Interesting old math book on Google books

[yslek]

I'm in the middle of reading Liping Ma's book (thanks to board peer pressure ;)) and was struck by the reversal in math instruction in the US & China mentioned in the preface to the anniversary edition. On p. xii, Ma mentions a book published in the 1800s by a Warren Colburn. I thought I'd check Google books, and found the full text: http://books.google.com/books?id=Msg2AAAAMAAJ&printsec=frontcover&dq=warren+colburn&hl=en&ei=sLjYTJjxKJO6sQOlsZmaBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q&f=false

 

I've only started perusing this, so don't really have an opinion yet. I did read the preface, though. Some interesting tidbits:

 

"Few exercises strengthen and mature the mind so much as arithmetical calculations, if the examples are made sufficiently simple to be understood by the pupil; because a regular, though simple process of reasoning is requisite to perform them, and the results are attended with certainty."

 

"After the pupil comprehends an operation, abstract examples are useful, to exercise him, and make him familiar with it. And they serve better to fix the principle, because they teach the learner to generalize."

 

"The examples are to be performed in the mind, or by means of sensible objects, such as beans, nuts, &c. or by means of the plate at the end of the book. The pupil should first perform the examples in his own way, and then be made to observe and tell how he did them, and why he did them."

 

"And the questions are asked in such a manner, that, if the instructor pursues the method explained in tho Key, it will be almost impossible for the pupil to perform any example without understanding the reason of it."

 

 

So...has anyone taken a closer look at this or even used it? Thoughts?

[AngelBee]

Who knew reading about math would be my venture for the day. :lol:

[Joyofsixreboot]

Hmm, off to check it out.

[Spy Car]

This really resonates with me:

 

The pupil should first perform the examples in his own way, and then be made to observe and tell how he did them, and why he did them."

 

"And the questions are asked in such a manner, that, if the instructor pursues the method explained in tho Key, it will be almost impossible for the pupil to perform any example without understanding the reason of it."

 

This really gets to the heart of how I'm trying to peruse math studies with my son. I want him to do the work then explain how he did it and why. Sometimes the reasoning is unexpected.

 

Last night, for example, he was asked what is 1/2 of 16? As an adult, I expected that he would say 8+8=16 and that means half of 16 is 8 (since he knows this).

 

But, being 6, and rather a new-comer to fractions he wanted to solve for 1/2 of 16. I could see the mind whirl a moment and he said: 8

 

I said that's right. How did you solve it?

 

He said: Half of 10 is 5, and half of 6 is 3, so half of 16 is 8.

 

Not necessarily the "most efficient" means of solving the problem, but the exercise revealed a certain understanding on his part that I would have been oblivious to had I simply accepted 8 as the "right answer."

 

Bill

[cathmom]

I'll have to read that later.

 

Bill, my issue is dc who cannot explain how they got something, wrong or right. :confused:

 

I really wish I could have a math do-over with my three oldest dc.

[Spy Car]

I'll have to read that later.

 

Bill, my issue is dc who cannot explain how they got something, wrong or right. :confused:

 

I really wish I could have a math do-over with my three oldest dc.

 

If I've done one thing right with math I think it has been making sure that at every step I had him explain his reasoning to me. When he has been "wrong" he usually corrects himself before I need to, and when the problem comes from semantics (or some other cause) I can respond with activities and lessons that clarify any misunderstandings he might have.

 

Having children explain and justify their answers is a very strong way of making sure they know what they are doing, and internalizes their own understandings as they explain. Good stuff.

 

Bill

[cathmom]

If I've done one thing right with math I think it has been making sure that at every step I had him explain his reasoning to me. When he has been "wrong" he usually corrects himself before I need to, and when the problem comes from semantics (or some other cause) I can respond with activities and lessons that clarify any misunderstandings he might have.

 

Having children explain and justify their answers is a very strong way of making sure they know what they are doing, and internalizes their own understandings as they explain. Good stuff.

 

Bill

 

Right. My 7 yo, the oldest of my second "batch" of children, is just like that. He hardly ever makes a mistake and if he does he usually catches it himself. He's only used RightStart Math.

 

It's my older ones who can't explain how they did something. :tongue_smilie:

[yslek]

This really resonates with me:

 

 

 

This really gets to the heart of how I'm trying to peruse math studies with my son. I want him to do the work then explain how he did it and why. Sometimes the reasoning is unexpected.

 

Last night, for example, he was asked what is 1/2 of 16? As an adult, I expected that he would say 8+8=16 and that means half of 16 is 8 (since he knows this).

 

But, being 6, and rather a new-comer to fractions he wanted to solve for 1/2 of 16. I could see the mind whirl a moment and he said: 8

 

I said that's right. How did you solve it?

 

He said: Half of 10 is 5, and half of 6 is 3, so half of 16 is 8.

 

Not necessarily the "most efficient" means of solving the problem, but the exercise revealed a certain understanding on his part that I would have been oblivious to had I simply accepted 8 as the "right answer."

 

Bill

 

That is so awesome! I have some of the same issues cathmom has.:glare: Usually when I ask my kids how they got an answer I get blank stare or "I don't know". I kind of gave up on even asking for a while, but I think I will again, at least with the younger ones since the olders prefer to do most of their math on their own. I've started modeling *how* to explain the thought process out loud. It seems to be helping, as D has been able to explain some of her reasoning to me. :hurray:

[JadeOrchidSong]

This really resonates with me:

 

 

 

This really gets to the heart of how I'm trying to peruse math studies with my son. I want him to do the work then explain how he did it and why. Sometimes the reasoning is unexpected.

 

Last night, for example, he was asked what is 1/2 of 16? As an adult, I expected that he would say 8+8=16 and that means half of 16 is 8 (since he knows this).

 

But, being 6, and rather a new-comer to fractions he wanted to solve for 1/2 of 16. I could see the mind whirl a moment and he said: 8

 

 

I said that's right. How did you solve it?

 

He said: Half of 10 is 5, and half of 6 is 3, so half of 16 is 8.

 

Not necessarily the "most efficient" means of solving the problem, but the exercise revealed a certain understanding on his part that I would have been oblivious to had I simply accepted 8 as the "right answer."

 

Bill

Bill,

My 5 yr old is just like your 6 yr old. I ask him why and I am often surprised how he gets the answer. He does things exactly like your son. He would break things into more parts and add them or multiply them. I just love that!!! He is really good at mental math and math is always easy for him.

June

[Spy Car]

That is so awesome! I have some of the same issues cathmom has.:glare: Usually when I ask my kids how they got an answer I get blank stare or "I don't know". I kind of gave up on even asking for a while, but I think I will again, at least with the younger ones since the olders prefer to do most of their math on their own. I've started modeling *how* to explain the thought process out loud. It seems to be helping, as D has been able to explain some of her reasoning to me. :hurray:

 

Bill,

My 5 yr old is just like your 6 yr old. I ask him why and I am often surprised how he gets the answer. He does things exactly like your son. He would break things into more parts and add them or multiply them. I just love that!!! He is really good at mental math and math is always easy for him.

June

 

Keep it up ladies! It is so much easier to have children memorize their "math facts" and to check their work against an answer key.

 

But having them in the routine of talking through their reasoning even for simple things like re-grouping to 10s really pays off. I'm also amazed at my son's ability to do mental math now. The grunt work pays off.

 

Bill

[~Jo]

Interesting conversation :)

 

One of the things my ds does when he gets stuck on an algebra problem is he asks me if he can teach me the problem. Once he starts to try and explain what he is doing things start to "click" and he figures out where he is making his mistake.

 

What I had to do though was model to him first how to explain a problem - step by step. Once he could figure out the small steps in explaining something it was very easy for him to do. Now I rarely get a whole problem explained to me anymore :001_huh: ...usually only about half and then he exclaims "I know what I'm doing wrong" and goes back to his work. This has also stopped the careless mistakes.

[FO4UR]

Bill, our ds's would have fun with some math games together. :001_smile:

 

I'll be reading this tonight..

 

I've taken the approach of getting to the how's and why's first and early, working on mastery of details after the over-arching concept is understood. The result is that I'm somewhat unsure what to do with this kid, looking into the long term. Miquon works so well for the basic concepts for him, especially b/c he's not a fluent reader yet. I kinda have an idea of what might work for him when he's middle school & high school...I just don't have a good grasp on what to do between Miquon and middle school...which might be why I'm always looking at other math currics. I keep thinking about what the author of LOF says...kids need to know the 4 operations very well, including long division before starting his series. I think my 7yo will get to that point very early, but I'm not sure he'd be ready for LOF that early. He gets burned out doing page after page of the same thing in math...I think the variety of Miquon is as important as the method itself...if he'd rather vomit than do one more page of x today, he can skip on over to fractions kwim. What does one *do* with a child like this when the Miquon runs out??? :lol: Maybe this book will give me some insight...

[Spy Car]

Bill, our ds's would have fun with some math games together. :001_smile:

 

I have no doubt about that :001_smile:

 

 

I've taken the approach of getting to the how's and why's first and early, working on mastery of details after the over-arching concept is understood. The result is that I'm somewhat unsure what to do with this kid, looking into the long term. Miquon works so well for the basic concepts for him, especially b/c he's not a fluent reader yet. I kinda have an idea of what might work for him when he's middle school & high school...I just don't have a good grasp on what to do between Miquon and middle school...which might be why I'm always looking at other math currics. I keep thinking about what the author of LOF says...kids need to know the 4 operations very well, including long division before starting his series. I think my 7yo will get to that point very early, but I'm not sure he'd be ready for LOF that early. He gets burned out doing page after page of the same thing in math...I think the variety of Miquon is as important as the method itself...if he'd rather vomit than do one more page of x today, he can skip on over to fractions kwim. What does one *do* with a child like this when the Miquon runs out??? :lol: Maybe this book will give me some insight...

 

Why do you think I bounce mine between Miquon, MEP, Singapore, as of this past week Primary Challenge Math, RS games, Indian math, just to name a few? :D

 

I am liking Singapore as a "spine" to make sure there is a method underlying the madness. Is this one not for you?

 

Bill

[FO4UR]

 

Why do you think I bounce mine between Miquon, MEP, Singapore, as of this past week Primary Challenge Math, RS games, Indian math, just to name a few? :D

 

I am liking Singapore as a "spine" to make sure there is a method underlying the madness. Is this one not for you?

 

Bill

 

I bounce between maths too...it just gets a little crazy doing that for 3 dc. I do like Singapore. We use the old CWP regularly, and enjoy the tb's (though he's beyond the tb's that we own at the present). When we've used Singapore tb & wb regularly, he has gotten that burned out attitude. I'd rather he have a few gaps to fill in the 4th grade than be burned out by monotony.

 

I think MOTL might be a good fit for him...if only it were written by Lore Rasmussen...why can't that exist???:tongue_smilie:

[Spy Car]

I bounce between maths too...it just gets a little crazy doing that for 3 dc. I do like Singapore. We use the old CWP regularly, and enjoy the tb's (though he's beyond the tb's that we own at the present). When we've used Singapore tb & wb regularly, he has gotten that burned out attitude. I'd rather he have a few gaps to fill in the 4th grade than be burned out by monotony.

 

I think MOTL might be a good fit for him...if only it were written by Lore Rasmussen...why can't that exist???:tongue_smilie:

 

You are even starting to call it maths :D

 

Mine is pretty good doing Singapore. Even there we bounce between books to avoid monotony, but he's pretty go with the flow.

 

I was going to ask what MOTL was, but then I remembered Math on the Level.

 

The good news is there is no shortage of great materials.

 

I am so grateful to the late Lore Rasmussen. I've thought many times I should write her family to express just how much goodness their mother's life and work have contributed to the richness of our lives. I need to get off the dime and do it.

 

Bill

 

Bill