why not delay math?

[shinyhappypeople]

I was reading (again) about L.P. Benezet's experiment last night. I find it intriguing.

 

Where did our tradition of starting formal math at 5/6 begin?

 

Why not wait until the brain is more mature (10/11) and they could, in theory, accomplish in a year or two what takes 4 or 5 years for younger students?

 

My younger DD is incredibly mathy and doesn't need or want to wait, but my I think my older DD would benefit immensely from extra time. Due to circumstances, I don't have the luxury of postponing math instruction, so she's stuck with a fairly "pushy" (her words) math schedule :(

 

This quote really resonated with me:

 

(link)

 

"Today whenever we hear that children aren't learning much of what is taught in school the hue and cry from the educational establishment is that we must therefore teach more of it! If two hundred hours of instruction on subject X does no good, well, let's try four hundred hours. If children aren't learning what is taught to them in first grade, then let's start teaching it in kindergarten. And if they aren't learning it in kindergarten, that could only mean that we need to start them in pre-kindergarten! But Benezet had the opposite opinion. If kids aren't learning much math in the early grades despite considerable time and effort devoted to it, then why waste time and effort on it?"

 

Thoughts? :)

[shinyhappypeople]

Here's an older (1986) NY Times article about this issue.

ABOUT EDUCATION; LEARNING MATH BY THINKING

 

Why is this point of view largely ignored in mainstream education and even mainstream homeschooling?

 

I'm guilty of ignoring it, too. I'd read about Benezet a couple of years ago, but didn't think much about it, to be honest.

 

Now, as I see my older DD suffering from the push-push-push of having to keep up with "grade level" for the sake of standardized testing I'm rethinking the issue. (For better or worse, we homeschool through a charter so the requirements exist and must be dealt with.)

 

I think that the "better early than late" approach to math ed has actually harmed older DD. I wish I could turn back the clock and spend the last 3 years limiting math instruction to playing games with her, measuring things, playing store (money) and giving her brain time to mature.

[BlsdMama]

When oldest DD hit a wall with algebra, we re-evaluated our math process, lol. :glare:

 

The Bluedorn's (Teaching the Trivium) also have written on delaying math.

 

So, about 3-4 years ago we decided to delay math for our daughter Elizabeth, then in the 1st grade. Poor little guinea pig. She is now ending her fourth grade year and has just turned 10. We are preparing to begin math. I did, slightly worried, pick up a 3rd grade math book last year and do 1-2 weeks worth of math to see if she would pick it all up as easy as all the articles promised. She did indeed. BTW, I will add that while she picks up things easily enough I would not qualify her as overly academic, just average in this area. She's a sweet little thing and not contrary so that certainly helps as far as a willing attitude, but I would not say she has an extraordinary natural aptitude towards all things mathy.

 

Without any formal math study she does understand math, money, multiplication, time, carrying in addition, borrowing, etc.

 

Honestly? I have NO regret and am consciously delaying math for all of my littles with ONE exception - we are having fun reading through some of the Life of Fred books. We also obviously tell time, cook, let them play with money, etc. I'm not one whit sorry AND Elizabeth and Rebecca think they "LOVE" math. :D Win/Win.

[Spy Car]

I was reading (again) about L.P. Benezet's experiment last night. I find it intriguing.

 

 

Where did our tradition of starting formal math at 5/6 begin?

 

 

Why not wait until the brain is more mature (10/11) and they could, in theory, accomplish in a year or two what takes 4 or 5 years for younger students?

 

 

My younger DD is incredibly mathy and doesn't need or want to wait, but my I think my older DD would benefit immensely from extra time. Due to circumstances, I don't have the luxury of postponing math instruction, so she's stuck with a fairly "pushy" (her words) math schedule :(

 

 

This quote really resonated with me:

 

 

(link)

 

 

"Today whenever we hear that children aren't learning much of what is taught in school the hue and cry from the educational establishment is that we must therefore teach more of it! If two hundred hours of instruction on subject X does no good, well, let's try four hundred hours. If children aren't learning what is taught to them in first grade, then let's start teaching it in kindergarten. And if they aren't learning it in kindergarten, that could only mean that we need to start them in pre-kindergarten! But Benezet had the opposite opinion. If kids aren't learning much math in the early grades despite considerable time and effort devoted to it, then why waste time and effort on it?"

 

 

Thoughts? :)

 

 

Why not delay speaking?

 

 

This makes no sense. Why be learning at 10 what you could be learning at 5? There are other things to learn at 10.

 

 

Young minds are amazing things. They are made to learn, and through the process of learning a neural network of wiring connections is formed in the brain. A brain that is stimulated with rich experience is very different that one that is not (all things being equal).

 

 

Obviously, doing so-called "formal" education is not the only way to stimulate a young developing mind. Creative play and exploration of their world are critical experiences for young children. But there are ways of capitalizing on children's propensity for play (and the good that comes from that) by using means that are both playful and effectively begin to develop number sense.

 

 

Just as language is a complex system that is best to introduce early (something that most of us don't even have to think about, because it happens naturally) so too can we naturally incorporate and exposure to math and number sense.

 

 

Then in the pre-K/K years there are developmentally oriented programs that help children learn, explore, create, and discover mathematical concepts in ways that "make them theirs." This makes math a native language.

 

 

I don't believe in a million years that a child whose math education is neglected for 10 years would ever develop the same number sense as if they'd started young. Brain connections are either formed or they wither.

 

 

While developmentally inappropriate teaching methods can be counter-productive, and I'm not arguing otherwise, cultivating young minds to develop number sense and mathematical reasoning in developmental appropriate ways makes sense. Where "delay" of important cognitive learning stages is a road to ignorance. The brain isn't built in a day. A brain that has not been exercised and strengthened though a host of means (including creative play) will not be the same in a 10 year old who has not had that advantage as it would be as they had been.

 

 

I think this is totally wrong-headed thinking.

 

 

Bill

[BlsdMama]

 

Why is this point of view largely ignored in mainstream education and even mainstream homeschooling?

 

 

Fear.

[BlsdMama]

Why not delay speaking?

 

 

Well, Bill, in a way we do. Think of it this way...

 

You COULD drill your six month old in speech, encouraging more sounds, correcting the sounds they make. You could set aside an hour each day to go ahead and "work with" your nine month old. By 12 months, she'll be making her first tentative words. Then, up the rigor of your program. Start working to get her to string together 2 words by modeling. Set aside an hour each day to this. Work with her. Visual aids will probably add to her learning. By 18 months she'll be putting two words together. Again, advance your program and expect more rigorous results. By two she'll be saying short sentences.

 

Guess what? So will MY child. And I didn't spend an hour each day "working" on speech. I just integrated speech all around her. I enjoyed her, played verbal games, and let her natural inclination come out.

 

There will very definitely be a time for me to correct any speech issues she has, correct wrong pronoun useage, encourage better grammar and sentence structure... However, the focused time is a little unnecessary.

 

Math is a little like this.

We push, in the name of rigor, abstract thinking on little people who are still in a concrete phase.

 

People who believe this don't AVOID math. They just don't "do" math like the parent above might "do" speech. They notice and appreciate math concepts in every day life and reinforce concrete thinking. They recognize and appreciate that their children will, very naturally, come to a phase where they are ready to think in abstract terms. This is the time in which all of first four YEARS of "stuff" the first parent did, is covered in four MONTHS... or possibly less based on my real life experience.

 

Thinking in theories - this is wrong thinking, is fine. But, studies are showing otherwise. There are studies showing that teaching math the way society is currently doing it is seriously undermining later, more advanced math. I really think they are correct. Early math did NOT help us.

 

It's the idea that if some is good, more is better. Great theory. Unfortunately it tends not to play out in real life.

Edited April 13, 2012 by BlsdMama

[WishboneDawn]

We "delayed" math.

 

Actually we delayed formal instruction as we were unschoolers but there was a lot of play, workbooks-by-choice, games, sorting beads, jigsaw puzzles, etc. The transition into formal math at around 8 or 9 was not so hard.

 

Kids are ready for a lot of math at a very young age and have a LOTS of fun with it. No need to deny them that fun either by starting formal work to early OR by not introducing math at all.

[Lang Syne Boardie]

I've seen children ages 10-12 who don't know basic math. 10-12 years old, unable to tell time, add a set of sums, work with the fractions required for cooking or dividing something among friends, handle money...they aren't happy that they can't do it. They're ashamed.

 

I can't imagine doing that to a child on purpose.

 

If the parent/teacher understands the math concepts, there is no reason that earlier math lessons should be drudgery to either parent or child. The concepts can be taught with games, manipulatives, and fun. My children all loved their preschool and kindergarten math lessons, and I enjoyed that time with each of them, as well.

[Down_the_Rabbit_Hole]

Delaying math does not mean you are not teaching ANY math skills, you are just not doing it in a formal manner. Sitting down and doing formal math with dd was counter productive. We ditched the math books and are just having fun, weekly we cover math skills but with games and hands on learning. We take games farther and discuss 'what ifs'. She is getting a grasp of numbers, methods, logic, and more just by playing math. She is taking math to a different level on her own. I will be doing this again next year and probably will not be doing "Formal math" until 4th.

[Spy Car]

Well, Bill, in a way we do. Think of it this way...

 

You COULD drill your six month old in speech, encouraging more sounds, correcting the sounds they make. You could set aside an hour each day to go ahead and "work with" your nine month old. By 12 months, she'll be making her first tentative words. Then, up the rigor of your program. Start working to get her to string together 2 words by modeling. Set aside an hour each day to this. Work with her. Visual aids will probably add to her learning. By 18 months she'll be putting two words together. Again, advance your program and expect more rigorous results. By two she'll be saying short sentences.

 

Guess what? So will MY child. And I didn't spend an hour each day "working" on speech. I just integrated speech all around her. I enjoyed her, played verbal games, and let her natural inclination come out.

 

There will very definitely be a time for me to correct any speech issues she has, correct wrong pronoun useage, encourage better grammar and sentence structure... However, the focused time is a little unnecessary.

 

Math is a little like this.

We push, in the name of rigor, abstract thinking on little people who are still in a concrete phase.

 

People who believe this don't AVOID math. They just don't "do" math like the parent above might "do" speech. They notice and appreciate math concepts in every day life and reinforce concrete thinking. They recognize and appreciate that their children will, very naturally, come to a phase where they are ready to think in abstract terms. This is the time in which all of first four YEARS of "stuff" the first parent did, is covered in four MONTHS... or possibly less based on my real life experience.

 

Thinking in theories - this is wrong thinking, is fine. But, studies are showing otherwise. There are studies showing that teaching math the way society is currently doing it is seriously undermining later, more advanced math. I really think they are correct. Early math did NOT help us.

 

It's the idea that if some is good, more is better. Great theory. Unfortunately it tends not to play out in real life.

 

But you are setting up a false dichotomy. One need not (and ought not) sit down with a infant and a stack of flash-cards. Defeating that idea is defeating a "straw-man."

 

There is a rich world that falls in the sensible Third Way of using neither developmentally inappropriate means and "delay." The creative enriching space between them is what we should hope to occupy.

 

Between two evils chose neither.

 

Bill

Edited April 13, 2012 by Spy Car

[Ellie]

I've seen children ages 10-12 who don't know basic math. 10-12 years old, unable to tell time, add a set of sums, work with the fractions required for cooking or dividing something among friends, handle money...they aren't happy that they can't do it. They're ashamed.

Delaying formal math doesn't mean not teaching children to tell time or handle money or being able to cook using measuring cups and spoons. We delayed *formal* math, although not on purpose--none of the things we like today were available in 1982 when I started hsing--but my dc learned to tell time and all those things in the course of normal life.

 

And the discussion is about delaying *formal* math, not withholding basic arithmetic knowledge and games and the things you said you did with your dc.

 

You should read the article. :)

[Lang Syne Boardie]

Those of us who teach math early with great success are teaching math formally (if by 'formally' we mean using curriculum and a scope and sequence) but we aren't sitting our toddlers down to math workbooks, either.

 

My children go through Ray's Primary Arithmetic at age 4 without ever picking up a pencil or looking at the book. "I" hold the book and follow the lessons as I chat and play with my child. We're just playing with blocks, buttons, and beans, and they easily learn all four basic operations and fractions. Bill 'plays' with Miquon. His child doesn't sit at the kitchen table with a stack of worksheets, either.

 

But Ray's and Miquon are both formal programs.

 

Don't most homeschooling parents play games and notice math (and science and language) concepts in daily life with their little children? That's something you do whether you use a formal program or not, or even whether you homeschool or not.

[WishboneDawn]

Well, Bill, in a way we do. Think of it this way...

 

You COULD drill your six month old in speech, encouraging more sounds, correcting the sounds they make. You could set aside an hour each day to go ahead and "work with" your nine month old. By 12 months, she'll be making her first tentative words. Then, up the rigor of your program. Start working to get her to string together 2 words by modeling. Set aside an hour each day to this. Work with her. Visual aids will probably add to her learning. By 18 months she'll be putting two words together. Again, advance your program and expect more rigorous results. By two she'll be saying short sentences.

 

Guess what? So will MY child. And I didn't spend an hour each day "working" on speech. I just integrated speech all around her. I enjoyed her, played verbal games, and let her natural inclination come out.

 

There will very definitely be a time for me to correct any speech issues she has, correct wrong pronoun useage, encourage better grammar and sentence structure... However, the focused time is a little unnecessary.

 

Math is a little like this.

We push, in the name of rigor, abstract thinking on little people who are still in a concrete phase.

 

People who believe this don't AVOID math. They just don't "do" math like the parent above might "do" speech. They notice and appreciate math concepts in every day life and reinforce concrete thinking. They recognize and appreciate that their children will, very naturally, come to a phase where they are ready to think in abstract terms. This is the time in which all of first four YEARS of "stuff" the first parent did, is covered in four MONTHS... or possibly less based on my real life experience.

 

Thinking in theories - this is wrong thinking, is fine. But, studies are showing otherwise. There are studies showing that teaching math the way society is currently doing it is seriously undermining later, more advanced math. I really think they are correct. Early math did NOT help us.

 

It's the idea that if some is good, more is better. Great theory. Unfortunately it tends not to play out in real life.

 

I think you and Bill actually agree.

 

Don't bother with the fussy formal math in the early years. Fill them up with developmentally appropriate play and activities that will give them a firm understanding of numbers, shapes, basic operations, etc.

 

Math is natural, inescapable and enjoyable. I think a lot of our issues with math would be solved if we looked at it like that rather then as some alien other that we have to impose on humans.

[Lang Syne Boardie]

Delaying formal math doesn't mean not teaching children to tell time or handle money or being able to cook using measuring cups and spoons. We delayed *formal* math, although not on purpose--none of the things we like today were available in 1982 when I started hsing--but my dc learned to tell time and all those things in the course of normal life.

 

And the discussion is about delaying *formal* math, not withholding basic arithmetic knowledge and games and the things you said you did with your dc.

 

You should read the article. :)

 

Ellie, I read the article. I saw a man experimenting on school children in ways that I do not agree with. He suggested teaching one to three 'mathy' concepts per year through sixth grade and then finally getting down to business.

 

I noticed the date of the article. The dawn of the progressive era was a horrible time for using children as guinea pigs in schools. My grandmother went to a school where they were first experimenting with whole language learning and informal math, and she never did learn math and English skills very well. Grandpa went to an old-fashioned school and studied Algebra and Latin in 8th grade. He was only one county away from his future bride, but they went to school in two different universes.

[Mrs Mungo]

Obviously, doing so-called "formal" education is not the only way to stimulate a young developing mind. Creative play and exploration of their world are critical experiences for young children. But there are ways of capitalizing on children's propensity for play (and the good that comes from that) by using means that are both playful and effectively begin to develop number sense.

 

 

I don't believe in a million years that a child whose math education is neglected for 10 years would ever develop the same number sense as if they'd started young. Brain connections are either formed or they wither.

 

?? Nobody is advocating not introducing kids to math. You are arguing against a claim that nobody has made.

[Spy Car]

If we are going to use the term *formal* as a synonym for "developmentally inappropriate" (something I think we ought not do) then I think many of us would find common ground. Don't use means that are developmentally inappropriate for a given child at their stage of development. That makes sense.

 

But DO use "developmentally" appropriate means (and the most creative ones one can come up with at that) to cultivate mathematical thinking in young children. Capitalize on "play" and children's love of interaction and discovery. Respect limits of attention spans. Honor the idea that everyday chores can be small "math lessons" but are not inherently so. Just as we can "narrate" what a young child's is experiencing in their immediate present to help them gain a sense of language, so we can do the same with developing number sense.

 

And there are ways that bridge the so-called "informal" means with the more "formal," but that retain developmentally appropriate (and fun, and effective) means. This is better than delay and better than using developmentally inappropriate means. But there really is a Third Way.

 

Bill

[regentrude]

I am all for delaying any kind of formal academics until maybe age 7. The push for academics in US preschools does not translate into a measurable gain at age 10 compared to countries where kids do not start school until age 6 or 7.

 

This said: age 10/11 is way too late. 11 year olds do geometry and algebra in other countries with better math instruction; the US are behind in math already compare to much of the world.

[catz]

?? Nobody is advocating not introducing kids to math. You are arguing against a claim that nobody has made.

 

:iagree: I think it might be more accurate to say unschooling math rather than delay? Every child is different. Some kids might do better with a more hands on approach to learning math.

 

Both my kids are mathy (DH and I have tech degrees, I also have a degree in math). My oldest raced through math curriculum and is doing algebra as a 5 th grader. My youngest loves games and puzzles (and I suspect shes every bit as mathy as ds) But getting her to do a written math curriculum is like pulling teeth. We are doing a little written work but I also am letting her run on computer games etc. she has not really done fractions in a curriculum, but now understands them and their basic operations. When we do go full bore into a curriculum I suspect we will need to do some skipping.

 

The thought that every kid needs to do X at age Y with curriculum Z is really contrary to what homeschooling is all about IMO.

[LittleIzumi]

?? Nobody is advocating not introducing kids to math. You are arguing against a claim that nobody has made.

 

:iagree::iagree: It's about developing mathematical reasoning and logic and pointing out math in context until a child is ready for formal math. (Rather like letting a child play with C-rods and pointing out interesting principles they discover, instead of sitting them down with a worksheet.) I could not fathom delaying until 7th grade, though. Probably 3rd.

Edited April 13, 2012 by LittleIzumi

[Ellie]

?? Nobody is advocating not introducing kids to math. You are arguing against a claim that nobody has made.

:iagree:

[catz]

I also want to say that a child that gets to the age of 10 without knowing about basic operations might have some neglectful parenting going on. We talk about math as applied to real life constantly. Once my youngest was introduced to the wonder of her own money, basic operations were a breeze. I just don't think a formal curriculum is necessarily the best approach for every kid. I know some ver successful homeschooled young adults that never used a curriculum until algebra level.

[Spy Car]

The thought that every kid needs to do X at age Y with curriculum Z is really contrary to what homeschooling is all about IMO.

 

Of course no one is arguing that every kid has to do X at age Y. What is being argued is that there are fun, effective, developmentally appropriate ways of cultivating mathematical thinking in young children. And that it is better to foster a rich and developmentally appropriate environment that it is to adopt inappropriate means or to "delay."

 

Creative engagement is the best path.

 

Bill

[Carol in Cal.]

Like every other 'better late than early' subject, the way this will play out depends to a tremendous degree on whether you're absolutely certain that your child will not need to go into a regular school or take achievement tests before the 'late' time has come and gone. Don't forget about this issue in considering this approach. If you're uncertain as to how long you can homeschool, then you need to consider how and when your child will transition into the mainstream very strongly in making these decisions.

[Jean in Newcastle]

Math builds so much on itself - esp. arithmetic. I think that playing games and tying it to real life is the way to go IF you have a system in place behind it so that you can build their understanding. For some kids that will be more step by step and systematic than with others. I suspect that those who object to not doing "formal" math are talking about not having a "system" that gives you a framework for building up the proper foundations in math.

[shinyhappypeople]

:iagree::iagree: It's about developing mathematical reasoning and logic and pointing out math in context until a child is ready for formal math. (Rather like letting a child play with C-rods and pointing out interesting principles they discover, instead of sitting them down with a worksheet.) I could not fathom delaying until 7th grade, though. Probably 3rd.

 

This is what I was thinking. Left to my own devices, I'd probably start requiring *formal* math (sit down, here's the math book, let's do the lesson whether you feel like it or not) at 9 or 10 so 4th/5th grade. Prior to that, concepts like money, time, measuring, counting, basic fractions, sums and differences could have been picked up in daily life.

 

However, I am not left to my own devices, so this discussion is theoretical for me at this point. I need to find a way to pull older DD off the math treadmill and unschool math with her, while still jumping through the charter's hoops. It *can* be done. The question is, am I brave enough to try it?

[Spy Car]

Plopping a kid down with a math book is lazy. Doing nothing is lazy.

 

Coming up with creative and exciting ways to turn-on their minds and open pathways of understanding takes work and engagement, but it is so worth it.

 

Bill

[Jean in Newcastle]

This is what I was thinking. Left to my own devices, I'd probably start requiring *formal* math (sit down, here's the math book, let's do the lesson whether you feel like it or not) at 9 or 10 so 4th/5th grade. Prior to that, concepts like money, time, measuring, counting, basic fractions, sums and differences could have been picked up in daily life.

 

However, I am not left to my own devices, so this discussion is theoretical for me at this point. I need to find a way to pull older DD off the math treadmill and unschool math with her, while still jumping through the charter's hoops. It *can* be done. The question is, am I brave enough to try it?

 

I took our curriculum, got the teacher's guide which has suggestions for extra games and activities, looked up stuff online, and have created my own program that follows the progression of the text without all the sit-down work. What work we do, is done on the write-erase board.

[SailorMom]

Like every other 'better late than early' subject, the way this will play out depends to a tremendous degree on whether you're absolutely certain that your child will not need to go into a regular school or take achievement tests before the 'late' time has come and gone. Don't forget about this issue in considering this approach. If you're uncertain as to how long you can homeschool, then you need to consider how and when your child will transition into the mainstream very strongly in making these decisions.

 

No doubt!

Just yesterday there was another thread on math suggestions for a kid who has to go back to middle school all of the sudden, has never really done math (it was 'un-schooling'), and now he needs to make up YEARS of formal instruction over the summer.

It's possible he and his parents could have made un-schooling work in the long run, but you just can't shift gears on a kid like that and expect success.

I'm all about teaching (anything and everything) at a developmentally appropriate age, and I agree we start 'formal' academics too early in this country ('formal' versus 'relaxed and learning naturally though play and experiences'), but I think 7 or 8 is as late as I'd dare go with formal (using a text book or curriculum) math.

[shinyhappypeople]

No doubt!

Just yesterday there was another thread on math suggestions for a kid who has to go back to middle school all of the sudden, has never really done math (it was 'un-schooling'), and now he needs to make up YEARS of formal instruction over the summer.

It's possible he and his parents could have made un-schooling work in the long run, but you just can't shift gears on a kid like that and expect success.

I'm all about teaching (anything and everything) at a developmentally appropriate age, and I agree we start 'formal' academics too early in this country ('formal' versus 'relaxed and learning naturally though play and experiences'), but I think 7 or 8 is as late as I'd dare go with formal (using a text book or curriculum) math.

 

That thread was actually what got me thinking in this direction. If it was possible (and it was) for him to be caught up in 6 mos. to a year fairly easily, why am I spending time now pushing something that causes mostly frustration and tears?

 

We're in this for the long haul with older DD, despite my occasional freak-outs, so I'm not too worried about whether or not she would fit (academically) in a classroom.

[SailorMom]

That thread was actually what got me thinking in this direction. If it was possible (and it was) for him to be caught up in 6 mos. to a year fairly easily, why am I spending time now pushing something that causes mostly frustration and tears?

.

 

Did you read that he was actually successful? So far, I don't think they've even started trying. So - we have no idea yet if that kid will catch up.....

[amsunshine]

That thread was actually what got me thinking in this direction. If it was possible (and it was) for him to be caught up in 6 mos. to a year fairly easily, why am I spending time now pushing something that causes mostly frustration and tears?

 

We're in this for the long haul with older DD, despite my occasional freak-outs, so I'm not too worried about whether or not she would fit (academically) in a classroom.

 

I don't know how old your dd is, but have you tried or looked at Right Start? Or at least the Right Start games? It's not exactly "unschooling" but it might provide the balance you need between unschooling and satisfying the charter.

[wapiti]

That thread was actually what got me thinking in this direction. If it was possible (and it was) for him to be caught up in 6 mos. to a year fairly easily, why am I spending time now pushing something that causes mostly frustration and tears?

 

Because, in all likelihood, he will not be caught up fairly easily. There will be nothing easy about it. It will take hours per day, with a talented tutor, and even then, it seems unlikely that his base of math skills will be anywhere close to as solid as it would be if he had been taught math all along. The path taken prior to the present was a mistake, not an example to strive toward. I'm sure you've heard the old saying: there is no royal road to learning.

 

I think there are two different questions that you are considering, though I admit I haven't read this whole thread. (1) whether you can you replace a math curriculum, or certain pieces of a math curriculum, with "living math," and (2) whether should you delay instruction and practice of certain math skills.

 

I think obviously the answer to the first question is yes, you can be creative in how you present lessons. A curriculum is but a tool. You'd want to be careful to include practice. At some point, work does need to be written, and a curriculum happens to be convenient for that, though certainly there are other ways to handle that. (Personally, I don't see a need to reinvent the wheel when someone else has already invented some pretty good ones.)

 

As for the second question, IMO purposely delaying instruction beyond what is reasonable developmentally (which, notably, may involve a different timing for different individual kids) is a mistake, and a move in the wrong direction.

[wapiti]

I don't know how old your dd is, but have you tried or looked at Right Start? Or at least the Right Start games? It's not exactly "unschooling" but it might provide the balance you need between unschooling and satisfying the charter.

 

This. Maybe what you need is a different curriculum, one that focuses more on concepts in a hands-on sort of way. ETA, what you might have liked for the early years is Montessori math, because it is very hands-on and conceptual with the addition of being interest-led, though it's difficult to replicate all of it in a home setting.

Edited April 13, 2012 by wapiti

[shinyhappypeople]

Did you read that he was actually successful? So far, I don't think they've even started trying. So - we have no idea yet if that kid will catch up.....

 

Of course no one knows yet how this particular kid will do. However, the experiment I linked to in the OP (um, I think I linked to it, anyway :tongue_smilie:) showed promising results. It's not the first time I've heard of a normal child mastering arithmetic quickly when they were motivated and ready.

[shinyhappypeople]

This. Maybe what you need is a different curriculum, one that focuses more on concepts in a hands-on sort of way. ETA, what you might have liked for the early years is Montessori math, because it is very hands-on and conceptual with the addition of being interest-led, though it's difficult to replicate all of it in a home setting.

 

Actually, conceptual math absolutely slays her. She hates it. Give her real-world problems (help me plan our garden, help me bake cookies, etc.) and straight forward strategies and she's fine. Try to teach her to "see" the 8 (or whatever) and she shuts down. It's just not how she learns.

[shinyhappypeople]

I don't know how old your dd is, but have you tried or looked at Right Start? Or at least the Right Start games? It's not exactly "unschooling" but it might provide the balance you need between unschooling and satisfying the charter.

 

We have Right Start C (I think it's C?) gathering dust.

 

What a cool program! She hated it.

 

We've also used Singapore in 1st grade. She STILL moans about that one if she sees anything that vaguely looks like the addition/subtraction-bubble things (I can't remember what it's called).

 

Math Mammoth was this last fall. I love, love, love, love Math Mammoth. I wish I'd been taught this way!

 

She hate, hate, hated it.

 

McRuffy was good, but that's a very straight-forward, gentle (mostly) and hands-on program. However, she hit a wall at trying to subtract numbers like 15-8. She needed more explicit instruction beyond "count / take away the bears"

 

Teaching Textbooks is working very well for her at the moment.

 

But...

 

(there's always a but)

 

But, she thinks of math as a pencil and paper exercise and not anything truly useful in real life. So, yeah, she can get the answers right, but I'm not sure what she's learning really matters if it doesn't occur to her to use those math skills in everyday life.

 

This is me: :banghead:

 

We have 6 weeks or so of school left. At the moment, I'm thinking of having her work strictly on puzzles, strategy and problem-solving games. Lots of Brick by Brick, Blokus, Sorry, Monopoly, that type of thing. Let's see if I can get creative and put game playing into math-speak. :)

 

Maybe when she starts 4th grade we can try again. I'm just weary of the whole math mess. And to think I could have skipped all the drama and just waited until 4th/5th to start (in my utopian, "If only I was able to homeschool independently" world).

 

Meanwhile younger DD is *flying* through math. Go figure.

[shinyhappypeople]

]Because' date=' in all likelihood, he will not be caught up fairly easily.[/b'] There will be nothing easy about it. It will take hours per day, with a talented tutor, and even then, it seems unlikely that his base of math skills will be anywhere close to as solid as it would be if he had been taught math all along. The path taken prior to the present was a mistake, not an example to strive toward. I'm sure you've heard the old saying: there is no royal road to learning.

 

What makes you think this?

 

A few years ago I would have agreed with you. But now I wonder if we view math as "hard" because it's introduced to early. My thinking is: wait for the right developmental window (probably later than we usually think) and the student picks it up much more quickly and with less frustration. That was the premise of the Benezet experiment, anyway. In that particular case, the strategy worked well for many (most?) of the kids in the experimental classes.

 

 

 

I think there are two different questions that you are considering, though I admit I haven't read this whole thread. (1) whether you can you replace a math curriculum, or certain pieces of a math curriculum, with "living math," and (2) whether should you delay instruction and practice of certain math skills.

 

I think obviously the answer to the first question is yes, you can be creative in how you present lessons. A curriculum is but a tool. You'd want to be careful to include practice. At some point, work does need to be written, and a curriculum happens to be convenient for that, though certainly there are other ways to handle that. (Personally, I don't see a need to reinvent the wheel when someone else has already invented some pretty good ones.)

 

As for the second question, IMO purposely delaying instruction beyond what is reasonable developmentally (which, notably, may involve a different timing for different individual kids) is a mistake, and a move in the wrong direction.

 

Is our idea of what's generally developmentally appropriate correct, though? Instead of pushing academics (specifically math) at younger and younger ages, would it be better to hold off a few years? The idea that "earlier is always better" deserves some push-back.

 

I'm not talking about denying instruction to an eager child (this would be my younger DD, btw). I'm not talking about refusing to answer questions or teaching appropriate life skills (money, clocks, etc.). But, there is something intriguing about letting the math curriculum be LIFE, at least until the child is a bit older (9? 10?).

[wapiti]

Actually, conceptual math absolutely slays her. She hates it. Give her real-world problems (help me plan our garden, help me bake cookies, etc.) and straight forward strategies and she's fine. Try to teach her to "see" the 8 (or whatever) and she shuts down. It's just not how she learns.

 

Problem-solving offers a great perspective for learning math skills. Problems can provide context for learning a concept. You might get more mileage from working toward application of the straightforward strategies she already knows as tools for solving many diffierent types of problems. When I see "real world problems," I see a call for hands-on context to learn a concept. There are lots of ways to teach concepts (and different sorts of curricula that are conceptual), but avoiding teaching a concept is not particularly helpful for problem-solving more generally.

 

We have Right Start C (I think it's C?) gathering dust.

 

What a cool program! She hated it.

 

We've also used Singapore in 1st grade. She STILL moans about that one if she sees anything that vaguely looks like the addition/subtraction-bubble things (I can't remember what it's called).

 

Math Mammoth was this last fall. I love, love, love, love Math Mammoth. I wish I'd been taught this way!

 

She hate, hate, hated it.

 

McRuffy was good, but that's a very straight-forward, gentle (mostly) and hands-on program. However, she hit a wall at trying to subtract numbers like 15-8. She needed more explicit instruction beyond "count / take away the bears"

 

Teaching Textbooks is working very well for her at the moment.

 

But...

 

(there's always a but)

 

But, she thinks of math as a pencil and paper exercise and not anything truly useful in real life. So, yeah, she can get the answers right, but I'm not sure what she's learning really matters if it doesn't occur to her to use those math skills in everyday life.

 

This is me: :banghead:

 

We have 6 weeks or so of school left. At the moment, I'm thinking of having her work strictly on puzzles, strategy and problem-solving games. Lots of Brick by Brick, Blokus, Sorry, Monopoly, that type of thing. Let's see if I can get creative and put game playing into math-speak. :)

 

Maybe when she starts 4th grade we can try again. I'm just weary of the whole math mess. And to think I could have skipped all the drama and just waited until 4th/5th to start (in my utopian, "If only I was able to homeschool independently" world).

 

Meanwhile younger DD is *flying* through math. Go figure.

 

That must be very frustrating. I think your idea of puzzles and strategy games is a good start. What particular skills was she successful/unsuccessful at learning this year? What are her weak spots, algorithmically or conceptually? I'm feeling the urge to brainstorm, lol.

 

This is a totally off the wall suggestion, because she would not be the typical student for BA, but what would she think of the comic book approach of BA? The practice books are a bit of the puzzle-sort. I have often wondered to what extent that program is really well-designed for kids who may think differently, kids who might struggle more with a more traditional presentation.

 

As far as MM, etc. go, I'd consider whether, in spite of her great dislike, it might be possible to get her through a grade-level of it (or NOT), even slowly and interspersed with something else like the TT. I'm quite certain that I've read more than one post about the long slog being worth it, resulting in a kiddo who understands math so much more after making a big effort to get through a year's worth or so. It really can be a challenging program, even moreso for kids who initially may not think that way, and therein lies the rub - the challenge to think about math another (better) way is the reason that it's good, even though it's hard. (I tell my kids I'm growing their brains, and sometimes that hurts, lol.)

[Mandy in TN]

Is our idea of what's generally developmentally appropriate correct, though? Instead of pushing academics (specifically math) at younger and younger ages, would it be better to hold off a few years? The idea that "earlier is always better" deserves some push-back.

 

I'm not talking about denying instruction to an eager child (this would be my younger DD, btw). I'm not talking about refusing to answer questions or teaching appropriate life skills (money, clocks, etc.). But, there is something intriguing about letting the math curriculum be LIFE, at least until the child is a bit older (9? 10?).

All children are so different. You may be right in thinking that your daughter would have been developmental more ready for math if you had held off a little bit. However, that is water under the bridge and there is no productive reason to chastise yourself for it now.

 

If TT is working, stick with it even if she decides she doesn't care for it. At this point, what will be detrimental is if you keep switching programs.

 

HTH-

Mandy

[SuperDad]

I am all for delaying any kind of formal academics until maybe age 7. The push for academics in US preschools does not translate into a measurable gain at age 10 compared to countries where kids do not start school until age 6 or 7.

 

This said: age 10/11 is way too late. 11 year olds do geometry and algebra in other countries with better math instruction; the US are behind in math already compare to much of the world.

:iagree: with the first part. Any programs used in our household with kids younger than 6/7 are done only when the child wants to. However, I can't speak for using this with typical children because my children are all neurologically atypical (they all test as "exceptionally gifted" or higher but several of them also have mental illnesses and/or developmental issues that affect their learning in both positive and negative ways).

 

The second part, however... I don't think age 10/11 is "way too late". For typical children I would probably start formal math somewhere around ages 8-10 (depending on the child's aptitude, interest, and learning style. It also depends on how much math the child is being exposed to in real life. For most children, I would lean towards the earlier age of 8 or possibly 9, but it all depends on the child and his/her environment). This positions a child to have 4-6 years to master arithmetic and prealgebra before beginning Algebra 1/upper level maths at the entirely respectable age of 14 (8th/9th grade).

Edited April 13, 2012 by SuperDad

[wapiti]

What makes you think this?

 

A few years ago I would have agreed with you. But now I wonder if we view math as "hard" because it's introduced to early. My thinking is: wait for the right developmental window (probably later than we usually think) and the student picks it up much more quickly and with less frustration. That was the premise of the Benezet experiment, anyway. In that particular case, the strategy worked well for many (most?) of the kids in the experimental classes.

 

Is our idea of what's generally developmentally appropriate correct, though? Instead of pushing academics (specifically math) at younger and younger ages, would it be better to hold off a few years? The idea that "earlier is always better" deserves some push-back.

 

I'm not talking about denying instruction to an eager child (this would be my younger DD, btw). I'm not talking about refusing to answer questions or teaching appropriate life skills (money, clocks, etc.). But, there is something intriguing about letting the math curriculum be LIFE, at least until the child is a bit older (9? 10?).

 

First, I agree that it's hard to know what is developmentally appropriate for content. But an even more difficult aspect of that question is developmentally appropriate for what type of instruction? Certainly, different curricula approach things in different ways, and some kids will learn better with more hands-on for longer than other kids. To complicate matters, the same kid might learn math facts and concepts on two slightly different timelines. Moreover, some kids do not develop in a linear fashion, but in fits and starts.

 

As an aside, if the window of "developmentally appropriate" is too wide, that makes it difficult to spot LDs, which then go unaddressed and the hole dug that much deeper.

 

As for why 10/11 would be too big of a delay in formal math instruction, I'm not sure whether I can articulate the reason. It just strikes me as absurd. Brains don't develop in a vacuum; use it or lose it. You can't know who needs more accelerated instruction if no one's getting instruction. (eta, I didn't intend to sound flippant :tongue_smilie: but I think a lack of challenge is a big problem. However, what is an appropriate challenge is the question...)

 

ETA, I should edit my other post but the board is loading too slowly :tongue_smilie:. I was thinking you might take a look at Kitchen Table Math - see the testimonials tab here. Might be a nice way to spend the summer :)

Edited April 13, 2012 by wapiti

[Corraleno]

But, she thinks of math as a pencil and paper exercise and not anything truly useful in real life. So, yeah, she can get the answers right, but I'm not sure what she's learning really matters if it doesn't occur to her to use those math skills in everyday life.

Have you seen the "Your Business" Math Series from Simply Charlotte Mason? They have three versions: bookstore, pet store, and sports store. The idea is that you learn/use math in the process of running your own virtual store.

 

Jackie

[Spy Car]

Because, in all likelihood, he will not be caught up fairly easily. There will be nothing easy about it. It will take hours per day, with a talented tutor, and even then, it seems unlikely that his base of math skills will be anywhere close to as solid as it would be if he had been taught math all along. The path taken prior to the present was a mistake, not an example to strive toward. I'm sure you've heard the old saying: there is no royal road to learning.

 

:iagree:

 

A mistake that should certainly not be emulated.

 

Bill

[regentrude]

I mean, seen a kid whose math instruction was delayed and who then later caught up and became really good at it?

I am not saying it is impossible, I just have never observed it. The kids whom I have personally seen whose homeschooling parents delay math education never caught up and ended up behind and struggling. Algebra 1 at age 17 is not a disaster, but not what I consider a particular success in math education if the child has no developmental issues.

So this whole "delay a few years and then the kid will breeze through because he is ready" may work in theory - just not with the kids I've seen. I'll be happy to hear examples to the contrary.

[Dana]

What makes you think this?

 

A few years ago I would have agreed with you. But now I wonder if we view math as "hard" because it's introduced to early. My thinking is: wait for the right developmental window (probably later than we usually think) and the student picks it up much more quickly and with less frustration.

 

If this were the case, I'd see a much higher pass rate in the developmental math courses I teach at the cc.

 

I see students who think math is hard and they are no good at it because they have never worked at it. They have never learned the foundational skills they need and haven't practiced enough. I use the analogy that I understood how to parallel park when learning to drive, but understanding how it worked was a lot different from actually doing it.

 

I may push my son too hard given what I see in my classes, but he's learning without the calculator, the importance of showing work, and drill with arithmetic facts. We do also do other math, but the basics are learned past mastery.

[Trilliums]

My kids have been doing pretty well with what I consider a delayed approach. We were, however, mathematically active.

 

DS does have LDs and formal math curricula caused a tremendous amount of frustration in an otherwise hardworking and compliant young person. We started homeschooling him in 1st grade. I tried math u see first. Oy! What a struggle. I stepped way back from demanding written math work from the kids and instead relied heavily on the Living Math website. For years their math primarily consisted of reading math readers, playing dice games, card games, using measuring cups/spoons, measuringg the perimeter of our yard and calculating how many laps made a mile, measuring the length of our cats' tails snd comparing it to the length if their whiskers,etc etc. I did actively strive to expose them to math concepts and to involve them in math processes. I would periodically try out math textbooks, but for the most part we continued on this path. By the time oldest son was in 7th grade, I afmittedly was concerned. In my mind, this was the time by which he should be transitioning to a math program in order to progress through high school math. He has always been interested in science and I wondered how in world he would manage any kind of career considering his attitude toward math curricula. I did discuss this with my kids--actually from the beginning I was open about the difference between what they were doi g and what schools did. DS just said he would find a way. Ok, to wrap this up, in 8th grade, DS worked through Saxon Alg 1/2 and Saxon Alg 1. Now, in 9th grade he is doing AoPS Geometry and Alg 2 w/ the public schools text book. He plans to go to ps precalculys in 10th grade. This mitivation came from within in order for him to meet his educational goals. So, in our experiences, kids can progress through high school level formal math curricula without having completed years of math worksheets. He is doing very well in his math although he works slowly. He is methodical and thoughtful in his approach: be it in math or any other subject. My younger son is in 8th grade and was having a rough patch with Alg. But, he is now on his second week of AoPS intro to algebra and doing great! To get to a point where he was ready to tackle AoPS, he did have gaps he needed filled in. Khan academy worked wonders for this and DS started AoPs at ch 4. I think both kids have strong analytical skills and they do not have the math phobia or hang ups I expect they would have developed had I continued to demand they follow formal math programs in elementary.

 

Sorry for so many typos! I am babysitting a sick neighbor and using my phone.

[garddwr]

What makes you think this?

 

A few years ago I would have agreed with you. But now I wonder if we view math as "hard" because it's introduced to early. My thinking is: wait for the right developmental window (probably later than we usually think) and the student picks it up much more quickly and with less frustration. That was the premise of the Benezet experiment, anyway. In that particular case, the strategy worked well for many (most?) of the kids in the experimental classes.

 

Is our idea of what's generally developmentally appropriate correct, though? Instead of pushing academics (specifically math) at younger and younger ages, would it be better to hold off a few years? The idea that "earlier is always better" deserves some push-back.

 

I'm not talking about denying instruction to an eager child (this would be my younger DD, btw). I'm not talking about refusing to answer questions or teaching appropriate life skills (money, clocks, etc.). But, there is something intriguing about letting the math curriculum be LIFE, at least until the child is a bit older (9? 10?).

 

I know this thread is a few days old--I subscribed when I first saw it but am just now getting around to reading, we've had a busy couple of days.

 

FWIW, I think that formal math instruction in the early years is often unnecessary and can be harmful (by pushing children who aren't ready to conceptually grasp an idea, especially in the abstract). I see math as a language, and view the early years as a time for exposure and immersion, but not for learning formal grammar. We play with cuisinaire rods, balance scales, abaci, money and other math manipulatives, and we cook and measure and weigh--but I haven't felt a need to follow a specific curriculum. Dd8 started MM2B in February, and will finish it this week and start 3A. It's the first time she has done more than an occasional page from any curriculum. I've tried occasionally in the past and it was obvious she wasn't ready. I won't say she loves math, but this time around she understands and can apply it, and is moving fast. I'm planning to start ds6 (almost 7) in Math Mammoth within the next month because I think he is ready (he frequently answers before dd when I am doing oral questions with her)--it really depends on the child.

I'm comfortable waiting until about 3rd grade before expecting a child to work through a curriculum largely because this was my mom's approach (she basically unschooled us in a very language and math rich environment for the early years, then sent us to the local school anywhere between 2nd and 4th grade). For my family, it work--I remember being introduced to a lot of things in third grade that I was seeing for the first time (addition and subtraction with regrouping, for example) and breezing right through because I had a very good understanding of what numbers were (I'd spent the previous summer selling vegetables from our small family farm, adding up prices and making change). I didn't pursue math past high school (majored in Anthropology!) but one of my brothers has engineering degrees from Stanford and MIT, another was just accepted as a PhD candidate in Statistics at Duke.

 

There is a math program on the market that can help a parent teach math primarily through real-life exposure and still track and document progress through the various concepts. If you're not familiar with it, you should look at Math on the Level. I used this program when I was working through a charter school program in California.

 

I do think it is important to young children to have lots of exposure to numbers and other mathematical concepts, and lots of opportunities to manipulate and make discoveries with them--but I believe this is best done in the context of life, not a do-the-next-lesson curriculum.

[BlsdMama]

I've seen children ages 10-12 who don't know basic math. 10-12 years old, unable to tell time, add a set of sums, work with the fractions required for cooking or dividing something among friends, handle money...they aren't happy that they can't do it. They're ashamed.

 

I can't imagine doing that to a child on purpose.

 

If the parent/teacher understands the math concepts, there is no reason that earlier math lessons should be drudgery to either parent or child. The concepts can be taught with games, manipulatives, and fun. My children all loved their preschool and kindergarten math lessons, and I enjoyed that time with each of them, as well.

 

But I guess this is my PERFECT example.

 

We did NO formal math. But they think they love math because math is part of their lives.

 

My 10yo can double or triple a recipe. She can tell time, count money, add, subtract, and multiply. How can a ten year old NOT?? This is without formal instruction.

 

Do the kids people are talking about do nothing but watch television? How do they know when their favorite show is on? How do they count money left over from birthdays? How do they make muffins?

 

How can you be TEN or TWELVE and have ZERO exposure to math?

And really, is PAPER math any type of substitution? Now I think I understand why some kids don't get math. They never had their hands on it. :glare:

[BlsdMama]

I think you and Bill actually agree.

 

 

Could be. Bill told me a great way to make coffee once upon a time. I am willing to concede on almost all terms in order to show my gratefulness.

 

Plopping a kid down with a math book is lazy. Doing nothing is lazy.

 

Coming up with creative and exciting ways to turn-on their minds and open pathways of understanding takes work and engagement, but it is so worth it.

 

Bill

 

I should have read further. Yes, yes, we do agree. ;)

Edited April 15, 2012 by BlsdMama

[NoPlaceLikeHome]

Well, Bill, in a way we do. Think of it this way...

 

You COULD drill your six month old in speech, encouraging more sounds, correcting the sounds they make. You could set aside an hour each day to go ahead and "work with" your nine month old. By 12 months, she'll be making her first tentative words. Then, up the rigor of your program. Start working to get her to string together 2 words by modeling. Set aside an hour each day to this. Work with her. Visual aids will probably add to her learning. By 18 months she'll be putting two words together. Again, advance your program and expect more rigorous results. By two she'll be saying short sentences.

 

Guess what? So will MY child. And I didn't spend an hour each day "working" on speech. I just integrated speech all around her. I enjoyed her, played verbal games, and let her natural inclination come out.

 

There will very definitely be a time for me to correct any speech issues she has, correct wrong pronoun useage, encourage better grammar and sentence structure... However, the focused time is a little unnecessary.

 

Math is a little like this.

We push, in the name of rigor, abstract thinking on little people who are still in a concrete phase.

 

People who believe this don't AVOID math. They just don't "do" math like the parent above might "do" speech. They notice and appreciate math concepts in every day life and reinforce concrete thinking. They recognize and appreciate that their children will, very naturally, come to a phase where they are ready to think in abstract terms. This is the time in which all of first four YEARS of "stuff" the first parent did, is covered in four MONTHS... or possibly less based on my real life experience.

 

Thinking in theories - this is wrong thinking, is fine. But, studies are showing otherwise. There are studies showing that teaching math the way society is currently doing it is seriously undermining later, more advanced math. I really think they are correct. Early math did NOT help us.

 

It's the idea that if some is good, more is better. Great theory. Unfortunately it tends not to play out in real life.

The example of the baby is incorrect IMO since by simply speaking and reading to our babies every day we are in a sense teaching them language and exposing them to language:) In fact they babies understand us long before they speak.

 

IMO it is not a good idea to delay math especially when there are plenty of age appropriate and fun ways to learn math for early ages.