[kenberg]

akwoo, on 2014-June-27, 01:14, said:

Sorry I'm replying so late to this.

First, I think intelligence is something that can be improved with training.

Second, I really think there is no solution (unless you count deciding as a society to limit the technology we will use) that will allow useful employment in large numbers of people not smart enough to be a farmer. If a robot can be programmed to do a job, the robot will be cheaper than any human.

So I think the only possibility is to keep this person in school long enough to get them smart enough to be a farmer. If it takes fifteen years of college, it takes fifteen years. Or we can decide it's not worth it to society to keep trying to educate this person, and that it's better (or at least cheaper) to let them be perpetually dependent. I hope such a decision would be made in recognition of the effects of having a large group of people who are widely regarded, by themselves and everyone else, as people on whom society has given up. (I would hope that, these days, we wouldn't consider just letting this person freeze or starve to death.)

What needs to stop is this business of awarding worthless degrees. All it does is keep people from having an education later on the grounds that, on paper, they already had one.

To begin at the bottom, I enthusiastically agree that this business of phony degrees is a serious problem. Some are more phony than others, but I have seen instances where it's pretty brash.

I also agree that people can learn. We develop our muscles through exercise and we can develop our brains as well. Furthermore, taking some courses in agriculture can provide information, even if it doesn't particularly raise reasoning ability or enhance creativity.

I think where we may, or may not, differ is this: We need to greatly enlarge opportunity for training. This includes college but is by no means limited to college. I have had the great good fortune to make my living in a career that I enjoyed. I'm 75, I am a retired math prof, I am currently working on a math problem with a friend, also retired. No pay, no nothing really, we just enjoy it. But not everyone likes mathematics. Time out for a true story: I was in the barbershop and the barber asked as they do, what I did for a living. "I'm a mathematician," "Oh, I really like mathematics". Not the usual response. He continued "Well, not he hard stuff, like algebra. I really like..." pause for thought "addition. I really like addition." Anyway, I would like to see expanded opportunity for those who not only don't like mathematics but also who are not very academic. This barber's brother owned the shop. I think that they both make a decent living. The barber has a family, owns his house, etc. The owner probably makes a better livingh. I imagine he has some business training. Did he go to college? Beats me.

A farmer today probably needs quite a bit of training that his father would have never heard of.. Sure. So make it available. But going off to a four year college and running up a lot oi debt studying a lot of stuff that is of no interest, maybe we could skip over that.

My own years in college were great. Great for me. I grew up in a neighborhood where my father's eighth grade education was about the norm. Here I was in college reading Aescculus, Dante, Goethe etc and studying mathematics and physics. I thought it was wonderful. But that was me. I am sure that if I ever came home and told my father I was quitting college and was going to become a carpenter like he was he would have told my mother "I was getting worried about the kid, but he has finally come to his senses". My parents were not paying the college bills, so it was completely my choice.

I am not really sure that we disagree. A modern farmer no doubt needs to know a lot of stuff. Soil, business, environmental issues, possibly some legal training. It's so much stuff that maybe a four year college, if it has a good program, is right for a farmer. But others, the barbershop owner for example, needs some business training and some specialized training in styling (not for me, I don't do "styling", my response to "How do you want it cut?" is "Shorter") but for him I think much of college would be, professionally, a waste. If he enjoys it, as I did, then fine. But he may not enjoy it and he may not need it.

My father was born in 1900, a very different era, but even so, as he was reaching retirement, technology was causing issues. The skills you learn when you are 20 may well be outdated when you are 40, or 60. So training and education has to be a lifelong commitment. Both the individual and society has to accept this fact of modern life. A college education, for some, and probably for many, can be part of this. But we need to cast a much larger net.

[akwoo]

You talk about training, but I think technology is going to make training itself mostly obsolete.

When I said someone was not smart enough to be a farmer, I did not mean they did not have enough farming training. I meant that their general intelligence, abstract thinking, reasoning ability, ability to learn, ability to come up with original solutions, et c was not good enough for farming. Even in your lifetime, Ken, I think it's possible we'll see farmers programming their combines to farm some of their fields without them actually sitting on the combine. If you're not smart enough to figure out how to program a 1980s VCR you're not going to be competitive as a farmer. And I explicitly mean 'figure out', not 'have taught to you' because it'll be just like 1980s VCRs; each model will be different and come up with its own weird arcane instructions.

So I think we are going to a society where almost any occupation which is reasonably useful to society is going to require a good deal of reasoning ability and abstract thought. Probably these abilities can be acquired through studying farming rather than literature or mathematics. But it won't be acquired by rote training in specific farming skills.

If we're talking about rote-learned skills, I think we are soon reaching the point that, in most occupations, the skills you learn when you're 20 will be outdated by the time you are 23. At that point rote training is useless.

There is also the political aspect. Many years ago I recall some story about a large number of small New England towns getting themselves into really bad deals with companies coming in to fix and modernize their (I think it was) water systems. Part of the original story was the confidentiality clauses in the agreements, so the towns had no way of finding out that similar deals had worked out poorly for other towns. But I remember looking into some of the details, and it was plainly obvious with any amount of thought that the deals were ticking time bombs for the towns. The problem was that these small towns had no one who could and would read the details and figure out what the deal meant in 5 or 10 years. The state government can legislate and regulate all they want to protect these small towns, but they can't anticipate every possibility, so frankly the best solution is simply for enough citizens to be smart enough to figure this out. This is small town New England, and these were big budget items for these towns, so the deals usually had to go through town meeting with a debate and vote of the whole town. (In small town New England, generally the whole town acts as the legislative and executive authority (i.e. the 'town council'), although a small group is empowered to handle minor or urgent business.) The citizens really did have input and a few townspeople who could and would read these deals would undoubtedly have been able to stop them.

[blackshoe]

It takes quite a bit of smarts to be a farmer, just like it takes quite a bit of smarts (more than in the past) to be a soldier. Technology changes everything.

There are, to my mind, two parts to "education". The first is to give people enough basic knowledge to function in their society. In a democracy that means, among other things, knowing how to reason. The second part is to teach people how to learn on their own. Currently, the system fails on both counts.

[kenberg]

akwoo, on 2014-June-29, 19:09, said:

You talk about training, but I think technology is going to make training itself mostly obsolete.

I take this seriously and to a fair extent I agree. Coping with the modern world, in particular making a living in the modern world, requires quite a combination of abilities. This relates back to Core and includes much else.

I have said, and I mean it with some seriousness, that the best thing that I did in my adolescence was to buy a car. A '47 Plymouth for $175 that needed work. My current car is a 2013 Honda and I know virtually nothing about what is under the hood. But I have confidence that if it became important for me to know about it, I could sit down and learn. No doubt a 2013 Honda is more complex than a 1947 Plymouth, but my early experience points the way.

Part of learning is reading and understanding. Part of it is thinking. Part of it is experience and discussion with others. My hope for a 17-year old is that s/he would have a decent grasp of this interplay, an appreciation of its importane, and some confidence that s/he can handle this. That's a tall order.

Here is a frequent problem (my view of course): Someone, say Core, comes up with some standards, promotes (often correctly) their importance, and there is broad agreement of those in power that this should be done. BUT THEN. Teachers, principals, administrators and so on have ther salaries and jobs dependent on getting good scores. Fair enough, sort of. But how to do this? What happens is that the questions and the answers become very formulaic. Doing well on these exams has more to do with training, using training in the sense that you are deploring, then it does with actual understanding and thought. And so we end up with high school graduates who have passed the required algebra exam but have no idea how to figure the change for a $100 bill if the cashier has inadvertently entered a $20 payment amount into the register.

I, and I think you, have faith that people can learn to think far more effectively if they are given proper guidance. Learning how to do routine tasks correctly is important, much of our lives are routine, but it is not enough. It probably never was enough, but today is is really not enough. . So we need to do a far better job than we do in encouraging independent thought..

It will not be easy. People are diverse in their approach to life, and more than a few are very insistent that learninig consists of memorizing the correct answers to a list of questions, and everything else is a waste of time. By the way, while college is better than high school at encouraging thought, it is far from being a paradise.

Anyway, I think that we are more in agreement here than you might believe that we are.

[kenberg]

blackshoe, on 2014-June-29, 21:17, said:

It takes quite a bit of smarts to be a farmer, just like it takes quite a bit of smarts (more than in the past) to be a soldier. Technology changes everything.

There are, to my mind, two parts to "education". The first is to give people enough basic knowledge to function in their society. In a democracy that means, among other things, knowing how to reason. The second part is to teach people how to learn on their own. Currently, the system fails on both counts.

Yep.

[barmar]

I got a new car last month. I had fun going through all the settings in the onboard computer, which is used for the navigation system, audio system, safety and security features, etc. But I'm a tech geek. I can easily imagine some people being totally overwhelmed by all the technology in a modern car.

And it's going to get even worse when we get the self-driving ones in a few years.

[kenberg]

barmar, on 2014-June-30, 10:31, said:

I got a new car last month. I had fun going through all the settings in the onboard computer, which is used for the navigation system, audio system, safety and security features, etc. But I'm a tech geek. I can easily imagine some people being totally overwhelmed by all the technology in a modern car.

And it's going to get even worse when we get the self-driving ones in a few years.

Indeed. I have had my car fora year and a half and I am still learning all of the features. the owner's manual, just the non-technical stuff written for everyone, is longer than the entire shop manual that i had fro my Plymouth.

I am by no means saying every kid should have a car to care for. This is probably not practical given the modern complexity. I meant it more as an illustration of something that I feel made a big difference in my early lie. I chose it myself, i paid for it myself, i cared for it myself. This was a very useful experience. I wish for a similar sort of experience for thday's mid-adolescent. It doesn't have to be a car, but a self-directed something, a something that he is really interested in, can be a great experience.

[barmar]

kenberg, on 2014-June-30, 11:30, said:

Indeed. I have had my car fora year and a half and I am still learning all of the features. the owner's manual, just the non-technical stuff written for everyone, is longer than the entire shop manual that i had fro my Plymouth.

Yeah, mine is huge as well, and it has a separate manual for the Navigation system. One thing that exacerbated it is that they use the same manual for both the traditional key ignition and the newer button. So every place where they say that you have to turn the key to On, they also have a footnote that says how to do it with the button; I guess they didn't think they could put something at the beginning of the manual that says "Whenever we say X, you should do Y if you have the other system." There are similar multiple explanations depending on whether you have the dual controls option with the computer display. They obviously never expected anyone to try to read the manual straight through -- it was exhausting.

Quote

I am by no means saying every kid should have a car to care for. This is probably not practical given the modern complexity. I meant it more as an illustration of something that I feel made a big difference in my early lie. I chose it myself, i paid for it myself, i cared for it myself. This was a very useful experience. I wish for a similar sort of experience for thday's mid-adolescent. It doesn't have to be a car, but a self-directed something, a something that he is really interested in, can be a great experience.

I didn't write about my car because of that, I brought it up in response to the post about how modern life requires understanding technology, e.g. farmers probably have to know more about programming their combines than about horticulture.

[kenberg]

barmar, on 2014-July-01, 09:17, said:

I didn't write about my car because of that, I brought it up in response to the post about how modern life requires understanding technology, e.g. farmers probably have to know more about programming their combines than about horticulture.

This issue is really fundamental. Akwoo has said, and I agree, that people can get smarter. Such a claim depends on definitions, but in some practical sense I believe it to be true. Still, the world becomes more and more complex.
Example, along the line of discussion. I have a cell phone but it's pretty basic. The new Honda allows me, so it says, to use Bluetooth so that I can use the cellphone inn a hands-free way. I tried to set it up, no luck. I now am reasonably convinced that the (cheap) cellphone I have is incompatible with the technology of the Honda. OK, I don't much use the cell and I can (and I do, I am convinced, it's not just a matter of not wanting a ticket) pull over if I am driving. I'll probably get a different cell eventually but I spent an embarrassing amount of time trying to get it hooked up through the Honda/Bluetooth system.
Example: Lately, but no longer, I had been having trouble with Shockwave freezing my computer. I could unfreeze it but it often closed what I was doing and it was annoying. Shockwave comes from Adobe so I kept looking at their site. Finally I found something about a "Hardware accelerator" and it suggested I disable it. But how to do this? A bit of searching around and voila, the accelerator is not part of Adobe, it is part of Firefox. It's an add-on (which I do not recall ever adding on) and I disabled it. Problem solved. Note; In my search of Adobe I found that there were some issues with Chrome and Shockwave as well. Bottom line: I coped, but it took a while.

Life was simpler in the 1950s, no doubt about it.

Part of being able to cope, including being able to earn a decent living, involves attitude. But there is also a real problem with complexity. If we are really moving into an era where a substantial portion of the population simply is not bright enough to cope, I think we are in serious trouble. I am not yet ready to concede we have reached this point, but I may be wrong or it may be that the time will soon come. To put it as mildly as I can, I would regard this as tragic.

Kathryn Hepburn once said that she thought she was born at exactly the right time and was dying not a moment too soon. I am not that pessimistic, but there are times that I can see her point.

[Zelandakh]

akwoo, on 2014-June-27, 01:14, said:

First, I think intelligence is something that can be improved with training.

I think you misunderstand the definitions. Intelligence is usually defined as general intelligence, i. This is by definition a constant for a given person. Our estimates of i for a person typically come from IQ tests; there is very strong evidence that IQ test scores can be heavily improved with training but this is not the same as your actual intelligence improving.

There is also good evidence that factors affected by i such as learning and memory are influenced by training. One famous early experiment was having Western subjects perform a memory game and comparing with a tribal group. The Westerners scored higher, which was initially taken as an indicator of higher intelligence. Then someone else performed as identical test using items for the test found in the wild as opposed to those found in a Western home. Now the Westerners scored lower and further testing suggested that intelligence levels between the two groups were roughly on a par.

The thing is that you do not have to be smart to program a combine. You have to have learned how to do it. Even a child of below average intelligence will be more effective at using a smartphone than me because they are used to it while I have never owned one. It is the same for farming technology. The farmer will have his son or daughter learn the interface young, just as city kids are learning to use their latest generation of smartphones and tablets. Then they are well placed to take over a farm when the time comes. It is no different from tractors taking over from horses. The bigger threat to farming probably comes from supermarkets collapsing the prices, thus meaning that potential farmers can often earn more for less effort by leaving the land and heading to the cities. But that is a social issue rather than one of education and intelligence.

[kenberg]

Zelandakh, on 2014-July-02, 03:01, said:

I think you misunderstand the definitions. Intelligence is usually defined as general intelligence, i. This is by definition a constant for a given person.

I don't at all see this as being part of the definition. I say this without being able to define "general intelligence". At any rate, I take akwoo (he can speak for himself of course) to be saying that college can develop mental ability in ways other than direct training for a specific job. At least that is my interpretation and I agree with it. I perhaps am more skeptical than he is on some fronts. A person who goes to college intending to get a degree while learning as little as possible will probably succeed, at least with the second part of this. And a person actively pursuing knowledge will increase his mental abilities, whether or not it is called general intelligence and whether or not it is done in college.

As to tests, IQ and otherwise, I am greatly skeptical. When I was a senior in high school we were given a vocabulary test. I did miserably. During my high school years I mostly read Scientific American, books on physics, Hot Rod Magazine, Motor Trend Magazine (I had a subscription to these last two) and Mad Magazine. There were no vocabulary questions on mesons or carburetors. I took a preference test intended to suggest a suitable career. It suggested that I be a farmer. I took an IQ test that also made career suggestions. It suggested semi-skilled labor. It was the "semi" that really amused me. I totally ignored all of this crap. I was, while in high school, better than any of my classmates (I helped some of them) at math, with one (very clear) exception I believed that I was better than anyone I knew, and I enjoyed it enough to pursue it outside of the demands of school, so I figured I should pursue a career in mathematics. But I might have liked farming, I'll never know. I need to get out now and water the strawberries, it's been very hot here.

[kenberg]

My wife, a more determined reader than I, finished Sonia Sotomayor's memoir My Beloved World.

There an aecdote that is perhaps relevant to testing.

I found something online so that I don't have to type it all in:


http://mathhombre.bl...-sotomayor.html

Quote

There was this geometry teacher nicknamed Rigor Mortis. Word had it that she'd been at Cardinal Spellman since before the invention of the triangle ... I was shocked when she called me into her office and accused me of cheating. The basis for her accusation was my perfect score on the Regents geometry exam. No one in all of her centuries of experience had ever scored a hundred on the Regents.

"So who did I cheat from?" I asked indignantly. "Who else got a hundred that I could have copied from?"

She looked flummoxed for a moment.

"But you've never scored higher than eighties or low nineties on the practice tests. How could you get a hundred?"

The truth, as I explained, was that I'd never once got an answer wrong on the practice tests; points had been deducted only because I hadn't followed the steps she had prescribed. I had reasoned out my own steps, which made sense to me, and she had never explained what was wrong with them. On the Regents exam we only had to give the answer; no one was checking the steps. What happened next truly amazed me. She dug out my old tests and reviewed them. Acknowledging the validity of my proofs, she changed my grades. Even Rigor Mortis, it turned out, wasn't quite as rigid as all that.

Perhaps there is some value in exams where the students are graded not only on whether they were able to solve the problem but also on whether or not they used the method that the teacher preferred. I am skeptical of this view, but I won't dismiss it. However, with large scale tests where one teacher teaches his/her preferred method and another person grades on the grader's preferred method, this has obvious dangers. The Regents Exam was sensibly designed so that the student who got the right answer was given credit for it. It takes some effort to design a test so that the student is unlikely to stumble into a right answer without actually understanding the problem, but largely it can be done.

As long as the test is prepared, administered and graded by the teacher, I have no problem, within broad limits, of just how this is done. I believe teachers should do as they think best (a somewhat old-fashioned view, I guess). But a high stakes common exam for everyone throughout the state or nation should be designed so that everyone is comfortable grading on whether the student did or did not submit the right answer. I realize that not everything in life is so simple that we can say "this is right, that is wrong" but for these exams, the scoring must be done in this way. That's if we have to give the damn things at all.

[barmar]

kenberg, on 2014-July-12, 07:07, said:

Perhaps there is some value in exams where the students are graded not only on whether they were able to solve the problem but also on whether or not they used the method that the teacher preferred. I am skeptical of this view, but I won't dismiss it. However, with large scale tests where one teacher teaches his/her preferred method and another person grades on the grader's preferred method, this has obvious dangers. The Regents Exam was sensibly designed so that the student who got the right answer was given credit for it. It takes some effort to design a test so that the student is unlikely to stumble into a right answer without actually understanding the problem, but largely it can be done.

It depends on what you're trying to teach. If you're teaching a specific process, such as long division, the student needs to demonstrate that he has learned the process. Just giving the answer, without showing your work, doesn't demonstrate that.

As an analogy, imagine a cooking school, with a test on baking. If the student just turns in a cake or a sheet of cookies, you can't tell whether he's actually learned how to bake from scratch -- he might have made it from a prepared mix.

[kenberg]

barmar, on 2014-July-12, 21:30, said:

It depends on what you're trying to teach. If you're teaching a specific process, such as long division, the student needs to demonstrate that he has learned the process. Just giving the answer, without showing your work, doesn't demonstrate that.

As an analogy, imagine a cooking school, with a test on baking. If the student just turns in a cake or a sheet of cookies, you can't tell whether he's actually learned how to bake from scratch -- he might have made it from a prepared mix.

There definitely are times when we want to teach a specific skill, carried out in a specific way. I think most of the time however we have different goals. I have not been following all of the debates here in Maryland but we appear to be switching from the MSA (Maryland School Assessment, I think it is) and HSA (High School Assessment) exams, aligned I think with NCLB, to exams aligned with Common Core. At any rate, the Maryland Department of Education refers us to the PARCC (Partnership for Assessment of College and Career Readiness). This, I gather, is a consortium of several states trying to set standards.


Earlier there were requests for sample problems, PARCC provides full sample tests:
http://www.parcconli...practice-tests.


I took the entire Algebra 1 test, two parts. I regard it as a substantial test. I brought up the Geometry test and took the first part, seven questions. It is also substantial. There is a longer second part I haven't looked at. By substantial I mean that if we are going to expect future farmers, plumbers and taxi drivers to do well on it, I think that the teachers will have their work cut out for them.

For example
Question 7 on the geometry exam gives the points A(1,-2), B(1,0.5), C(2,1), D(4,-3), E(4,2), and F(6,3). : The students are told that triangle DEF is the image of triangle ABC under a dilation, and asked to find the center and the scale factor of the dilation.

Now there is more than one way to do this, including trial and error since this one is multiple choice (not all questions are multiple choice and I don't really see why this one is, but it is). Even trial and error requires some knowledge, although I assume that is not what they hope to be testing so it would have been better to have students put in the answer. I am going to go out on a limb and guess that some WC Forum posters cannot work this problem. We are having an election this fall and I think it would be amusing to ask the candidates if they can work this problem.

Of course students can be taught to work this problem, but there are many problems.

I would be very interested in hearing from teachers as to whether their students can, in large numbers, work this problem. Ditto for the other problems.

[hrothgar]

kenberg, on 2014-July-13, 05:58, said:

Question 7 on the geometry exam gives the points A(1,-2), B(1,0.5), C(2,1), D(4,-3), E(4,2), and F(6,3). : The students are told that triangle DEF is the image of triangle ABC under a dilation, and asked to find the center and the scale factor of the dilation.

Now there is more than one way to do this, including trial and error since this one is multiple choice (not all questions are multiple choice and I don't really see why this one is, but it is). Even trial and error requires some knowledge, although I assume that is not what they hope to be testing so it would have been better to have students put in the answer. I am going to go out on a limb and guess that some WC Forum posters cannot work this problem. We are having an election this fall and I think it would be amusing to ask the candidates if they can work this problem.

I've long felt that Presidential Candidates should be forced to take GREs and have their scores published as part of the vetting project.

With this said and done, I had never heard of applying scale or dilation to a triangle, however, I'm pretty confident that I worked out the right answer in a few seconds. (Its really easy to look at the coordinates and see the parallel line segments). The only complicated part was double checking whether there was any rotation...

[kenberg]

hrothgar, on 2014-July-13, 07:16, said:

I've long felt that Presidential Candidates should be forced to take GREs and have their scores published as part of the vetting project.

With this said and done, I had never heard of applying scale or dilation to a triangle, however, I'm pretty confident that I worked out the right answer in a few seconds. (Its really easy to look at the coordinates and see the parallel line segments). The only complicated part was double checking whether there was any rotation...

Yes, I don't have a doubt in my mind that you could do this quickly. Same for several others who contribute. I am guessing though that some thoroughly intelligent people would have little idea of how to approach this. Not just farmers and plumbers but, quite possibly, governors. And heads of state education departments. Now this does not either disqualify the person to be governor or disqualify the question as an exam question. Still...

Here is a scene that I have often seen play out: Everyone agrees that high standards are a good thing. So we set some. Then it becomes apparent that quite a few people will not meet these standards and therefore not graduate. So then we set out to see how we can get them through this stuff. It's remarkable how much can be done to get students through an exam, without them much understanding what is going on, by Pavlovian training. You set very tight limits on how a question is phrased and specify exactly what can get asked, and then you set out to train the kids. At one time, for questions on adding fractions, there was a short list of allowed denominators. Knowing how to add 5/7 to 3/11 was not a required skill.

If we can really get students to understand geometry and algebra well enough so that they can do well on tests such as these, I will be delighted. I don't mean getting a thirteen year old version of you through, I mean getting a replica of my friend Fred the future plumber through. And, on that score, Fred was no dummy. We were in Minnesota, where all of the children are above average. But he did take shop math, not algebra. Was he really up for dilations? I don't know.


Anyway, Common Core is a very live topic around here. I am hoping I can contribute concrete suggestions, something beyond "Common Core is good because it has good intentions" or "Common Core is bad because it is different so who needs it". First I have to grasp what really is involved. So far, looknig at the PARCC questions, it is clear to me that considerable thought has been put into them. I believe that the PARCC questions are an attempt to implement Common Core, although I am not even completely sure of that.

[Elianna]

kenberg, on 2014-July-13, 05:58, said:

At any rate, the Maryland Department of Education refers us to the PARCC (Partnership for Assessment of College and Career Readiness). This, I gather, is a consortium of several states trying to set standards.


...

I would be very interested in hearing from teachers as to whether their students can, in large numbers, work this problem. Ditto for the other problems.

PARCC and Smarter Balanced are the two test makers (and are basically private companies) that have vied with each other to have states sign up with them for testing. (These tests being private is another thing that has people upset about CC.)

It's interesting to compare PARCC with SBAC (the one that CA signed up for). SBAC has only one test for HS - in 11th grade covering Alg 1, Geo, and Alg 2. We're working out how to test at the end of the year so that we know how students are doing BEFORE the big test.

As to whether my students could solve that problem, I honestly highly doubt it. Especially since they would be taking it at least one year after they've had Geometry. I would guess that many would do it with trial and error if they could do it.

[kenberg]

Elianna, I was hoping you would weigh in on this, thank you. And I would be glad to hear from other teachers.

A word or two about the dilation problem: It's not clear to me what exactly they have in mind. As Richard essentially notes, the line AB is parallel to the line DE, and the segment DE is twice as long as the segment AB. Starting with this, you can move quickly through the problem Still, when I see a sample question such as this, I expect that the intended message is that students will be expected to find the center and the scale factor in many general situations. Moreover, the less mathematically talented students expect questions to test their ability to apply a general procedure rather than their ability to pick out a feature unique to the problem.


Along these same lines, take a look at geometry problem 2. There is a picture of a trapezoid, the bottom and the top parallel, the sides not. There are two lines r and s meeting at a point P inside the trapezoid. We are told:

The lines r and s are perpendicular. Line r is parallel to the bases and bisects both legs of the trapezoid. Line s bisects both bases of the trapezoid.

We are given a list of 5 transformations and told to select all of those which carry the trapezoid onto itself. Now here a clever test taker could observe that four of the five quite obviously don't take the figure onto itself so probably the remaining one is the right answer (in general, these "select all that apply" often have more than one choice that should be slected but I didn't see any where no choice should be selected). But if we really are to see why reflection in s takes the figure onto itself we presumably need to reason that it suffices to check that the two lower vertices are interchanged and the two upper vertices are interchanged, and that this follows from s being a perpendicular bisector (and they must know why s is perpendicular to the bases, we are not directly told that) of each of the two bases. Simple enough, or simple enough for you, for me, for Richard, but is it really simple enough for a random 13 or 14 year old in a geometry class that s/he is taking because s/he must, rather than because s/he enjoys it? (Edit: I recall now that I was 15 when I finished geometry class.)


Anyway, there are quite a few people that are pretty up in arms about all of this. Some years back, Maryland put a system of statewide exams into place. After some pushing, some shoving, some adjusting, they got something that people are more or less accepting of. And it seems to help. I saw something put out by NAEP that ranked Maryland as the top state for improvement based on the NAEP exams, and somewhere else Maryland was in the top ten, maybe sixth or so, for their test scores. So resistance to change here is not all just smoke. A lot of work went into the exam structure that we have, including aligning the courses with the exams. Starting over with a new exam structure is not something to be taken lightly. Still, the PARCC questions seem pretty decent to me. Hard, for a general population, but decent for content.

I think that the decision to go with PARCC is now a fait accompli, but there is considerable pushback so who knows? Honestly I am not sure where I come down on this. It's a big deal, I think. Or, to quote our Veep on a different matter, a big....deal.

[hrothgar]

kenberg, on 2014-July-14, 07:30, said:

Simple enough, or simple enough for you, for me, for Richard, but is it really simple enough for a random 13 or 14 year old in a geometry class that s/he is taking because s/he must, rather than because s/he enjoys it?

I don't expect every person who takes a test to get every question correct...

If you make the questions too easy, you have no ability to differentiate between the students on the right hand tail.
If you make the questions too hard, you can't differentiate between your C, D, and F students.

One of the consequences of this is that there are going to be questions that the average 14 year old doesn't get right or will take too long to solve...

[kenberg]

Yes, a good point, at least potentially. With the current (or the until recently current) version of Maryland's test, the main purpose and possibly the only purpose is/was to determine minimum competency. You need to pass the thing or you can't graduate from high school. As I think I mentioned earlier, my granddaughter, and I think most opf her classmates, got the math exam out of the way at the end of eighth grade, so these minimal requirements are in fact minimal. The kids got grades, but not from these exams.

So it all depends on purpose. If they are going to sort into failing/basic/proficient/advanced then indeed they need some tough questions. I need to check on how these are to be used.

This testing business is intricate.