So what's up with Common core?

[Justice Hunter]

The new curriculum schools are teaching now for math in elementary is Common core, which is a visual representation of addition, subtraction, multiplication etc...

I've seen a couple videos, articles and stories of some, what i believe to be, outrageous accounts of unfairness towards the answers given to some of the questions they have on tests.

A recent example is the teacher that marked a 3rd grader wrong for answering the following question, in the following manner :

Q: What is 5x3?
A: 5+5+5

the "correct answer" was 3+3+3+3+3.

Now I can sort of see why the students answer might not be the most mathematically correct answer, but i think it urks me to think that they are still "wrong" according to this new curriculum.

I think the most important concept in physics and mathematics, is that there are multiple ways to arrive at the same answer. Mathematics and physics have evolved through out history to find the most simple and mathematically beautiful paths to an answer, but i think this is getting out of hand. If students aren't challenged to think in ways different to the mainstream, i fail to see how there will be any advancement at all in future generations to come, if we are all thinking the same way.

Also, for those familiar with common core, why is it that 3+3+3+3+3 is more correct then 5+5+5 if they are both non factor-able(prime numbers)?

Couldn't an even more correct answer be 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 ?

I just don't see how this can even be a question in the first place, when it can be answered in so many different, equally logical ways.

 

[Student100]

The new curriculum schools are teaching now for math in elementary is Common core, which is a visual representation of addition, subtraction, multiplication etc...

I've seen a couple videos, articles and stories of some, what i believe to be, outrageous accounts of unfairness towards the answers given to some of the questions they have on tests.

A recent example is the teacher that marked a 3rd grader wrong for answering the following question, in the following manner :

Q: What is 5x3?
A: 5+5+5

the "correct answer" was 3+3+3+3+3.

Now I can sort of see why the students answer might not be the most mathematically correct answer, but i think it urks me to think that they are still "wrong" according to this new curriculum.

I think the most important concept in physics and mathematics, is that there are multiple ways to arrive at the same answer. Mathematics and physics have evolved through out history to find the most simple and mathematically beautiful paths to an answer, but i think this is getting out of hand. If students aren't challenged to think in ways different to the mainstream, i fail to see how there will be any advancement at all in future generations to come, if we are all thinking the same way.

Also, for those familiar with common core, why is it that 3+3+3+3+3 is more correct then 5+5+5 if they are both non factor-able(prime numbers)?

Couldn't an even more correct answer be 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 ?

I just don't see how this can even be a question in the first place, when it can be answered in so many different, equally logical ways.

What do you mean? The question was to find 5x3 using repeated addition. 5x3 should be read off as 5 groups of 3, not 3 groups of 5, although they're the same using the commutative property of multiplication. The students answer is perfectly "mathematically correct", but isn't what the problem asked and it's possible they haven't covered the commutative property yet. I doubt the student lost full credit either.

 

[DiracPool]

I think the most important concept in physics and mathematics, is that there are multiple ways to arrive at the same answer. Mathematics and physics have evolved through out history to find the most simple and mathematically beautiful paths to an answer

That's a nice fantasy, but in practice (in my experience) there is no provision or reward for original thinking in pretty much any mainstream culture. If you want to be an original thinker, you're facing a steep uphill battle that's going to roll you back down to the base faster than sisyphus. If somehow you are miraculously able to scale and bifurcate the precipice, then perhaps you will be rewarded. But I think Einstein is the only case history of that.

In the real world, what we mere mortals have to contend with is a system that forms a model of conformity and then tests you on how well you conform to that conformity (in academia specifically). Case in point, the USA's graduate record exam. I personally just took this recently and about 1/3rd of the test (in my estimation) actually tests what your knowledge is, and the the other 2/3rds of the test tests how well you can answer the question within their guidelines. The first time I took the test I didn't prepare for that and actually ended up walking out of the test center infuriated. The second time I took it was after several months of equally infuriating indignation that I had to learn the twists and turns of the battery of essentially "trick" questions that comprises the GRE.

So what's the reason for all this? Well, the reason (again in my estimation) is that it's much easier for administrators to narrowly define a requisite paradigm of performance and then test on that paradigm than it is for them to entertain the creative abilities of "outlier" students that are not so easily defined. And since the administrators make the rules (after all, it's the administrators that administrate), then we are left with essentially no choice than to go along with this.

But what's the end result? The end result is that we are stamping out "professionals" in all walks of scientific fields that are cookie cutter clones of each other. Not very much original thinking is going on here, IMHO. In fact, at least until perhaps you reach tenure, original thinking is punished far more than encouraged.

Also, for those familiar with common core

I'm not familiar with "common core," but from what you've posted, it has that same smell of the GRE

 

[Student100]

I think the most important concept in physics and mathematics, is that there are multiple ways to arrive at the same answer. Mathematics and physics have evolved through out history to find the most simple and mathematically beautiful paths to an answer, but i think this is getting out of hand. If students aren't challenged to think in ways different to the mainstream, i fail to see how there will be any advancement at all in future generations to come, if we are all thinking the same way.

I also couldn't disagree more with this line of thinking. The most important concept in physics and mathematics is the work leading up to the solution. Solutions are trivial, all the physical insights come from the method of solution.

 

[Justice Hunter]

In the real world, though, what we mere mortals have to contend with is a system that forms a model of conformity and then tests you on well you conform to that conformity. Case in point, the USA's graduate record exam. I personally just took this recently and about 1/3rd of the test (in my estimation) actually tests what your knowledge is, and the the other 2/3rds of the test tests how well you answer the question within their guidelines. The first time I took the test I didn't prepare for that and actually ended up walking out of the test center infuriated. The second time I took it was after several months of equally infuriating indignation that I had to learn the twists and turns of the battery of essentially "trick" questions that comprises the GRE.

This seems to be the sad truth. I was helping my brother out with his math homework, and i couldn't believe the amount of trick questions i encountered. And these trick questions had no rhyme or reason, but had the sole purpose of just to get you to answer the question wrong. On top of it, teachers aren't actually teaching the concepts, but rather are teaching how to answer the questions to get a good score on the test...

I also couldn't disagree more with this line of thinking. The most important concept in physics and mathematics is the work leading up to the solution. Solutions are trivial, all the physical insights come from the method of solution.

I agree with this, the work leading up to the answer is the bread and butter. But... there are many different ways to lead up to that solution as well. For example, just because Issac Newton wasn't 100% on gravity, doesn't make his work wrong, in fact, without it, we wouldn't be here today with general relativity, which isn't 100% correct either.

Saying that one way to a solution is wrong, is just completely nonsensical. This applies in real life also, where we thrive in a world, that all sell the same merchandise, but everyone has a different way to sell them, which equally make them all successful.

 

[DiracPool]

This seems to be the sad truth. I was helping my brother out with his math homework, and i couldn't believe the amount of trick questions i encountered. And these trick questions had no rhyme or reason, but had the sole purpose of just to get you to answer the question wrong. On top of it, teachers aren't actually teaching the concepts, but rather are teaching how to answer the questions to get a good score on the test...

Couldn't have said it better myself...

 

[Student100]

This seems to be the sad truth. I was helping my brother out with his math homework, and i couldn't believe the amount of trick questions i encountered. And these trick questions had no rhyme or reason, but had the sole purpose of just to get you to answer the question wrong. On top of it, teachers aren't actually teaching the concepts, but rather are teaching how to answer the questions to get a good score on the test...

But you can't see the logic behind common core? The entire purpose is to teach concepts in addition to calculation techniques. The student didn't miss the question because he came to the wrong "solution", but because he arrived at it possibly incorrectly applying the concepts.

I agree with this, the work leading up to the answer is the bread and butter. But... there are many different ways to lead up to that solution as well. For example, just because Issac Newton wasn't 100% on gravity, doesn't make his work wrong, in fact, without it, we wouldn't be here today with general relativity, which isn't 100% correct either.

Saying that one way to a solution is wrong, is just completely nonsensical. This applies in real life also, where we thrive in a world, that all sell the same merchandise, but everyone has a different way to sell them, which equally make them all successful.

I've looked up the problem on Google. The question wants him to use repeated addition to find 5x3. His only work states 5+5+5=15. If the student had said applying commutative law 3x5=5x3, and then expanded his work he would have gotten the problem correct. His work leading up to the solution shows a lack of understanding, and in that case, it isn't "nonsensical" to mark him down.

In lieu of common core, what type of pedagogical techniques would you suggest should be taught to teach both concepts and calculation techniques? Certainty not back to the days of rote memorization? In which the "genius" students were the ones that had the multiplication tables memorized or x numbers of digits of pi. I find that cringe worthy.

I find nothing in modern science that stifles creativity, quite the contrary.

 

[Student100]

That's a nice fantasy, but in practice (in my experience) there is no provision or reward for original thinking in pretty much any mainstream culture. If you want to be an original thinker, you're facing a steep uphill battle that's going to roll you back down to the base faster than sisyphus. If somehow you are miraculously able to scale and bifurcate the precipice, then perhaps you will be rewarded. But I think Einstein is the only case history of that.

Evidence of this please?

In the real world, what we mere mortals have to contend with is a system that forms a model of conformity and then tests you on how well you conform to that conformity (in academia specifically). Case in point, the USA's graduate record exam. I personally just took this recently and about 1/3rd of the test (in my estimation) actually tests what your knowledge is, and the the other 2/3rds of the test tests how well you can answer the question within their guidelines. The first time I took the test I didn't prepare for that and actually ended up walking out of the test center infuriated. The second time I took it was after several months of equally infuriating indignation that I had to learn the twists and turns of the battery of essentially "trick" questions that comprises the GRE.

The GRE is only meant to measure basic understanding, not the ability to create new work. Undergraduate research experience is supposed to demonstrate that.

So what's the reason for all this? Well, the reason (again in my estimation) is that it's much easier for administrators to narrowly define a requisite paradigm of performance and then test on that paradigm than it is for them to entertain the creative abilities of "outlier" students that are not so easily defined. And since the administrators make the rules (after all, it's the administrators that administrate), then we are left with essentially no choice than to go along with this.

Most tests are meant to test the basic understanding of a subject, not creative ability.

But what's the end result? The end result is that we are stamping out "professionals" in all walks of scientific fields that are cookie cutter clones of each other. Not very much original thinking is going on here, IMHO. In fact, at least until perhaps you reach tenure, original thinking is punished far more than encouraged.

This isn't the case at all, do you have evidence of this statement?

 

[phinds]

... able to scale and bifurcate the precipice ...

Just out of curiosity, how does one bifurcate a precipice ?

 

[Student100]

Just out of curiosity, how does one bifurcate a precipice ?

Dynamite, obviously.

 

[collinsmark]

The concept that [itex] 5 \times 3 = 5 + 5 + 5 [/itex] is wrong is not Common Core. It has nothing to do with Common Core.

What it is is bad journalism, pigeonholing a bad grading decision by a teacher to be used as a straw-man argument to blame Common Core. For shame.

Yes it's shameful, but let's place the blame where it's due. It has nothing to do with Common Core. The blame lies on a poor pedagogical decision by an individual teacher, and even more-so the blame lies on the journalist who misattributed the mistake to Common Core.

 

[OmCheeto]

Odd. I had the same problem when I was about 13, way before CCM.
I got an F on an exam, as I didn't show any of my work, as instructed.
All the answers were correct though.

I'd probably be a poster child of anti-CCM on the internets nowadays...

I never followed the instructions...

let's place the blame where it's due. It has nothing to do with Common Core. The blame lies on a poor pedagogical decision by an individual teacher, and even more-so to the journalist who misattributed the mistake to Common Core.

Doh!

 

[phinds]

Dynamite, obviously.

Well, yeah, but you're not supposed to do that in the classroom

 

[collinsmark]

The concept that [itex] 5 \times 3 = 5 + 5 + 5 [/itex] is wrong is not Common Core. It has nothing to do with Common Core.

What it is is bad journalism, pigeonholing a bad grading decision by a teacher to be used as a straw-man argument to blame Common Core. For shame.

Yes it's shameful, but let's place the blame where it's due. It has nothing to do with Common Core. The blame lies on a poor pedagogical decision by an individual teacher, and even more-so the blame lies on the journalist who misattributed the mistake to Common Core.

As a matter of fact, this is straight from the common core standards themselves:

Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)​

Source: http://www.corestandards.org/Math/Content/3/OA/

So what this whole issue is really about is bad journalism, journalists reporting problems where there are none, and other journalists merely repeating nonsense without performing their due diligence of fact checking. That's the real problem here.

 

[phinds]

So what this whole issue is really about is bad journalism, journalists reporting problems where there are none, and other journalists merely repeating nonsense without performing their due diligence of fact checking. That's the real problem here.

So you don't consider it a problem that a teacher says an answer is wrong when it is right?

 

[Student100]

So you don't consider it a problem that a teacher says an answer is wrong when it is right?

I still feel as though the teacher wasn't completely wrong, one element of CCM is to teach students to think about multiplication as groups of things. I don't like that they took what appears to be full credit away, and provided no more explanation for the lose of credit other than 3+3+3+3+3. If the justification was the students lack of work, then the teacher is also guilty!

Other than that, I don't think a teacher making a mistake is a news worthy incident. It happens.

 

[collinsmark]

So you don't consider it a problem that a teacher says an answer is wrong when it is right?

Yes, that's a problem. I agree. It was a poor pedagogical decision by the teacher.

The teacher probably misinterpreted the Common Core standards themselves. In the link I quoted above (in the standards, http://www.corestandards.org/Math/Content/3/OA/) there is an earlier part that reads,

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.​

The teacher probably misinterpreted that 5 groups of 7 as a the only way to end up with total number of 5 × 7. But that standard doesn't specify that that is the only way. The wording was more as an a way. As a matter of fact, it says later down the page,

Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) ​

So yes, the teacher marking the student's answer wrong is a problem. But the bigger problem is the journalists blaming Common Core for the whole mess.

 

[OmCheeto]

I just learned what "repeated addition" is, as explained by the Khan Academy.
The question has two answers according to them:

3+3+3+3+3+3
and
5+5+5​

It seems very "first grade-ish" to me.
The wording of the exam does not seem at that level.
"Math Formative"?
"2. Draw an array..."?

I'm pretty sure I didn't know what "formative" and "array" meant when I was 6.

This is all very strange. I think I'll unsubscribe, and go watch some TV.

 

[edward]

Grade 3 » Operations & Algebraic Thinking » Represent and solve problems involving multiplication and division. » 1

http://www.corestandards.org/Math/Content/3/OA/A/1/

IMHO it is a waste of time to push this concept in 3rd grade to 8 year olds. The concept will fall into place all on it's own down the road a few years.

For this age group this type of learning is not age appropriate.

The makeup of the work groups helps to explain why so many people in the field of early childhood education find the CCSS to be developmentally inappropriate. There was literally no one on the writing committee (with one possible exception) with any knowledge of how very young children learn. The same concern applies to those who educate children in the middle-school years or children with disabilities or English language learners. The knowledge of these children and their needs was not represented on the working group.

The makeup of the work groups helps to explain why so many people in the field of early childhood education find the CCSS to be developmentally inappropriate. There was literally no one on the writing committee (with one possible exception) with any knowledge of how very young children learn. The same concern applies to those who educate children in the middle-school years or children with disabilities or English language learners. The knowledge of these children and their needs was not represented on the working group.

http://dianeravitch.net/2014/04/28/...4-people-who-wrote-the-common-core-standards/

American children are not learning nearly as well as they did in the past. There are always a few exceptions to this, but in reality we are behind nearly every other 1st world country. No new methodology of teaching concepts is going to change that. It all started 60 years ago with "Why Johnny Can't Read" and Johnny still can't read.

If parents are concerned they might start by taking away the TV, electronic gadgets, and four hours of soccer practice per week plus a game on Saturday. (choose your own sport}

 

[Student100]

http://www.corestandards.org/Math/Content/3/OA/A/1/

IMHO it is a waste of time to push this concept in 3rd grade to 8 year olds. The concept will fall into place all on it's own down the road a few years.

For this age group this type of learning is not age appropriate.
The makeup of the work groups helps to explain why so many people in the field of early childhood education find the CCSS to be developmentally inappropriate. There was literally no one on the writing committee (with one possible exception) with any knowledge of how very young children learn. The same concern applies to those who educate children in the middle-school years or children with disabilities or English language learners. The knowledge of these children and their needs was not represented on the working group.

http://dianeravitch.net/2014/04/28/...4-people-who-wrote-the-common-core-standards/

American children are not learning nearly as well as they did in the past. There are always a few exceptions to this, but in reality we are behind nearly every other 1st world country. No new methodology of teaching concepts is going to change that. It all started 60 years ago with "Why Johnny Can't Read" and Johnny still can't read.

If parents are concerned
they might start by taking away the TV, electronic gadgets, and four hours of soccer practice per week plus a game on Saturday. (choose your own sport}

Where's the evidence that american students are behind nearly every other first world country?

 

[phinds]

Where's the evidence that american students are behind nearly every other first world country?

I read several weekly magazines including The Economist and I assure you that every poll any of them report on shows the US way down the list in verbal skills and even further down the list in math.

 

[edward]

Where's the evidence that american students are behind nearly every other first world country?

You apparently don't live in this country.

American Students Fall in International Academic Tests, Chinese Lead the Pack

http://www.usnews.com/news/articles...national-academic-tests-chinese-lead-the-pack

Study finds U.S. students lag behind those in other industrialized countries

http://www.washingtonexaminer.com/s...ther-industrialized-countries/article/2548346

The U.S. education system is mediocre compared to the rest of the world, according to an international ranking of OECD countries.

http://cdn.theatlantic.com/assets/media/img/posts/pisa-2012-results-overview graph 1_larger.jpg Scroll down to the chart on this one.

 

[Silicon Waffle]

They make use of so many *big* words in several places in the problems, which I think should be taught later in higher grades.
The wording of the problem question (e.g 5x3) confused and almost misled me about the Common core's standard for maths multiplication itself as if I weren't allowed to interpret it as 3x5.

 

[DiracPool]

Just out of curiosity, how does one bifurcate a precipice ?

Took me years of practice. The key, though, is to cut across the grain

 

[jack476]

I thought that the problem was that the student didn't show his work. He wrote "5+5+5" in the blank space, when he should have finished the argument and written "5+5+5=15". That's the kind of thing I remember getting in trouble for all the time as a kid, the expectation is to write down your entire thought process. In this context that might seem trivially simple, but it's a habit that it's best to get into as early as possible.

Or maybe he was expected to write it both ways, thereby demonstrating understanding of the fact that multiplication is commutative on the integers? That also seems pretty likely.

I also find it unlikely that this is specifically a common core thing. All common core requires is that states codify standards for teaching, it doesn't provide a specific set of standards. If you find that concept troubling then there are some barely-accredited Bible schools you can send your kids to where they can learn all about Adam and Eve riding velociraptors when the world was created 6000 years ago, why evolution is a lie straight from the pits of Hell, how the atheist communists have infiltrated the government, and why you should therefore always vote Republican, none of that useless ivory tower academic "math" and "science" stuff.

None of us were in the classroom at the time so we can't know for sure what the teacher's instructions were. But my guess is that what happened is that specific instructions were provided for the quiz and that they somehow were not followed. And honestly I don't trust a third-grader's word on the claim that he only got a bad grade because the government's allegedly keeping him down.

 

[jackwhirl]

I was upset when I first saw that picture, but looking again just now I realized that if you read 5x3 as "five of three" the correction makes a whole lot more sense.

The concept that [itex] 5 \times 3 = 5 + 5 + 5 [/itex] is wrong is not Common Core. It has nothing to do with Common Core.

What it is is bad journalism, pigeonholing a bad grading decision by a teacher to be used as a straw-man argument to blame Common Core. For shame.

I'm inclined to agree with you with the exception that I believe this was spread predominately by social media.
Common core is a, particularly popular, unpopular political punching bag. What do you suppose the intersection of the set of people who know common core and the set of people who blame problems on common core looks like?

 

[Justice Hunter]

So ya, in response to everyone here :

I understand that the question did ask for a specification as to answer the question, so that's understandable.

However, doesn't anyone find it strange that this has to deal more with a really specific sector of computer science? Most adults, and i mean parents, don't know what an array is...and 70% of the time, that's where most of these kids reinforce their learning, which is at home.

Now, I have a small story.

I us-to be an assistant teacher at a recreational program, and i had this really inspiring young man (about 5th grade or so) who was really into science and technology. He always talked to me about how he wanted to build spaceships and time-travel machines, and a lot of other inquisitive things that'd he would always ask me, to some of which i didn't even know the answer to.

Now this bright young man, filled with ideas, when presented with some things he would need to know, particularly math and physics, he could not articulate the concepts mathematically, which is perfectly understandable, so instead, i just fed him a bunch of cool ideas, like bose-einstien condensates, black holes, and other really cool physics stuff. He didn't have to understand how it worked, he just needed to be driven to learn them when he gets older.

Now looking at this new curriculum, these concepts to me at least seem way to complicated to be teaching to someone in 3rd grade, hell, i didn't even know i had male genitalia until 2nd grade, and we expect kids to learn this kind of stuff and stay interested in math and science? The bigger problem here is that it's already apart of american culture that being bad at math is a GOOD thing...and these problems are making the anti-math culture even worse, with what seems to be over complexifing math at these levels of education.

And one more thing, off the subject of CCM, why do teachers insist on using the division sign? This is such an outdated symbol, and serves no purpose, since we turn them into fractions anyway...does common core even address that?

 

[gleem]

I thought the CC curriculum was is response to the request by industry to produce students competent in the 3 R's. How does telling a student the 5x3 is not equal to 5+5+5 meets that criterion.

BTW I have always interpreted (or was taught I can't remember because it was 65 years ago) 5x3 as 5 things taken 3 times.