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why not delay math?

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#51 garddwr

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Posted 15 April 2012 - 10:56 AM

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.


I agree with you, unfortunately I think math is often taught in ways that are not developmentally appropriate. I think we should look more closely at the language model--find ways to expose children to math through daily life just as we expose them to language. What many children experience is I think rather like taking a 5 year old and trying to teach them a language to which they have had almost no exposure by having them conjugate lists of verbs--they can learn to put the right endings on the verbs, but they are not really learning to use and understand the language. And they can come to think that all there is to the language is conjugating verbs on a page. Children need to experience math as a living, breathing language, an integral part of living in and navigating and manipulating the world around them--THEN when you show them a verb conjugation (mathematical algorithm) on a page they will know what it is all about.

It is possible to use a curriculum as a framework for age-appropriate math exploration, it is equally possible to do it in a more organic way without a curriculum.

#52 shinyhappypeople

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Posted 15 April 2012 - 11:57 AM

I agree with you, unfortunately I think math is often taught in ways that are not developmentally appropriate. I think we should look more closely at the language model--find ways to expose children to math through daily life just as we expose them to language. What many children experience is I think rather like taking a 5 year old and trying to teach them a language to which they have had almost no exposure by having them conjugate lists of verbs--they can learn to put the right endings on the verbs, but they are not really learning to use and understand the language. And they can come to think that all there is to the language is conjugating verbs on a page. Children need to experience math as a living, breathing language, an integral part of living in and navigating and manipulating the world around them--THEN when you show them a verb conjugation (mathematical algorithm) on a page they will know what it is all about.

It is possible to use a curriculum as a framework for age-appropriate math exploration, it is equally possible to do it in a more organic way without a curriculum.


I love how you expressed this. I think that with my older DD most math is really as meaningless to her as conjugating verbs in Russian. She catches on, she can DO it, but she has no idea why.

Now, hand the kid a cookbook and she can bake almost anything from scratch. Fractions in that context makes perfect sense to her.

#53 NASDAQ

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Posted 15 April 2012 - 12:02 PM

Speech is natural. All people in all societies at all times learn to speak. Math is, sadly, not naturally. Whether people learn math or not, and whether they are successful at higher math, is highly dependent on the quality of their math instruction from an early age. Speech is walking. Math is skiing. People do not learn to ski unless taught.

I don't want my children to figure (math) things out on their own. I'm a great fan of guided instruction that is carefully oriented towards success in higher mathematics. My child might look at everyday math and "discover" the base ten system, number bonds, and so on. But he might not. If I guide him thoughtfully through those discoveries, he will make the appropriate discoveries, and he will do so in a reasonable time.

I think the widespread approval for delaying mathematics among classical types is a sign that, by and large, classical home schoolers just don't value math that much. Exactly the same progressive era arguments apply to reading as apply to math.

If anything, I think the North American standards are to go too slowly with math, especially after third grade.

If a child is struggling with math, the solution isn't "do nothing." It's "do something else." That said, a child may well be struggling because he needs to go back and work through an earlier level, because he never really mastered the previous material. I definitely wouldn't put him further behind in such a situation by adding a delay before addressing that problem.

#54 LeslieAnneLevine

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Posted 15 April 2012 - 12:14 PM

I don't want my children to figure (math) things out on their own.


I understand not wanting to leave everything math-related to be figured out (or not), but it's pretty cool when kids discover some stuff themselves. I remember my son realizing you just add 2 each time you add two of the same number together when he was 4, figured out out odd and even numbers when he was 5 ("some numbers have middles and some numbers don't have middles") and square numbers when he was 7.

I didn't start any formal math with him until he was nearly 9 and we don't overdo it.

#55 Trish

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Posted 15 April 2012 - 12:15 PM

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.


:iagree:

An added disadvantage of pushing advanced concepts too early is it gives kids the feeling they're "not good at math" when in fact their brains might just need a little more maturing. As the author of Life of Fred says, algebra is extremely difficult for kids who are not ready for it. The same child can find it easy and fun a year or two later.

#56 Minniewannabe

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Posted 15 April 2012 - 12:28 PM

Personally, I believe nothing should be delayed, nor should anything be advanced too quickly. As a parent, my job is to stay one step a head of my kiddos' brains. I should be teaching just one micro step out of reach especially until about age 6 or 7 when the greatest number of brain synapses are created. It's the reason why kids who have been exposed on average perform academically better than kids who have not. Delaying for the sake of delaying can be just as detrimental as teaching young ones to the point of frustration. And this thought carries to all learning in life including physical skills, music, potty training, etc.

In regards to most homeschoolers, however, what is regarded as purposeful delay is merely waiting on a formal textbook or program. The actual learning is still happening in some form or another which is fine.

:)

#57 shinyhappypeople

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Posted 15 April 2012 - 01:16 PM

Speech is natural. All people in all societies at all times learn to speak. Math is, sadly, not naturally. Whether people learn math or not, and whether they are successful at higher math, is highly dependent on the quality of their math instruction from an early age. Speech is walking. Math is skiing. People do not learn to ski unless taught.

I don't want my children to figure (math) things out on their own. I'm a great fan of guided instruction that is carefully oriented towards success in higher mathematics. My child might look at everyday math and "discover" the base ten system, number bonds, and so on. But he might not. If I guide him thoughtfully through those discoveries, he will make the appropriate discoveries, and he will do so in a reasonable time.

I think the widespread approval for delaying mathematics among classical types is a sign that, by and large, classical home schoolers just don't value math that much. Exactly the same progressive era arguments apply to reading as apply to math.

If anything, I think the North American standards are to go too slowly with math, especially after third grade.

If a child is struggling with math, the solution isn't "do nothing." It's "do something else." That said, a child may well be struggling because he needs to go back and work through an earlier level, because he never really mastered the previous material. I definitely wouldn't put him further behind in such a situation by adding a delay before addressing that problem.


Delaying math doesn't mean never teach it at all. It means (to me) holding off on formal instruction for a few years and guiding a child as he/she explores math in the context of life. The more I think and read about this approach, the more I wonder why it's so controversial.

#58 regentrude

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Posted 15 April 2012 - 01:53 PM

Delaying math doesn't mean never teach it at all. It means (to me) holding off on formal instruction for a few years and guiding a child as he/she explores math in the context of life. The more I think and read about this approach, the more I wonder why it's so controversial.


I think the reason it is controversial is a lack of success stories: the delayed kid who then went on to excel at math. Not merely catch up and become average in math, but really good. (On this whole thread, I think there was one single person who could share a successful experience for her older kids.)
All the families I personally know who delayed math have produced students who are severely behind now that they are approaching college. Unfixable? No. But an endorsement for the method? No.

Edited by regentrude, 15 April 2012 - 01:56 PM.


#59 shinyhappypeople

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Posted 15 April 2012 - 01:58 PM

I think the reason it is controversial is a lack of success stories: the delayed kid who then went on to excel at math. Not merely catch up and become average in math, but really good. (On this whole thread, I think there was one single person who could share a successful experience for her older kids.)
All the families I personally know who delayed math have produced students who are severely behind now that they are approaching college. Unfixable? No. But an endorsement for the method? No.


How long did they delay for?

#60 NASDAQ

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Posted 15 April 2012 - 01:58 PM

Delaying math doesn't mean never teach it at all. It means (to me) holding off on formal instruction for a few years and guiding a child as he/she explores math in the context of life. The more I think and read about this approach, the more I wonder why it's so controversial.


Right, and I wouldn't do that with reading, so I don't do it with math. I don't put a bunch of books around my children and wait until they figure it out. I directly instruct them in phonics. I do the same thing with math.

It's controversial because there's precious little evidence, anecdotal or otherwise, that it ever works out better than either "acceptable" or "a total disaster." And the systems in the world that teach math better than we do have a number of things in common:
- Formal math instruction beginning in earnest by age 5-7;
- Intensive teacher training;
- A combination of direct instruction and guided discovery;
- Time devoted to math practice.

Nowhere do we see formal instruction delayed until 10-11, children left to essentially unschool (or discover through life) arithmetic, an absence of direct instruction, or a lack of deliberate practice of math skills.

#61 Mynyel

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Posted 15 April 2012 - 02:22 PM

I think one of the main problems with this whole thread is everyone is basing opinions off a supposed "norm". But "norm" by whose standards? If we compare ourselves to X country then we stink. If we compare ourselves to a different country then we excel. Who made it a rule that children needed to know all the multiplication facts at 9 or 10? I remember memorizing them, I had no idea what for (when I was 9 and 10). There are teachable moments in children's lives. For instance counting can be taught when they want to know how many ladybugs they just caught in a jar. Money when they want to buy things.

My ds isn't as far "ahead" as his cousin (who is in PS). Does this mean he is "behind"? No, it doesn't.

One poster mentioned kids are ashamed if they don't know these things. Why are they ashamed? Because others make them feel that way. As adults we aren't (generally:glare:) ashamed of things we don't know (because we haven't learned them). Math is the same way. Now before you start in on analogies, to children it is all the same. Something they do not know. Yes it is a life skill and they will need it, but why do kids at such a young age need so much of it?

Who is anyone to say whether delaying is right or wrong for anyone else? Just because one person says "You shouldn't delay" doesn't make them right. Regardless of reasoning. Just because another says "Delaying is good" doesn't make them right. Regardless of reasoning.

All you can go by is your own experience with your own children. This is why we homeschool. So we don't have to conform to the ideas of someone else.

In my experience, with my children, delay of "formal" (read textbook) math would have and has been a good thing. My dd would have benefited greatly. Md ds who has only done "formal" math in the last year has sailed through math where dd struggled as she was much younger when doing the same concepts. She laments over this almost daily:glare:. I have found that as an adult I have learned things a heck of a lot better than when I was younger or even a teenager.

Having a lively debate is all well and good but in the end it doesn't really matter. As long as the child grows into a decent adult that can support himself (or herself!) and family and be happy then who the heck cares if they are doing multiplication at 8 or 10 or 12? Does it really matter *when* they learned it?

#62 shinyhappypeople

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Posted 15 April 2012 - 02:27 PM

Right, and I wouldn't do that with reading, so I don't do it with math. I don't put a bunch of books around my children and wait until they figure it out. I directly instruct them in phonics. I do the same thing with math.

It's controversial because there's precious little evidence, anecdotal or otherwise, that it ever works out better than either "acceptable" or "a total disaster." And the systems in the world that teach math better than we do have a number of things in common:
- Formal math instruction beginning in earnest by age 5-7;
- Intensive teacher training;
- A combination of direct instruction and guided discovery;
- Time devoted to math practice.

Nowhere do we see formal instruction delayed until 10-11, children left to essentially unschool (or discover through life) arithmetic, an absence of direct instruction, or a lack of deliberate practice of math skills.


In the US, earlier rather than later is the status quo, but it doesn't mean it's the best way. It's just the usual way.

The result of early instruction here (US) is not a nation of adults with excellent (or even adequate) math skills. It's produced a society filled with math phobes and, conversely, people who are "good" at math (ie good at plugging in numbers) but have no idea what it all means or why the algorithms work.

I think the risk is in continuing on the same path that has produced such poor results. If what we're doing isn't working (and clearly it isn't), then why not change things up? Why not tweak the variables and see if waiting a few years might actually help.

If the worst happens and the kids end up not retaining math and requiring remedial math work in college, they'll be in good company, as quite a few of their "early math" instructed peers will be right there in class with them.

Edited by shinyhappypeople, 15 April 2012 - 02:31 PM.


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Posted 15 April 2012 - 02:32 PM

Earlier rather than later is the status quo, but it doesn't mean it's the best way. It's just the usual way.

The result of early instruction is not a nation of adults with excellent (or even adequate) math skills. It's produced a society filled with math phobes and, conversely, people who are "good" at math (ie good at plugging in numbers) but have no idea what it all means or why the algorithms work.

I think the risk is in continuing on the same path that has produced such poor results. If what we're doing isn't working (and clearly it isn't), then why not change things up? Why not tweak the variables and see if waiting a few years might actually help.

If the worst happens and the kids end up not retaining math and requiring remedial math work in college, they'll be in good company, as quite a few of their "early math" instructed peers will be right there in class with them.


That's because our early instruction isn't very good. In other nations, we have people who are taught early but are much more competent than ours. That strongly suggests that early instruction isn't the problem; The problem is poor quality of instruction.

We could change an infinite number of variables in North American math. We all live in the short term and I think we should limit ourselves to changing those variables that make us more like countries with successful math programs, or variables that otherwise seem tied to evidence that they may actually be useful. We could decide that all children need to do math on blue paper with red pens, which is changing a variable, but it isn't particularly likely to be helpful.

If math instruction isn't particularly important to you, and so you're willing to just experiment and see what happens, and if they end up in remedial math, so be it, that's fine. We all have different priorities. I don't think, though, that you should be surprised that most people are somewhat more invested in the subject.

#64 ssavings

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Posted 15 April 2012 - 02:35 PM

Curious, why math, specifically? Why not delay all formal academics?

Edited to add: not that this is the way I've chosen to go. I'm just wondering why just math, rather than everything?

Edited by ssavings, 15 April 2012 - 02:38 PM.


#65 shinyhappypeople

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Posted 15 April 2012 - 02:48 PM

That's because our early instruction isn't very good. In other nations, we have people who are taught early but are much more competent than ours. That strongly suggests that early instruction isn't the problem; The problem is poor quality of instruction.

We could change an infinite number of variables in North American math. We all live in the short term and I think we should limit ourselves to changing those variables that make us more like countries with successful math programs, or variables that otherwise seem tied to evidence that they may actually be useful. We could decide that all children need to do math on blue paper with red pens, which is changing a variable, but it isn't particularly likely to be helpful.

If math instruction isn't particularly important to you, and so you're willing to just experiment and see what happens, and if they end up in remedial math, so be it, that's fine. We all have different priorities. I don't think, though, that you should be surprised that most people are somewhat more invested in the subject.


Actually, it's because math is so important to me that I'm willing to take a second and third look at the way things are done and consider an alternate path.

#66 shinyhappypeople

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Posted 15 April 2012 - 02:50 PM

Curious, why math, specifically? Why not delay all formal academics?

Edited to add: not that this is the way I've chosen to go. I'm just wondering why just math, rather than everything?


In our case it's because both of my girls were eager to read pretty early on (3 to 4 yo) so it's never been an issue one way or the other. I'm not into denying an eager child instruction in any age-appropriate skill or topic. Had to add the "age-appropriate" disclaimer, because my 8 year old would love to learn to drive :)

#67 MelAR05

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Posted 15 April 2012 - 03:08 PM

Actually, it's because math is so important to me that I'm willing to take a second and third look at the way things are done and consider an alternate path.


:iagree:

When my oldest daughter hates math and I want her to enjoy it, then I look at other options as well. She picks up mathematical concepts very quickly but hates doing the sit-down formal math. I started off with a formal math program because I thought that was best. I wasn't so concerned then about her loving math but learning math. Now I am questioning it because I feel like I did not help her to enjoy it.

She loves all things to do with science, but I know if I make her sit-down and do formal science it would take away her enthusiasm for the subject.

#68 thefragile7393

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Posted 15 April 2012 - 03:33 PM

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.

Exactly! So true!!! I have my son in a gentle math curriculum right now, but we do a lot of Family Math and Kitchen Table Math, games, cooking, etc. Once I saw how Singapore EB math BOMBED, I went back exactly to what Down_the-Rabbit_Hole is doing. We're going slowly as much as he can handle, and I DO NOT go by the state requirements for each grade, I go by my son and how well he has mastered concepts before moving on. So there is a big difference between doing math and doing formal math. I do wish schools would delay formal math. And while yes other countries with higher math skills then the US start early (and do it for longer hours) how about the kids that don't get it? That can't keep up? I know they are often times given extra help but there's always the few that don't adapt well. Not every system is ideal for every child-but that's the way outside schools make their curriculum. If it works for your child that's great! If not, then you'll have someone like me who struggled horribly with math up to right now in college.

There aren't any big studies done on this because I highly doubt the USDE would dare to find an independent way to do a study. I care about what is the best way for my son to learn. If being unconventional gets him learning and retaining math, then so be it. Same with reading, although reading is a different skill and many kids can't learn to read until they are developmentally ready-which isn't always at age 3,4, or 5. Again, there's a difference between not doing any reading and a formal reading sit down program.
If waiting until later helps a child be a fluent reader (and extra points if he can enjoy it and not find it a drudgery) then that is all that matters. Delaying any type of formal study does not mean kids are running around doing nothing and not learning-I think people are just NOT getting that point at all. Reading the book Better Late Than Early was such a great eye opener. I don't agree with everything that is written, but it helped me to realize that my son just isn't going to fit into the Western "early is better" thinking. That is the beauty of homeschool-you can adapt learning to your child's pace.

#69 Marylou

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Posted 15 April 2012 - 03:34 PM

I started this thread a few years ago on the same topic.

I did not delay math with my girls; I just did the fun hands-on stuff K-2 instead of the worksheet approach which I think many schools use. I would get so frustrated that my DDs would give me the 'deer in the headlights' look when we would use flashcards in 2nd grade. You know, those tricky 7 + 8 and 6 + 7 !!!! Then I started showing them the side of the flashcards that have the answers. What a good tip that was for my situation. I also taught them lots of skip counting songs which came in quite handy when they started learning the multiplication facts (around 9 years old). Sometimes I would just make up completed math sheets and hang them around the house w/o saying anything. IF you want your kids to see something, just hang it on the wall w/o mentioning it :D

My girls both scored great on the ITBS math (6th grade). I do not regret for a moment not keeping up with what the PS say I should be teaching and when.

The fact that one of them keeps begging me to buy the other 2 Ray's Arithmetic books so that she can complete her set and do math in her room on her own time makes all the previous frustration seem like nothing now. Her birthday is coming up soon, and I can't wait to see her smile when she opens a math book as one of her gifts.

OP, thanks for starting this thread!

#70 4blessingmom

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Posted 15 April 2012 - 03:35 PM

Haven't we had this conversation before!?!:tongue_smilie:



Early math? Yes.

Early workbooks/drill & kill? No.



I do think it would be beneficial for many children to do math mainly orally and with manipulatives, or in real-life situations until age 9-10yo. That said, mine do pencil/paper math before then.

#71 4blessingmom

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Posted 15 April 2012 - 03:36 PM

I started this thread a few years ago on the same topic.

.



I knew this all sounded familiar.:lol:

#72 Marylou

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Posted 15 April 2012 - 03:36 PM

That's because our early instruction isn't very good. In other nations, we have people who are taught early but are much more competent than ours. That strongly suggests that early instruction isn't the problem; The problem is poor quality of instruction.

We could change an infinite number of variables in North American math. We all live in the short term and I think we should limit ourselves to changing those variables that make us more like countries with successful math programs, or variables that otherwise seem tied to evidence that they may actually be useful. We could decide that all children need to do math on blue paper with red pens, which is changing a variable, but it isn't particularly likely to be helpful.

If math instruction isn't particularly important to you, and so you're willing to just experiment and see what happens, and if they end up in remedial math, so be it, that's fine. We all have different priorities. I don't think, though, that you should be surprised that most people are somewhat more invested in the subject.


Bolded part not necessary.

#73 cottonmama

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Posted 15 April 2012 - 03:39 PM

I'm speaking more from my own educational experience than from any teaching experience, because... well... see my signature. :D

I don't think anyone should start out planning on a "better late than early" approach to math. It is not better for a child to spend four years of his elementary education without much of a mathematical education. Math can and should be a delight. Just because he will "catch up" by age 10 doesn't mean that he hasn't lost something by not receiving a well-rounded math education.

Of course it seems like the people who support this idea the most are parents whose kids just will. not. delight in math. I'm not going to tell you those kids need you to push math. I'd like to believe that you can always turn it around and help those kids delight in math, but I've never tried. Maybe for some kids it is better to delay.

But I would never make that apply to all kids. I know for a fact that there are kids who will suffer if you don't keep them challenged mathematically.

Edited by cottonmama, 15 April 2012 - 05:39 PM.
Omitted a very important "not". :-P


#74 thefragile7393

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Posted 15 April 2012 - 03:43 PM

:iagree:

When my oldest daughter hates math and I want her to enjoy it, then I look at other options as well. She picks up mathematical concepts very quickly but hates doing the sit-down formal math. I started off with a formal math program because I thought that was best. I wasn't so concerned then about her loving math but learning math. Now I am questioning it because I feel like I did not help her to enjoy it.

She loves all things to do with science, but I know if I make her sit-down and do formal science it would take away her enthusiasm for the subject.

:iagree:I found that too....finding ways to teach without a huge formal curriculum can be a hassle but worth it. I don't expect all kids will enjoy everything, no matter how you try to present it, but if you can at least find ways to teach without killing off too much joy, then you're doing well. My son is the same way with...well..everything lol. I do stuff in small chunks, and find ways to do a lot of science-related, math-related, history-related things without having it be formal.

#75 SuperDad

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Posted 15 April 2012 - 03:48 PM

Bolded part not necessary.


:iagree:

We can disagree civilly.

#76 NASDAQ

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Posted 15 April 2012 - 03:50 PM

Bolded part not necessary.


If someone says "It's fine if my kids end up in remedial math, no big deal because PS kids end up there too," then I don't think that high achievement in math is that important to them.

Lots of things aren't that important to me. I don't particularly mind if my children never learn Latin. I don't mind if they never develop a nice hand. It's not terrible to have different priorities.

If it _is_ important to someone that their child perform as well as that child is able to in math, then what's being suggested makes no sense. We have an idea for which we have no evidence, either locally or internationally, and defending it because "what we do in North America doesn't work very well" (but what is being advocated looks _less_ like countries that do have math instruction than works), isn't a particularly sensible way of approaching the problem.

#77 SuperDad

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Posted 15 April 2012 - 03:58 PM

If someone says "It's fine if my kids end up in remedial math, no big deal because PS kids end up there too," then I don't think that high achievement in math is that important to them.

Lots of things aren't that important to me. I don't particularly mind if my children never learn Latin. I don't mind if they never develop a nice hand. It's not terrible to have different priorities.

If it _is_ important to someone that their child perform as well as that child is able to in math, then what's being suggested makes no sense. We have an idea for which we have no evidence, either locally or internationally, and defending it because "what we do in North America doesn't work very well" (but what is being advocated looks _less_ like countries that do have math instruction than works), isn't a particularly sensible way of approaching the problem.

I see where you're coming from and what you're trying to get across. But the way you phrased your post implied that it was your way or the highway. There are many paths which we can take to reach the same end point. Your path is not necessarily superior to someone else's path. This thread is for discussing, not bashing.

#78 wapiti

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Posted 15 April 2012 - 04:11 PM

I think that there's a little bit of confusion going on in this thread, and I think it would be very helpful to be especially clear about a few things. When we say "delay math", I take that to mean doing very little in the way of math outside of some discussion here and there in everyday life. If we say "delay formal math instruction," that could mean more than one thing: at the very least, it would mean not using a formal curriculum. However, it could mean, on the one hand, not doing much more than a little discussion of math as things come up in everyday life, OR on the other hand, it could mean pulling together numerous interesting resources and giving non-traditional lessons. Or, something in between. I'd be a proponent of the latter but not the former. There ARE non-traditional resources available, and a lot of people use materials from more than one type of resource, and of course from life, to enrich their children's math education. However, I'm concerned that "delay formal math instruction" for some people may mean what I believe is too little math instruction, or an attempted excuse for procrastinating on what has been deemed an unpleasant or difficult task. This is why I think it is important to be clear, and why I chafe at the word "delay" where what is intended is a REPLACEMENT of a formal curriculum with an informal manner of teaching roughly the same content that would be studied in a formal curriculum. In such case there may not be an actual delay of teaching.

And, while I may have mentioned this the other day, I aslo get concerned that actual delayed instruction - delayed beyond typical grade level material for a particular age - may make LDs go unnoticed and unaddressed. (ok PSA over for now ;))

#79 Marylou

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Posted 15 April 2012 - 04:52 PM

If someone says "It's fine if my kids end up in remedial math, no big deal because PS kids end up there too," then I don't think that high achievement in math is that important to them.

Lots of things aren't that important to me. I don't particularly mind if my children never learn Latin. I don't mind if they never develop a nice hand. It's not terrible to have different priorities.

If it _is_ important to someone that their child perform as well as that child is able to in math, then what's being suggested makes no sense. We have an idea for which we have no evidence, either locally or internationally, and defending it because "what we do in North America doesn't work very well" (but what is being advocated looks _less_ like countries that do have math instruction than works), isn't a particularly sensible way of approaching the problem.


Okay. But she didn't say it would be fine. You did not quote her correctly. She not only did NOT say it was "no big deal", she admitted that it would be the "worst case scenario".

If someone starts a thread about something as they are "thinking out loud" and tossing around ideas so that they can make an informed decision about doing the right thing for their precious children, and then one of us makes the comment "if it's not important to you . . . " it just sounds like an insult.

But I don't think you meant it as an insult. I just think it is unnecessary (unhelpful).

#80 Jean in Newcastle

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Posted 15 April 2012 - 05:26 PM

The problem I have with the "teach them naturally until age 9/10" is the age limit. By age 10 (my dd's age), we are (hopefully) beyond the basic fractions found in baking. We are beyond being able to simply measure or tell time or count or the simpler parts of the 4 operations. I'm not saying that you can't teach the concepts she needs at that level without a textbook - you can. But I at least, would need to have a curriculum to walk me through the steps needed to understand long division etc. Also- while I understand that people can learn to do some pretty amazing mental math, I need a paper and pencil to be able to keep everything straight! I can get behind the "teach them naturally until 7 (and possibly 8)" argument but not older than that because I think that most kids are able to do more complex things after that age and that I would be holding my child back if I didn't allow them to progress mathematically.

#81 Butter

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Posted 15 April 2012 - 05:27 PM

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


Yes.

When I was homeschooled we knew another family who homeschooled (unschooled) their kids. One of the boys, about 10 years younger than me, did NO math formally until he was 14 or 15. At that point he decided he wanted to learn math so his mom got him textbooks to facilitate that. He taught himself math and taught it to himself well. By 16 or 17 he was doing calculus.

However, I don't think that is common. Not even close. I think he was probably quite the exception. His younger brother (and older siblings) certainly didn't do the same thing. They all learned math and do not have problems with it as adults. That kid was pretty darn amazing.

#82 Bluegoat

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Posted 15 April 2012 - 06:04 PM

Speech is natural. All people in all societies at all times learn to speak. Math is, sadly, not naturally. Whether people learn math or not, and whether they are successful at higher math, is highly dependent on the quality of their math instruction from an early age. Speech is walking. Math is skiing. People do not learn to ski unless taught.


This is not true. People who live in societies that have not developed any sort of formalized mathematics do, on their own, develop very good number sense and problem solving abilities. As a most basic example, a hunter gatherer in the desert can tell you that three antelopes and two wildabeasts makes five animals, even if he has no symbols for numbers or addition. In fact people who come from those kinds of societies often surprise those from more "developed" societies with the kinds of problems they can tackle conceptually and find solutions for, without formalized notation.

Which I think is what the study in question is really asking about. The kids in that study who had delayed instruction did not just catch up to the normal group - their problem solving skills were actually better. Why would that be? The questions it raises for me are: whether our systems tend to try and teach some concepts too early and so actually stunt real intuitive number sense and problem solving ability later on - this seems quite possible because when we learn an abstraction befor the concrete thing it represents it is often difficult for the brain to really marry the two up; and possibly more seriously, whether giving children the abstraction or formalized notations can actually, in itself, condition the way in which they take in the concrete experience, and perhaps limit it.

To me no math program is going to be able to give the opportunities that a varied everyday life is going to for experiencing the numerical world, so while that can be fun and beneficial to do puzzles and problems aimed at developing numeracy, I don't think it is absolutely necessary. And I tend to think around grade four or five is probably the time when kids have made enough of their experiential learning that adding in formal structures and notations and approaches will open new avenues rather than closing them down. I don't see kids being handicapped by it myself - leaning how to formally deal with things one knows intuitively doesn't take that long nor is it very arduousness.

#83 Jean in Newcastle

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Posted 15 April 2012 - 06:16 PM

This is not true. People who live in societies that have not developed any sort of formalized mathematics do, on their own, develop very good number sense and problem solving abilities. As a most basic example, a hunter gatherer in the desert can tell you that three antelopes and two wildabeasts makes five animals, even if he has no symbols for numbers or addition. In fact people who come from those kinds of societies often surprise those from more "developed" societies with the kinds of problems they can tackle conceptually and find solutions for, without formalized notation.


I'm sorry but I do not consider being able to figure out 3 + 2 = 5 as being anywhere near "good number sense or problem solving abilities". I understand that it is only an example but you're going to have to find much more complicated examples to convince me that this has any comparison to math with formalized notation. This is what I was talking about in my previous post. It is fine for 1st and 2nd grade level mathematics but once you get beyond that I think you need something more.

#84 wapiti

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Posted 15 April 2012 - 06:34 PM

This is not true. People who live in societies that have not developed any sort of formalized mathematics do, on their own, develop very good number sense and problem solving abilities. As a most basic example, a hunter gatherer in the desert can tell you that three antelopes and two wildabeasts makes five animals, even if he has no symbols for numbers or addition. In fact people who come from those kinds of societies often surprise those from more "developed" societies with the kinds of problems they can tackle conceptually and find solutions for, without formalized notation.


This post raises an important point, though perhaps not one you intended. Problem-solving ability is developed from having been made to solve hard problems, even with limited tools. Most of the curricula used widely by public schools (and a lot of the curricula used by homeschoolers as well) give problem-solving short shrift. Certainly, NOT doing significant problem-solving, which for the most part is the case in a situation of delayed use of formal math curricula, isn't going to help develop problem-solving skills. Quite the contrary. (If developing problem-solving abilities interests you, check out AoPS.)

#85 Bluegoat

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Posted 15 April 2012 - 08:14 PM

I'm sorry but I do not consider being able to figure out 3 + 2 = 5 as being anywhere near "good number sense or problem solving abilities". I understand that it is only an example but you're going to have to find much more complicated examples to convince me that this has any comparison to math with formalized notation. This is what I was talking about in my previous post. It is fine for 1st and 2nd grade level mathematics but once you get beyond that I think you need something more.


You can look into ethnomathematics if you are interested in seeing how non-literate societies or other cultures treat mathematical concepts - the things mathematics are about. Some examples of complex conceptual understanding can be seen in art, or in strategy games, or in astronomical prediction, or in building techniques, or in methods of navigation. Polynesian navigation is particularly interesting as a very impressive system of navigation that was done without Western formal mathematics but shows an extremely sophisticated intuitive grasp by individuals of mathematical concepts.

But that is largely missing the point. Mathematical notations are not random things - they represent something real (particularly in the beginning stages of learning math, that is the what is being taught.) People can have experiences of these real things and learn to deal with them, whether or not they have a way to write them down or a formal process for dealing with the problems. For a person who has not had the experience of the thing - who has never encountered it and cannot conceptualize it - formalized ways of dealing with it will be meaningless. Like teaching someone who has never heard language what a verb is.

Of course there are huge advantages to having formalized mathematics. But that doesn't in itself tell us much about whether it is advantageous to teach younger children, who have limited personal, concrete experience with the world, formal mathematical ways of organizing what they are experiencing.

Children's ability to abstract from their experience tends to coalesce at certain ages, and teaching the abstraction before that point is not only pretty meaningless, it could potentially make it hard for the child to connect the formal technique to the concrete reality later on. So the question is - at what age does that tend to happen, and when have they acquired enough experience to provide the raw material for the abstraction?

#86 ssavings

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Posted 15 April 2012 - 08:23 PM

Children's ability to abstract from their experience tends to coalesce at certain ages, and teaching the abstraction before that point is not only pretty meaningless, it could potentially make it hard for the child to connect the formal technique to the concrete reality later on. So the question is - at what age does that tend to happen, and when have they acquired enough experience to provide the raw material for the abstraction?


So... Is there honestly a possibility that I'm harming my children's future math abilities by not delaying?? **worried**:001_huh:

Edited by ssavings, 15 April 2012 - 08:26 PM.


#87 Bluegoat

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Posted 15 April 2012 - 08:30 PM

This post raises an important point, though perhaps not one you intended. Problem-solving ability is developed from having been made to solve hard problems, even with limited tools. Most of the curricula used widely by public schools (and a lot of the curricula used by homeschoolers as well) give problem-solving short shrift. Certainly, NOT doing significant problem-solving, which for the most part is the case in a situation of delayed use of formal math curricula, isn't going to help develop problem-solving skills. Quite the contrary. (If developing problem-solving abilities interests you, check out AoPS.)


Developing problem solving abilities doesn't have to be done with formal mathematical tools, even for adults. There can sometimes be real advantages to giving people the problem before giving them the solutions and ready made tools. The problems exist before the tools to solve them do.

But in this case we are talking about the introduction formal learning and we are not talking about the kinds of problems that can only be solved with specialized tools. We are talking about ways of noting and dealing with very down to earth and fairly concrete problems. It does not make sense to give problems they are not yet able to conceptualize. It doesn't make sense to give techniques to solve those problems either, because they will learn the technique in isolation from the problem.

But I think what is the most important thing to consider is that by giving a standard way of looking at or approaching problems while young children are still in the process of accruing their basic experiences with real problems they encounter, we may actually limit the way they approach and even understand the problem. We know this happens when children approach new complex toys, for example. At what age might the same be true of mathematical concepts?

That is what the results of the study suggest to me as one possibility, and it is too bad it would be hard to develop a new study to look into it more in terms of teaching math.

#88 Jean in Newcastle

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Posted 15 April 2012 - 08:30 PM

Children's ability to abstract from their experience tends to coalesce at certain ages, and teaching the abstraction before that point is not only pretty meaningless, it could potentially make it hard for the child to connect the formal technique to the concrete reality later on. So the question is - at what age does that tend to happen, and when have they acquired enough experience to provide the raw material for the abstraction?


Oh, I agree and I suspect that almost everyone else would too. Isn't that why even in "formal" math curricula they start out with manipulatives? I realize that the age is going to vary some, just like it does in reading and other skills that have a developmental component, but I still think that 3rd grade to 4th grade, when most texts start to veer away from the concrete to the abstract to some degree is when it "tends" to happen. Even then, when there is a new concept, many programs will go back to the concrete and build it from there.

#89 Bluegoat

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Posted 15 April 2012 - 08:36 PM

So... Is there honestly a possibility that I'm harming my children's future math abilities by not delaying?? **worried**:001_huh:


I don't think there has been much real study into this as far as teaching math goes, aside from the one presented in this thread. I think there are lots of kids who have done fine with the standard North American approach, so it doesn't seem to be a way of dooming them to mediocrity. There also isn't any evidence that I know of that waiting a few years while pursuing other ways of approaching math in the mean time is harmful, and there is no way to know if it might be better.

#90 Bluegoat

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Posted 15 April 2012 - 08:44 PM

Oh, I agree and I suspect that almost everyone else would too. Isn't that why even in "formal" math curricula they start out with manipulatives? I realize that the age is going to vary some, just like it does in reading and other skills that have a developmental component, but I still think that 3rd grade to 4th grade, when most texts start to veer away from the concrete to the abstract to some degree is when it "tends" to happen. Even then, when there is a new concept, many programs will go back to the concrete and build it from there.


Yes, I think that is exactly why they use manipulatives and such up to that point. I suppose what we could ask ourselves, in light of the study presented, is whether it would actually be better to go a bit further and give children fairly free concrete problem solving situations up to that point, and then spend a small amount of time teaching how to show those and deal with them formally. If the kids have managed to experience and find ways to deal with those situations, that should not be terribly difficult. The advantages, if there is onare any, would I think be that they would have really learned in a deeply intuitive way how the most basic mathematical ideas work, and that they would have a very open and positive approach to problem solving. That would be a great foundation for going on to the next stage of study.

#91 SweetIrony

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Posted 15 April 2012 - 09:30 PM

Polynesian navigation is particularly interesting as a very impressive system of navigation that was done without Western formal mathematics but shows an extremely sophisticated intuitive grasp by individuals of mathematical concepts.


This is actually exactly what I was thinking of right before I read this reply! Wayfinding just flabbergasts me... how did they do that??

I don't have anything to add to the discussion, but I wanted to thank everyone for this very interesting thread! :lurk5:

#92 ChristineW

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Posted 15 April 2012 - 10:02 PM

So... Is there honestly a possibility that I'm harming my children's future math abilities by not delaying?? **worried**:001_huh:


Don't worry. The best predictor of academic excellence is proficiency at math in the early grades. Not only for mathematics but also literacy.

The effective early programs don't drill and kill but focus more on problem solving, grouping, estimating, patterns, skip counting, etc--Activities that are fun for the primary grade set anyway. Of course, if a kid doesn't have a good mental picture of "5" or "7" then flashcards for 7+5 aren't going to be useful. However, there are great resources (even free ones like MEP) which focus on the basic number sense that needs to come first.

Christine

Edited by ChristineW, 15 April 2012 - 10:39 PM.
spelling


#93 Ray

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Posted 15 April 2012 - 10:33 PM

So... Is there honestly a possibility that I'm harming my children's future math abilities by not delaying?? **worried**:001_huh:


No.
Learning happens all of the time (good or bad) so when exactly do ideas of; 'more', 'less', 'up', down, left, and right begin? These relationships happen to be math. Formal math programs can build off of these relationships.

#94 shinyhappypeople

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Posted 15 April 2012 - 11:08 PM

This is actually exactly what I was thinking of right before I read this reply! Wayfinding just flabbergasts me... how did they do that??

I don't have anything to add to the discussion, but I wanted to thank everyone for this very interesting thread! :lurk5:


:iagree: I'm learning a lot from this thread!

#95 garddwr

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Posted 16 April 2012 - 08:30 AM

So... Is there honestly a possibility that I'm harming my children's future math abilities by not delaying?? **worried**:001_huh:


I think it is possible for certain types of early instruction to be harmful, but that does not mean all early instruction is harmful.

Purely anecdotal, so take it for what it's worth, but I always felt that my parents' decision to delay formal school entry until age 8/third grade COMBINED with providing a learning-rich environment at home had a hugely positive effect on my own and my siblings' (there are a bunch of us) ability to think for ourselves and solve problems creatively. From the time I entered school and repeatedly over the years I was surprised at how passive nearly all of my peers were in their approach to learning. Left largely to my own devices (again, in an environment where thinking and learning were obviously valued) I had spent my early years exploring, trying things out, making mistakes (with no-one to mark them wrong!), and thinking for myself. That joy in discovery and spirit of independence has remained with me and served me well throughout my life. I still remember how excited I was when I figured out what the word "times" meant when someone said "five times three"--the fact that I figured out the meaning of the operation on my own, not in the context of any teaching or lesson, was immensely satisfying to me.
Over the years, I have thought many times about what it was in my parents' approach to raising children that made us different (in a positive way) from most of the people around us--different in our willingness to tackle hard problems and our eagerness to learn. I am convinced that one of the keys was their giving us those early years to explore and experience the joy of discovery.
Now, in the context of homeschooling, I think we have a real advantage: when we do provide early instruction, we can do so in ways that are geared to the needs and readiness of our particular child. Our children are not sitting in a classroom with 20+ other children who are all supposed to simultaneously understand the same concept and fill out the same worksheet. If there is a risk in providing early academic instruction, I think it lies as much or more in the environmental constraints of the school setting as it does in the instruction itself. Several people here have pointed out that programs such as Miquon or MEP are designed with a young child's developmental readiness in mind and with the intent to capitalize on, not squash, the child's innate creative problem solving ability. In the end, how we teach is probably more important that what and when we teach. And it may be what is happening outside of lesson time that matters most--our children are not confined to a classroom for the best portion of the day. Once lessons are done (at least if we limit lessons to what I would consider appropriate for young children) they still have many, many hours to climb trees, build with blocks, help mom cook, and cut up thousands of sheets of paper (or does that only happen in my house???)--they are using and developing all their mental faculties. I suspect that in the end it is the amount of time spent engaging in active, creative thinking and problem solving (AKA play of the open-ended type) that has the greatest impact on their development of thinking and problem solving skills.

Edited by thegardener, 16 April 2012 - 08:33 AM.


#96 Spy Car

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Posted 16 April 2012 - 10:41 AM

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.


:lol:

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


The problem with these discussion is people seem to talk past one another. Like many disagreements, part of the problem involves "defining ones terms. Or rather, not defining ones terms.

The big culprit here is the word *formal* with a supporting role for the word *delay*.

As I suggested earlier, I think many people use *formal* as a synonym for advancing developmentally inappropriate means to force learning on young children who simply are not ready for the means employed. At the extreme this would include using math fact flashcards with infants, or chaining young kid's to desks and giving them hours upon hours of seat-work with drill sheets.

But that sets up a straw-man, as I don't think any sane person believes that is a good idea.

Some use *formal* to mean using anything published as a curriculum, without (from my POV) recognizing that there are published programs designed precisely to help parents teach young children in developmentally positive ways using means that capitalize on play, problem solving, activity based learning, developing understanding using concrete means, learning though real world experiences, and the like.

There are (to my mind) *formal* math resources (under this use of the term) that are very well suited to learning/teaching math with young children, and there are published programs that are not well suited for this aim.

To me, *formal* means "intentional, regular, deliberate, and methodical."

There are all sort of ways to build mathematical understanding in ways that are intentional, regular, deliberate, and methodical" that have nothing to do with seat-work. I can't say how much value we got out of shopping in the produce aisles combined ith deliberate and intentional questions. If these real life activities are "methodical" are they formal or not formal?

If children play with C Rods and base-10 "flats" I'd this formal or not formal?

If children engage in creative activities of the sort outlined in the MEP Lesson Plans is it formal or informal?

If they work on problems that build on ideas they have learned in concrete ways that involve paper is this formal or not formal?

Personally I think it is a mistake to conflate *formal* with "developmentally inappropriate." I think there are many ways to creatively engage with young children with the intention of fostering learning into the play. This does not negate the idea that children left to their own devices (as they should be at times) will find their own ways to learn through play. But these things should be complementary and not antagonistic activities.

I made up all sort of games and activities to bridge the understanding of my young child from the concrete towards the more abstract, and freely borrowed, modified, or used directly ideas from many published sources. This is what I would call "creative engagement."

There is no doubt in my mind that a child who grows up in a home where there is "creative engagement" happening on a regular basis will develop cognitive skills (and actually develop a physically more densly wired brain) than a child who grows up in an unstimulating environment. "Math-play" is surely not the only way to stimulate a young brain, but why exclude it?

And why exclude the interesting and helpful resources that help parents create a rich learning environment for young children? And why not give children opportunities to test their knowledge in ways that might involve paper? There are many fun leaning problems that come in published form that do not destroy children's childhoods.

We really do not need to choose between two bad options. One being forcing developmentally inappropriate work on kids who are not ready for it, and the other of letting them rot. There is a rich alternative of creative engagement, and that is the best path.

Bill

#97 Marylou

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Posted 16 April 2012 - 12:03 PM

Right on, Bill!

I just saw this in an old book (1984) yesterday:

Too much drill without understanding merely causes frustration. Not enough practice after understanding will leave it not well enough developed. There's nothing wrong with practice. Practice is good. But drill without understanding is debilitating to the mind just like bad food is to the stomach. Monroe Morford

Edited by dmmosher, 16 April 2012 - 12:55 PM.


#98 Marylou

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Posted 16 April 2012 - 12:03 PM

Now I need that coffee recipe :D

#99 shinyhappypeople

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Posted 16 April 2012 - 12:09 PM

Look what I found on my math shelf this morning: Afterwards: Folk Tales and Fairy Tales with Mathematical Ever Afters 1-2

I'm wanting to take a big step back from formal (contextless, standards-driven) math and give DD practice problem solving and playing with numbers. The books contains 9 short fairy tales. Each story is followed by a half dozen or so activities. There's a sample page at the link.

Anyway, I love it when I find treasures in my curriculum stash that I'd totally forgotten about. :)

#100 Marylou

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Posted 16 April 2012 - 12:56 PM

Look what I found on my math shelf this morning: Afterwards: Folk Tales and Fairy Tales with Mathematical Ever Afters 1-2

I'm wanting to take a big step back from formal (contextless, standards-driven) math and give DD practice problem solving and playing with numbers. The books contains 9 short fairy tales. Each story is followed by a half dozen or so activities. There's a sample page at the link.

Anyway, I love it when I find treasures in my curriculum stash that I'd totally forgotten about. :)


:thumbup: Yay! I love *shopping* in my own house!



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