Common Core Standards

[Dancing David]

I'm referring to this:

[qimg]http://i.imgur.com/N3CePB6.jpg[/qimg]

Um, was that from the test or from the math booklet?

our district uses Everday Math, which makes sense in context but not if you just take a problem page out of context.

 

[Minoosh]

Dear Jack,

On the number line you took away 3 hundreds ok but then you only took away 6 instead of 16.

This explanation doesn't match what I see on the page - in fact I can't tell what Jack's answer is. Poor sot. I'm not sure that exercise is considered "Common Core" - such devices predate the development of the national standards.

I find number lines very useful for certain applications, usually having to do with the existence of negative integers. I've also had to break things down when students, given mpg, couldn't calculate how many gallons you'd need to drive 400 miles. Some automatically divided, but most didn't. I had them draw a diagram seeing how far they'd get on 1 gallon, 2 gallons, etc. That did involve crescent shapes.

It turns out their difficulty was partly due to not know the word "per." When I told them to substitute "for each" or "cada uno" they had a better idea what to do.

I love teaching small-group math and wish there was a model for making this the prime mode of math instruction with resources already in place. IMO it makes it much easier to diagnose conceptual difficulties and provide immediate feedback/correction.

 

[Daald]

This explanation doesn't match what I see on the page - in fact I can't tell what Jack's answer is.

I was confused at first as well.

The problem is that someone has written all over the problem and that throws you off. If you just look at the typed numbers (right below where every arc ends and ignore everything else) you see he is removing by hundreds then by ones forgetting to remove the tens. I think the parent just got confused because he is not used to the method.

(PS: The arcs where he is subtracting by one are filled by the parent...just look at the last typed number)

 

[arthwollipot]

Um, was that from the test or from the math booklet?

That was from Teh Intarwebs.

 

[Dancing David]

That was from Teh Intarwebs.

 

[Paul C. Anagnostopoulos]

What do you base this statement on? Would it sound reasonable to apply this to other subjects, or are you making math the exception?

It's reasonable to apply it to any subject, but I think math illustrates the point most clearly. I base my statement on knowing multiple kids whose math careers I have followed very closely.

It's perfectly valid to say, "I counted with my fingers." You seem so certain kids won't be able to explain. What gives you that confidence?

See above.

I've had to deal with kids who said they couldn't do math when in fact they were doing it at the time!

Then you haven't seen the kids I'm talking about.

~~ Paul

 

[Paul C. Anagnostopoulos]

Hi Paul, this is SOP for the 'extended response' in the ISAT test that Illinois has used for at least ten years.

The teachers go over it with the students and have sample rubrics on the walls in poster forms. So for our state it is nothing new.

None of that would help the kids I know with math disabilities.

What exactly is the difference between requiring a common math test to graduate high school and requiring a common physical education test? I often ask people this question and it leads to interesting discussions about the supposed difference between physical abilities and "mental" abilities.

~~ Paul

 

[DallasDad]

What exactly is the difference between requiring a common math test to graduate high school and requiring a common physical education test? I often ask people this question and it leads to interesting discussions about the supposed difference between physical abilities and "mental" abilities.

~~ Paul

By "physical education test," do you mean demonstrating push-ups and running laps, or do you mean answering questions about physical education?

 

[Minoosh]

Then you haven't seen the kids I'm talking about.

If there is a specific math-related disability, that's diagnosable and comes with varying degrees of modification, including not having to pass the test. Sometimes probably not even taking the test, in the case of, say, Down syndrome and serious head trauma.

I have dealt with 20-year-olds still barely fluent in single-digit addition, and often there were environmental/cultural factors (like never having attended school). I've seen others who understood some algebra concepts, but insisted they could not learn multiplication tables. If they could add, I had them do that.

But if you are talking about non-disabled or at least non-diagnosed kids, IMO U.S. culture reinforces widespread math phobia, even among elementary teachers. When I hear a very bright person say, "I can't do fractions," I sometimes suspect they have a psychological block, rather than some native lack of ability.

If people can count, add single digits and recognize shapes, they are doing math, and there's work available for their level. In case of severe disability, teachers generally don't want to torture students, but they do tend to encourage progress. Can you explain more specifically what you mean by "some kids can't do math"? You mean at any level?

BTW education standards far predate the current "Common Core" hoopla - do you disapprove of them in general? A lot of teachers aren't wild about them, but until the last 20 years or so, except in a few states, there was no performance bar at all to graduate high school. If you accumulated the credits, you graduated. High-stakes tests are more a function of NCLB and before that a bipartisan standards movement. From what I've heard, states may have more flexibility now to drop that requirement. Not totally sure about this.

 

[marplots]

Let's face it: parents are stupid.
Evolution requires it.

 

[Minoosh]

Let's face it: parents are stupid.
Evolution requires it.

At least, it rarely seems to occur to bad parents that they might be bad parents. It's people who are, or would be probably be, good parents that have the doubts.

 

[fuelair]

This convinces me even more that the folks coming up with the core requirements and tests have no concept that some kids simply cannot do math. At least those kids have a vague chance with rote problems, but certainly not with explanations.

Again, I want to add three physical education requirements to the core.

~~ Paul

Damn it man, you're not supposed to be paying attention to actual children, you are supposed to be teaching!!!!!!!

 

[Paul C. Anagnostopoulos]

By "physical education test," do you mean demonstrating push-ups and running laps, or do you mean answering questions about physical education?

I mean actually performing certain physical acts, which is equivalent to performing certain "mental" acts, since mental acts are physical acts.

~~ Paul

 

[Paul C. Anagnostopoulos]

If there is a specific math-related disability, that's diagnosable and comes with varying degrees of modification, including not having to pass the test. Sometimes probably not even taking the test, in the case of, say, Down syndrome and serious head trauma.

In Massachusetts, you must pass the test in order to receive a high school diploma. It's actually more complicated than that, but kids are denied diplomas.

But if you are talking about non-disabled or at least non-diagnosed kids, IMO U.S. culture reinforces widespread math phobia, even among elementary teachers. When I hear a very bright person say, "I can't do fractions," I sometimes suspect they have a psychological block, rather than some native lack of ability.

That is certainly true in many cases, yes.

If people can count, add single digits and recognize shapes, they are doing math, and there's work available for their level. In case of severe disability, teachers generally don't want to torture students, but they do tend to encourage progress. Can you explain more specifically what you mean by "some kids can't do math"? You mean at any level?

No, but some kids cannot do math at the level required to pass the standardized tests and receive a diploma.

BTW education standards far predate the current "Common Core" hoopla - do you disapprove of them in general? A lot of teachers aren't wild about them, but until the last 20 years or so, except in a few states, there was no performance bar at all to graduate high school. If you accumulated the credits, you graduated. High-stakes tests are more a function of NCLB and before that a bipartisan standards movement. From what I've heard, states may have more flexibility now to drop that requirement. Not totally sure about this.

It's not that I disapprove of standardizing tests per se. I simply think that the assumption that such standards pertain to everyone is based on an incorrect model of how the "mind" works. That is why I suggest a physical education test, too, since it highlights the absurdity of assuming that everyone has the same physical abilities.

Perhaps many people believe it's okay to deny the diploma, since, after all, the kid simply can't do all the standard high school work. I'd rather see a diploma with a caveat, but perhaps that's just me.

~~ Paul

 

[Minoosh]

Perhaps many people believe it's okay to deny the diploma, since, after all, the kid simply can't do all the standard high school work. I'd rather see a diploma with a caveat, but perhaps that's just me.

Where I live, idiom for graduation with a diploma is you "get to walk." The state, to its horror, gradually recognized that it was mandating itself to extend high school to age 22, if that's what it took to pass the test. Hence a variety of workarounds made it into the process - "augmentation" became permitted. I'm fairly certain these workarounds ended up giving quite a bit of leeway to principals. But principals also had to bend over backward to prove they were doing everything possible to boost student test performance. No child left behind.

This helped my bottom line, as a grant-funded tutor, and gave me the pleasure (the luxury) of working with small groups. In that context I could find work for anyone, because students' abilities and aptitudes were much easier to perceive than they would be with a class of 30 (let alone five or six classes of 30).

You passed if you got 53% of the problems right, and chance alone would give you 25 percent. If they knew an additional 25 percent, and could narrow down choices just a little bit on the others, they would squeak by.

It was very funny to see one girl who stated "I can't do math" looking over her math test data sheet and calculating that she could get every algebra problem wrong and still pass on the strength of logic, geometry, probability and statistics. (I didn't check her math). She did all kinds of math in her everyday life, but foundered as topics grew more abstract. Or as she said, "I was good at math until they put the alphabet in it."

In my state the high-stakes test is going away, at least temporarily, as legislators decide whether to make passing the Common Core exam (PARCC) a graduation requirement. Having students explain how they got their answers is a good classroom tool but I would not make it a significant part of a high-stakes assessment.

I wish all math could be taught in small groups.

 

[Slowvehicle]

In Massachusetts, you must pass the test in order to receive a high school diploma. It's actually more complicated than that, but kids are denied diplomas.

<polite snip for space>

Perhaps many people believe it's okay to deny the diploma, since, after all, the kid simply can't do all the standard high school work. I'd rather see a diploma with a caveat, but perhaps that's just me.

~~ Paul

It ought to mean something (other than a specific number of birthdays) to have been granted a diploma, or a diploma "with a caveat".

A student who has not mastered (for instance), high school mathematics should not possess an academic diploma.

It may be time to bring back trade schools, and apprenticeships.

 

[MortFurd]

"The Feeling of Power" by Isaac Asimov.

And you both missed the point of the story. Everyone had used calculators and computers to do math for so long that no one could do maths manually anymore.

The military was looking for a way to make their missiles cheaper, and discovered this old guy who had rediscovered how to do arithmetic by hand. This brought them to the brilliant idea of replacing the expensive computers with people - basically making a missile into a piloted vehicle, and incidentally killing the pilot when he hit his target.

The old fellow who rediscovered math killed himself for having made such a horrible thing possible. The story closes with the general who ran the project thinking some (humdrum) arithmetical thing (some simple addition or multiplication) and being proud of "the feeling of power" it gave him to be able to do math in his head without needing a computer or calculator.

 

[Dancing David]

None of that would help the kids I know with math disabilities.

l

I have to respectfully disagree, having worked with some of those students in grade school and middle schools, during ISAT.

They get lots of practice "I counted out loud from 8" is an acceptable.

 

[Paul C. Anagnostopoulos]

It ought to mean something (other than a specific number of birthdays) to have been granted a diploma, or a diploma "with a caveat".

Agreed.

A student who has not mastered (for instance), high school mathematics should not possess an academic diploma.

I understand what you're saying, but I disagree. This is based on the assumption that everyone can do everything. Again, let's add a physical education requirement that everyone must pass and see how that works out for some kids. When it doesn't, let's figure out whether there is a difference between "mental" and physical requirements.

It may be time to bring back trade schools, and apprenticeships.

Absolutely. Go tell the public school systems.

~~ Paul

 

[Paul C. Anagnostopoulos]

I have to respectfully disagree, having worked with some of those students in grade school and middle schools, during ISAT.

They get lots of practice "I counted out loud from 8" is an acceptable.

I think you're talking about explaining how they solved the problems. That is irrelevant for kids who can't solve the problems. Lack of practice is not the culprit for the kids I've worked with. (Note that I'm not saying these kids can't do any math at all, but not enough to pass the standardized tests.)

I can think of no magic reason why we should assume that every kid can handle any given discipline X. I'm not sure what to do about it.

~~ Paul