[mycroft]

 Cyberyeti, on 2014-May-26, 05:55, said:

It's terribly easy to get this wrong, what's half of 2 + 2 ?

2 ⫞ ?

Spoiler

sorry, did you want the top half?

[barmar]

The only test I remember taking in grade school that had a "trick" to it was the one that begain with "Read the entire test before answering any questions." The trick was that at the end of of the test there was an instruction saying to answer only question 1. So if you just started in answering all the questions, it meant you didn't properly follow the first instruction.

While the wording of some questions may not be perfect, if you just interpret them according to normal common sense you'll usually come to the right conclusion. Like the question about credit cards. Deciding that b is the correct answer because they say "accrued interest" rather than "accrual of interest" means you're expecting it to be a trick question based on grammar, not a normal question about how credit cards work. Basically, unless the question is something like "Which of the following is has correct/incorrect grammar?", I wouldn't expect a detailed grammatical analysis to be necessary.


Regarding the reindeer question. The right way for reading comprehension tests to be worded is to start with something like "Based on the text you've just read, answer the following questions." It's been a while, but I think that's how the SAT English Comprehension tests were written. So if the text says that reindeer are the largest deer, you can't argue that "moose" is the correct answer -- it may be true, but this isn't a biology or zoology exam, it's a reading exam, and you're supposed to show that you understood what you read.

[blackshoe]

 gwnn, on 2014-May-26, 16:31, said:

Anyway, moving on, I was very much serious in that in my opinion, linguists are better equipped to interpret day-to-day communication than logicians. (I am unable to provide evidence for this and your opinion may well differ. I don't think it's a kind of statement that is easy to (dis)prove with concrete evidence, anyway)

What you said was "logicians describe how people ought to think and speak in an ideal world that is nowhere to be found in our galaxy". First, I don't know that logicians actually do that - sure they describe what logic is and point out the illogic in some speech or writing, but I don't think I've ever seen one try to define an "ideal world" where people think and speak in the way the logician thinks they should. IAC, the thrust of my objection was that you cannot have evidence that your statement about "nowhere to be found in our galaxy" is true - unless you've been everywhere in our galaxy or know someone trustworthy who has. I will grant that the assumption is probably pretty safe but it's still an assumption.

I do agree that linguists are generally better equipped to interpret day-to-day communication.

[PassedOut]

I thought of this thread when I read this article today: How Bill Gates pulled off the swift Common Core revolution

Quote

Bill Gates was de facto organizer, providing the money and structure for states to work together on common standards in a way that avoided the usual collision between states’ rights and national interests that had undercut every previous effort, dating from the Eisenhower administration.

The Gates Foundation spread money across the political spectrum, to entities including the big teachers unions, the American Federation of Teachers and the National Education Association, and business organizations such as the U.S. Chamber of Commerce — groups that have clashed in the past but became vocal backers of the standards.

Money flowed to policy groups on the right and left, funding research by scholars of varying political persuasions who promoted the idea of common standards. Liberals at the Center for American Progress and conservatives affiliated with the American Legislative Exchange Council who routinely disagree on nearly every issue accepted Gates money and found common ground on the Common Core.

One 2009 study, conducted by the conservative Thomas B. Fordham Institute with a $959,116 Gates grant, described the proposed standards as being “very, very strong” and “clearly superior” to many existing state standards.

Gates money went to state and local groups, as well, to help influence policymakers and civic leaders. And the idea found a major booster in President Obama, whose new administration was populated by former Gates Foundation staffers and associates. The administration designed a special contest using economic stimulus funds to reward states that accepted the standards.

The result was astounding: Within just two years of the 2008 Seattle meeting, 45 states and the District of Columbia had fully adopted the Common Core State Standards.

The math standards require students to learn multiple ways to solve problems and explain how they got their answers, while the English standards emphasize nonfiction and expect students to use evidence to back up oral and written arguments. The standards are not a curriculum but skills that students should acquire at each grade. How they are taught and materials used are decisions left to states and school districts.

With my sons out of school, I hadn't focused on how the Common Core had been developed and implemented, so lots of the information in the article was new to me. Surely something needs to be done to improve US education, particularly in the area of drawing conclusions based on evidence and reason. I hope this approach helps.

[kenberg]

 PassedOut, on 2014-June-08, 07:44, said:

I thought of this thread when I read this article today: How Bill Gates pulled off the swift Common Core revolution


With my sons out of school, I hadn't focused on how the Common Core had been developed and implemented, so lots of the information in the article was new to me. Surely something needs to be done to improve US education, particularly in the area of drawing conclusions based on evidence and reason. I hope this approach helps.

I also heve not been following it closely, I also hope for the best. As with so many things, a lot depends on interpretation and implementation. Based on experience, I am concerned about "explain how they got their answers".

I have encountered more than few people who have very rigid ideas about what the correct explanation should be. There are a great many students taking the test, and so a large supply of graders is needed. More often than you might think, "correctly" explaining how the answer was obtained means conforming rather rigidly to something that has been put on a list of acceptable explanations. I have not kept close track of the story here in Maryland, but I am pretty sure that there has been a significant reduction in the number of "explain your reasoning" questions. This is not because anyone is opposed to reasoning, rather it comes from the difficulty of fairly and consistently evaluating responses with a large number of test takers and a large number of test graders. Perhaps they can cope with this, but it is tougher than it sounds.

Imo, the best way to test and encourage reasoning is to give problems where getting the right answer requires careful reasoning.

[PassedOut]

 kenberg, on 2014-June-08, 15:29, said:

Imo, the best way to test and encourage reasoning is to give problems where getting the right answer requires careful reasoning.

I certainly agree. My interpretation of:

Quote

The math standards require students to learn multiple ways to solve problems and explain how they got their answers, while the English standards emphasize nonfiction and expect students to use evidence to back up oral and written arguments.

is "show your work," as my math and geometry teachers required all through school. Harder to grade than multiple-choice questions for sure, but then I think that US teachers should be paid a lot more than they are now...

[barmar]

 PassedOut, on 2014-June-08, 17:00, said:

Harder to grade than multiple-choice questions for sure, but then I think that US teachers should be paid a lot more than they are now...

And we should have more of them so the class sizes will be manageable.

Unfortunately, public school teachers are paid out of tax dollars, and no one wants their taxes to go up so we can have more and better paid teachers. Everyone says it's a crime that teachers are paid so little, but few people are willing to put their money where their mouth is.

[PassedOut]

 barmar, on 2014-June-08, 17:04, said:

And we should have more of them so the class sizes will be manageable.

Unfortunately, public school teachers are paid out of tax dollars, and no one wants their taxes to go up so we can have more and better paid teachers. Everyone says it's a crime that teachers are paid so little, but few people are willing to put their money where their mouth is.

I think that the US anti-tax propaganda is short-sighted to the point of being nuts, and I gather that you agree. Our parents and grandparents paid plenty of taxes to build roads and schools for us to use, and they supported an exciting space program to boot. Today's it's-all-about-me politicians and voters seem happy to let that decay around us instead of improving the country for those who follow.

[kenberg]

We have to take people as they are. I was in high school in the mid 1950s in St. Paul. The schools needed more money and, at the time, this had to be put to the voters. It failed. So some big cheese in the school system announced that there simply was not enough money to do everything, so as of next fall there would be no high school football games. They put the funding up for another vote. It passed. Fast forward fifty years or so. I am at one of these 4th of July lakeside galas where politicians and their flunkies, oops I mean top level assistants, come to press flesh. I am speaking to this guy about funding for the University. He wants to talk about the Terps (Terps=Terrapins, Fear the Turtle is our school slogan). I do not have a solution for this.

Some things seem very clear to me, for example it seems clear that education benefits society as well as the individual. For some reason this is not so clear to everyone.

[Elianna]

A bit of background for those who don't know me: I teach HS Math, and have been to many district meetings about common core (at least at the MS/HS level).

The "explain your reasoning" types of questions take place in different forms: (I'm using VERY simple Math so everyone could understand)

1) x + 3 = 5

a) x= 8 because 3 + 5 = 8
b) x = 8 because you have to add 3 to both sides
c) x = 2 because 2 + 3 =5
d) x = 2 because 7-5 =2

Basically, students have to not only choose the correct answer, but have to choose the correct reasoning. Note, the choice between c and d could be confusing if d said "because 5 - 3=2", but I haven't seen ones where there is a distractor (incorrect choice) with plausible reasoning.

2) Constructed response questions where students have to come up with answer and explain their reasoning. As a teacher, as long as the reasoning is mathematically valid (i.e. I couldn't use the same logic to reach an incorrect answer) I accept their reasoning, but like others have said, I worry about the readers on the actual test.

I should note that my students are much more taken aback by the multiple choice questions than by the constructed response. They especially struggle with MC questions that require multiple responses, and are right if they only if they choose EXACTLY the correct responses.

[nigel_k]

 Elianna, on 2014-June-08, 23:03, said:

Note, the choice between c and d could be confusing if d said "because 5 - 3=2", but I haven't seen ones where there is a distractor (incorrect choice) with plausible reasoning.

I would have said "because 5 - 3 = 2" was the correct choice. The actual choice C is simply stating an answer rather than providing a reason to believe it is correct.

[akwoo]

I am a math professor, and I can say that some of the secondary math education majors who graduate from my department cannot follow (much less come up with) any but the simplest mathematical arguments. (They would have to spend a couple minutes to parse that previous sentence.)

These graduates get jobs teaching high school. Their deficiencies are obvious from their transcripts and not a secret.

All I can say in our defense is that many universities have even lower standards.

The Common Core Standards are going to be a failure, because we do not have enough teachers who can teach it. The schools and the politicians won't say so; they'll just gradually dumb down the tests so that they can be taught to by rote and declare success.

Until we make teaching a respected career that many of the smartest people in the country want to pursue, we won't be able to teach reasoning to all of our kids.

[PassedOut]

 Elianna, on 2014-June-08, 23:03, said:

A bit of background for those who don't know me: I teach HS Math, and have been to many district meetings about common core (at least at the MS/HS level).

The "explain your reasoning" types of questions take place in different forms: (I'm using VERY simple Math so everyone could understand)

1) x + 3 = 5

a) x= 8 because 3 + 5 = 8
b) x = 8 because you have to add 3 to both sides
c) x = 2 because 2 + 3 =5
d) x = 2 because 7-5 =2

Basically, students have to not only choose the correct answer, but have to choose the correct reasoning. Note, the choice between c and d could be confusing if d said "because 5 - 3=2", but I haven't seen ones where there is a distractor (incorrect choice) with plausible reasoning.

2) Constructed response questions where students have to come up with answer and explain their reasoning. As a teacher, as long as the reasoning is mathematically valid (i.e. I couldn't use the same logic to reach an incorrect answer) I accept their reasoning, but like others have said, I worry about the readers on the actual test.

I should note that my students are much more taken aback by the multiple choice questions than by the constructed response. They especially struggle with MC questions that require multiple responses, and are right if they only if they choose EXACTLY the correct responses.

Thanks much for taking the time to explain this! I see now how the multiple choice questions can be implemented in the way you've shown.

My favorite HS class (by far) was geometry, which I took as a sophomore. It was my introduction to formal proofs, and I remember thinking, "Now we are getting somewhere!" I don't see how constructing proofs would be compatible with multiple choice questions, nor how one could actually learn math without working through lots of problems and proofs. But perhaps I am not distinguishing carefully enough between the learning process and the testing process.

[barmar]

 nigel_k, on 2014-June-09, 00:47, said:

I would have said "because 5 - 3 = 2" was the correct choice. The actual choice C is simply stating an answer rather than providing a reason to believe it is correct.

But that wasn't one of the choices; the choice with subtraction said "because 7 - 5 = 2" -- it has the right value of x, but the wrong reason, and the test-taker has to recognize this.


If they gave both this answer and the actual C, I think it would have to be in a question that allowed you to select multiple answers, since both are correct. One just requires you to understand how variables are used in equations, the other also requires you to know the process used to solve algebraic equations (e.g. changing an addition on one side of the equation to a subtraction on the other side).

[Elianna]

 PassedOut, on 2014-June-09, 06:49, said:

Thanks much for taking the time to explain this! I see now how the multiple choice questions can be implemented in the way you've shown.

My favorite HS class (by far) was geometry, which I took as a sophomore. It was my introduction to formal proofs, and I remember thinking, "Now we are getting somewhere!" I don't see how constructing proofs would be compatible with multiple choice questions, nor how one could actually learn math without working through lots of problems and proofs. But perhaps I am not distinguishing carefully enough between the learning process and the testing process.

One would not be able to have students construct a whole proof in multiple choice questions, but what I see on the state tests goes something like this:

Alex is trying to prove that vertical angles 1 and 3 are congruent. (I'm using <1 as meaning "angle 1")

Statements Reasons
1. m<1 + m<2= 180 1. <1 and <2 are a linear pair
2. m<3 + m<2= 180 2. <3 and <2 are a linear pair
3. m<1 = 180 - m<2 3.____
m<3 = 180 - m<2
4. ____________ 4. Transitive Rule of equality

And students would be given a multiple choice question to fill in the blanks.

[Zelandakh]

 Elianna, on 2014-June-08, 23:03, said:

1) x + 3 = 5
c) x = 2 because 2 + 3 =5
d) x = 2 because 7-5 =2

It strikes me that d is just as correct as c since x = 5 - 3 = 7 - 5 = 2. In the old days we also had to show our working and sometimes 60% of the marks were on that so it was important. How hard is it for the students to writesomething of the form in the first sentence rather than resorting to multiple choice? Incidentally, the multiple choice maths tests I did as a child all had negative marking for incorrect answers to prevent guessing and the resulting statistical anomalies this creates. Do the American tests also include this?

[PassedOut]

 Elianna, on 2014-June-09, 18:11, said:

One would not be able to have students construct a whole proof in multiple choice questions, but what I see on the state tests goes something like this:

Alex is trying to prove that vertical angles 1 and 3 are congruent. (I'm using <1 as meaning "angle 1")

Statements                            Reasons
1. m<1 + m<2= 180             1. <1 and <2 are a linear pair
2. m<3 + m<2= 180             2. <3 and <2 are a linear pair
3. m<1 = 180 - m<2            3.____
m<3 = 180 - m<2
4. ____________               4. Transitive Rule of equality

And students would be given a multiple choice question to fill in the blanks.

Thanks again! I do see that this testing approach allows for useful and measurable results. With uniform measurements over large populations, the effectiveness of different teaching approaches can be compared and tweaked. Looks reasonable and promising to me.

[PassedOut]

 Zelandakh, on 2014-June-10, 07:21, said:

It strikes me that d is just as correct as c since x = 5 - 3 = 7 - 5 = 2. In the old days we also had to show our working and sometimes 60% of the marks were on that so it was important. How hard is it for the students to writesomething of the form in the first sentence rather than resorting to multiple choice? Incidentally, the multiple choice maths tests I did as a child all had negative marking for incorrect answers to prevent guessing and the resulting statistical anomalies this creates. Do the American tests also include this?

To me, the word "because" rules out d.

In my (long ago) school days, professionally developed multiple choice tests did penalize incorrect answers. Perhaps Elianna will update us on this too.

[kenberg]

Actually, the word because is at least a little tricky. If you believe that the equation x+3=5 leads to x=2 because 2+3=5 then you might also reason that x^2+3=7 leads to x=2 because 2^2+3=7. This would be wrong, all we can conclude from x^2+3=7 is that either x is 2 or x is negative 2. Really, in the problem as stated, we need to say that x+3=5 leads to x=2 because 2+3=5 and, if x is taken to be any number other than 2, the sum of x and 3 is not 5.

I was reluctant to note this (yes of course it is picky) until your post because I absolutely do not think this issue would cause trouble for any student, and anyway Elianna was just illustraing an idea. But if we get down to saying that we really are going to teach reasoning, then the fact is that 2+3=5 is only part of the reason that we can conclude from x+3=5 that x=2.

I find most "because" problems to be iffy when push comes to shove. I very much favor teaching reasoning, and although testing on reasoning is, I think, very difficult I favor that also. I also favor listening to teachers such as Elianna. But I think that it is tough.

I know I have told this before, but it bears on the issue of reasoning and shows just how widespread the problem is. I was in a Burger King or its equivalent when, next line over, a woman paid for her order and got the change back for a 20. But she had given the cashier a 100, not a 20. The cashier looked in the drawer and agreed. The cash register announce the change for a 20, no one in the BK had any idea how to cope with this. No one knew how to reset the cash register. I barged in. Thankfully everyone agreed that 100 was 80 more than 20, and they then accepted my solution that the woman should receive an extra 80 in change. Whew!

This very basic reasoning is useful, and you would think anyone with an 8th grade education could do it. My father in fact had an 8th grade education and I am confident that he could have done it. But many can't, so I heartily endorse teaching this basic reasoning., My preference would be to place such reasoning, most of the time at least, in a real world setting. Part of the problem with the x+3=5 setting is that the student has learned that you subtract 3 from both sides of the equation and so, from his view, the answer "because 5-3=2" would make sense to him, while the answer "because 2+3=5" may not seem right. True, he is possibly confusing technique with logic, but if we look at a real world situation often we get more clarity.

I want to repeat that I do not mean to dis Elianna's example. Rather I think that as soon as words such as "because" get into the act, there almost always can be issues. Often, as with this example, the "problem" is really a non-problem But things can, and sometimes do, go wrong.


Final comment: Three cheers for Bill Gates fro taking this on. I hope he and everyone involved can make it work.

[Elianna]

 PassedOut, on 2014-June-10, 10:43, said:

In my (long ago) school days, professionally developed multiple choice tests did penalize incorrect answers. Perhaps Elianna will update us on this too.

Historically, the ACT did not penalize incorrect answers, and the SAT did on the multiple choice sections. (Both of these are used as college entrance exams.)

I know that the old California Standardized Tests did not penalize, but I am not sure about the new tests. What I do know is that as they are adaptive, my guess is that students cannot skip questions, and so they do not penalize per se for missed questions, but they adjust future questions based on results of the previous questions, so if you miss the middle-of-the road questions you will start getting easier questions, but have less of an opportunity of getting a higher score.

There are two companies that are making tests for common core, and states have signed up for them in roughly equal proportion. California signed up for Smarter Balanced (SBAC), and I forget the other one.

I know that the example I came up with was not great, but on my behalf, I thought of it in 5 minutes. If someone wants to see actual sample questions, they can go to the smarter balanced webpage, and try out the sample test: http://sbac.portal.a.../practice-test/