how to game the exam?

As far as I was concerned, I decided that teaching English and passing entrance exams were 2 different things. I taught English for those students who were interested. I gave up a lot of my free time (a few hours every day) to help them do that. When exam time came, though, I taught no English at all. I taught them how to do what they needed to do to be successful. Every one of my colleagues did the same thing. Probably every teacher in the country does the same thing.

Standardized tests that grade you and decide your future are insane.

It sounds like it's gameable because it's predicatable.

Imagine the next year's Todai entrance exam was totally different and unpredictable (say, transcribing an Eminem song or something similarly off-the-wall), then all the people who studied ways to game last year's exam would be SOL and only the people who actually know English would get in.

That's the kind of system I'm advocating for: get a bunch of smart test writers together with the express intent of coming up with novel ways to destroy the people who game the exams.

The reason they can't reasonably make ungameable tests is that they have tens of thousands of applicants. The need for an easy to mark test is more important than the need for an ungameable test. Otherwise you could simply interview applicants in English. (Todai actually considered this approach, but I understand that they abandoned it as being impractical).

In my more cynical periods, I suspect that they don't mind people gaming the exams. After all, most Todai students don't actually need to speak English (or know crazy details of history, or write thousands of kanji, or whatever). They are more interested in clever students who are willing to study like insane people and practice boring stuff over and over again. That's what you need to do to game the exams. In a twisted way, it works...

Making test questions more difficult won't help. More people will make simple stupid mistakes, so it's going to be more like a lottery. If you forgive simple stupid mistakes, the test is becoming subjective again.

Here's an example of a bad question: what is the area of the right triangle with hypotenuse 10 and height 6 (height is measured from the vertex opposite to the hypotenuse)? It does not test understanding. The optimal algorithm for the student is to parse the question looking for keywords - "triangle", "area", "height", recalling the formula, and plugging the numbers into it to get the answer 30.

The question is from the real test, and by the way, this answer is incorrect. Why it is incorrect is a better question.

Here's an example of a good question: prove the Pythagorean Theorem. You can't answer it by picking the right answer from the multiple choice list. You have to explain your line of reasoning to the examiner and be able to answer question like "why you say these two triangles are congruent". Such interactive process is much better at determining student's skill level, and you can't prepare for it by simply memorizing stuff without understanding.

The student might not like the proof in the textbook and prefer another proof. It take a human to understand whether this other proof holds water.

Ooh yay, a topic I can speak fairly well-informed on.

>> You can make it multiple-choice (objective) difficult, non-algorithmic math problems comprising multiple concepts each and then grade the whole test on a curve.

You do realize that that's what Olympiads are right? https://en.wikipedia.org/wiki/International_Mathematical_Oly... You can be fairly confident the Chinese "teach for the test" to a few handpicked kids who can perform well on those problems (in the same way they select children with an aptitude for gymnastics at an early age). Nearly 20 wins, not one Fields Medal. You can 'teach to the test' at any level up to the 400 levels, at which point you start creating new ways to approach the test, solving problems which weren't solved for a couple hundred years, or founding problems which won't be solved for another couple hundred.

The problem with applying this sort of measuring regime against education or medicine vs. a sales team or IT service operation is that the outcomes are difficult to assess, because he assessments are bogus.

A high quality general education should lead to a good outcome on a standardized test, (Say the SAT) right?

The reality is the complexity of the assessment requires preparation. Without understanding SAT test strategy, you won't do well. When I took AP US History, the difference between a 4 and a 5 (the highest score) was understanding how to "stage" essays for the graders.

Instead of worrying about red teaming standardized tests, we should think log and hard about the cultures being created in these environments.

FWIW, the SAT is a terrible example of a gameable test. Test prep is consistently shown to affect scores by a mere 20-40 points.

> well designed test will touch on so many concepts that only a education that is broad will work.

So you create an education system that's a mile wide and an inch deep.

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