"Postponing" Math until 10-12 y/o

[css3238]

Has anyone ever tried postponing formal math until the child is 10-12 years old? There is a significant amount of research that shows that there is no benefit, and perhaps a detriment, to starting formal mathematics training before around age 10, and I was curious if anyone had tried this. Also please note this is formal mathematics training. All of the studies have seen still advocate for informal math training via money, measurement, etc.

[TippyCanoe]

.

[serendipitous journey]

Has anyone ever tried postponing formal math until the child is 10-12 years old? There is a significant amount of research that shows that there is no benefit, and perhaps a detriment, to starting formal mathematics training before around age 10, and I was curious if anyone had tried this. Also please note this is formal mathematics training. All of the studies have seen still advocate for informal math training via money, measurement, etc.

 

Can you reference the primary literature on that? I disagree that the current literature shows that best practices in math are to delay formal training until age 10, though I have seen one paper done in one school that makes that argument.

[css3238]

Thanks Doodler. By "formal" I would mean textbook/curriculum based things: teaching operations and the such. What you are describing is very much like what I am thinking. There is no disability for my 6 y/o that I have noticed, but I am a research based kind of guy and go where the methods point me. She's the first one I had that I could do this with and wondered how many others had done the same. Thanks for the input!

[Momling]

I've heard about it anecdotally and read an article once posted here about a larger scale study done (possibly in the 1930's? My memory is shot...) Maybe somebody else remembers.

 

Anyway, I would guess that it would be an efficient use of time to wait to begin formal math. But I could imagine problems if the child had to take a standardized test or ended up being enrolled in school or ever was questioned by friends or family not on board with Homeschooling.

 

What about doing something less formal like LOF through early elementary and then jump in with a more comprehensive program around 5th grade that either doesn't make assumptions about previous knowledge (Jump math?), a spiral program that will review concepts previously taught (Saxon), or accelerating through a math program. My dd's homeschool buddy, for instance, started SM2a in 5th grade and is now working in 5a in 6th grade.

[sweetpea3829]

I haven't heard anything of the like, but given the severe math difficulties my DD6 has (she has not mastered a single mathematical concept since we started schooling, with the exception of rote counting....which she still occasionally struggles with), I'd be willing to give it a try, lol.

 

Except, NY has those pesky standardized testing requirements, and if I wait until DD is 10, she'd probably not be prepared for the 4th or 5th grade assessments she would have to take.

[momma2three]

I've only heard of one study done recently, and so I wouldn't consider it a "significant" amount of research. I seem to remember reading some things that really picked it apart, too.

[css3238]

Can you reference the primary literature on that? I disagree that the current literature shows that best practices in math are to delay formal training until age 10, though I have seen one paper done in one school that makes that argument.

 

Here is a good synopsis: http://www.triviumpursuit.com/articles/research_on_teaching_math.php though that is not my only source. I can provide more if you really want them, but it will take some time to collect them all again.

 

And I do not disagree that current literature shows that "delaying" formal mathematics training are not best practices, but current best practices are also leaving three out of five high school graduates unprepared for college according to ACT results released today. As a rule, I do not trust government funded studies that show more government paid for teachers teaching lessons earlier and earlier is the answer.

[stripe]

The only group I know who believes in this is the Waldorf crowd. Anecdotally, they never seem to become magically mathy when it is introduced. And the one paper about the group that held off. But they still did math things -- wasn't it tons of estimating?

 

I certainly wouldn't and haven't held off on math, since my kids asked about math, and I can't stop talking (or singing? ;) ) about it.

 

I haven't held off teaching my kids to read until age 10, either. I believe there is a lot to be gained in encouraging thinking in a young child. I am not aware of a substantial body of literature pointing to a detriment in education beginning before the age of 10. Perhaps you could share with us what has convinced you that that is the case.

 

For what it's worth, I don't believe in extremely early academics, either.

[css3238]

To make sure we are clear, let me change the phrase "formal math education" to "arithmetic." There would still be a lot of emphasis on math skills, again like money, time telling, measuring, etc. just not formal addition, subtraction, multiplication, and division.

[sweetpea3829]

To make sure we are clear, let me change the phrase "formal math education" to "arithmetic." There would still be a lot of emphasis on math skills, again like money, time telling, measuring, etc. just not formal addition, subtraction, multiplication, and division.

 

But wouldn't one kind of automatically use arithmetic skills when learning concepts such as money and measuring? I mean, if you're counting money, you're adding, subtracting, etc.

[css3238]

Another study/experiment. Probably the one that most caught my attention and got me thinking about it: http://www.ithaca.edu/hs/mathcs/compass/storyI-III.htm

[css3238]

But wouldn't one kind of automatically use arithmetic skills when learning concepts such as money and measuring? I mean, if you're counting money, you're adding, subtracting, etc.

 

Right. :glare: Maybe we should go with "formal arithmetic?" Or perhaps "arithmetic our of context." So instead of 2+5 it is always "these apples and those apples are how many?" Does that make sense? I know it's hard to come to an answer when the question is ambiguous so I am trying.

[Hunter]

This topic comes up every few months. I wish I knew of keywords to search for to find old threads :tongue_smilie:

 

Anyone interested in this topic might like the free African Waldorf math pdfs

 

Free vintage teacher's manual that is the basis of most conceptual methods. Grube's Method

 

Professor B has a lot of finger work and recitation.

 

The RightStart games look good.

[Dolphin]

To make sure we are clear, let me change the phrase "formal math education" to "arithmetic." There would still be a lot of emphasis on math skills, again like money, time telling, measuring, etc. just not formal addition, subtraction, multiplication, and division.

 

Another study/experiment. Probably the one that most caught my attention and got me thinking about it: http://www.ithaca.edu/hs/mathcs/compass/storyI-III.htm

 

I would look for more current research before going down that road. The article you linked was originally printed in 1935 based on research from 1929....

[css3238]

I would look for more current research before going down that road. The article you linked was originally printed in 1935 based on research from 1929....

 

See my previous on current research. Newer does not automatically equal better. Especially in education.

[css3238]

This topic comes up every few months. I wish I knew of keywords to search for to find old threads :tongue_smilie:

 

Anyone interested in this topic might like the free African Waldorf math pdfs

 

Free vintage teacher's manual that is the basis of most conceptual methods. Grube's Method

 

Professor B has a lot of finger work and recitation.

 

The RightStart games look good.

 

Ironically I am finding more threads on this here through a Google search than I am the built in search. Speaking of, I found your Grube's Method post. I was thinking of using MEP before I saw these studies. You think they are that similar?

[Tawlas]

This topic comes up every few months. I wish I knew of keywords to search for to find old threads :tongue_smilie:

 

Anyone interested in this topic might like the free African Waldorf math pdfs

 

Free vintage teacher's manual that is the basis of most conceptual methods. Grube's Method

 

Professor B has a lot of finger work and recitation.

 

The RightStart games look good.

 

This is one link i saved:

 

http://forums.welltrainedmind.com/showthread.php?t=128114&highlight=Unschooled+math

 

I think it's a great idea, althoug in reality well probably only delay until third grade or so here. I can't say how it's going as we're only just starting lol.

[stripe]

Ironically I am finding more threads on this here through a Google search than I am the built in search. Speaking of, I found your Grube's Method post. I was thinking of using MEP before I saw these studies. You think they are that similar?

You may be interested in MEP's approach of no writing in Reception Year (as in Hungarian kindergarten), and dealing with only numbers 0-20 in Year 1. Liping Ma mentions the emphasis in Chinese schools of more time on smaller numbers first, instead of rushing to larger numbers.

[JennyD]

It seems pretty clear to me that people who are not me can do a spectacularly good job educating their elementary schoolers in math without using a formal comprehensive curriculum, a la Doodler's post above. Others on this board have also done this, IIRC, and I inevitably find it extremely impressive.

 

However, I can't imagine why you'd want to delay actually teaching them arithmetic. It's so useful! I find the idea -- espoused in the 1935 article you linked -- that the only time children need arithmetic is when they're making change to be frankly bizarre. My 7yo asks me to help him solve complicated arithmetic problems all the time, just based on stuff he's been reading, some craft project he wants to do, etc.

[FO4UR]

Right. :glare: Maybe we should go with "formal arithmetic?" Or perhaps "arithmetic our of context." So instead of 2+5 it is always "these apples and those apples are how many?" Does that make sense? I know it's hard to come to an answer when the question is ambiguous so I am trying.

 

 

 

I understand what you are asking, I think. Formal math = workbook/textbook. Informal math = real life, games, stories, etc.

 

 

 

On one hand, I think it would be a terrible idea to just not think about teaching math until the child is 10. Terrible!

 

 

 

On the other hand, I think it's vital to teach those basics early AND in a way that they truly understand...which is most often through real life, games, stories, etc. That said, it's important for the parent/teacher to have a plan in place (however flexible) for teaching and giving the child enough practice to own that math (especially the 4 operations).

 

 

Practically speaking...b/c I have 3 dc (4th on the way) and more than math to teach...I find it best to find curricula that fit out learning styles rather than reinvent the wheel and rely entirely upon my ability to find/plan/implement informal math regularly. There are SO many wonderful resources that are SO far removed from the typical early 1900's math books that birthed that article (I read it long ago.). The author there was not referring to Miquon or RightStart or LOF or even Singapore....or MEP (check out MEP!)...or Beast Academy...or TOPS Get a Grip...

 

 

 

My POV is probably tainted b/c my oldest is a mathy kid who has struggled in reading/writing so just handing him a traditional math worksheet does not happen. He *has* to have that math pulled off the worksheet for him - though not always in real life context. He thrived with Miquon and MEP in K-2nd.

 

 

My 7yo is highly insulted at the math I gave her today. She wants TOUGH problems! :tongue_smilie: I've been pretty laid back with her so far, but she's taking the reigns...You tell her she has to wait until she's 10.:lol:

 

 

The problem with research and statistics is that it takes the focus off of the child who learns in *YOUR* home. You aren't educating the masses, just your 6yo. What does she know? What can you show her next? Carry on... Try a lesson. What does she remember tomorrow? What seems kind of fuzzy? Try another lesson and carry on...

[serendipitous journey]

Another study/experiment. Probably the one that most caught my attention and got me thinking about it: http://www.ithaca.edu/hs/mathcs/compass/storyI-III.htm

 

oh well. I detest that article!!! :tongue_smilie: The post question at the end bugs the heck out of me:

 

"Here is a wooden pole that is stuck in the mud at the bottom of a pond. There is some water above the mud and part of the pole sticks up into the air. One-half of the pole is in the mud; 2/3 of the rest is in the water; and one foot is sticking out into the air. Now, how long is the pole?"

 

I detest it. It the sort of thing that made me think I wasn't designed to like math; it is the sort of question the Math Literacy books often have -- "About how many quarters high is the Statue of Liberty?" Really, having been around poles & ponds & boats too, I ask you: how often does a person know that half of a pole is in mud, 2/3 of what is not in mud is in water; and one foot is neither in mud nor water. If one foot of a pole is sticking up in the middle of a lake, slapping a buoy on it is more urgent than meditating on its length.

 

But at any rate, that is article gives an example from one group; and it is not a study, but an intervention. I myself would find it much harder to provide Button with the sort of "informal" maths they used than with the formal maths we employ, and with Button, I cannot take things any harder than they already are.

 

Here is a good synopsis: http://www.triviumpursuit.com/articles/research_on_teaching_math.php though that is not my only source. I can provide more if you really want them, but it will take some time to collect them all again.

 

And I do not disagree that current literature shows that "delaying" formal mathematics training are not best practices, but current best practices are also leaving three out of five high school graduates unprepared for college according to ACT results released today. As a rule, I do not trust government funded studies that show more government paid for teachers teaching lessons earlier and earlier is the answer.

 

Well, that is not really research; the bits of it I am unfamiliar with are poorly done and do not at all show that formal maths should be delayed. If there is a part of it you find esp. robust you can quote it and I'll think over it more carefully; to be honest, it is too full of conceptual gaps for me to address all of them. The myelination of the brain is one that touches on my own specialist training, and is utter hooey. The brain of a 6-year-old has perfectly lovely myelination for thinking purposes and readily generalizes abstract rules from specific inputs. It is much more plastic (learns and forgets more easily), much more full of cells & synapses, and much less full of prefontal cortex than an older child's; but recent work has shown that the brighter the child, the longer the brain takes to move from child-like to adult-like connectivity and nobody suggests that the brightest children should not be taught math until they are older than their slower peers.

 

I do agree that government best practices & studies are to be viewed carefully. The best practices I have in mind are those that target specific populations and seem to get the desired effects; particularly gifted or at-risk children. I have never seen those suggest delayed formal maths.

 

By formal you seem to mean abstract. As in, 2 + 2 = 4 as opposed to 2 apples + 2 apples = 4 apples. Now if you want to keep your children in concrete maths until they are 10, and you are doing lots of enriching with concrete concepts and are as dedicated to education as you seem, I am sure they will turn out fine. And if you forced them to do unpleasant abstractions when they were 5 I bet that would be a worse outcome. But at our house we like thinking about infinity. And negative numbers. And numerical series; &c. It seems to me that the best, most mathematically apt materials I have seen -- MEP comes to mind -- introduce abstract concepts naturally, well, and early.

 

Here's a preview of a scholarly article that touches on formal ed, and suggests formal math ed closes the gap btw. US and Korean children in maths by age 7/8. As in, the Korean children start out farther behind b/c of differences in home environments but rapidly close the gap. They seem to still be ahead of US children, on average, at graduation so the early formal stuff doesn't seem to have damaged their long-term math prospects on that front.

 

This article suggests a link btw. earlier formal education and the rising mean IQ in populations. Now I have no special regard for IQ tests and please do not flame me or suggest I think IQ is an important measure of child education! I only mention this because I learned recently (this is quoted in Pinker's recent book on the decline of violence) that the rise in mean IQ is specifically due to the rise in abstract thinking skills. These same abstract thinking skills seem to underlie not just abstract math thought, but abstract personal arguments: imagining a counterfactual (say, asking a man how he would feel if he were a women denied equal access to education; or a white person how she would feel if she woke up one morning black, and her children were black, and they were treated differently). While I am not arguing that children grow up less empathetic if they don't have early formal maths, I am arguing that the formal thinking skills -- those of being able to abstract -- seem to be at least somewhat generalizable, and no one would delay teaching general empathy which requires considerable abstraction.

 

This article seems to find the formal/informal distinction artificial ... and I'm stopping there, having looked at about the first 15 or so abstracts to pop up on a Google Scholar search for [begin/delay] formal math education. I came across none that argued for delaying, by the way -- these are simply all the articles that seemed to address this issue at all.

 

Stripe's good point RE Liping Ma and also MEP reinforces, to my mind, the value of abstraction -- young children have a much easier time imagining small numbers and manipulating them, and can develop great formal sophistication early (as these sources, to my reading, suggest) when values are kept small.

 

at any rate: we disagree, I hope respectfully; I just wanted to throw out some pro-formal ideas for future thread-searchers. I don't imagine I will change the OPs mind, and I have no concern for the quality of his children's math education anyhow, nor for the neighbor children he is teaching :). They are fortunate to have such a dedicated papa & mentor.

Edited August 23, 2012 by serendipitous journey

[regentrude]

And I do not disagree that current literature shows that "delaying" formal mathematics training are not best practices, but current best practices are also leaving three out of five high school graduates unprepared for college according to ACT results released today. As a rule, I do not trust government funded studies that show more government paid for teachers teaching lessons earlier and earlier is the answer.

 

In that case, I would have a look and see how math education is accomplished in countries that are more successful than the US.

Many other countries with good educational outcomes delay all formal academics until the kids are 6 or 7 years old; but once they start, they work more efficiently and get to higher math quicker than the traditional US curriculum (they don't spend four years trying to teach fractions, as it is done here in grades 5 through 8). Of course it also plays a role that math teachers are trained much better than they are in this country. But in any case, none of the successful countries delay formal math until age 12; at that age, the students are covering algebra and geometry topics taught in US high schools.

Edited August 23, 2012 by regentrude

[kitten18]

And I do not disagree that current literature shows that "delaying" formal mathematics training are not best practices, but current best practices are also leaving three out of five high school graduates unprepared for college according to ACT results released today. As a rule, I do not trust government funded studies that show more government paid for teachers teaching lessons earlier and earlier is the answer.

I agree with you but I don't think it's because they started too early. I just think they're using inferior curricula. ;)

 

I could see just playing with numbers for the first couple years of school. There is some really, really great math curricula out that starts out as playing with and exploring numbers: Miquon, RS, MEP, etc.

[Free]

There is wonderfully inspiring article by Louis P. Bénézet which talks of the same thing. It makes for a very interesting read. Here is the link: The Teaching of Arithmetic : The Story of an experiment

 

I do not believe in delaying mathematical instruction, however I do agree that mathematical instruction does not have to be through textbooks and worksheets. If you can find creative ways to teach the same concepts, then it may actually turn out to be better for the child.

 

ETA: Oops, sorry I missed your earlier link to the same article.

Edited August 23, 2012 by Free

[Elizabeth in MN]

The only group I know who believes in this is the Waldorf crowd.

 

Waldorf introduces math in first grade.

[css3238]

oh well. I detest that article!!! :tongue_smilie: The post question at the end bugs the heck out of me:

 

"Here is a wooden pole that is stuck in the mud at the bottom of a pond. There is some water above the mud and part of the pole sticks up into the air. One-half of the pole is in the mud; 2/3 of the rest is in the water; and one foot is sticking out into the air. Now, how long is the pole?"

 

I detest it. It the sort of thing that made me think I wasn't designed to like math; it is the sort of question the Math Literacy books often have -- "About how many quarters high is the Statue of Liberty?" Really, having been around poles & ponds & boats too, I ask you: how often does a person know that half of a pole is in mud, 2/3 of what is not in mud is in water; and one foot is neither in mud nor water. If one foot of a pole is sticking up in the middle of a lake, slapping a buoy on it is more urgent than meditating on its length.

 

But at any rate, that is article gives an example from one group; and it is not a study, but an intervention. I myself would find it much harder to provide Button with the sort of "informal" maths they used than with the formal maths we employ, and with Button, I cannot take things any harder than they already are.

 

 

 

Well, that is not really research; the bits of it I am unfamiliar with are poorly done and do not at all show that formal maths should be delayed. If there is a part of it you find esp. robust you can quote it and I'll think over it more carefully; to be honest, it is too full of conceptual gaps for me to address all of them. The myelination of the brain is one that touches on my own specialist training, and is utter hooey. The brain of a 6-year-old has perfectly lovely myelination for thinking purposes and readily generalizes abstract rules from specific inputs. It is much more plastic (learns and forgets more easily), much more full of cells & synapses, and much less full of prefontal cortex than an older child's; but recent work has shown that the brighter the child, the longer the brain takes to move from child-like to adult-like connectivity and nobody suggests that the brightest children should not be taught math until they are older than their slower peers.

 

I do agree that government best practices & studies are to be viewed carefully. The best practices I have in mind are those that target specific populations and seem to get the desired effects; particularly gifted or at-risk children. I have never seen those suggest delayed formal maths.

 

By formal you seem to mean abstract. As in, 2 + 2 = 4 as opposed to 2 apples + 2 apples = 4 apples. Now if you want to keep your children in concrete maths until they are 10, and you are doing lots of enriching with concrete concepts and are as dedicated to education as you seem, I am sure they will turn out fine. And if you forced them to do unpleasant abstractions when they were 5 I bet that would be a worse outcome. But at our house we like thinking about infinity. And negative numbers. And numerical series; &c. It seems to me that the best, most mathematically apt materials I have seen -- MEP comes to mind -- introduce abstract concepts naturally, well, and early.

 

Here's a preview of a scholarly article that touches on formal ed, and suggests formal math ed closes the gap btw. US and Korean children in maths by age 7/8. As in, the Korean children start out farther behind b/c of differences in home environments but rapidly close the gap. They seem to still be ahead of US children, on average, at graduation so the early formal stuff doesn't seem to have damaged their long-term math prospects on that front.

 

This article suggests a link btw. earlier formal education and the rising mean IQ in populations. Now I have no special regard for IQ tests and please do not flame me or suggest I think IQ is an important measure of child education! I only mention this because I learned recently (this is quoted in Pinker's recent book on the decline of violence) that the rise in mean IQ is specifically due to the rise in abstract thinking skills. These same abstract thinking skills seem to underlie not just abstract math thought, but abstract personal arguments: imagining a counterfactual (say, asking a man how he would feel if he were a women denied equal access to education; or a white person how she would feel if she woke up one morning black, and her children were black, and they were treated differently). While I am not arguing that children grow up less empathetic if they don't have early formal maths, I am arguing that the formal thinking skills -- those of being able to abstract -- seem to be at least somewhat generalizable, and no one would delay teaching general empathy which requires considerable abstraction.

 

This article seems to find the formal/informal distinction artificial ... and I'm stopping there, having looked at about the first 15 or so abstracts to pop up on a Google Scholar search for [begin/delay] formal math education. I came across none that argued for delaying, by the way -- these are simply all the articles that seemed to address this issue at all.

 

Stripe's good point RE Liping Ma and also MEP reinforces, to my mind, the value of abstraction -- young children have a much easier time imagining small numbers and manipulating them, and can develop great formal sophistication early (as these sources, to my reading, suggest) when values are kept small.

 

at any rate: we disagree, I hope respectfully; I just wanted to throw out some pro-formal ideas for future thread-searchers. I don't imagine I will change the OPs mind, and I have no concern for the quality of his children's math education anyhow, nor for the neighbor children he is teaching :). They are fortunate to have such a dedicated papa & mentor.

 

Humbled by your closing words and thankful for them all, especially the links. I have still not decided what to do, though I still leaning very much in favor of MEP which does seem to address the ideas that make sense to me (ensuring mastery with small numbers first) without doing away with curriculum or structure or whatever you want to call it. The idea of not having a plan does terrible things to my nerves, but as a former teacher it is oooooh soooooo easy to slip into old paradigms. Thanks for all the input! :grouphug:

[kiwik]

I know people who take the same approach to reading. If your life turns to custard and you kids have to go to school how will they feel about your decision?

[Janice in NJ]

We did not delay. Two of my kids were ready for algebra by 6th grade. One began in the 5th grade - the wiggly one.

 

Independent seat work in arithmetic is one of the few things kids can do on their own at age 6. Short times working alone. Neatly. Carefully. With an end goal in mind. Yes, kids can read on their own. But an arithmetic paper is different; it's output. Verifiable proof of hard work. And it's good for kids - especially the wiggly ones who don't seem ready for it. In the beginning, I needed to keep the paper-pencil time short with my wiggly guy, but it was still important to do it.

 

The Bluedorn's materials have been out for a while. No, I do not agree with their methods. Arithmetic at our house was a fun, hands-on lesson together. Seat work - including spiraling review. Followed by a short time of evaluation by mom.

 

No one here dislikes mathematics. It's hard to dislike something you are good at. :001_smile:

 

Peace,

Janice

 

Enjoy your little people

Enjoy your journey

[Down_the_Rabbit_Hole]

You could do "formal Math' in a non formal way. My dd was struggling with math so we dropped her math curriculum and started playing math. I had a book by Katheryn Stout (Maximum Math) that listed math skills needed at different grades. How these skills were taught was up to you. The pressure was off dd and she blossomed in her math ability simply by playing with math and writing math and performing math in a natural way. I used her skills...drawing and writing...and we created a wonderful math notebook.

 

I think it is possible to not approach math in a traditional way but arithmetic skills are needed. To not get these skills until later, in my opinion, would hinder a child in so many ways.

[boscopup]

If you delay 2+2=4 because it's too abstract (and I don't think it is), why not delay reading as well? Afterall, it's also just as abstract.

 

I don't think you should look at what the schools are doing and assume that homeschool curricula will be the same way. Homeschool has the advantage of one on one teaching with curriculum geared toward that particular child. Pick one that takes the child from concrete to visual to abstract. Go at your child's pace. Pay attention to your child's needs.

 

My children start math at a young age. They love it. They're good at it. They have strong conceptual understanding of it. I can't even imagine the work I would have to put in to make sure we covered math topics informally, and one child actually learns better with a workbook combined with manipulatives than with manipulatives alone. He couldn't figure out colors by just pointing then out in real life. He needed a workbook. Same goes for counting. He's now figuring out multiplication at age 5, and he can do a bit of subtraction into negative numbers (2-5= -3). Negative numbers are abstract, but both my school aged kids understood them at age 5. I think people sometimes underestimate the abilities of young children.

 

I would suggest checking out Life of Fred if you're wanting â€informal mathâ€. DS2 is finishing up Apples today, and he can now read a clock to 5 minutes. :) We love informal math here, but I'm not throwing the baby out with the bath water. My kids love their Singapore also, and it's a textbook and workbook. Gasp! Hasn't hurt them one bit. I wouldn't torture them with endless drill of concepts they fully understand already (as pubic schools often do), but I do formal math. In a homeschool setting, it looks a lot different.

[Hunter]

How to Tutor has some interesting information on arithmetic vs math in general before launching into the lessons. I think "arithmetic" meant something different to the old timers, than it does to us now. The old timers took arithmetic very seriously.

 

I've seen reports comparing education around the world. Some European countries that outperform the USA with less hours and less money, don't teach reading until 7, or math until 9. They wait until the vast majority of children are developmentally ready, they clear the schedule of all the clutter, and teach the priority subject.

 

Classroom study and homeschool study are different. In a classroom it is just efficient to wait until the vast majority of students are developmentally ready before introducing a subject. The delayed "arithmetic" (be sure you know what the author means by the term) approach is often to make more time for early reading instruction, which the students are fully developmentally ready for.

 

In the further past, arithmetic was delayed until after students were reading Latin fluently. Some of the delayed arithmetic is in this tradition, even if fluency switched from Latin to English.

[SorrelZG]

If it is the difference between loving math and hating it, and between a joyful, rich childhood and a miserable one, then I would chose whatever path resulted in the former. For us that has meant leaving off formal curricula and it hasn't delayed anything (im not sure how to delay math in general, it has proven unavoidable) and has redeemed much time and effort for other things.

[FairyMom]

The only group I know who believes in this is the Waldorf crowd.

 

Just a slight disagreement. Although I'm not a Waldorf purist, they teach math in 1st grade, multiplication, division, addition and subtraction at the same time, not at 10. Unless that particular mom is into delaying.

[regentrude]

I've seen reports comparing education around the world. Some European countries that outperform the USA with less hours and less money, don't teach reading until 7, or math until 9. They wait until the vast majority of children are developmentally ready, they clear the schedule of all the clutter, and teach the priority subject.

 

 

Do you have an example of countries where they wait with math until age 9? I know that many do not start formal schooling until age 7, but I can not think of a European country that does not start with math right away.

[EKS]

So what makes something formal training? If you used a program that didn't require paper and pencil work, would that be considered informal? Because learning about money and measurement still requires a lot of understanding of math concepts.

 

I'm going to go out on a limb here and say something utterly un-PC.

 

I believe all the hooha about what age to start various levels of math education (most notably Algebra I, but arithmetic as well) really boils down to the fact that learning math (or learning *anything* for that matter) requires a certain level of intelligence. Up to a certain age on an absolute scale, people get more intelligent as they get older. So, frankly, smarter kids will be ready for math instruction earlier.

 

When people put ages on things, what they're really doing is trying to ensure that a certain percentage of the population will "get it." So if you raise the age on teaching single digit addition and subtraction from 6 to 12, you go from having maybe 50% of the kids successfully mastering it to 99% mastering it (I'm making these numbers up BTW).

 

IMHO.

[ErinE]

I'm not sure what makes 10 a more developmentally appropriate age for beginning math than six. If a child can perform basic math with fiat money (a highly abstract concept), than that same child should be able to understand 2+2=4. Basic math is getting familiar with math relations. If you start at 10, even a child particularly gifted at math will be working at a level other children his age began 4 years prior.

 

In the US, another problem with a delayed approach is if the child is on a college prep route, Algebra I needs to be completed in ninth grade. If it's a rigorous college prep, Algebra I needs to be done in eighth grade. Assuming average American school age, the child is 13 or 14 when he begins algebra. He only has 3-4 years of formal mathematics, assuming you start at the lower end of your suggested range. I honestly don't think that's enough time to quickly perform a broad range of calculations before beginning a higher level of abstract study.

[regentrude]

In the US, another problem with a delayed approach is if the child is on a college prep route, Algebra I needs to be completed in ninth grade. If it's a rigorous college prep, Algebra I needs to be done in eighth grade. Assuming average American school age, the child is 13 or 14 when he begins algebra. He only has 3-4 years of formal mathematics, assuming you start at the lower end of your suggested range.

 

And actually, schools in the US are starting algebra and proof based geometry already late, compared to higher performing countries.

[stripe]

Just a slight disagreement. Although I'm not a Waldorf purist, they teach math in 1st grade, multiplication, division, addition and subtraction at the same time, not at 10. Unless that particular mom is into delaying.

I take back my Waldorf comments. I was apparently misinformed, or there are some differences in approaches.

 

So are there any groups who delay math en masse?

[SorrelZG]

It's been a while but from what I recall from the 1930s article, those they worked with on the delayed scheduled started out behind in certain things at the beginning of the year but by the end had completely surpassed their age peers (due to various factors described). The whole point (from what I recall) was the belief that by rearranging when things were taught, time could be used more efficiently to the increase and even acceleration of the child.

 

.. and I thought when the Bluedorns started formal curriculum it was right on level, not behind.

[stripe]

I believe all the hooha about what age to start various levels of math education (most notably Algebra I, but arithmetic as well) really boils down to the fact that learning math (or learning *anything* for that matter) requires a certain level of intelligence. Up to a certain age on an absolute scale, people get more intelligent as they get older. So, frankly, smarter kids will be ready for math instruction earlier.

I saw the DVD "Finland Phenomenon," and in it, an American teacher who now lives and teaches middle school (? this is my memory, based on how they looked) aged students. Anyway they showed him asking his student -- in English, mind you -- at what age they learned to read, and I think most of them said 6. (They can all read now, incidentally.) He then asked them if they had trouble or were ever worried/stressed about learning, and they sort of laughed and said, of course not. His feeling was that when you set up an expectation of success at an age/stage when a large number of children won't be capable of doing that, then you start in motion a feeling of failure, both on the part of the children themselves AND a sort of branding by the school/teacher that these children are failures.

 

It is a show worth watching, in my opinion.

[SorrelZG]

It is a show worth watching, in my opinion.

 

Oh great, and it's on YouTube .. there goes an hour of my day. :tongue_smilie:

[serendipitous journey]

Humbled by your closing words and thankful for them all, especially the links. I have still not decided what to do, though I still leaning very much in favor of MEP which does seem to address the ideas that make sense to me (ensuring mastery with small numbers first) without doing away with curriculum or structure or whatever you want to call it. The idea of not having a plan does terrible things to my nerves, but as a former teacher it is oooooh soooooo easy to slip into old paradigms. Thanks for all the input! :grouphug:

 

:) and :grouphug:. MEP is terrific, if time-intensive (that is just a heads-up, I never feel good about rec'ing it to somebody teaching many children without the qualifier that it takes a chunk of time) .... I really am sure that the children you are teaching will be learning math well; but that's easy for me to say b/c you are so clearly conscientious. It is rather more work, and less certainty, on the end of being the conscientious one!!!

 

ETA: I'm PMing you with this link as well: have you seen the livingmath site?

Edited August 23, 2012 by serendipitous journey
adding link.

[TippyCanoe]

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[TippyCanoe]

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[serendipitous journey]

I saw the DVD "Finland Phenomenon," ... His feeling was that when you set up an expectation of success at an age/stage when a large number of children won't be capable of doing that, then you start in motion a feeling of failure, both on the part of the children themselves AND a sort of branding by the school/teacher that these children are failures.

 

It is a show worth watching, in my opinion.

 

thank you for this! I've been chatting with folks about the need to not-fret about reading in the pre-primary years; I'm looking forward to watching this & am glad to have something to recommend to people ...

[ErinE]

And actually, schools in the US are starting algebra and proof based geometry already late, compared to higher performing countries.

 

I think this is a problem in the US. Children should receive greater exposure to algebraic concepts and geometry proofs before reaching the courses designated "Algebra" and "Geometry." For American students, it segregates basic math practices into arbitrary buckets. But I don't need to tell you that, regentrude! I follow your posts closely when it comes to schooling.

[stripe]

I've read quite a bit about math instruction in Japanese primary schools just from curiosity. They seem to have highly scripted lessons in a way, but they are all based on stories or hands-on activities in the early grades.

 

Some years ago, I watched a video online of a Japanese elementary math class.

I think it was the ones at Global Education Resources

http://www.globaledresources.com/resources.html (go to the bottom)

But the teacher, Hiroshi Tanaka of the Univ of Tsukuba has a bunch on his website too

 

http://www.criced.tsukuba.ac.jp/math/video/previous/

 

Watch them when you have time.

(ETA: I am not really sure these are the ones I first watched, but they're interesting nonetheless!)

 

I've long thought Japanese elem schools sound really great. I have middle grade math bks (7-9?) in English translation from Univ of Chicago and they are organized around the daily problem to be solved as well. For what it's worth Global Ed Resources now has gr 7-9 texts from Tokyo Shoseki for sale as PDF download. http://www.globaledresources.com/products/books/mathematics-international/index-7-9.html

Edited August 23, 2012 by stripe

[Hunter]

My preference is to hear about efficient methods, more than the methods of the highest ranking countries that require LONG hours and highly trained teachers.

 

Also I have no interest in studies based on students that are not representative of the total population, and are just the cream skimmed off the top.

 

I know I'm throwing out the baby with the bath water by not spending more time studying Asian math methods, but I have only so much time to study, and I choose not to invest much of my time studying a time intensive method best practiced by highly trained teachers.

 

It's in some countries' current best interest to invest heavily in raising the math scores of all, or just a small segment, of their population, at the expense of other things. Their methods and sacrifices are not always worthy of copying for people with other priorities and resources. "The best" are not always worth attempting to copy, for so many reasons. I don't try to make very child/student into an elite gymnast, sprinter, marathon runner, writer, mathematician, artist, etc. Trying to be the "best" in EVERYTHING and in areas where the student is average results in failure and injuries and confusion. "Successful" methods need to be looked at in context.

 

In GENERAL math instruction should be based upon average child development. Gifted children should be ALLOWED to move ahead if the child AND mom want to make math a priority and ENJOY moving ahead. GENERAL math instruction shouldn't be based on the development and abilities of children capable of COMPETING for limited spaces designed to prepare GIFTED people to further the interests of mankind or the power of a country.

 

Stripe thanks for the tip on the Finland video. It sounds interesting.

Edited August 23, 2012 by Hunter

[regentrude]

My preference is to hear about efficient methods, more than the methods of the highest ranking countries that require LONG hours and highly trained teachers.

 

This is a contradiction as the most efficient method is to have a highly trained teacher. there are subjects that can not be effectively taught by somebody who has not mastered the subject material levels above what is taught.

As for the long hours: time on task is the second ingredient for mastery. Nobody would expect a violinist to play well without hours of practice; the same goes for every skill.

There is no such thing as an efficient math teaching method that involves minimal time and a clueless teacher.

 

Also I have no interest in studies based on students that are not representative of the total population, and are just the cream skimmed off the top.

Finland does not differentiate at all; all student receive pretty much the same education.

 

It's in some countries' current best interest to invest heavily in raising the math scores of all, or just a small segment, of their population, at the expense of other things...

Can you name an example of that "expense"? I find US public schools to be lacking in almost all subjects compared with general schools (i.e. not for small segments) elsewhere: math is behind, foreign language instruction is almost nonexistent, science education is sorely lacking... I can not identify a single discipline where the schools are performing better than in my European home country, which, incidentally, accomplishes the outcomes with much shorter school days than in the US. So, at what 'expense" do the better math scores come? (Btw, those countries usually have better reading and science scores as well. Kids in Singapore, which is top performing, are all bilingual... so they are certainly not sacrificing in the language department)

 

In GENERAL math instruction should be based upon average child development.

I do not believe that American children are developmentally delayed compared with their peers elsewhere in the world - but what is considered developmentally appropriate for the average child in the US is years behind what other countries deem suitable for their average children. Hm..... Edited August 23, 2012 by regentrude