WTM vs the Bluedorns RE math

[k3bzr18]

Hello all,

 

We really just started following the WTM, we were sidetracked and have come around full circle. Anyways I do also like the Bluedorns "Teaching the Trivium" book but they advocate no formal math texts until age ten because children will not be able to process it correctly. They do NOT say not to introduce concepts, but they feel money, time,addition, subtraction, 10's can be done without texts. They say with that you should be able yo jump into Saxon 6/5 without issue.

Has anyone done this? I see their logic but.......my daughter has never been great at grasping concepts from texts.

Thoughts?

[Soror]

Have you checked out the placement test for 6/5? I don't think what you are describing would adequately prepare a child for that level. If one could find a way to hit those basics without a text more power to you I guess but I would at least want to you some guide for the parent like Kitchen Table Math to make sure I gave them a good base so they don't end up frustrated.

[wapiti]

Anyways I do also like the Bluedorns "Teaching the Trivium" book but they advocate no formal math texts until age ten because children will not be able to process it correctly. They do NOT say not to introduce concepts, but they feel money, time,addition, subtraction, 10's can be done without texts. 

 

It is one thing to undertake math instruction without a specific text.  It is quite another to believe that kids can't "process correctly" math in "texts" before age 10 - it boils down to what exactly they are talking about regarding "formal math texts."

 

A math text is simply a particular program of study set forth in an organized manner, in a book.  That doesn't have to mean that all, or even any, of the instruction is received by the student reading the text.  There are loads of math programs that involve the teacher giving instruction, often with manipulatives.  (Maybe their experience is limited to Saxon?  Not my cup of tea, but from what I've read here, even Saxon uses some manipulatives in the early stages, no?)

 

Editing heavily to add:  if what the Bluedorns were trying to convey by the term "formal math text" is a very particular style of instruction, then I might tend to agree with them that certain styles of instruction may be less-optimal for certain individual students.  However, the term "formal math texts" is far too broad, vague and ambiguous, as that term would ordinarily include texts with other styles of math instruction that IMO would be quite appropriate for this age range.

 

They say with that you should be able yo jump into Saxon 6/5 without issue.

 

I agree w/soror that 6/5 probably assumes prerequisite skills that involve working on paper, including long division.

 

I've gone off on a tangent.  OP, essentially what I think you're talking about is cobbling together your "own" formal math program from a variety of resources, custom-fit to your student's needs.  Which can be a wonderful approach  :).  Somewhere there's a really long thread started by soror that lists loads of resources.  There are other threads as well - at what level is your child working currently?  Kitchen Table Math might be a good place to start. 

Edited January 12, 2016 by wapiti

[maize]

Hmm, I don't do formal math before age 8 or 9; we do living math books, play games, use math in daily life. But when we switch to a formal program I start at a 2nd or 3rd grade level to make sure we cover the basics thoroughly, I just accelerate through the program until we hit a level that is challenging for the child then we slow down (with my oldest two we have been able to cover 1.5-2 grade levels a year until they hit 5th or 6th grade material, at which point they are working slightly ahead of where they would be by age/grade).

[shinyhappypeople]

I think jumping into Saxon 65 is a bit optimistic, but I could totally see a typical 10 yo with a living math background jumping straight into 54 and doing very well.

[kiana]

Quite honestly, anything that says "no x before age y because their little minds just can't handle it" sticks in my craw. Kids are ready for the same thing at different ages.

 

Now, as far as not doing formal math with a curriculum before a certain stage of readiness, I think it'll work just fine if whichever parent is doing the educating is aware of mathematics in daily life and makes an effort to discuss it. I don't think it would take very long to learn the pencil-and-paper algorithms for arithmetic for someone who's good at mental computations with small numbers. I doubt, though, that it's necessary to follow this route, and it seems like a lot more work than just finding a curriculum that's a good fit for both of you.

[maize]

Quite honestly, anything that says "no x before age y because their little minds just can't handle it" sticks in my craw. Kids are ready for the same thing at different ages.

 

Now, as far as not doing formal math with a curriculum before a certain stage of readiness, I think it'll work just fine if whichever parent is doing the educating is aware of mathematics in daily life and makes an effort to discuss it. I don't think it would take very long to learn the pencil-and-paper algorithms for arithmetic for someone who's good at mental computations with small numbers. I doubt, though, that it's necessary to follow this route, and it seems like a lot more work than just finding a curriculum that's a good fit for both of you.

 

I don't know, my older kids picked up basic addition, subtraction, and multiplication concepts without a huge amount of effort (for us, significantly less effort than it would have taken to get them through standard curricula). Other things too--one day I realized my son could tell time from an analog clock, I don't really know when or where he picked that up. Now, we do have a lot of math resources, we have played games, they read books, we talk about concepts--but it's not something I make sure we do on a daily or close to daily basis.

 

I have wondered at times if there would have been a benefit to doing formal paper and pencil math earlier, but unless I could run a concurrent experiment with identical children I really have no way of knowing which would be better. I do know that what I am doing has worked for two children so far :P

 

Oh, and I agree completely with children's minds developing in different ways at different times.

[Rosie_0801]

I don't understand why avoiding a maths curriculum is a virtue, but if they say that because they think of maths curricula as being drier than stale bread, they haven't looked at enough of them. My dd is not developmentally ready for arithmetic, but that's not the only maths to be found in the curriculum we use, thank goodness.

[Arcadia]

They do NOT say not to introduce concepts, but they feel money, time,addition, subtraction, 10's can be done without texts.

K-8 math can easily be done without text. The person can just explain with pen and paper, whiteboard, chalkboard. Addition and subtraction can easily be taught with an abacus. Money can be taught with kids paying for grocery with cash during off peak hours. Computation and word problems can be invented on the spot to test understanding.

 

Whether you want to teach your kids math without texts is up to you.

[maize]

I don't understand why avoiding a maths curriculum is a virtue, but if they say that because they think of maths curricula as being drier than stale bread, they haven't looked at enough of them. My dd is not developmentally ready for arithmetic, but that's not the only maths to be found in the curriculum we use, thank goodness.

 

I think it depends on the child. My mom took a "better late than early" approach and didn't send me to school until I was 8. At that point I had never done formal math, and had just barely learned to read (in the summer before school started). I had, however, grown up in a very resource and idea rich home, had been read to, had participated in a family business (including selling and making change). The formal stuff was easy to pick up because I had a rich background in informal learning. I'd caught up within a couple of months on whatever I was behind in, and there were plenty of areas I was ahead in. I just can't imagine that formal math workbooks would have been better for me than the excitement of figuring out from context and practice how to understand and work with numbers.

 

Now, that is the story of one child, one experience. I trust you as a mother to figure out how best to work with your own child. 

[kiana]

I don't know, my older kids picked up basic addition, subtraction, and multiplication concepts without a huge amount of effort (for us, significantly less effort than it would have taken to get them through standard curricula). Other things too--one day I realized my son could tell time from an analog clock, I don't really know when or where he picked that up. Now, we do have a lot of math resources, we have played games, they read books, we talk about concepts--but it's not something I make sure we do on a daily or close to daily basis.

 

I have wondered at times if there would have been a benefit to doing formal paper and pencil math earlier, but unless I could run a concurrent experiment with identical children I really have no way of knowing which would be better. I do know that what I am doing has worked for two children so far :p

 

Oh, and I agree completely with children's minds developing in different ways at different times.

 

I do think the kid matters somewhat. A bright kid who is at least not non-mathy is going to pick a lot of stuff up just from being around it, just like some kids are natural readers and spellers and easily pick it up without any sort of curriculum. It works beautifully for some.

 

I also still think that the parent has to be at least educated enough to discuss it -- just like even a natural reader is going to have more difficulties (I am NOT saying it can't be done) learning to read if their mum never has any reading material in the house, but only watches television. So I think that if the parent is not confident around basic arithmetic, advocating that they eliminate a curriculum and use only living math could be a bad idea. I don't like that they seem to be claiming that a curriculum is bad, I really don't.

 

FWIW, I didn't have formal math before we started (concurrently) a book very similar to BCM and hands-on equations, and it worked beautifully for me, but I have seen it work quite badly for others.

 

All of this blather could be summed up as "keep an eye on your kid and what's working for them -- and if it's NOT working, CHANGE"

[Rosie_0801]

I think it depends on the child. My mom took a "better late than early" approach and didn't send me to school until I was 8. At that point I had never done formal math, and had just barely learned to read (in the summer before school started). I had, however, grown up in a very resource and idea rich home, had been read to, had participated in a family business (including selling and making change). The formal stuff was easy to pick up because I had a rich background in informal learning. I'd caught up within a couple of months on whatever I was behind in, and there were plenty of areas I was ahead in. I just can't imagine that formal math workbooks would have been better for me than the excitement of figuring out from context and practice how to understand and work with numbers.

 

Now, that is the story of one child, one experience. I trust you as a mother to figure out how best to work with your own child. 

 

Certainly not, if you're talking about drill and kill maths. If you're talking about some of the more eclectic programs, you might have thought they were fun supplements to the rest of your life. Not that it matters since you turned out fine. :)

 

 I've heard a few people lately talking about maths curriculums as though it is a virtue not to use them, is all. Doing without is fine if you don't need one. Doing without things you don't need is never a bad thing, as far as my imagination can inform me. However, I know someone who is maths phobic and doesn't want to use a curriculum on principle. (I'm not sure what principle.) I've not read the Bluedorns so I don't know why they are against maths curricula for smaller kids. I was offering that if it was because they imagine them all to be miserably drill and kill, there are other options that aren't in case the OP hasn't discovered them yet. I don't think there are any homeschool mum points to be gained by avoiding curriculum when it would be easier or more efficient to use one. Or in my case, three plus real life, plus supplements. (Very much taking the "throw everything at the wall and hope  to goodness something sticks" approach here. No one knows how to teach maths to echolalic kids so I'm making it up with no reason to expect success.) â€‹As you said, you should do whatever works. Or at least seems most likely to work with the least pain to everyone involved. :p

[TGHEALTHYMOM]

I don't have the book anymore... I did read it through :)

 

In my memory I do think there was a reason for not pushing math in very young children ( pre-K) and some reference to possible brain damage due to over stimulation was mentioned.  

Did they state that it would be ok to start formal math at age 8 or 9 or heavily endorse it? I can't remember the details clearly.

 

I have heard on Focus on the Family ( years ago), that Formal Schooling could be started around the same age ( 8 or 9) if a child was in a healthy, happy home with good parents ( my paraphrasing) 

and that the child should be able to catch up quickly.  

 

Our 2 year old wants to "do" her math!! I do not push math or reading lessons early but exposure or trickling down does occur here.  It also produces more desire in our younger children if they see their older siblings reading or doing math.  

 

I use Pattern blocks, RS math games, Lego's, and other "hands on" approaches to learning colors, shapes, and counting for our younger children.  I also have workbooks if they desire to do a page.  I used to push math and reading earlier until I got so busy I simply did not have time.  I also use Funnix and Big Brainz on the PC as well as Reader Rabbit and Charlie Church Mouse.  This helps tremendously as 3 children gather around and stay motivated to learn for 15-20 minutes.  

 

Dh does Skip counting with our young children and drills them on math facts.  

 

I ask them to help me count my change when it piles up.

 

One thing that helped too was a pretend cash register.  Hours of Playing store have kept our girls so busy.  They still need to know how to handle "real" money.  

 

 

[Hunter]

Bluedorn was published in 2001 and based off of 1990's experiences. Lots of people started 10 year olds in the FIRST edition Saxon 54 after a real hodgepodge of other math, and it worked just fine. I would NOT start a child on the CURRENT 65 at 10 years old. That is about a 3 year leap from the FIRST edition 54. The series is getting progressively wider, more rigorous, requires more time on task, and is harder to teach. And people are using it a year or two earlier. Mr Saxon must be rolling over in his grave to see what is being advocated in his name.

 

I do not believe in rigorous math at early ages. I do agree with classical ideas about math being better for older students. I also believe that some gifted children can handle math MUCH earlier than the average child. I had a gifted and radically accelerated math student and I had an average math student. My younger son was sometimes 5-6 years ahead of his older brother in math. 

 

Simply Charlotte Mason has a wonderful and very affordable pdf about teaching hands on math.

https://simplycharlottemason.com/store/mathematics-an-instrument-for-living-teaching/

 

You might like this thread on Grube's Method.

http://forums.welltrainedmind.com/topic/409801-grubes-method-of-teaching-arithmetic-why-havent-i-heard-of-this/

 

 

[Hunter]

Free Waldorf Maths

http://www.entwicklungshilfe3.de/media/Bilder_ZSE/UEber_Uns_Dateien/Grundlagentexte/MATHEMATICS_GRADES_1_2_TRAINING_MANUAL.pdf

http://www.entwicklungshilfe3.de/media/Bilder_ZSE/UEber_Uns_Dateien/Grundlagentexte/GRADE_3_TRAINING_MANUAL.pdf

 

Free Arithmetic Village

http://arithmeticvillage.com

 

 

[Hunter]

And I believe that inflicting the current most rigorous internationally competitive math scope and sequences on NORMAL children is a human rights violation. I'm not talking about gifted children; I'm talking about NORMAL children.

[Coco_Clark]

I think it COULD be done, but I'm with Rosie in thinking there's no particular virtue in it.

 

Personally, I need a math curriculum because I am not confident in math (not even truly confident in addition and subtraction). I need the handholding to know how to present things, and I need the plan because I'm sure without there would be gaps. And I don't say that as a curriculum lover. 80% of our schooling is momma-designed.

 

I also feel like my oldest DS, who is very give-it-to-me-straight, and however else you'd describe the opposite of discovery-led, needs a straightforward curriculum. He's the kid that would flail in montessori.

 

But I could see myself, two or three kids later perhaps, ditching the curriculums and feeling like I knew the subject well enough to go freestyle. And I can see with my very discovery-led DS5 how it might work for certain students.

[boscopup]

My little kids enjoy doing math curriculum. It's their favorite subject. Both the little ones are doing CLE Math, which is traditional and includes plenty of math fact drill, yet a nice variety of things at a developmentally appropriate level. I've been very happy with it (I do use it a little ahead for my kids, as the whole family is good at math). I'm not sure what is so scary about math for young children. Frankly, math has been the best way to get my kids writing at young ages, since they find numbers easier than letters, and that helps build up their hand strength for writing.

 

I also disagree with the Bluedorns' (and their Classical Conversations) philosophy for young elementary kids in general though. I fail to see how using a developmentally appropriate math curriculum is detrimental, yet cramming a gazillion science, history, math, Latin, and grammar facts into their heads with no concept of what they are is beneficial. I've seen young kids stressed out by their memory work program, when those same kids were fine using an on grade level math program. So yeah, I take the Bluedorns' advice with a huge grain of salt.

[k3bzr18]

 

In my memory I do think there was a reason for not pushing math in very young children ( pre-K) and some reference to possible brain damage due to over stimulation was mentioned.  

Did they state that it would be ok to start formal math at age 8 or 9 or heavily endorse it? I can't remember the details clearly.

 

 

 

Here is what it says in part. "  A ten-year old us perfectly capable of jumping right into a sixth grade math textbook, such as Saxon 6/5 with no previous experience with math workbooks or textbooks. Skipping Kindergarten through fifth grade in math will in no way hinder your child's success in math.  You do not need to wear our your child's interest and your own patience attempting to make him understand what his brain is not yet wired to handle.  Waiting until age ten, when your child is developmentally prepared to handle mathematical concepts readily, makes instruction in arithmetic very easy.  What was painfully spread over five previous years, may here be compressed painlessly into as little time as a month.

We are NOT saying that you should keep your child away from numbers before age ten.  Not at all.  By age four, most children have discovered money, and you will not be able to hide numbers from them after that.  Children encounter numbers all of time.  If you encourage learning, then they will be asking plenty of questions, and you will have plenty of opportunities for informal instruction in numbers and measurements.  But we would not encourage formal workbook instruction before age ten unless the child shows a genuine interest and genuine competency to handle the work.   (Bluedorns, Teaching the Trivium, p.369)

[ByGrace3]

But we would not encourage formal workbook instruction before age ten unless the child shows a genuine interest and genuine competency to handle the work. (Bluedorns, Teaching the Trivium, p.369)

My kids all show a "genuine competency" around age 4. My issue with the idea of "wait until they are 10 and it will be so much easier!"-- I am sure it will be easier, but what about diligence, perseverance, hard work pays off, not everything is easy we have to work at it-- these attitudes are built from the working out of math.

 

I am not super familiar with the upper levels of Saxon, but looking at what my dd is doing in MM 4, I cannot imagine it being easy to get someone to that level from no formal math in a short time. No textbook is a whole other story...

[maize]

My little kids enjoy doing math curriculum. It's their favorite subject. Both the little ones are doing CLE Math, which is traditional and includes plenty of math fact drill, yet a nice variety of things at a developmentally appropriate level. I've been very happy with it (I do use it a little ahead for my kids, as the whole family is good at math). I'm not sure what is so scary about math for young children. Frankly, math has been the best way to get my kids writing at young ages, since they find numbers easier than letters, and that helps build up their hand strength for writing.

 

I also disagree with the Bluedorns' (and their Classical Conversations) philosophy for young elementary kids in general though. I fail to see how using a developmentally appropriate math curriculum is detrimental, yet cramming a gazillion science, history, math, Latin, and grammar facts into their heads with no concept of what they are is beneficial. I've seen young kids stressed out by their memory work program, when those same kids were fine using an on grade level math program. So yeah, I take the Bluedorns' advice with a huge grain of salt.

You're confusing the Bluedorns with someone else. The Bluedorns are not associated in any way with Classical Conversations nor do they recommended similar methods in the early years. I think the person behind CC is Leigh Bortins.

[EndOfOrdinary]

I would worry about push back.  I mean, cooking with math, playing with math, math games and all sorts of math in art is a lot of fun.  Then to go from that to Saxon?!  My son would be in tears!  I don't care if he was ten, he would still go from very fun and playful worldly math to dozens of problems only because he passed some magical age barrier.  That just seems like a really great way to turn a kid off from math in general and destroy any fostering of joy from learning.

[maize]

I would worry about push back.  I mean, cooking with math, playing with math, math games and all sorts of math in art is a lot of fun.  Then to go from that to Saxon?!  My son would be in tears!  I don't care if he was ten, he would still go from very fun and playful worldly math to dozens of problems only because he passed some magical age barrier.  That just seems like a really great way to turn a kid off from math in general and destroy any fostering of joy from learning.

 

Not necessarily. Milestones with new responsibilities and challenges often make kids feel more grown up. 

[Dmmetler]

I would worry about push back. I mean, cooking with math, playing with math, math games and all sorts of math in art is a lot of fun. Then to go from that to Saxon?! My son would be in tears! I don't care if he was ten, he would still go from very fun and playful worldly math to dozens of problems only because he passed some magical age barrier. That just seems like a really great way to turn a kid off from math in general and destroy any fostering of joy from learning.

I agree! My junior high used Saxon Algebra 1/2 for the advanced kids, and I remember HATING that book with a passion at age 12 or so. It was just so boring, so dry, and so tedious to have to do 50-zillion problems. And that was coming from K-6 PS math which was similar, just not quite as dry as Saxon. I can't imagine going from living math to Saxon and not having a kid decide that math just isn't worth the time.

[Hunter]

My kids all show a "genuine competency" around age 4. My issue with the idea of "wait until they are 10 and it will be so much easier!"-- I am sure it will be easier, but what about diligence, perseverance, hard work pays off, not everything is easy we have to work at it-- these attitudes are built from the working out of math.

 

I am not super familiar with the upper levels of Saxon, but looking at what my dd is doing in MM 4, I cannot imagine it being easy to get someone to that level from no formal math in a short time. No textbook is a whole other story...

 

Children from large oldschool rural and conservative families worked. They learned to work by working. They learned their attitudes of perseverance and problem solving with sweat, blisters, pulled muscles, and sometimes blood.

 

Developmentally inappropriate book learning has to be the single most inefficient way to teach children to work.

 

Some oldschool kids looked forward to book learning as it was an excuse to get out of the real work.

[Hunter]

I would worry about push back.  I mean, cooking with math, playing with math, math games and all sorts of math in art is a lot of fun.  Then to go from that to Saxon?!  

 

I don't think the Bluedorns used a lot of games and fun. I think the kids were WORKING with math. I think when they were cooking, they were working not playing at cooking. I think they were expected to handle money in real life situations, not play with it. And I don't think the kids even knew the definition of "push back" :lol:

 

My kids barely knew the definition of "push back". That just didn't happen in a lot of conservative oldschool families. Back in the 80's people still spanked their babies' hands in public, if they reached for something again after being told not to ONCE. I wouldn't do that now, but I did it back then. These kids were conditioned to obey. It was a whole other world.

[maize]

But what do you in a society where there isn't that much work to be done, especially for under 10 year olds? Back in the day, the mother spent hours on household chores and her daughters were expected to assist her. There were plenty of necesssary chores for boys too.

 

Is there enough work in the average American middle class suburban household to occupy the time of under 10 year olds to provide them with the experience to learn how to work? And if there's not enough work to occupy them and they can't play all of the time, then what else can they do but schoolwork or sports? I think there are activities that can be devised to occupy a child's time but it's not the same thing as the work done by children in prior centuries because it's work that's a choice instead of a necessity. No one is going to go hungry or not have any clothes to wear if the work isn't done.

 

My mom used music to teach us to work hard and persevere. She didn't believe in early academics, but I started violin at age 3 :)

[Hunter]

But what do you in a society where there isn't that much work to be done, especially for under 10 year olds? Back in the day, the mother spent hours on household chores and her daughters were expected to assist her. There were plenty of necesssary chores for boys too.

 

Is there enough work in the average American middle class suburban household to occupy the time of under 10 year olds to provide them with the experience to learn how to work? And if there's not enough work to occupy them and they can't play all of the time, then what else can they do but schoolwork or sports? I think there are activities that can be devised to occupy a child's time but it's not the same thing as the work done by children in prior centuries because it's work that's a choice instead of a necessity. No one is going to go hungry or not have any clothes to wear if the work isn't done.

 

I certainly don't have the answers to how to navigate modern society. I'm just trying to provide some background to the oldschool books published pre-Y2K or soon after.

 

I do see immigrant families running stores and restaurants where kids are given a "break" to do homework. This lifestyle is not over for everyone.

[k3bzr18]

You're confusing the Bluedorns with someone else. The Bluedorns are not associated in any way with Classical Conversations nor do they recommended similar methods in the early years. I think the person behind CC is Leigh Bortins.

That is correct.  Leigh Bortin started CC and her son now runs it.  Definitely different.  We started with this when we first started homeschooling a few years ago and now have really gone back to the WTM ...CC is a different world, not for us.

 

My DD8 is definitely one who doesn't grasp the concepts of math easily.  I feel like a combo of fun and text would work,  its finding the right text where I don't loose her.  It's funny (and I know this is not education) but we started swimming lessons in May and she has advanced 4 classes since then because she is "ready".  She wanted nose plugs before we started lessons lol and now she is literally a fish.  I see the wisdom, I am just not convinced I would cover all the necessary milestones myself...

[boscopup]

You're confusing the Bluedorns with someone else. The Bluedorns are not associated in any way with Classical Conversations nor do they recommended similar methods in the early years. I think the person behind CC is Leigh Bortins.

Ah, you are correct. My bad! Didn't Leigh Bortins recommend something similar though? Learning math facts and then starting Saxon 5/4?

[maize]

Ah, you are correct. My bad! Didn't Leigh Bortins recommend something similar though? Learning math facts and then starting Saxon 5/4?

 

I don't think so. If memory serves, in The Core she talks about doing math every year, in fact every day, and that sometimes her kids would work through a level twice to make sure they have mastered it. She's an engineer, and math was obviously a priority in her homeschool. I do think she used Saxon.

 

It's been a long time since I read that book though.

[Hunter]

Robinson Curriculum has always been math facts and then Saxon 54. And that did work fine for the FIRST edition of 54.

[BlsdMama]

I've actually tested this theory ON one of my children due to the the Bluedorn's recommendation with an average mathy child

 

It worked.

 

They talk about their " Ten Things to do Before Age Ten."

 

Essentially, so as to not overwhelm the child, they prioritize. FORMAL math study lower on the list. They, in no way, advocate avoiding math. Remember, they are still classical educators. They simply believe there is really little to be gained in K -4/5 grade math that couldn't quickly and easily be taught to your average fifth grade child.

 

It doesn't mean at age 11 I handed Elizabeth a grade level text and expected her to teach herself. No, when they've not had any formal math teaching there is some initial hand holding to be done.

However she was able to process the concepts quickly and easily and start with very little issue.

[Penelope]

I don't know anything about old vs. new Saxon, but I have no doubt a child with no learning blocks could progress through K-4 math much quicker than in 4-5 years. Don't people do that here all the time with Singapore or a Math Mammoth, and I doubt that all of our children who do this are geniuses.

 

I guess, though, I don't see the point in shunning a program that is written out for you. Why reinvent the wheel when there are perfectly good, child-appropriate options? I understand wanting to avoid the lower levels of a program like Saxon, but Saxon and Abeka are no longer the only options for elementary math.

[maize]

I don't know anything about old vs. new Saxon, but I have no doubt a child with no learning blocks could progress through K-4 math much quicker than in 4-5 years. Don't people do that here all the time with Singapore or a Math Mammoth, and I doubt that all of our children who do this are geniuses.

 

I guess, though, I don't see the point in shunning a program that is written out for you. Why reinvent the wheel when there are perfectly good, child-appropriate options? I understand wanting to avoid the lower levels of a program like Saxon, but Saxon and Abeka are no longer the only options for elementary math.

For my family, delaying formal math has allowed me to meet the individual developmental needs of my children and focus on other priorities during the primary years. My oldest struggled a lot with anxiety and perfectionism, when she was younger math would paralyze her because there were right and wrong answers and she might make a mistake. So we didn't do math until she had matured to a point where she could work through those issues. It didn't hurt her. Now I have five children and limited time to work with each. I prioritize reading and music for individual time with my youngers; math can wait.

[ElizaG]

I guess, though, I don't see the point in shunning a program that is written out for you. Why reinvent the wheel when there are perfectly good, child-appropriate options? I understand wanting to avoid the lower levels of a program like Saxon, but Saxon and Abeka are no longer the only options for elementary math.

I agree with maize's point about different levels of maturity, but I think there might also be other benefits that would apply to all children, whatever their "developmental readiness."

 

For one thing, one could argue that the most highly touted features of primary math curricula -- e.g., the use of manipulatives; solving different types of problems; lessons based on discovery (usually with guidance from teachers or peers when needed) -- are just attempts to replicate the experiences that children will go through when learning math in everyday life.

 

Even if the school curricula sometimes get the concept into the child more efficiently (and I'm not sure that they do, in general), I don't think they're anywhere near as effective as the real-life situations in developing the child's powers of observation, reasoning, and hard work.   And in the primary years, this is the sort of foundation we need to be thinking about.   

 

To put it another way -- why use wheels at all, if you can walk?

[Hunter]

 

 

For one thing, one could argue that the most highly touted features of primary math curricula -- e.g., the use of manipulatives; solving different types of problems; lessons based on discovery (usually with guidance from teachers or peers when needed) -- are just attempts to replicate the experiences that children will go through when learning math in everyday life.

 

 

 

:iagree:

[Penelope]

In asking why reinvent the wheel, I guess I'm also thinking about busy moms with multiple children who have limited time with each. It is easy for me to teach K-3 math without a program. But I don't necessarily want to sit and create the number of problems that they need for adequate practice. I do some of that, but for the most part, why would I if they are there in a book for me and I can pick and choose? And by the time we get to working with fractions and long division, it is nice to have problems with answers written for me when I'm short on time and can barely keep up with everyone's lessons.

 

Maybe some families have home businesses and endless time at the grocery store to give their children all of the necessary practice using real life, but as a mom mostly on my own all day taking the kids with me everywhere and living in suburbia, I don't think we have enough opportunities for practice arithmetic at these younger ages. We certainly do some of that with having them tell time, manage some of their own money, and measuring and building things. But I don't think it's enough, and to create more experiences like that would take more of my time and energy than just getting out a math book for a few minutes a day.

[maize]

In asking why reinvent the wheel, I guess I'm also thinking about busy moms with multiple children who have limited time with each. It is easy for me to teach K-3 math without a program. But I don't necessarily want to sit and create the number of problems that they need for adequate practice. I do some of that, but for the most part, why would I if they are there in a book for me and I can pick and choose? And by the time we get to working with fractions and long division, it is nice to have problems with answers written for me when I'm short on time and can barely keep up with everyone's lessons.

 

Maybe some families have home businesses and endless time at the grocery store to give their children all of the necessary practice using real life, but as a mom mostly on my own all day taking the kids with me everywhere and living in suburbia, I don't think we have enough opportunities for practice arithmetic at these younger ages. We certainly do some of that with having them tell time, manage some of their own money, and measuring and building things. But I don't think it's enough, and to create more experiences like that would take more of my time and energy than just getting out a math book for a few minutes a day.

 

 

I don't sit and create problems, nor do I spend tons of time creating extra experiences.  We incorporate numbers and math talk into everyday life, occasionally play games--and mostly just wait to introduce more formal math at a time when the kids brains are more mature and they pick up the concepts quickly (what they haven't figured out already).

 

It's not a matter of making sure I cover everything that would be covered in a primary grade math program without using  program, it's a matter of living life, letting kids grow, focusing on other priorities--then when the kids are nine or ten pulling out the formal math program and going from there. 

[ElizaG]

Maybe some families have home businesses and endless time at the grocery store to give their children all of the necessary practice using real life, but as a mom mostly on my own all day taking the kids with me everywhere and living in suburbia, I don't think we have enough opportunities for practice arithmetic at these younger ages. We certainly do some of that with having them tell time, manage some of their own money, and measuring and building things. But I don't think it's enough, and to create more experiences like that would take more of my time and energy than just getting out a math book for a few minutes a day.

As someone who's trying to move toward more of a "living math" approach with the younger ones, it does seem like it takes more work for me, too.   But I'm not sure if this is because of our lifestyle, or because I have warped perceptions.  My feeling is that it's more the latter.  

 

For instance, I've noticed that when we do a page or two from a workbook, I'm fairly confident that that's "enough" math for the day.  On the other hand, doing a few everyday activities (folding napkins in half, reading time on the clock, sharing out a bag of almonds) seems like "not enough."  But if you look closely, where's the evidence that they're learning more with the former?   

 

YMMV, but I suspect that my main problem is that I've come to take the primary school sequence for granted, and assume that we have to work to match that in terms of the number of problems, the age at which topics are covered, etc.   But then there are people like the Bluedorns, Benezet, and Ella Frances Lynch -- to name a few who've been discussed on these boards -- whose experience seems to turn this assumption on its head.   They start with real-life math as the standard for young children, and show that even the best-designed school curriculum is deficient in comparison.  

 

I think this sort of "re-education" is valuable, even if we don't choose to follow their whole system.   

[dauphin]

It is sort of revolutionary thinking. I read Bluedorn's book and kind of said "yeah right how do you do that in today's culture?" But I'm so glad to hear from some who have successfully gone this route. I'd love to hear how some think this might relate to how Montessori teaches math? Is it perhaps an intermediate stop? (More concrete and more real-life but not quiiiite as real life as...well...real life.

[Hunter]

I don't sit and create problems, nor do I spend tons of time creating extra experiences.  We incorporate numbers and math talk into everyday life, occasionally play games--and mostly just wait to introduce more formal math at a time when the kids brains are more mature and they pick up the concepts quickly (what they haven't figured out already).

 

It's not a matter of making sure I cover everything that would be covered in a primary grade math program without using  program, it's a matter of living life, letting kids grow, focusing on other priorities--then when the kids are nine or ten pulling out the formal math program and going from there. 

 

:thumbup:

 

I'm not saying anyone NEEDS to wait, but this is an excellent reason to wait, and how best to wait. Waiting can be ultra efficient, or it can be a lot of work if you don't know why you are waiting.

[ElizaG]

I'd love to hear how some think this might relate to how Montessori teaches math? Is it perhaps an intermediate stop? (More concrete and more real-life but not quiiiite as real life as...well...real life.

It might be that -- trying to come up with a compromise, for children who are in a classroom environment.   But I think it's also related to her being heavily influenced by Pestalozzi.   As I understand it, he was the first pedagogue to make math a main part (maybe even the main part) of the elementary curriculum.  

 

His reasons were different from the ones that are given today.  It wasn't because he thought it was necessary to start the children early so that they could do calculations in daily life, or so that it would be easier for them to learn advanced math later on.  And he certainly wasn't intending to prepare them for "STEM careers," which scarcely existed at the time.   He was going more by theories about what types of learning were most appropriate for developing young children's minds.   

 

Pestalozzi's ideas were very popular right around the time when mass education was being developed in Europe and North America.  He also influenced other famous pedagogues, such as Froebel, the inventor of kindergarten.   As a result, pretty much all mainstream schools, and a lot of alternative ones, take this early emphasis on math for granted. The 19th century American common school approaches such as Grube's, Ray's, etc., all follow more or less from his ideas.

 

Montessori was even more of an admirer of Pestalozzi than most other people were, so she put an especially high priority on introducing small children to math, and developed the materials to do this.   It seems as if her methods are better than many of the others.  But the more I learn about this, the less I'm sure that the whole endeavor is really necessary, or even beneficial.  

 

In contrast to this trend, traditional classically-oriented systems of education, and many of today's advocates of "delayed formal math" (which, as the Bluedorns rightly point out, isn't "delayed" at all by historical standards), put a much heavier emphasis on verbal skills in the early years.   Depending on the particular system, oral reading and listening, memorization, recitation, paraphrasing, conversation, copywork, and foreign language study could all be part of this.   For those who saw the arts of language (i.e., the trivium) as the foundation of learning, it wouldn't make much sense to take time and energy away from these activities, to teach more advanced mathematics than the children needed in their daily lives.  

 

By the way, my impression is that Montessori's original method also had a lot of rich verbal content, but for some reason -- trouble adapting it to different countries?  lack of literary culture among the teachers?  not enough time to cover it all? -- most schools and teacher training programs tended to neglect that area, so it's ended up pretty unbalanced.  But maybe it was already somewhat unbalanced to begin with.  IDK.

[Hunter]

 

 

… Pestalozzi's ideas were very popular right around the time when mass education was being developed in Europe and North America.  ...  As a result, pretty much all mainstream schools, and a lot of alternative ones, take this early emphasis on math for granted. ...

 

… In contrast to this trend, traditional classically-oriented systems of education, and many of today's advocates of "delayed formal math" (which, as the Bluedorns rightly point out, isn't "delayed" at all by historical standards), put a much heavier emphasis on verbal skills in the early years.  ...

 

I, too, question the whole idea of early math as being the best possible scope and sequence. I was first introduced to the idea of later math when studying Latin and Greek centered versions of classical education–LCC the method, not the book.

[Hunter]

I've been studying Greenleaf's 1875 math books. Here is a link to the primary book.

http://books.google.com/books?id=S78yL5CtGgQC&dq=inauthor:%22Benjamin+Greenleaf%22&source=gbs_navlinks_s

 

It seems like older arithmetics included a lot more reciting and writing. Advanced vocabulary was taught and comprehension questions were asked. As math was inflicted more harshly on younger children, the beginner methods needed to be changed. Also, at the same time the trivium ideas of having children memorize what they might not be able to understand and use yet, became unpopular.

 

I really like Greenleaf's New Primary Arithmetic for remediating older students. But really, is it remediation, if many college students struggle with the vocabulary and comprehension questions of this primary book. In the past, I was sometimes using an older version of Ray's (not the Mott Media books) for the verbal and written emphasis in them. I like Greenleaf better though. He retained the more classical methods longer than Ray did.

[ElizaG]

Which methods of actually teaching math are "the most classical" is a whole other question, and it gets pretty murky.

 

In ancient and medieval times, basic arithmetic would have been part of primary education, which wasn't generally considered to be part of the classical curriculum.   In ancient Rome, this stage was taught either at home, or by the litterator, who came before the grammaticus.   In the middle ages and colonial America, it would often have been taught in a petty school or dame school.   None of these schools had much prestige, and from what I've read, they seem to have used a hodge-podge of methods.  

 

A couple of years ago, I came across an interesting e-book about math teaching in the ancient world.   I can't find it now, but the search did turn up these two, by Florian Cajori:

 

The Teaching and History of Mathematics in the United States (1890)

 

A History of Elementary Mathematics (1901)

 

I'm too burned out on vintage pedagogy to read them any time soon, but thought maybe someone else might be interested.   :001_smile:

 

(If there's a problem with the scans, archive.org has several other copies.  Most of them look pretty fuzzy, though.)  

[Elisabet1]

I think that sounds great and fine. But I would throw in memorizing multiplication facts. But, if you have the desire to teach it all on your own..wing it..then go for it. I actually happen to love math, so I would be happy to wing it myself. I noticed when touring some expensive private schools, a lot did not use formal math in the early years....as in before 3rd, 4th, or even 5th grade in some cases. They had lots of hands on games and activities and such, but there were no textbooks for it.

[birchbark]

I am kind of doing this with my 2nd DS. We will begin formal arithmetic next year in 3rd grade, which is age eight, so a little earlier than the Bluedorns' rec. The plan is to use Strayer Upton, which begins at the 3rd grade level. Even so, we are not completely math-curriculum-less as I've been using Ray's Primary Arithmetic the last couple years. This level of Ray's is almost entirely oral story problems. No pencil and paper and no algorithms. So I'm not a purist yet! Perhaps I'll be more confident with the next kiddos. 

 

The Bluedorn's article is available online. Ruth Beechick and of course the Moores have similar recommendations. I was also influenced by the fascinating write-up on Benezet's experiment. Paul Ziegler, of Systematic Mathematics, also recommends informal math before 3rd grade. He has a video module for parents on this.

[Hunter]

Yup, Strayer-Upton book 1 was written for 3rd graders with no previous formal math, as that was so common when the book was written.

 

In the 1920's, math was started in grade 3, and formal grammar/composition was started in grade 3 or 4. Home geography was usually started in 3 and the elementary geographies were usually not started until grade 4 or 5. Before that, in grades 1 and 2, the focus was on phonics, literature, nature study and paper crafts. CM and Waldorf are just products of their time.

[Amy M]

Ah, you are correct. My bad! Didn't Leigh Bortins recommend something similar though? Learning math facts and then starting Saxon 5/4?

 

I recently read The Core's math chapter, and it struck me as very "drill and kill." Bortins suggests Saxon all the way up, including K-3, and just as a pp mentioned, sometimes had her children repeat a level just to really glue in the material. Her children do all the problems assigned on the page, even if she feels that they're not struggling with the material.

 

Bluedorn's Teaching the Trivium was my first introduction to both classical and Charlotte Mason philosophies of education, actually; it's funny that you've connected CC with the Bluedorns. There's really no connection, and in many ways I don't think the Bluedorns would like CC's approach to the different subjects.

 

In their chapter discussing different methods in the light of the trivium, they very briefly described CM philosophy. I didn't get it when I first read it, but in a chart at the end of that section, they prefer using either CM or a unit study approach for before age 10, and starting the classical approach around age 10. This is over-simplifying what they say, but anyway, it stuck with me because I had never heard of CM before, and here were the "classical" guys saying it was a good approach to use before age 10. That to say, that they would lean more CM in many regards than CC. They recommend Beechick as well in their recommended reading list.

 

For the OP: I remember when I first read Bluedorn's section on math, I rolled my eyes. Yeah, right. But now that I've taught one child up through 3rd grade math, I realize that it can be done! I still prefer using a curriculum to keep me on track and save me work, but maybe I'll be more relaxed after teaching a few more kids. One lady I know told me she sort of follows Bluedorn's recommendations in grammar and math--she uses the old MUS Foundations and Intermediate levels for math in elementary before switching over to upper level maths.

 

Here are some quotes that might help clarify what the Bluedorns think about memorization in particular.

 

 

There is some discussion over what to have the child memorize. Some say the time should be spent memorizing facts: dates, Latin verb endings, miscellaneous scientific and geographic data, etc. Maybe so, but there is only so much time in the day, so we, as the parents, need to determine what is the best use of that time. If it is important to you that the child have all the states and capitals memorized by age ten, then by all means do it. Both parents could sit down and write out a list of those things they think are important for their children to memorize, and adjust this list as different priorities emerge. Bare facts, divorced from their contexts, can become a drudgery. Facts are best planted as seeds in the fertile context of their story....

 

In their section on the CM method:

 

Karen Andreola noted... that "...Charlotte's method is in disagreement with Dorothy Sayers' strong emphasis on memory work in the early grades." "A true intellectual life is not achieved by exercising children's minds as if they were nothing but memory machines." We also would diverge from Dorothy Sayers here. Though there may be some value, at a young age, to memorize groups of facts (dates, geographical facts, Latin chants, etc.), there is much more value in memorizing passages of literature -- both prose and poetry -- and in more than one language. An early and high degree of mastery of the language is more valuable than an early mastery of the presidents. Besides that, facts are better learned and are less of a drudgery when they are placed within a setting instead of isolated as abstractions.

 

A bit of an aside from just the discussion on math, but wanted to make sure that Bluedorns were not connected to CC. ;)