What is 5x3?

[Patler]

Apparently, 5x3 is not 5+5+5. It is 3+3+3+3+3.

http://www.aol.com/article/2015/10/26/why-5-5-5-15-is-wrong-under-the-common-core/21254219/?cps=gravity_4816_-643180647726459443

Apart from the arithmetic calculation, is one restatement of the problem more correct than the other?

Does 5x3 mean five groups of three, not three groups of five?

Linguistically speaking, aren't both correct?

[mraynrand]

You should take theological questions to FYI

[Joemailman]

I would think the commutative law of multiplication makes either answer correct.
https://books.google.com/books?id=bNUSAQAAMAAJ&pg=PA4&lpg=PA4&dq=principle+of+5x3%3D3x5&source=bl&ots=oJxAKgSsCD&sig=c79SoqP66aV1vL0_ElGn5N_-LzY&hl=en&sa=X&ved=0CDYQ6AEwA2oVChMIp9PG8s3myAIVTBkeCh37QQNM#v=on epage&q=principle%20of%205x3%3D3x5&f=false

[Patler]

I would think the commutative law of multiplication makes either answer correct.
https://books.google.com/books?id=bNUSAQAAMAAJ&pg=PA4&lpg=PA4&dq=principle+of+5x3%3D3x5&source=bl&ots=oJxAKgSsCD&sig=c79SoqP66aV1vL0_ElGn5N_-LzY&hl=en&sa=X&ved=0CDYQ6AEwA2oVChMIp9PG8s3myAIVTBkeCh37QQNM#v=on epage&q=principle%20of%205x3%3D3x5&f=false

Apparently not, under the common core concepts discussed in the article.

This intrigued me, so I did some online research into what "common core" is all about. It seems to be an approach to teaching math that has its own set of "rules" that are claimed to be consistent with how math is taught in countries recognized to turn out better math students than the US. It's goal is to actually change the traditional ways that we think of or apply mathematical concepts. The website actually gave a similar example, stating that students are taught to understand that the phrase "5x7" means 5 groups of 7 items (apparently rather rigidly, because seven groups of five is not given full credit for an answer). It said that better prepares a young student for more advanced concepts down the line.

I could not find an example for addition; however it seems to me that we have traditionally taught that "2+4" means starting with a group of two and combining it with another group of four. The first group is changed by the addition of the second group. Applying that understanding to multiplication would seem to present the opposite result from what the common core example provides, that is "5x7" should mean a group of five replicated seven times. Common core teaches that it means five replications of a group of seven. If that sequence of understanding is applied to "2+4", are they now teaching the student to think that a group of two is added to an existing group of four?

It will be interesting to see what formulas common core teaches are correct answers from simple addition and multiplication fact patterns

[mraynrand]

Once you confuse the people, get them to distrust their own thoughts, convince them that only you know how to think, you have them.

[Patler]

Once you confuse the people, get them to distrust their own thoughts, convince them that only you know how to think, you have them.

Smacks of that, doesn't it?

[swede]

Apparently not, under the common core concepts discussed in the article.

This intrigued me, so I did some online research into what "common core" is all about. It seems to be an approach to teaching math that has its own set of "rules" that are claimed to be consistent with how math is taught in countries recognized to turn out better math students than the US. It's goal is to actually change the traditional ways that we think of or apply mathematical concepts. The website actually gave a similar example, stating that students are taught to understand that the phrase "5x7" means 5 groups of 7 items (apparently rather rigidly, because seven groups of five is not given full credit for an answer). It said that better prepares a young student for more advanced concepts down the line.

I could not find an example for addition; however it seems to me that we have traditionally taught that "2+4" means starting with a group of two and combining it with another group of four. The first group is changed by the addition of the second group. Applying that understanding to multiplication would seem to present the opposite result from what the common core example provides, that is "5x7" should mean a group of five replicated seven times. Common core teaches that it means five replications of a group of seven. If that sequence of understanding is applied to "2+4", are they now teaching the student to think that a group of two is added to an existing group of four?

It will be interesting to see what formulas common core teaches are correct answers from simple addition and multiplication fact patterns


Once you confuse the people, get them to distrust their own thoughts, convince them that only you know how to think, you have them.

I think you are correct, but crony capitalism--and not local ambitions--are the source of this kind of nonsense.

Throughout the entire arc of my teaching career, reading has been the focus of most of the research that has led to positive changes in classroom approaches. Simply enough, balanced reading programs incorporate early instruction in phonics, guided practice in well-matched materials, independent practice, and integrated writing tasks. Math programs have suffered greatly from a lack of serious effort to provide a similar theoretical bridge between research into the process of acquiring math skills and classroom instruction. Math and literacy are very different beasts, though, and classroom teachers at the elementary level are forced to trust the materials given to them.

The tragedy is the metestasizing of centralized educational bureaucracies that force high-functioning school districts to adopt mediocre, faulty, or incomplete k-12 curriculum guides. And many of the architects of the Common Core are representatives of Pearson, Heinemann, and other textbook giants. Design a mandated curriculum not much different from previous iterations, convince inexpert consumers of its essential nature, and then sell bazillions of dollars worth of Common Core-linked materials. What could go wrong?

Patler, any school board would be fortunate to have you as a member asking such questions. The fight for educational independence has to start at the local levels.

[wist43]

The purpose of government education is to "train", not teach.

Going back to Hegal, John Dewey, Pavlov, and B.F. Skinner... it's all about "behavior", self-esteem, and coming to "acceptable" conclusions in lieu of using logic, reason, and being able to think critically.

It's all about dumbing down the population to make them as ignorant and controllable as possible; while at the same time giving them enough technical skills to be able to semi-function in a tech economy.

Kids today, and Amerikans up into their 40's, are completely ignorant of history, the principles of freedom, the rule of law - and of course lack the skills to reason their way out of the trap they've been led into by the government schools.

Make no mistake - the elites who are pushing the buttons have no interest whatsoever in "educating" and producing self-sufficient, functioning citizens.

[red]

now i will admit, that when you see this stuff about the common core it seems pretty insane and stupid to me

but on the other hand, we aren't the world leaders in education by quite a ways, so maybe they way things are taught do have to change

and just because it doesn't make sense to us, doesn't mean its wrong. we just don't get it

when you first look at 5x3, i said its 15, and who gives a fuck how i came out with that. and i've thought that way ever sense i first read about common core, it all seems overly complicated. But then i just read that part that patler wrote about it "building" towards something, and trying to get kids to think in a different kind of way, and i thought, "ok, i do kinda get that idea"

so now i don't know what to think

[mraynrand]

I'd like to take a 2x4 to the Common Core

[3irty1]

I don't think this conspiracy goes all the way to the top or even past the creator of the idiotic quiz. Here's a link to the common core math standards (http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf). 3rd grade math starts on page 21, but you won't see any of the above nonsense codified in there. Its a short list of concepts a 3rd grader should understand, none of them particularly controversial. Nothing the national policy does or doesn't do is going to make the math teacher who gave this quiz a competent educator.

[wist43]

Try on this logic fellas...

Would any of you argue that the nuclear physicists, doctors, engineers, astronauts, mathematicians, et al that the Soviet Union, Russia, China, India, et al have produced - would you argue that they received a quality education??

If they can cipher better than Jethro Bodine, surely that speaks well of the education they received - no??

-----------------------------------------------------------------

What is wrong with that picture, and what is wrong with the United States and the top-down indoctrination system that is in place in this country?? Just like the average communist citizen, serf, caste victim, etc, Americans have been deliberately deprived a proper education from which they can use critical thinking skills to arrive at principled positions which would ensure that liberty survives for posterity.

Liberty is not on the agenda. The proper teaching of history is not on the agenda. Logical, rational, honest, scientific, critical thinking - is not on the agenda.

Math is important - but it is not the most important subject. Get the leftist, PC, authoritarian curriculum out of the schools - and the monsters that reside within the institutions that drive that curriculum out of the education process altogether, and I think you'd find the state of America's educational system improve immediately.

Sadly, we are well past that... too many generations have been subjected to the brain washing.

[mraynrand]

Try on this logic fellas...

Would any of you argue that the nuclear physicists, doctors, engineers, astronauts, mathematicians, et al that the Soviet Union, Russia, China, India, et al have produced - would you argue that they received a quality education??

If they can cipher better than Jethro Bodine, surely that speaks well of the education they received - no??

-----------------------------------------------------------------

What is wrong with that picture, and what is wrong with the United States and the top-down indoctrination system that is in place in this country?? Just like the average communist citizen, serf, caste victim, etc, Americans have been deliberately deprived a proper education from which they can use critical thinking skills to arrive at principled positions which would ensure that liberty survives for posterity.

Liberty is not on the agenda. The proper teaching of history is not on the agenda. Logical, rational, honest, scientific, critical thinking - is not on the agenda.

Math is important - but it is not the most important subject. Get the leftist, PC, authoritarian curriculum out of the schools - and the monsters that reside within the institutions that drive that curriculum out of the education process altogether, and I think you'd find the state of America's educational system improve immediately.

Sadly, we are well past that... too many generations have been subjected to the brain washing.

If I knew any history or was able to think logically, scientifically, ethically, honestly and rationally, I might agree with you. Otherwise - hey "The Apprentice" is on !!!!

[swede]

Try on this logic fellas...

Would any of you argue that the nuclear physicists, doctors, engineers, astronauts, mathematicians, et al that the Soviet Union, Russia, China, India, et al have produced - would you argue that they received a quality education??

If they can cipher better than Jethro Bodine, surely that speaks well of the education they received - no??

-----------------------------------------------------------------

What is wrong with that picture, and what is wrong with the United States and the top-down indoctrination system that is in place in this country?? Just like the average communist citizen, serf, caste victim, etc, Americans have been deliberately deprived a proper education from which they can use critical thinking skills to arrive at principled positions which would ensure that liberty survives for posterity.

Liberty is not on the agenda. The proper teaching of history is not on the agenda. Logical, rational, honest, scientific, critical thinking - is not on the agenda.

Math is important - but it is not the most important subject. Get the leftist, PC, authoritarian curriculum out of the schools - and the monsters that reside within the institutions that drive that curriculum out of the education process altogether, and I think you'd find the state of America's educational system improve immediately.

Sadly, we are well past that... too many generations have been subjected to the brain washing.

Outside of history/government classes it really isn't the curriculum that is the problem. Most kids are too shallow to benefit from the indoctrination anyway.

However, I would be inclined to accept your position that the entirety of all that is wrong with education is the covert insinuation of a vast liberal scheme to co-opt American education if you would agree with me that the path forward is not the insinuation of a vast conservative scheme to repair education (NCLB...cough cough) but a rapid and complete move to return educational control to states and communities and outlaw talk of federal "investments" in education forever.

Then you can run for your local school board and watch like a hawk to make sure that the commie pinkos can no longer run amok and subvert our youngsters. Or, better yet, you can work to convince your state to drop public education efforts in entirety and you can pay out of pocket to educate your children or attend to that matter in august halls of your own domicile without fear of intrusion. Whatever. I just don't want JEB! Bush involved any more than I want Hillary Clinton involved. Neither of them know my students as well as their parents and I do.

[Patler]

I don't think this conspiracy goes all the way to the top or even past the creator of the idiotic quiz. Here's a link to the common core math standards (http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf). 3rd grade math starts on page 21, but you won't see any of the above nonsense codified in there. Its a short list of concepts a 3rd grader should understand, none of them particularly controversial. Nothing the national policy does or doesn't do is going to make the math teacher who gave this quiz a competent educator.

It wasn't just the teacher, because I found a Common Core website that gave examples (mentioned in my second post) and did the same thing, full credit for one answer, partial for the other. Even your website hints at it:


Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each.


It makes no mention of 7 groups of 5 objects, even though in following statements it refers to the commutative property.

[swede]

It wasn't just the teacher, because I found a Common Core website that gave examples (mentioned in my second post) and did the same thing, full credit for one answer, partial for the other. Even your website hints at it:


It makes no mention of 7 groups of 5 objects, even though in following statements it refers to the commutative property.

I had a second grade student protest after I demonstrated that zero added to any number resulted in a sum identical to the number added to zero, even to numbers beyond tens and hundreds of thousands. This student, the intellectually pampered son of college professors, vigorously argued--upon the authority of his first grade teacher--that there was no mathematical number in excess of 15,000.

Suspecting that such a barrier had been set in place to keep the student from wandering off into esoteric distractions that interfered with his mastery of simpler concepts, and annoyed to boot, I sent him back to his first grade classroom with a note outlining the point in debate. He returned a few minutes later to inform us, and I quote, "Apparently I was mistaken."

So Patler, there is almost no mischief that can be done to students that cannot be undone later through instruction or the inductive self-monitoring of intelligent beings.

[mraynrand]

14k/student in Detroit. How many of you think that you, or someone you know, could educate 20 kids to fantastic success with $280,000/nine months?

[Patler]

I had a second grade student protest after I demonstrated that zero added to any number resulted in a sum identical to the number added to zero, even to numbers beyond tens and hundreds of thousands. This student, the intellectually pampered son of college professors, vigorously argued--upon the authority of his first grade teacher--that there was no mathematical number in excess of 15,000.

Suspecting that such a barrier had been set in place to keep the student from wandering off into esoteric distractions that interfered with his mastery of simpler concepts, and annoyed to boot, I sent him back to his first grade classroom with a note outlining the point in debate. He returned a few minutes later to inform us, and I quote, "Apparently I was mistaken."

So Patler, there is almost no mischief that can be done to students that cannot be undone later through instruction or the inductive self-monitoring of intelligent beings.

Ya, things can be fixed, but not always for everyone. The thing I worry about is that many students grow to fear or hate math and sciences, because they don't understand them. When a student loses points for rewriting 5x3 as 5+5+5 instead of 3+3+3+3+3 I expect another brick is added to the wall between the student and enjoyment of math class.

Particularly with sciences, most young kids have extremely high levels of interest. They are curious about everything. When my kids were young, keeping a cub scout or brownie scout pack's interest with kitchen chemistry was a piece of cake. They were fascinated with anything about plants, animals, insects, etc. They would push each other to be able to see or attempt to do. Yet, by 7th grade many of my kids' friends hated anything to do with sciences, and couldn't understand why my kids were still fascinated by it.

I'm not here to criticize teachers, they have a lot of obstacles. Too often in younger grades, we expect teachers to teach all subjects, even the subjects they disliked as students. Kids pick up on that. Answering a student's question by saying "the book says....... " doesn't help the student's understanding. But, if the teacher doesn't have a solid understanding, they can not present it in a different way that can help the student understand.

With that in mind, I am not opposed to new ways of teaching any or all subjects. However, an approach that adds to a student's frustration is probably not a good thing.

[Patler]

Patler, any school board would be fortunate to have you as a member asking such questions. The fight for educational independence has to start at the local levels.

Thanks Swede. True story:

In the 1960's a friend of mine considered, and ultimately did run for school board. I naturally agreed to help. We had both attended school board meetings regularly for quite sometime, but had not said much much, so while our faces may have been familiar, the existing board had no reason to know us.

When he was first thinking about running, he and I wrote letters to the editor identify issues and our thoughts on them, to gauge other reactions. The next month I appeared at the meeting, and one of the members approached me with a copy of one of the newspapers with one of my letters. He asked if I was the one who wrote it. When I confirmed that I was, he asked me to leave! When I explained that it was a public meeting so I had a right to be there, he turned and talked to a group of them. He came back and said I could stay, but I wouldn't be allowed to speak! I kept quiet that night. My intent was to listen and gather information, not argue or campaign. My friend ran and ultimately won a landslide election.

We were young rebels in the eyes of the city fathers. Many were accustomed to "choosing" who would run, and most often win. Small town, mid-western politics. Gotta love it!

[mraynrand]

I had a second grade student protest after I demonstrated that zero added to any number resulted in a sum identical to the number added to zero, even to numbers beyond tens and hundreds of thousands. This student, the intellectually pampered son of college professors, vigorously argued--upon the authority of his first grade teacher--that there was no mathematical number in excess of 15,000.

Suspecting that such a barrier had been set in place to keep the student from wandering off into esoteric distractions that interfered with his mastery of simpler concepts, and annoyed to boot, I sent him back to his first grade classroom with a note outlining the point in debate. He returned a few minutes later to inform us, and I quote, "Apparently I was mistaken."

So Patler, there is almost no mischief that can be done to students that cannot be undone later through instruction or the inductive self-monitoring of intelligent beings.

a second grader used 'apparently?'

[3irty1]

It wasn't just the teacher, because I found a Common Core website that gave examples (mentioned in my second post) and did the same thing, full credit for one answer, partial for the other. Even your website hints at it:


It makes no mention of 7 groups of 5 objects, even though in following statements it refers to the commutative property.

There is certainly no shortage of garbage materials vomited out and marketed as common core compliant. The nonsense is probably just in there just to differentiate from the existing materials and imply that if you stick with your old materials you'll be out of compliance. Its clearly not ideal but ultimately its the teacher responsible for the implementation of whatever standards their state/district have adopted. They need to know the standards and align their lesson and that includes filtering out nonsense from whatever materials they might have. When I see a quiz like in the OP I can't imagine how lazy and incompetent the teacher giving it must be.

[red]

i think my question would be. if the teacher is teaching the kids that 5x3 = 3+3+3+3+3

then where would the kid come up with 5+5+5? is it the parents interfering and telling the kids to do it a different way then what the teacher said, or is it the student just trying to do it their own way?

if a teacher asks me to write an essay about why the civil war happened, and i respond by answering with "the south wanted to leave the union over states right about slavery", i would be right, however i would not get full credit because i didn't give all the possible reasons, and i didn't use 500 words to do it.

i remember getting points off for using the wrong punctuation on history and econ papers? wtf did that have to do with the answer at hand?

sometimes you have to do what the teacher tells you to do in order to get full credit, and sometimes you have litle smart ass kids who think they are entitled to do things their way. and in other cases you have asshole parents who want things done their way

the kid in the OP still got the question right, but they just didn't get full credit because they didn't do it the right way.

remember our math classes when the teacher would say "show your work". what would happen if you didn't show your work? you didn't get full credit

[swede]

a second grader used 'apparently?'

That's part of what makes the story so memorable for me, and, as I said, he was the progeny of college professors and the sun and moon orbited his unique only child realm. He went through 180 days without using the restroom at school--ever. He only cried once, and that was the day his father cut his daily peanut butter and grape jelly sandwich into rectangles instead of triangles as his mother customarily did. As he moved through the grades his fifth grade teacher--a varsity assistant football coach--used to yell "No mincing!" whenever this particular child pranced down the hallway. The 90's might have been the last decade a teacher could create a "No Mincing!" rule and not get fired.

[swede]

i think my question would be. if the teacher is teaching the kids that 5x3 = 3+3+3+3+3

then where would the kid come up with 5+5+5? is it the parents interfering and telling the kids to do it a different way then what the teacher said, or is it the student just trying to do it their own way?

if a teacher asks me to write an essay about why the civil war happened, and i respond by answering with "the south wanted to leave the union over states right about slavery", i would be right, however i would not get full credit because i didn't give all the possible reasons, and i didn't use 500 words to do it.

i remember getting points off for using the wrong punctuation on history and econ papers? wtf did that have to do with the answer at hand?

sometimes you have to do what the teacher tells you to do in order to get full credit, and sometimes you have litle smart ass kids who think they are entitled to do things their way. and in other cases you have asshole parents who want things done their way

the kid in the OP still got the question right, but they just didn't get full credit because they didn't do it the right way.

remember our math classes when the teacher would say "show your work". what would happen if you didn't show your work? you didn't get full credit

Red, you scoundrel, I would love teaching next door to you. You are seeing the moving parts in education--sliding scales that encompass teachers, parents, and students of all stripes and attitudes from excellent to horrible. You see the power in having kids navigate successfully past tough teachers, demanding teachers, even crappy teachers and survive with good stories to tell. I think you are even seeing that curriculum is no more constant than human nature and all the personality types inherent in the species.

The 5x3 question may be explained one way by the Common Core, but most experienced teachers have handled the development of that concept so long that they employ a multitude of strategies for developing concrete understandings with arrays, expanded addition, commutative and associative properties, and applications with problem-solving. Once again, Common Core is not the enemy. Administrators and math series have paid lip service to it, but teachers are not yet being held accountable to its constraints and vagaries, although some mediocre teachers will hide behind it when the pedagogy fails. Common Core is a paper face pasted to the front of the real monster...federalized education.

[swede]

There is certainly no shortage of garbage materials vomited out and marketed as common core compliant. The nonsense is probably just in there just to differentiate from the existing materials and imply that if you stick with your old materials you'll be out of compliance. Its clearly not ideal but ultimately its the teacher responsible for the implementation of whatever standards their state/district have adopted. They need to know the standards and align their lesson and that includes filtering out nonsense from whatever materials they might have. When I see a quiz like in the OP I can't imagine how lazy and incompetent the teacher giving it must be.

Mr. 3irt1, I agree with every word of this. Bad teachers can take cover behind the Common Core Standards. Good teachers can make sense of it and translate past absurd notions such as 5x3 has only one meaning--instead of many.

[wootah]

No written word, no spoken plea can teach our youth what they should be.
Nor all the books on all the shelves, it's what the teachers are themselves.

[mraynrand]

No written word, no spoken plea can teach our youth what they should be.
Nor all the books on all the shelves, it's what the teachers are themselves.

That's poetry, right? We're not required to know about that. STEM.

[mraynrand]

Common Core is a paper face pasted to the front of the real monster...federalized education.

http://vignette2.wikia.nocookie.net/starshiptroopers/images/3/3c/Vlcsnap-193764.png/revision/latest?cb=20090102235449
http://i.dailymail.co.uk/i/pix/2013/05/22/article-2328880-19ED414F000005DC-196_964x642.jpg
http://www.edweek.org/media/2007/06/05/39china-fss-0419.jpg

[sooner6600]

Swede;

Are teachers day care attendants, educators, or ideology guards?

How did this happen?

Sign me Over PC'd.

[George Cumby]

My oldest is in fourth grade. Part of the issue is the teachers are trying to learn how to teach the Common Core. It's the blind leading the blind out there.

He'd come home with his math homework the last few years and my reaction would be "What the FUCK are they teaching?" He's all, 'You shouldn't use that word, Dad.'

They are trying to get the kids to think algebraically earlier, which is fine, but IMO they are ignoring the basics like memorizing addition, subtraction, multiplication and division. You know, the foundation of mathematics.

The bottom line is education starts and begins at home. If a parent relies on the schools to educate their kids, the kids are gonna' suffer.

[woodbuck27]

This is interesting. I taught Math and In feel this way:

I always tried too keep Math fun and described it as something that is all around you in a visual sense.

A Math Teacher might and especially with young students 'keep it simple'.

Before the student is taught Multiplication that student is taught Addition and Subtraction.

5 X 3 = 15 .... may alternatively be expressed as the Number on the Number Line defined as FIVE multiplied by the Number THREE on that same Number Line and....is the same as and related to Addition:

3 + 3 + 3 + 3 + 3 = 15

15 = 5 X 3 = 3 + 3 + 3 + 3 + 3 = 15