# DailyDirt: No More Teaching To The Test?

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A Singaporean math test question went viral not too long ago, confusing some people and making others wonder how American kids should be taught math. Plenty of other countries perform better on international standardized tests than US kids do, but it doesn’t always mean the US should adopt other countries’ lesson plans and policies. However, there’s always some political pressure to try to change things (not always for the better). Check out some links on Finland and how it has been working to improve its school system since the 1960s.

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## Comments on “DailyDirt: No More Teaching To The Test?”

Anonymous Coward says:

Just to clarify, this is not a math test. Has nothing to do with math. It’s a logic puzzle.

Different Anonymous Coward says:

# Re: Re:

If you think any given logic puzzle has nothing to do with math you either need to go deeper into logic until you hit math, or deeper into math until you hit logic.

Zonker says:

# Re: Re:

Abstract and Discrete Mathmatics, the highest level of math class offered at my undergraduate college, is all about formal logic rules and mathematical proofs.

Math absolutely has everything to do with logic. The logic gates in your computer before you operate on mathematical logic: AND, OR, NOT, NAND, NOR, EOR, and ENOR logic gates. The basic building block of your computer, the flip flop circuit, is a combination of these logic gates that can mathematically represent one bit of information as a zero or one. The Singapore math test can be solved with a written mathematical proof.

This is why college level Computer Science programs include so much math curriculum, and are often part of the Mathematics department itself.

Anonymous Coward says:

Of what value is learning how to pass a test when you are not understanding that which the test is intended to measure?

Let’s face it, No Child Left A Dime is a complete and utter failure. Attempts to prop it up and claim success have also failed. Maybe it is time to go back to what worked in the past, how much worse could it be ….

Oh wait, I get it now, They are trying to destroy our education system not improve it. Well then, the effort has been a stunning success!

Anonymous Anonymous Coward says:

# Put the tests online

I read or heard (could have been a books on tape thing) long ago about or by Tom Peters, author of In Search of Excellence. He was on his first day as an instructor at some college, and he was in the process of handing out the final exam to his students when another professor, walking by, noticed what he was doing and interjected. Peters’ response was not only was he giving them the final exam now, he was going to spend the rest of the semester, giving them the answers.

Seems to me the whole testing process is a run on game of gotcha, and is more about the test designers making money than the students learning. One of the major functions of a school is to get the students to KNOW the answers.

Anonymous Coward says:

# Re: Put the tests online

Place I work for does the same thing.
They start with an exam on day one of your training but don’t tell you which questions you got right/wrong.

The rest of the training goes as planned.

They then repeat the same test and see how many more questions you got right than previous.

Then they tell you just how much you’ve improved….

And damn if it doesn’t seem to be working 🙂

Ehud Gavron (profile) says:

# Logic indeed

It’s a good puzzle.

One day I hope to foster a society where everyone is clever enough to solve this puzzle

and whip to death anybody who holds a spray-paint can.

E
oh wait, you mean some of them didn’t die? Good at puzzles not so good at whipping then.

Bill Jackson (profile) says:

# It is all about what you are brought up to want.

You want to get laid, you learn to run with the pack, conform and try to be alpha male/female.
As we see, a large portion of our youth do this.
An offshoot of the alpha male path is football = guarantee of plenty of sex.
The girls flock to them = that is what they want, laid and kids.
Our co-ed system is complicit in this.

In Singapore the youth are prevented from these paths by more restrictive parents and social rules. I am not sure how separated the sexes are in Singapore schools?

So if we want to eventually be a nation in decline – carry on.
High school teachers are greedy and incompetent and sacred = can not be fired for being bad.

Richard (profile) says:

# Re: It is all about what you are brought up to want.

High school teachers are greedy and incompetent and sacred = can not be fired for being bad.

Actually what is wrong with the system in the UK is precisely the threat of being fired for being bad. If that is not yet the case in the US then that is the one good thing left in the system

The trouble is that no one knows what “bad” actually is – let alone how to measure it reliably enough to make any use of the results.

In the UK we have used exam results – but the problem here is that when the teacher’s job depends on the students’ results then the students’ results can no longer be allowed to depend on the students.
Since the exam boards are now also “commercial” operations then they are motivated to collude with the schools to corrupt the system. As a University Lecturer I have seen the sorry results of this year by year as the exam scores get better yet the students’ ability to actually understand anything gets progressively worse.

A teacher’s job should be made more difficult to get in the first place, and well enough paid to attract the best. After that however you have to take the risk of trusting those people you have employed to remain professional.

There will always be a few who will take advantage of this – but the alternative is infinitely worse.

Anonymous Coward says:

# Re: It is all about what you are brought up to want.

“High school teachers are greedy and incompetent and sacred = can not be fired for being bad.”

This is in reference to schools in Singapore?

Bill Jackson (profile) says:

# Re: Re: It is all about what you are brought up to want.

No, many schools in the USA. High wages, low performance, protected jobs

eye sea ewe says:

# Teaching how to think and solve what is before you

In my first two years at University, we had a lecturer by the name of Dr. Fitzgerald. He stuttered which at times made his lectures somewhat difficult. The defining feature of him was not his stuttering but the fact that he taught you to methodically work through any problem (from first principles) and get the solution.

He had a eidetic memory and so he never brought in any notes other than the specific problems he was going to use as examples for the lecture. As a result he use to cover blackboard after blackboard with details, much faster than we could copy them down.

One of his favourite activities for us was deliberately making a mistake and then calling for us to determine what that mistake was. This meant we all had to catch up and comprehend what he was doing and hence fix the specific problem.

His semester examinations were always different year by year, but if you learned the processes, methods and principles he taught, you would be able to solve anything he set.

Whereas, other would expect you to learn by rote and just regurgitate the “facts” without necessarily understanding anything of what it was all about.

David (profile) says:

“Teaching to the test” is kind of a stupid phrase. If the test properly covers what was supposed to be taught, wouldn’t “teaching to the test” and “teaching the required curriculum” be the same thing?

Derek Kerton (profile) says:

# Re: Re:

Either way, it’s a negative. We’re supposed to be teaching kids to prepare them for life’s tests. Not for academic tests.

“Teaching to the test” is negative because the focus is on creating the appearance of an education, but the kids may have no clue how to apply that lesson to real world situations.

Richard (profile) says:

# Re: Re:

If the test properly covers what was supposed to be taught, wouldn’t “teaching to the test” and “teaching the required curriculum” be the same thing?

True – Google “constructive alignment” and you will find out that this is part of educational theory. Sadly it rrarely gets applied properly.

The problem is that people set tests that are too similar year by year – and so it becomes possible to teach to the answers rather than teaching to the problems.

When the test setters and the teachers are measured by the exam results then this kind of corruption is inevitable.

Proper education is too risky when your job is on the line!

Anonymous Coward says:

# Re: Re: Re:

“Proper education is too risky when your job is on the line!”

Teachers in the US used to have input when the curriculum was set, now in many districts it is determined by politicians who may lack the credentials and probably lack the motivation to provide an adequate education.

Anonymous Coward says:

# Re: Re:

Teaching to the test is a stupid phrase because the concept is stupid.

Setting the level of education funding to be directly proportional to test results is stupid.

Perhaps you could present your question to teachers, what might they have to say?

Anonymous Coward says:

Trick question: if the student does not show excessive praise to the state of Singapore when they answer, they will be imprisoned.

Ehud Gavron (profile) says:

# Teaching to the test

Often the test focuses on the specific solution to the problem, not how to get to the solution given that problem.

Students [kids, adults, etc.] who are working to ACE THE TEST are working to regurgitate the solution, not understanding the problem, the steps required to solve it, nor how the solution is proven to exclude type-I or type-II errors.

We create tests and we create “grading curves” and “people who break the curve” and we turn education into a competition. Competitive vs cooperative is good for SGE but the lesson from that is that it’s NOT good for the goals of education.

These winners [grow up to] become researchers who repeat this fallacy.

Teaching to the test is not a good thing if our goal is to increase the spread of knowledge [education].

E

Anonymous Coward says:

# Re: Teaching to the test

Yup, in addition, in advanced math one can arrive at the solution in several different ways and a good teacher will give more points for doing it the easy way.

Richard (profile) says:

# Re: Re: Teaching to the test

a good teacher will give more points for doing it the easy way.

Which way is the easiest will vary from person to person.

A good teacher will reward a student whose method of solution displays a greater degree of understanding.

Anonymous Coward says:

# Re: Re: Re: Teaching to the test

“Which way is the easiest will vary from person to person.”

In showing ones work, the difference between one page and three pages is sufficient to determine which way is easiest.

“method of solution displays a greater degree of understanding.”

Correct.

John Fenderson (profile) says:

# Re: Re: Re:2 Teaching to the test

“In showing ones work, the difference between one page and three pages is sufficient to determine which way is easiest”

I don’t think so. “Easiest” is highly subjective as it depends heavily on how the person doing the work thinks. The approach that requires three pages of work may in fact be easier than that approach that takes one page for some people.

Anonymous Coward says:

# Re: Re: Re:3 Teaching to the test

“The approach that requires three pages of work may in fact be easier than that approach that takes one page for some people.”

In that case, those individuals should get credit for a correct answer, but not extra points for understanding the most expeditious or eloquent solution.

Almost anything is better than common core. Considering the author behind most of the history part of it makes up complete nonsense and portrays it as fact.

Lets not forget the infamous and completely illogical math courses.

Anonymous Coward says:

# Re: Re:

I agree that revisionist history is a bad thing. Several states have recently made the news when they decided that AP history was too critical of the US and did not want certain aspects taught. To replace these anti-US items they want things that show how exceptional the country is/was/will be … ad nauseum.

And that new math, what a waste. The only ones who benefit from these new math books are the publishers.

John Fenderson (profile) says:

# Re: Re: Re:

“these anti-US items”

Omitting or misrepresenting the unflattering aspects of US history is, in itself, an anti-US act.

Anonymous Coward says:

# Re: Re:

Considering the author behind most of the history part of it makes up complete nonsense and portrays it as fact.

I’m not sure what you’re talking about. The Common Core has no true history portion. Within the literacy standards are standards specific to history/social studies (e.g., “Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights gained from specific details to an understanding of the text as a whole”), but there aren’t any standards about, for example, the Civil War.

To address your other point, I have seen a lot of poorly-designed math curriculum that’s Common Core aligned, that seems to be primarily the fault of the people writing the curriculum, not the standards themselves. Lousy textbooks/curriculum existed before the Common Core and they will continue to exist after the Common Core is replaced.

I’m not saying that the CCSS are perfect or undeserving of criticism, but criticism that isn’t rooted in fact is meaningless and solves nothing. Blaming the CCSS for textbook writers who have an agenda and/or are incompetent is not going to fix the actual problem.

David (profile) says:

Random idea that came to mind from a couple bits from the article and comments, along with another vaguely related idea on human motivations. Probably won’t ever be applied, but it seemed interesting, and I might as well write it down somewhere.

Right now we take a test and create a ‘grade’ — what percentage of the test did we successfully complete?

So how about changing that to instead create a ‘score’ — not the score we usually see on a test, but a score like you’d get in a video game. A progressively advancing achievement number.

Possible implementation: Every single test given over the course of the school year is exactly the same (with random variations for each individual question, of course). For example (simplified view), 10 questions on addition/subtraction; 10 questions on multiplication/division; 10 questions on fractions; 10 questions on decimals; 10 questions on variable substitution; etc, etc. Adjust to the actual subject as appropriate. Higher tier questions get more points per question.

Each question is given a point rating, and the further into the test you get, the higher points per question. You accumulate points based on the number of questions you successfully answer, with the goal of getting the highest number of points by the end of the year.

You then have a final class grade that’s a composite of your best total score, and the rate of improvement over the year.

For the improvement side, since the test is essentially the same throughout the year, you can then graph the results and see how the student is progressing over time, when they seem to get stuck (plateauing of the score), when they find stuff easy (spike in the score), etc.

The same simple questions are kept on each test, repeated over and over, that the students will answer because even if they don’t give many points each, they’re guaranteed easy points. And that constant refreshing of the basics helps solidify understanding to an instinctual level.

The test is still limited by time, so it’s not just a matter of “do you understand this specific topic, and are able to regurgitate the answer”, but “do you understand this topic well enough to answer it quickly along with all the other stuff you’ve learned this year?”

I’d also suggest making the tests with several dozen variants for each individual question, and have a program that can spit out a randomized version of each test for each student, to make sure it’s not just a test of memorization (as well as avoid some types of cheating).

Anyway, make it so that you’re essentially trying to get a “high score” by the end of the year, and where the actual improvement over the course of the year is just as significant as the final score. You can then use the final score to determine whether someone is qualified to move on to the next course in the subject, and the improvement rate to collect students together with those of similar learning rates.

Note that while technically this is doable with typical scantron methods, I personally find such testing methods cheap and lazy, and would avoid them if possible. It probably wouldn’t work well with the randomized test questions, either.

David (profile) says:

# Re: Re:

Note that the above was just a bit of an idea that related to the test-taking stuff that was mentioned, and I wanted to write it out before I forgot it. On the Finnish educational system side, with more focus on personalization than scores, it’s somewhat of a secondary consideration.

Anonymous Coward says:

The Common Core and now the PARCC tests are facing a lot of criticism, but that is mostly driven by teachers and their union. PARCC is designed to measure teachers more than students, but you have parent groups out there protesting it.

In terms of teaching to the test, if the test measures what the kids should be learning, shouldn’t they be teaching to the test?

It is all about money. Why do our highschools need different curriculum in math at one highschool but a different way in the town next door, or in multiple states? Why are new algebra books coming out regularly, forcing students or districts to buy new ones? Did we suddenly find new thoughts from Al-Khwarizmi?

Education should be about preparing kids for the future, but it is about money.

Oh, and if you are a parent holding your kid out of the PARCC test, if you are not a teacher, you are an idiot.

Bill Jackson (profile) says:

# Re: Re:

No math has not changed, instead something far worse has occurred – the royalty stream has stopped as books are good year after year and unchanging – as it should be – HS math, Algebra and geometry is a stable topic.
So these new books are created and the teachers who wrote them want them sold, the publisher wants them sold…need I say more.
there is a need for a public domain set of math books, year by year, with online ability to read. Such books can have lives in decades and the only changes will be typos etc and wear and tear. That would give books printable in runs of 100,000 or more = low price.

The conflict in the system allows this, even promotes it.
In college you even have profs printing books to sell to students directly.

Max (profile) says:

# Hard, you say?

Not sure what age group that problem was meant for, but even I could solve it with a bit of logical thinking – and frankly I’m absolutely, completely rubbish at math in general and strict logic in particular. The steps to solve it are effectively laid out right in front of everyone, in the wording of the puzzle itself.

The thing to consider is that even back in school when I was slightly better at this sort of thing, I remember finding math olympiad stuff staggeringly hard indeed (never got anywhere with that, told you it’s not my thing). In contrast, if this was considered mind-boggling around the world, I have to take a rather dim view indeed of our ability as a species to use our brain… 🙁

Anonymous Coward says:

In terms of “easy” ways to come up with an answer, have a junior high or high school kid that is brilliant at math come up with the correct answer without showing their work because they did the problem in their head.

See how many points you get for that.

He said if he couldn’t do them in his head then I must be cheating.
Jack Hall: Well, that’s ridiculous! How can he fail you for being smarter than he is?
Sam Hall: That’s what I said.
Jack Hall: [smirks] You did? How’d he take it?
Sam Hall: He flunked me, remember?

Anonymous Coward says:

A major topic taught in math is proof or derivation.
Not sure how one conveys this without showing your work.
Mental telepathy?
Osmosis?
Or maybe the proof is left to the reader? I’m sure that would be welcomed with open arms by the scientific community.