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Related: Editorials & Other Articles, Issue Forums, Alliance Forums, Region ForumsHow would you answer this 1st grade test question. Explain your reasoning.
Yes, I know the answer, but it took a few minutes. And I am smarter than a first grader.
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bettyellen
(47,209 posts)msanthrope
(37,549 posts)B2G
(9,766 posts)How in the FUCK are parents supposed to help kids with homework??
Common Core is the devil. Period.
petronius
(26,602 posts)domino-looking hieroglyphics are supposed to symbolize... 
arcane1
(38,613 posts)Codeine
(25,586 posts)and they seem to work. My little monkey uses that style of math with great facility. It allows kids to internalize the sort of shortcuts we taught ourselves to use As we navigated maths.
I'm old, so it looks like nonsense to me, but who cares? He's the learner and it works. He just knows when I look at his homework there's always going to be a bit of a WTF? moment. 
stevenleser
(32,886 posts)It seems awkward to someone who was not taught this way but after thinking about it a bit, I can see how understanding this kind of shortcut would work for doing all kinds of computation in ones head relatively quickly.
joshcryer
(62,270 posts)Count the dots. It's literally giving the visualization of the answer.
uppityperson
(115,677 posts)Last edited Sat Nov 22, 2014, 11:24 PM - Edit history (1)
14-4=10
then -2 to get the whole 6 because 6-4=2
arcane1
(38,613 posts)But 14-4-2 is the same as 14-6. But WTF does "make a ten" mean?
LuvNewcastle
(16,845 posts)There's got to be a better way to phrase that question so that it makes sense.
Tuesday Afternoon
(56,912 posts)but, when I was in first grade I would have asked the teacher to explain that question.
sammytko
(2,480 posts)You wouldn't be expected to just jump in and see how this works without some background.
It's hard for us old timers to comprehend sometimes. I took a course in teaching grade school math and it involved lessons like this.
Vocabulary is also very important. They would know what make a ten means. Most, not all.
arcane1
(38,613 posts)demwing
(16,916 posts)Because we have 10 fingers, an we operate on a base 10 counting scale.
(14-6) = (14-(4+2)) = (14-4-2) = (10-2) [make a 10!] = 8
yurbud
(39,405 posts)
RoverSuswade
(641 posts)"Making a box with ten dots then crossing out 2 which leaves 8 (14 minus 6)
madfloridian
(88,117 posts)The problem is first grade minds don't really work that way....even if they have been taught the concept.
joshcryer
(62,270 posts)I can't see how this would be difficult to a first grader. It's telling them to reduce the number to 10 intuitively, then subtract the remaining numbers. It's visualized to make it quite simple.
I think this would be quite difficult for a parent who doesn't know these methods, however.
sammytko
(2,480 posts)Why we should keep an open mind. I'm old and I find this very interesting.
joshcryer
(62,270 posts)I don't have kids but I have a nephew I'm quite involved with. These methods, to me, are really foreign, but I can see them working. They make sense, once you give them a bit of thought.
There is a DUer here who has admitted having to use Google search to figure out WTF is going on, but she is glad to do it, because she herself has had difficulty learning stuff and she wants her daughters to succeed.
I think 99% of the backlash is from parents who don't want to go that extra mile to figure out what the teachers are teaching (who, btw, 99% of the time, are implementing things themselves, not by some evil corporate hierarchy). It's so disappointing and saddening because I think the new methods help children, and don't hinder them.
I'll relate a personal issue I had with algorithmic addition / subtraction. It was so difficult for me to understand the inverse relationship between addition and subtraction. It literally made me fail algebra. I didn't get it. I was so confused and lost. "New math" tries to get rid of that algorithmic methodology and teach kids "number sense."
AgingAmerican
(12,958 posts)nt
RKP5637
(67,108 posts)
brewens
(13,585 posts)college algebra in the 90's and got an A in that class.
Dyedinthewoolliberal
(15,574 posts)maybe because I was taught the old way?
RKP5637
(67,108 posts)cherokeeprogressive
(24,853 posts)
Downwinder
(12,869 posts)6 = 1 hand and 1 toe.
left wifh 1 hand and 3 toes = 8
pacalo
(24,721 posts)It doesn't make sense. Why not teach math as simplistic as possible?
Codeine
(25,586 posts)It just looks weird and convoluted to us. But I submit that simplifying manual calculations by using tens is about as natural and instinctive as mathematics can be.
I'm raising a kid who is learning like this and it's nothing like failure. He's learning and internalizing number theory with great success. It's not how learned, but there's no failure involved.
AtheistCrusader
(33,982 posts)Our kids are going to kick our asses in math, and that's awesome.
I might get my flying car yet.
Control-Z
(15,682 posts)But why?
Rex
(65,616 posts)Who wrote that question, is my question.
Codeine
(25,586 posts)"Make a ten" has a specific, defined meaning to kids taught to use this ten-box system. I'm not sure I like it but they seem to be learning quite well at my kid's school.
Jenoch
(7,720 posts)Since when are 1st grade children challenged in this manner.
I remember learing to read, plus simple addition and subtraction. I also temember the future homecoming queen sitting at her desk with a puddle of urine on the floor under her desk. I don't recall arithmatic problems such as this one.
Codeine
(25,586 posts)It seems challenging and weird because it's not the system we learned, but this is brilliant. This breaks down things into tens, which is the basis for all maths and numbers. Kids GET tens -- ten fingers and ten toes and "can you count to ten" are the building blocks of our earliest mathematical learning.
I'm watching this system work every day. As goofy as it looks to us it's a successful educational model.
Jenoch
(7,720 posts)about children 'getting' tens. They might even 'get' the metric system, something their parents and grandparents had trouble grasping.
Jenoch
(7,720 posts)I work from left to right instead of the traditional right to left.
Threedifferentones
(1,070 posts)This is basically just a formalization of what myself and most of the more clever students realized on our own as kids: when you do arithmetic in your head, it is best to reduce the problem to a serious of more simple calculations. Of course for an adult 14-6 is obviously 8. But with just slightly bigger numbers, I do the same thing this system would do, albeit without any formal concept of a "ten box" or whatever.
If someone says "what's 124 minus 47," I first subtract 4 in my head to get the number to an even 120, then I subtract the 40 to get to 80, and then I subtract the remaining 3 to get to 77.
Similarly, if someone asked me to add 47 and 77, I would first calculate that 40 and 70 make 110, and then that 7 and 7 make 14, and then that 110 and 14 make 124.
In my life I have met many educated people who cannot do that sort of arithmetic in their head, even though they easily could with pen and paper. I have realized that's because they never figured out these little mental shortcuts, which I assume is why schools are now formalizing them and teaching them to kids early.
csziggy
(34,136 posts)"Which way to make a ten to solve 14-6?" Instead of teaching the kids math by rote, they are teaching them to break it down to get to a round number, then finish the equation.
The part before the | shows ten dots and four dots in ten cell boxes. You cross out the box with four dots so you have "a ten." Then you cross out the remaining two of the six you're subtracting from the ten you have left to get the solution.
Convoluted and not likely to teach kids how to solve simple math problems quickly, in my opinion. But then, I am not a teacher, not a mathematician, and don't have kids.
Wella
(1,827 posts)Write memorization is quick, once it's done. This roundabout way is an interesting way to think about it, but kids will always be counting, and the retrieval will be slow, not quick. You can't do advanced math without the basic stuff being rote.
csziggy
(34,136 posts)For long division. I could do it in my head, but that wasn't "good enough" for the teachers - I had to write out all the steps. Basically, they told me to unlearn what I intuitively knew. It made math bring and slow so I lost interest in doing it. If they had originally made me learn math the way it is being taught in that example, I never would have gotten as far as long division - I would have given it up at subtraction!
Maybe it works for some of the students, but for any with a talent for numbers, it would be torture!
Wella
(1,827 posts)I think it's way to hold students back.
csziggy
(34,136 posts)Because it doesn't seem to be designed to actually teach math!
Wella
(1,827 posts)As you found with long division, slowing down math will create disinterest.
csziggy
(34,136 posts)No wonder this country is deficit in technology students. We've gotten really good at teaching kids to not like math and science.
Wella
(1,827 posts)The service economy doesn't need people with math and science. Underpaid foreign workers on H-1 Visas will take care of any needs stateside.
csziggy
(34,136 posts)And it seems the next generation is getting an even poorer quality education. I'm so glad I don't have children - but I wish the kids out there were being better taught.
Bandit
(21,475 posts)All workers in the service industry are underpaid. The key word so far being workers.
Wella
(1,827 posts)Companies can hold their H-1 Visas over their heads and force them to accept insane work hours and extremely low pay. The US still has laws on the books against that sort of thing but they only apply to citizens. That's why companies prefer to hire foreigners with H1 Visas.
Nay
(12,051 posts)your head. Now, it's perfectly fine for the teacher to suggest that students try to do these simple problems in their heads by imagining a 4 subtracted from 14, making a ten, from which you can mentally subtract the remaining 2 to get the answer for the original problem (14-6), but to put such stuff on a test? Madness.
My grandson and I do the above sort of mental math all the time, but in an effort to make computation in his head easier and quicker, thus making the answers come faster and faster, and in the end, memorized.
IMO, it's a way of making math harder, not easier, especially considering the reaction on this thread to what the question wants. It took me a minute to realize what the hell they were getting at, even though I've used this very idea all my life to do math in my head.
Wella
(1,827 posts)That is why everyone--irrespective of party--must fight against Common Core.
AgingAmerican
(12,958 posts)This just shows the mechanics of what goes on under the hood. That is what number theory does, helps you understand it better.
But then, I am not a teacher, not a mathematician, and don't have kids.
I've never heard of 'make a ten.' It seems to me that memorizing your numbers is a faster way. Tedious, yes, but once you know them, you simply recall them.
I read an article about 7 years ago, that stated that young people who don't know how to tell time on a clock with a face do not have as good a grasp of the passage of time. There was something about seeing an hour split into quarters that helped with that sense. My first thought was, "Who wouldn't know how to read a traditional clock?" but a young woman once asked me the time & I told her it was a quarter till four & she gave me a blank look & asked, "But what time is it?" I remembered the article & said, "It's 3:45."
And then there are the threads about whether we should still teach cursive.
Times change.
csziggy
(34,136 posts)When I was a very young kid we had what is called a flip clock. If you Google "vintage flip clock" one just sold on Etsey very much like the one my parents had.
It looked like a digital clock, but flipped numbers over to tell the time. We had regular dial clocks at various points in the house, but the flip clock was the one in the family room and the one I learned to tell time by. It was hard to learn to use the dial face clock when I started to school - it's as if a dial clock face hits a different part of my brain than the clock with digits. I still have a bit of a dichotomy about how I think about time depending on which type of clock I read. If I read a digital clock, I don't think in quarter hours, just in digits, while I am less accurate in my time sense with a dial clock and just approximate the time - quarter hour or in fives and tens (ten 'til, twenty after for example).
gollygee
(22,336 posts)That's how I've always done it. 14-4 brings it to 10, then -2 more
bhikkhu
(10,715 posts)That's more or less how I do mental math, but I've never really seen it taught visually.
joshcryer
(62,270 posts)That's why people are upset, because it's teaching the intuitive methods, that you learn much later on in life, though real world experience.
The taught methods before were algorithmic, without paying any mind to the shortcuts available.
Codeine
(25,586 posts)all the shortcuts and tricks we taught ourselves and derived from experience. I'm always surprised by the antipathy a progressive board has to new learning and teaching techniques.
Just because we learned the old way doesn't mean it was the best way -- our way taught generations of children to hate and fear mathematics.
Perhaps teaching kids that every problem has - at its core - a simple solution that can be derived with an equally simply operation should be heralded as a good thing.
bhikkhu
(10,715 posts)and I wound up working out my own methods over the years, and especially before going back to college algebra (which really made no sense when I took it in high school. I don't have any problem with new methods, as I don't have much confidence that the old ways were the best.
Starting kids off in first grade with the reasoning skills behind the math, before all the rote memorization, is probably a very good idea.
As an aside, probably everyone here knows how to multiply two large numbers together using the usual method, and probably thinks that's the best way to do it (lacking a calculator). A friend of mine from India showed me once how they did it using a completely different "matrix method". It took a couple minutes to learn, but then it was ridiculously easy, same results in a third of the time with much less opportunity for error.
Tree-Hugger
(3,370 posts)Go ahead....give it a Google. Makes the head spin.
Warpy
(111,256 posts)at least in the first grade.
The question in the OP was as clear as mud. It was either poorly worded or poorly drawn.
Tree-Hugger
(3,370 posts)Everyday Math makes the simplest of equations into nonsense.
AgingAmerican
(12,958 posts)...when it isn't familiar. Long division is a good example.
Yavin4
(35,438 posts)Some poor kid is going to get this wrong and get shoveled into the "slow" learners track and never reach his/her potential.
Codeine
(25,586 posts)because we lack the educational context they all possess. As mystifying as "make a ten" is to us older folks it's so everyday and internalized to children taught that way that they don't need to parse it out.
Every kid in my son's first grade class would understand this question. It's no as though this question is just sprung on them without lessons. They know this stuff.
AgingAmerican
(12,958 posts)...would be incoherent to us had we not been taught it in grade school. It's all relevant.
AtheistCrusader
(33,982 posts)You and I? Calcified old-school methodology. Makes it harder for us to see.
It's easier to learn, than to un-learn.
U4ikLefty
(4,012 posts)I can't understand adding additional confusion in math skills.
Teach basic calcs first & then add more aids as needed. I recall teaching Korean & Chinese kids who spoke NO English, but we could communicate because they had such a good command of the language of math.
pnwmom
(108,978 posts)Last edited Sat Nov 22, 2014, 11:57 PM - Edit history (1)
against a heavy reliance on word problems. It is so unfair to them.
Math is a language unto itself. Children who understand the language of math shouldn't have to prove that by translating it into English.
U4ikLefty
(4,012 posts)They used to use a translation dictionary & would score consistently in the 90% range by my pointing out "key" words. Color me impressed!!!
Still, I believe that the hard skills come first & then teach how to use them in a word problem, which should come later...after they have a command of the basic math skills.
pnwmom
(108,978 posts)AND the basic reading comprehension skills!
Another group of children who are disadvantaged by the current teaching fad is comprised of dyslexics and others with learning differences. My nephew, an engineer, was years behind in his reading skills compared to his math skills. Fortunately, he never had to cope with the "Common core." And sometime in high school, his reading skills suddenly improved. Math will always be his first love, however.
glowing
(12,233 posts)And it stems from this common core crap starting in 2nd grade and continuing on. What the kids at this level need most of all is boring old repetitive flash cards, multiplication tables... There's a way to make it into fun learning, but it is necessary items that your brain just needs to remember and know. So, now, because the 3rd grade didn't make these kids learn their multiplication skills like they should know them, they are struggling with long division and understanding how it works.
I've literally had to take the BS out of the hands of the school and teach him methods that work and will always work before his frustration overwhelms his love of learning. For all this fancy "new math" that is going on, they haven't shown the kids what the math is doing and why they are using it at all. They have all these different techniques to solve the problem that end up feeling like they are doing several different things when really they are just solving long division problems with an occasional remainder left over. So, now its flash cards and multiplication tables and learning what he needs to know. (When we were taught these things, there might have been a couple of "hey try this or that" if you were struggling, but never a mandate that you do all these techniques over multiple days and on a test in these different manners of solving the same damn equation.) There is nothing wrong with making kids remember there simple add, subtract, multiplication and division problems... Once they have these items down, there's no where they can't go with their math. (I had to do this in 2nd grade with adding and subtracting.. should have known better than to think anyone would smarten up with 3rd and 4th grade math).
dumbcat
(2,120 posts)why are they trying to make this so hard for the kids?
I went through calculus and analytic geometry in high school. Then in college took more differential and integral calculus, differential equations, and finally a course called Advanced Engineering Math, which was third order partial differential equations (which is where they started to lose me) needed to grok field theory, heat flow and a lot of other engineering problems.
And somehow I managed to do all that with a basic arithmetic education in grade school where I learned the subtraction, multiplication and division tables by rote, just like millions of other successful kids have done. Why did the eggheads have to come up with BS like the above to make things "better"?
pnwmom
(108,978 posts)so they assume most other kids do, too.
WinkyDink
(51,311 posts)Try blaming MATH MAJORS.
Codeine
(25,586 posts)to understand the system in question. My first grader and his peers wouldn't find it confusing at all.
The first time I saw it I was flabbergasted, of course. But it makes sense.
WinkyDink
(51,311 posts)however, is the incredibly nonsensical re-inventing of a wheel to the extent that a 1960's rocket scientist would ask, "WTH?"
pnwmom
(108,978 posts)WinkyDink
(51,311 posts)
DeadLetterOffice
(1,352 posts)pnwmom
(108,978 posts)that people with college degrees can't instantly solve.
I mean unless I am way out of touch and this is what 1st graders are learning. Maybe children develop abstract and concrete learning at earlier stages now.
pnwmom
(108,978 posts)They haven't changed -- and they shouldn't.
The educational system should adapt to them, not the other way around.
Codeine
(25,586 posts)In seeing it in my grade school kids. I went to grade school in the 70s-80s and these little buggers are learning faster and I believe deeper than we ever did.
This shit looks stupid (believe me, it looks like gibberish at first) but I'm watching it succeed in my own home every day.
bhikkhu
(10,715 posts)Now its precalculus. My kids both studied areas that neither my wife nor I could make heads or tails of, though I always enjoyed math and she was an honor student.
I think its great that teaching methods are changing, and I cringe reading upthread about how rote memorization should be the bedrock of understanding math. I think the bedrock should be understanding - as in, it doesn't matter how many tables you can recite unless you can solve real-world word problems.
JEFF9K
(1,935 posts)The same as when I was in school.
In the words of Paul Simon:
"When I think back on all the crap I learned in high school,
It's a wonder I can think at all."
Peregrine
(992 posts)This is how subtraction and addition is taught.
world wide wally
(21,743 posts)Too complex?
840high
(17,196 posts)joshcryer
(62,270 posts)Different problem but doing it the way we learned.
Codeine
(25,586 posts)This internalizes it. When we learned 14-6 I think a lot of us did think 14-4=10-2=8 the first few times. It's a standard mental shortcut, the sort of breaking things down to building blocks that allows people to do very complex calculations mentally.
They aren't really drawing ten-boxes and crossing stuff out after the first few lessons. The boxes illustrate a concept that cements base-ten reasoning and number theory in little brains. My lid learned this way and he does mental math as quickly as anyone taught our old-school way did at that age.
AgingAmerican
(12,958 posts)Rather than them being taught this in addition to rote memorization. Number theory isn't a means to an end, rather it's just a way to expose the mechanics of what is going on.
Because it isn't instantly obvious to us, some assume it is hard. It isn't instantly obvious because we weren't taught how to do it. We would react the same way to simple adding and subtracting if we had never been exposed to it. Context.
Brigid
(17,621 posts) SheilaT
(23,156 posts)are about. And I took calculus for fun when I was 46.
A couple of months ago I saw a posting on FB that turned a simple subtraction problem into a series of addition problems and I never could get anyone on that thread to explain it to me.
I honestly think things like this problem and the one on FB make very simple math far more complicated than it needs to be.
Has anyone reading this ever heard of UICSM math?
ManiacJoe
(10,136 posts)
SidDithers
(44,228 posts)Sid
KingCharlemagne
(7,908 posts)Rex
(65,616 posts)Hopefully not in my pants.
stone space
(6,498 posts)KingCharlemagne
(7,908 posts)has happene to the notion of 'carrying a ten' (or a 'hundred' or a 'thousand,' etc.), which is the way I learned to do sbutraction? Do kids not learn\memorize addition and subtraction tables any longer?
Silent3
(15,211 posts)...selling parents courses for their children to be able to pass these crappy tests.
Live and Learn
(12,769 posts)jamzrockz
(1,333 posts)This is another lousy money making scheme. But this time, it is the children that are going to summer for it. How about we stick with the system that has served humanity for all these years of great innovation and discoveries?
hunter
(38,311 posts)It's a cruel joke of the universe that humans have two-times-five fingers.
All the cool space-faring species have multiples of two and/or three manipulative digits.
Base 2,4,6,8,9,12,16, and so on. There's a tentacled species, I can't remember the name, with three "arms" and nine "fingers" on each "hand." Watching those kids do base 27 and base 24 math on their "fingers," sometimes before they even climb out of the nursery tank, is awesome!
Okay, space and time travels aside, the rote way most of us adults were taught math leads to a certain rigidity of thinking about numbers, as evidenced by many of the replies on this thread. I have some appreciation for what this "spiral review" (wtf?) is trying to do here, but it's probably not the way I'd teach it.
I was obsessed with computers as a kid, but this was before ordinary people had electronic calculators. My parents gave me an abacus, a slide rule, and a few sorts of mechanical calculators. I could play with them for hours (whenever I wasn't playing with fire, which may be why they were so generous) and that influenced the way I think about numbers.
One of the little mechanical calculators I had was a "Magic Brain." Here's the youtube video of a guy still has the one his parents gave him:
http://americanhistory.si.edu/collections/search/object/nmah_694509
One of my younger siblings broke mine.
In kindergarten and first grade we ought to be getting the kids excited about reading and writing and learning in general. Kids that age really shouldn't be exposed to rote learning of "facts" or standardized "bubble" tests.
Shankapotomus
(4,840 posts)Um, what space-faring species? 
stone space
(6,498 posts)The species that works base 27 says that 14-6=14-4-2=10-2=P.
(P in base ten would be 25.)
The species that works base 24 says that 14-6=10-4-2=10-2=M.
(M in base ten is 22.)
The method described in OP works in any base. It is not specific to base ten.
It's just based on an understanding how positional notation for numbers works in any base.
Shankapotomus
(4,840 posts)how do would hunter know what the number systems of other space-faring species are based on when we have yet to make contact with any?
stone space
(6,498 posts)If our toes were more flexible and we commonly went around barefoot, we'd probably use base twenty.
hunter
(38,311 posts)Base 5 (or in our case, Base 2 X 5 ) counting systems obscure early intuitive understandings of certain dimensional relationships.
It's interesting that the traditional system of Chinese units of weight were hexadecimal, and complex hexadecimal calculations could be quickly accomplished on a suanpan (Chinese abacus).
Language, including our systems of measure and math notation, has a very large influence on the way humans think about things.
Methods we learn as children tend to stick. Look at the reluctance of the U.S.A. to switch entirely to the metric system, or imagine how difficult it must have been for literate Europeans taught to use Roman numerals (I,V,X,L,C,D,M) to accept and manipulate Indo-Arabic numbers (0,1,2,3...).
hunter
(38,311 posts)... I'm a very dangerous fellow when I don't know what I'm doing, and I've traveled quite a bit.
My mind takes me places my physical body wouldn't function in.
ohheckyeah
(9,314 posts)Are you shitting me?
fob
(5,578 posts)They have filled in the first two 10 count blocks with 14 dots, creating a full 10 dot block and a 4 dot block. Then they subtracted the 4 dots in the second block to leave a single 10 count block with all dots filled in.
Then there is a bar after the X'd out 4-dot block, so the second operation, after the bar, depicts the 10 dot block with the remaining 2 dots subtracted(X'd out), leaving the answer of 8. If you had to fill in the last empty 10 count block you would fill in the 8 dots.
Not the best way to teach someone, but not terrible either.
::::: ..... <-- 14
::::: <-- 14-4 The "10" is now "made"
:::.. <-- 10-2
bravenak
(34,648 posts)I suppose 14-4-2 is correct but I have no idea why we need to make a ten.
It makes sense in a way though.
LibDemAlways
(15,139 posts)dreads spending the day in the primary grades because of this crap. I've encountered it and basically told the kids to save their questions for the regular teacher. However, chances are he or she is muddling through it, too.
cwydro
(51,308 posts)by math lol.
Just looking at that - gah!
Liberal_in_LA
(44,397 posts)Live and Learn
(12,769 posts)
HereSince1628
(36,063 posts)trying to learn basic arithmetic this way? I don't actually know.
I don't challenge that it works. It does.
It seems it's a way of doing subtraction without the concept of "borrowing" a unit from the next larger order to the left. But it still seems as though it requires memorizing all the differences possible between 0 an 10.
I'm fairly sure no one setting up a spreadsheet or entering values into a calculator would do math that way. So I'm not sure what this approach foreshadows that benefits later computational skills.
For a person like me who in learning arithmetic had to also learn to be very careful about misperceiving written 3's, 5's, and 8's as the same number every step represents a risk for a mistake. So, I'm not fond of things that add steps.
I do get that the structure of presentation during early learning has a very long lasting effect.
55 years ago when I was learning numbers and basic arithmetic Miss Elledge presented numbers 1 through 12 as upward steps on a cartoon staircase...later numbers greater than 10 were presented as columns of 20's, 30's, 40's, etc. I've never been free of that visual and if asked to rate something on a scale from 1 to 10 I visualize it as a position on that staircase. I'm not sure that did me much good with thinking in terms of number lines or coordinate planes. Things which are necessary if you are going to solve a system of equations for a dominant eigenvalue.
If this is really a better system for learning foundational skills that facilitate learning advanced math practice I'd be good with that.
madfloridian
(88,117 posts)It has been taught in schools for years, but more as a way to understand the procedure.
I worry now that it is being included on a high-stakes test that determines teachers' jobs and students' futures.
Inkfreak
(1,695 posts)
DeadEyeDyck
(1,504 posts)TransitJohn
(6,932 posts)What is 'making a ten'? What the heck has changed that simple arithmetic of whole numbers has to be so convoluted? 14-6=8.
muriel_volestrangler
(101,316 posts)and '5' is completely irrelevant to the question. '14-4' does 'make (a) ten'. Having worked that out, I can then interpret the picture as a two step '14-4=10' and '10-2=8'. But if I wanted a picture to help me subtract 6 from 14, I'd just draw 14 objects, and cross out 6 of them in one picture, not divide it up into 2 pictures. When you've gone pictorial, you don't need to keep thinking in tens.
stone space
(6,498 posts)WinkyDink
(51,311 posts)stone space
(6,498 posts)I don't have a very good memory when it comes to stuff like that.
rock
(13,218 posts)Alpha sub 0 + Alpha sub 0 = Alpha sub 0; Or if you prefer infinity + infinity = infinity.
sir pball
(4,742 posts)That said, you have a much better concept of number theory than the people upthread claiming that this round about idiocy is teaching "number theory".
If I had been intellectually crippled this way I never would have been able to normalize triple integrals in my head in Phys Chem 
Oh, to answer your questions: 1. it's because aleph-0 is 'countably" infinite and 2. the arithmetic of true infinity (which aleph-0 isn't, but that's dark arts indeed) is so simplistic to be understandable by a (non-CC) first grader.
rock
(13,218 posts)or maybe you already knew that. thanks.
sir pball
(4,742 posts)But I figure if somebody knows what the cardinality of infinite sets is, they deserve to at least be able to talk about it properly 
Iggo
(47,552 posts)...then, I would use the knowledge gained on those days to answer the questions correctly during the test.
WinkyDink
(51,311 posts)Iggo
(47,552 posts)
MineralMan
(146,308 posts)The children don't have the experience to know the answer to the question instantly.
So, they use the "make a ten" method to get to the answer. It works just fine.
The method I learned in grammar school, back in the 1950s was to ask "What number, if added to six, makes 14?" Early algebraic reasoning.
Of course, the answer ends up being instantly recognized very quickly for most children, but the "make a ten" method is one good way to arrive at the correct answer, too.
We don't recognize the method, because it isn't how we learned arithmetic. If we were in that first grade class, we would have learned that method.
joshcryer
(62,270 posts)It disappoints me that people seem to think that kids can't understand stuff like this. Frankly, the more I look at issues like this, and with my personal experience raising my nephew, we probably can do a lot better. Kids, they literally are information sponges, they soak it up, they're brilliant little learners.
The key is producing an environment where they learn. Sadly I think institutionalized education is limited in many respects. The "sit down, shut up" model is good for industrialized society, but it is a complete failure in the information age.
AgingAmerican
(12,958 posts)Because of the wording of the question. More like fourth or fifth.
I agree that we freak out because it isn't the way we were taught. Imagine how we would react to long division had we never been exposed to it.
PCIntern
(25,544 posts)it is a tribute to my inherent math skills that I survived it.
I wasted so much time deciphering the hieroglyphics that although I was placed into 5th grade class in 3rd grade, I could have been in 7th grade (except for the lack of socialization of course). they dispensed with the program, to their credit, after a year and a half of ridiculousness. I knew exactly what this problem was about and I am ashamed to admit it…I taught/tutored math and science to work my way thru school and cannot believe that this is 'back'.
moriah
(8,311 posts)The written manipulatives show you first subtract the four in the second block, then 2 from the first block.
Sneak the freak
(14 posts)first graders could read at that level.
Codeine
(25,586 posts)reinforces reading lessons by integrating it into maths. It's an interesting exercise in dynamic learning, I think.
AgingAmerican
(12,958 posts)My first reaction was the wording if fourth or fifth grade level, not first grade. I notice the OP has no source. IT's from photo bucket.
Codeine
(25,586 posts)It's simple subtraction
AgingAmerican
(12,958 posts)nt
Codeine
(25,586 posts)This is how he does his math, and it works fine. It's gibberish and occasionally frustrating to me because I learned math differently, but this is natural to him and he's internalized mathematical thinking to a surprising degree already.
His reading and writing are coming along a bit more slowly, but that seems to be normal in the family -- his sister didn't really hit her stride in that area until second grade and then she advanced rapidly.
In short, it looks stupid to us but it works.
MineralMan
(146,308 posts)unless that's how you learned it. What does "carry the one" mean after all? Where will you carry it? How much does it weigh, exactly?
From what I understand, teaching arithmetic today is designed to instill calculation methods of various types in the students' minds. Looking back on how I learned math, I can see now that the methods being used were designed to lead me to understand algebra later. Nobody told me that at the time, because I wouldn't have understood what they meant.
There are many ways to solve arithmetic problems. They all work just fine, but most of us know only the one we learned, way back in grammar school. Because of that, different methods seem strange to us and are hard to understand, because we learned a different method.
I was trying the other day to remember how I learned to calculate square roots. I couldn't remember it, and it has no purpose any longer, since I have a calculator nearby wherever I am. There's one on my phone. There's a really cool one on my desktop PC. I have no need to manually calculate a square root, and really never did have such a need.
I don't care how today's kids learn math, as long as they learn it.
muriel_volestrangler
(101,316 posts)And cross out another 2 from that? It's that diagram that I think is the most confusing part of the question. Why do they draw a second diagram of 10?
Codeine
(25,586 posts)Once the "ten-box/tens-block" system is laid out it becomes as instinctive and immediate as any other simple mental math, but because it uses the simplicity of tens it seems to lead to right answers more often.
The best part is that a child with facility for math can immediately move past the physical tens-box stuff and do the two-step operation in her head while a kid who learns more slowly can stick with the boxes for a few more lessons, and each time she does it she's further reinforcing the mental-math concepts at the core of the lesson.
Honestly, it looks stupid but it seems to work. Common Core (our kids' school has an even more demanding curriculum called Core Knowledge that goes even further) is making some pretty surprising demands of youngsters but the underlying lessons seem to be giving them the tools they need to rise to the challenge.
muriel_volestrangler
(101,316 posts)And it makes the child have to think 'what is 6-4' before proceeding to the next step of crossing out another 2 items. If they just crossed out 6 items in one go, it'd be faster.
Codeine
(25,586 posts)a total of two times ever in his learning before he moved on and never bothered again. That does seem pretty immediate to me. He doesn't use the ten-boxes at all anymore because he's long since absorbed the underlying conceptual operation. He does it in his head, just as fast or faster than any of us very did mental math at that age and with greater accuracy because finding the ten cuts down on mistakes.
And they don't cross out six boxes all at once because that cancels out the universality of the operation and requires thinking about each problem as a whole new situation, which is silly. If everything breaks down to tens then the same lesson, the same solution, can be applied to multiple problems.
This system is creating a learning tool, a way of thinking that can be used for multiple solutions. I fail to see the problem everyone has with it.
muriel_volestrangler
(101,316 posts)A group of 10; a group of 4, all crossed out; a group of 10, with 2 crossed out; and an empty group. So the group of 10 was drawn twice.
This seems, to me, to be a slow way for the work to be done, and I wondered if 'draw the 10s twice' is a standard part of the process (for that matter, if they needed to work out '24-6', would they have to draw 2 boxes of 10, twice, for a total of 4?). If they're not crossing out six boxes all at once, it also implies an intermediate stage of '6-4=2' which, strangely, didn't get a diagram, even though I'd say that's 'harder' than '14-4=10'.
RKP5637
(67,108 posts)WinkyDink
(51,311 posts)
rickford66
(5,523 posts)Then try to explain how you did it. We all use self-taught short cuts like rounding up or down, adding before subtracting etc. Memorizing math tables only goes so far without pencil and paper.
JoePhilly
(27,787 posts)Some people are more visually oriented, and this approach works for them. That's why the little dots are there.
Back when I was a kid, I struggled doing math.
Take an easy problem like 8+7. I hated that one. You had to memorize it, and I couldn't.
Then I noticed that 8+2=10. So I took the 2 from the 7, leaving 5. So now 8+7 becomes 8+2 (=10)+5 = 15.
This approach was really good for problems like 26+37. I'd find all the 10s. So 20+30 = 50. And that left 6+7 ... which was 13. So 50+13 = 63.
Thing is, I could SEE it in my head. Suddenly I was great at math. I could add, subtract, multiple and divide this way.
So why not teach it as another way to do it?
Lots of kids won't who could benefit from this approach won't "invent" it on their own like I did.
I have three kids, one of them uses this approach, the other two had no problem with the standard way.
TexasMommaWithAHat
(3,212 posts)Kids who learn their "doubles" first (2 + 2, 3 +3) know that "6 +7" is just one more than "6 + 6."
There aren't that many math facts to memorize once you get the "+ 1's," the "2's" and the "3's". Then there's the "9 +'s," which are one less than "10 +'s." Think "9 + 7"...back up one to "6," and the answer is "16."
I made sure that my kids memorized their math facts at an early age, accompanied by lots of play time with math manipulatives so they could "see math."
It might be an old fashioned method, but it works beautifully, imo.
LWolf
(46,179 posts)And young children CAN learn the concepts behind the facts or procedures, and it DOES make them better mathematicians down the road.
The question and the visual here are confusing; first graders MIGHT understand it if this is the way they've been working in class, where as the rest of the public who didn't work this way would be confused.
Still, there are better ways to achieve the goal, if learning concepts as well as procedures IS the goal. I know, because I've taught it.
What I'm seeing here, though, is not something appropriate for actual learning OR testing. If I'm trying to teach place value, and how to use it to solve things, I'm not going to be working with paper and pencil, or drawings, or bubbles. I'm going to be working with manipulatives, and having conversations about what we're doing with them.
Even if I want to test them...which is actually not really necessary when done well.
This isn't about learning, or about demonstration of that learning. This is just about trying to create standardized paper/pencil tests for things that aren't suitable for that format, because the standardized score is GOD in the corporate reform world.
Buns_of_Fire
(17,175 posts)(Oh, keep in mind he did this in 1965!)
madfloridian
(88,117 posts)I never saw that before, but so true. Yes, we did have to do other bases in the 6th grade I taught. Horrible. That video was true in the 60s, but even more true for the 80s new math.
They have done this before. We always teach WHY and HOW, but it wasn't used on a high stakes test.
Even in 2nd grade we would have subtraction in the 100s with a problem so long it ran off the page.
Now they are doing it again.
WinkyDink
(51,311 posts)
OregonBlue
(7,754 posts)I have found that when it's explained to me, it all makes sense but somehow, it seems more complicated than the old method. According to their teachers, it's part of the new core principals which are supposed to teach children how to think and give them shortcuts for learning. Who knows, the kids are both getting A's in math.
Codeine
(25,586 posts)It seems to work for my kids, despite the fact that when I first encountered it I thought it was a convoluted mess.
OregonBlue
(7,754 posts)I find it a bit confusing and have to reread problems a number of times to get what they are talking about. Also, it's interesting that they are not always going for an exact number but rather approximations and simple methods for getting there. Different but not bad.
Smarmie Doofus
(14,498 posts)What's " a ten"?
Codeine
(25,586 posts)when you're doing math in your head. Rather than figuring out that 14-6=8 the idea is that you "make a ten" by subtracting the four, then take the remaining two off that ten for eight. For simple problems like this it seems silly, but it's the sort of tool that can make more complex problems much easier to solve in the future. It reminds me of the tricks people use to quickly multiply very large numbers in their heads -- breaking down bigger problems into a few smaller, simpler ones that take advantage of the simplicity of tens. It's a building block that's probably unneeded at this stage, but by establishing that mode of thought now you're setting the stage for future success.
I thought it was dumb the first time my kid showed me his homework with that, but after I adjusted I began to see the underlying brilliance in it; sure you can just teach them arithmetic, but with this they're learning how to think, how to break difficult things into discrete, simple steps that can be dealt with easily. I like it.
WinkyDink
(51,311 posts)Codeine
(25,586 posts)It's about larger figures and more complex calculations later on. This is a tool that allows them to understand number theory in a very simple, easily-grasped fashion.
ScreamingMeemie
(68,918 posts)
AgingAmerican
(12,958 posts)The words are too big for first graders.
Codeine
(25,586 posts)That's standard it's grade stuff now. Those words aren't "too big."
AgingAmerican
(12,958 posts)Words like, "Spiral" "review" "which" "solve". Those are not words learned in the first grade. Perhaps the fourth grade.
Warren Stupidity
(48,181 posts)Therefore I will declare it stupid and wrong and prove that by stating that it isn't the way I learned math.
Or I could ask a first grader.
yurbud
(39,405 posts)
Contrary1
(12,629 posts)ancianita
(36,055 posts)Codeine
(25,586 posts)I'm seeing this stuff in action. It works.
Paula Sims
(877 posts)Understanding lambda and matrices are simpler than this.
Then again, I have dyslexia. . .
AgingAmerican
(12,958 posts)nt
Blue_In_AK
(46,436 posts)When my 12-year-old grandson and I play Yahtzee, he's got the dots on the dice totaled up before I can even line them up in my head. He's also already taking real algebra.
madfloridian
(88,117 posts)I understand it well because I taught it. I also saw the harm done to those who could learn the procedures but simply did not have the thought process maturity to get the rest of it.
I guess I saw so much harm done to those who did not get it. The strange thing is we always taught math this way. Even my 2nd graders could add 100 + 20+ 4 to another number in that format. They got the ones, tens, hundreds part.
But I worry now that such high stakes testing is being used that more will be harmed.
So many really don't get it, yet they could do okay in math by performing procedures the simpler way.
It's about teaching why, when some can barely function in math anyway.
Yes, many do understand it right away. Yet many in spite of all our place value blocks and the hands on we did....just do not.
I think it should be taught, but I think a child should be judged on mastery on such a vital test.
davidpdx
(22,000 posts)
AtheistCrusader
(33,982 posts)THIS math is fucking awesome. If I had been taught this method in school, my life would be totally different. TOTALLY DIFFERENT.
When I became aware of Common Core, I started investigating the math, and re-training myself. It's excruciating as an adult, to try and re-learn such basic, core code by which our brains were taught to operate. It's fucking painful.
But I am getting there. A 20 something at a fast food joint took a 20 dollar bill from me, and then entered exact change, so the register didn't do the work for him. Using this method, I snapped out the correct change in about 2 seconds, doing the math in my head.
5 years ago, I'd have needed pencil and paper to work it out. Not anymore.
(Kid had to go get a calculator, to verify I was correct (I was))
I felt like a fucking champ for the first time, and it was probably a first or second grade level problem. That's how ingrained a hatred of math I got from the system we were taught in the Seattle Public School System 20 years ago. It crippled me. I couldn't do it. I couldn't muster the energy to figure that shit out and memorize it by rote. Flunked out of math classes over and over. Had to repeat a grade, largely because of math.
But now... I'm getting there. Bit by bit. Using THIS system. I will do it. I will be there for my child when he needs help with this, because *I* will understand it.
Codeine
(25,586 posts)It's a THINKING system. It trains kids to understand, to work their way around numbers rather than memorize things or count on fingers. I went through to calc and trig with the old system, but I think this new way of thinking is brilliant.
muriel_volestrangler
(101,316 posts)You've had to do both "6-4=2" and "10-2=8"; but you've had to memorise just 36 combinations of "bigger number minus smaller number" (some of which are fairly trivial, such as "bigger number minus 1"
, and 9 "what is 10 minus this number" facts (arguably 5, since those come in pairs) for that, without the other 36 "10 plus smaller number minus bigger number" that the 'traditional' way uses - such as "14-6=8".
This test question, however, is not a great way of demonstrating the way the answer is found. This may be a reflection of the problem with insisting on multiple choice questions to test a child's knowledge of a method.
WinkyDink
(51,311 posts)"Alzheimer's Practice: No Memorization Required!"
ecstatic
(32,704 posts)Go back to rote memorization, get rid of calculators (until algebra), and let the kids come up with their own methods and shortcuts.
The problem is, they're forcing kids to use one person's idea of a shortcut. I'm pretty sure the techniques I came up with were superior to this crap. I can do some pretty advanced calculations in my head and it doesn't involve dots, ffs. But I would never dream of forcing all students to learn my technique! If anything, my techniques would be in the teachers manuals to provide instructional guidance.
magical thyme
(14,881 posts)My IQ has tested as high as 155. I have no idea what the fuck they're asking.
NCTraveler
(30,481 posts)Teaching children the proper way to do mathematics while also showing them how most of us do it in the real world. It covers both at the same time.
Without the lesson plan or context very little can be made of the image in your op. You are asking a bunch of adults to show up for elementary school for one day in order to make a point. A point not backed up by context or the lesson plan involved before the study. Still neat the as it seems much more real world than what I learned twenty years ago. Seems to be what I leaned with real life usage added. Pretty cool.
yellowcanine
(35,699 posts)You need the parenthesis to tell you to do that part first. Otherwise if you subtract 4-2 first you get 12, and the correct answer is 8.
Bettie
(16,107 posts)And they are doing fine, even my oldest who isn't a natural with math is doing fine in Algebra right now because the idea of equations was introduced early on with this kind of math.
My middle one just looks at a problem and knows the answer. Just like my husband who is a math guy by natural ability.
My little one is getting it quickly and he's only in Kindergarten.
I learned math by rote memorization and had a terrible time once we got past basics. This style of teaching would probably have benefited me a lot.
But, I can perform the basic math my current life requires, so it's all good!
WinkyDink
(51,311 posts)Bettie
(16,107 posts)well, except for a pencil and paper.
But, as we get older, we use the same tools we learned with, so automatically that we don't even realize it.
Codeine
(25,586 posts)Voice recognition software doesn't mean we stop teaching writing, yes?