Liping Ma book

[ScoutTN]

Thank you to those who have recommended this book!

I am reading it and learning so much! I am not a math person, generally, but I am finding this fascinating. It will certainly shape how I teach.

Thanks!

[Dina in Oklahoma]

Hello ~

I was considering this book. What specifically has been of help to you?

THANKS!

Dina :001_smile:

[TracyP]

Thank you to those who have recommended this book!

I am reading it and learning so much! I am not a math person, generally, but I am finding this fascinating. It will certainly shape how I teach.

Thanks!

 

:iagree: I just recently got it through ILL. Unfortunately, I ran out of time and had to return it before I finished but what I great recommendation! I will be getting it again both to reread and finish (hopefully).:tongue_smilie:

 

Hello ~

 

I was considering this book. What specifically has been of help to you?

 

THANKS!

 

Dina :001_smile:

 

Have you seen some of the "define conceptual math" posts? I now understand what it means to have a true understanding of math. I also see what a difference a teacher with a true understanding can make. Seeing math this way will help me to be a better teacher. Now I am struggling with how to apply what I learned going forward.

 

BTW, I thought I understood what it meant to have a conceptual understanding of math but I did not in the way Ma describes in her book.

[Spy Car]

Have you seen some of the "define conceptual math" posts? I now understand what it means to have a true understanding of math. I also see what a difference a teacher with a true understanding can make. Seeing math this way will help me to be a better teacher. Now I am struggling with how to apply what I learned going forward.

 

BTW, I thought I understood what it meant to have a conceptual understanding of math but I did not in the way Ma describes in her book.

 

What a good answer! :001_smile:

 

Then I'm going to speak "generally" at not at you :tongue_smilie:

 

In my case I had an intuitive understanding that the sort of math education I had as a child (not horrible, but typical of American public school education in the 60s and 70s) was inadequate. But I wasn't 100% sure what the alternative was, at least not in "particular terms."

 

What Ma does (for those who have not read her book) is to go through some of the basic operations of math, including adding and subtracting. Then she analyzes how specific (typical) American teachers understand and teach the mathematics, and compares and contrasts the kind of "procedural" math we tend to teach here (learning how to plug numbers into a formula that is provided) with the way Chinese teachers (some who are even more impressive than others) understand and teach the math.

 

The differences are staggering! There are no other terms to use. Ma's book solidified by understanding that "something is broken" in the way we teach math. It gave me a vision of the kind of math education that is possible, and inspired me to have this sort of education as a goal.

 

It did not really tell me HOW to provide that education exactly, but I've been able to figure that part out (so far).

 

If you go read the book, you will never look at "how do I get my child to memorize math facts?" threads the same way. Oh dear, oh dear.

 

It is a profoundly important book I wish every teacher and every parent would read. If the lessons of the book were taken to heart it would revolutionize math education. But if we can't revolutionize math education everywhere, we can do it in our own homes. If we choose.

 

I vote: Yes!

 

I will fully credit Dr Ma with crystalizing my feelings about what sort of math education I would not perpetuate, and what the alternative aspirations involved. It was a life-changing read. One doesn't experience many of those (at least I don't) but for me this book goes on a very short lists to the most influential works I've ever read.

 

It doesn't necessarily need to be owned (library is fine) as it is not a "how to" so much as a "why to." Fortunately there is an ever-growing circle of people who are successfully home educating using the "conceptual math" model here on the boards, and there are a number of great math programs that support this sort of education.

 

Read the book if you are open to making changes in the way you treat math.

 

Bill

Edited May 18, 2010 by Spy Car

[Doubleblessings]

what is the name of the book?

[TN Mama]

What is the title of the book, please?

[Spy Car]

The book is called: Knowing and Teaching Elementary Mathematics.

 

There was just a 10th Anniversary edition released recently. I can't speak to the value of any added material. I read the "old edition."

 

Bill

[Doubleblessings]

I think I found it...

KNOWING AND TEACHING ELEMENTARY MATHEMATICS

 

I am reading this blog about it now

http://rationalmathed.blogspot.com/2007/06/what-does-liping-ma-really-say.html

[EKS]

It was a life-changing read.

 

:iagree:

 

Life changing for me and (more importantly) life changing for my children.

[mo2]

If you go read the book, you will never look at "how do I get my child to memorize math facts?" threads the same way. Oh dear, oh dear.

 

 

THis particular statement got me curious. Does Ma encourage the memorizing of math facts or is she against it?

 

I checked the book out once but life got in the way and I had to return it before I got very far into it.

[Spy Car]

THis particular statement got me curious. Does Ma encourage the memorizing of math facts or is she against it?

 

I checked the book out once but life got in the way and I had to return it before I got very far into it.

 

Enough time has passed that I would want to speak for Dr Ma on this, so I'll speak for myself. It is not as if anyone teaching "conceptual math" doesn't feel it is "necessary" or utilitarian to have a quick recall of math facts. It is about how you get there.

 

With conceptual math there is a great deal of ground-work that is done to make sure a child really understand the mathematical operations "first." I read a comment in a thread yesterday where a husband asked incredulously, "so you make it more complicated than it needs to be?"

 

And maybe, on some level the answer is: Yes!

 

So while it is "necessary" to learn math facts, it not a "sufficient."

 

Think about reading. Almost everyone on this forum is convinced that learning reading using phonics is vital. People follow up with phonics based spelling programs, and then teach grammar (English and maybe even Latin) because they want their children to have a full comprehension of how language works.

 

Then, many of those very same parents, will turn around and teach math using flash cards. Does this make sense? Would they teach reading with sight-word flash-cards? Obviously not.

 

There is a "grammar" of math, just as there is a "grammar" of language. The "grammar stage" is the time to learn that grammar. That is a lesson than has not fully penetrated this community. But that is going to change.

 

I hope.

 

The people who advocate for "conceptual math" do so for a reason. The same reason those who wanted phonics and grammar to be the focus of language arts do. As people decided the schools were failing with "whole language" and would take matters into their own hands, the same thing can be (and should be) done with math education.

 

Bill

[Halcyon]

The single most important book I've read on educating my child mathematically ever. Hands down. I've read it several times and it always recenters my math teaching.

 

Without a doubt, everyone on these boards who wants their child to have a strong math education needs to read it.

[mo2]

Enough time has passed that I would want to speak for Dr Ma on this, so I'll speak for myself. It is not as if anyone teaching "conceptual math" doesn't feel it is "necessary" or utilitarian to have a quick recall of math facts. It is about how you get there.

 

With conceptual math there is a great deal of ground-work that is done to make sure a child really understand the mathematical operations "first." I read a comment in a thread yesterday where a husband asked incredulously, "so you make it more complicated than it needs to be?"

 

And maybe, on some level the answer is: Yes!

 

So while it is "necessary" to learn math facts, it not a "sufficient."

 

Think about reading. Almost everyone on this forum is convinced that learning reading using phonics is vital. People follow up with phonics based spelling programs, and then teach grammar (English and maybe even Latin) because they want their children to have a full comprehension of how language works.

 

Then, many of those very same parents, will turn around and teach math using flash cards. Does this make sense? Would they teach reading with sight-word flash-cards? Obviously not.

 

There is a "grammar" of math, just as there is a "grammar" of language. The "grammar stage" is the time to learn that grammar. That is a lesson than has not fully penetrated this community. But that is going to change.

 

I hope.

 

The people who advocate for "conceptual math" do so for a reason. The same reason those who wanted phonics and grammar to be the focus of language arts do. As people decided the schools were failing with "whole language" and would take matters into their own hands, the same thing can be (and should be) done with math education.

 

Bill

 

Thank you. The phonics comparison makes perfect sense. What are some programs that teach math in this (conceptual) way, for those of us who need a lot of hand-holding?

[SophiaH]

Thank you. The phonics comparison makes perfect sense. What are some programs that teach math in this (conceptual) way, for those of us who need a lot of hand-holding?

 

For hand-holding, I prefer RightStart. Actually, hand-holding or not, I prefer RightStart. :D

 

And it seems from the consensus on the board that Math Mammoth would be a very good choice as well.

[Doubleblessings]

Ok, you all convinced me. :) (not really too hard to convince me to order a math book :D) I ordered it used. Neither of the library system's I am a member of had it and I didn't want to mess with ILL.

[Ali in OR]

Teaching a conceptual understanding of mathematics is important, and Ma's book can help you understand how a good teacher of mathematics will do that. And that China seems to have more of those good teachers than we do!

 

But having a good conceptual knowledge doesn't mean that you don't teach math facts. Students with a good conceptual knowledge will also know their math facts. IMO, you can't have a good conceptual knowledge and not know the basic math facts. And I think that in reading Ma's example problems, it is pretty clear that knowledge of math facts is foundational. You can't even talk about place value issues and division of fractions if you can't do basic addition, subtraction, multiplication, and division.

 

If the goal of the parent or teacher is only to get the basic facts and algorithms mastered, the child's math education will be lacking the conceptual understanding that will make him/her truly math literate. But you also can't have true mathematical literacy without mastering those elements. I think it's okay to post those math fact threads, and I'll optimistically submit that the posters know there is more to math than just facts. But in order to take part in the "Great Conversation" of mathematics--to be able to grapple with the ideas in algebra or trig or beyond, you do need to be able to "speak the language" and have the math facts down.

[Spy Car]

Thank you. The phonics comparison makes perfect sense. What are some programs that teach math in this (conceptual) way, for those of us who need a lot of hand-holding?

 

I'd guess I'd second Heather and say probably Right Start and Math Mammoth would have the most "hand holding."

 

I'm particularly happy with our Miquon-Singapore-MEP combo with RS elements thrown-in, as it suits our eclectic style.

 

Moving further out there, the CSMP materials add interesting things. There is Japanese Math (Tokyo Shoseki).

 

I'm sure there are others I'll regret not mentioning. But those are a few for the early years.

 

Bill

[Spy Car]

But having a good conceptual knowledge doesn't mean that you don't teach math facts. Students with a good conceptual knowledge will also know their math facts. IMO, you can't have a good conceptual knowledge and not know the basic math facts. And I think that in reading Ma's example problems, it is pretty clear that knowledge of math facts is foundational. You can't even talk about place value issues and division of fractions if you can't do basic addition, subtraction, multiplication, and division.

 

There is no argument here. As I said, it is "necessary" but not "sufficient" to have a good grasp of math facts. Memorizing math facts alone, without a rock-solid foundation to support those facts, can lead to the deception that a child "understands" what they are doing, when they do not.

 

If the goal of the parent or teacher is only to get the basic facts and algorithms mastered, the child's math education will be lacking the conceptual understanding that will make him/her truly math literate.

 

Exactly.

 

But you also can't have true mathematical literacy without mastering those elements.

 

I agree.

 

I think it's okay to post those math fact threads, and I'll optimistically submit that the posters know there is more to math than just facts. But in order to take part in the "Great Conversation" of mathematics--to be able to grapple with the ideas in algebra or trig or beyond, you do need to be able to "speak the language" and have the math facts down.

 

What I guess I wasn't clear about, is that in many of these "math fact thread" it is crystal-clear that a great deal of math education in the home school community never gets beyond the memorization of math facts, and how to plug numbers into a (provided) formula. There, I said it.

 

Knowing the math facts (once you really know what they involve) is necessary, just as one needs to be able to decode words quickly (and even by sight) to enter the Great Conversation via reading. But that does not mean you learn to read by memorizing sight words.

 

And that Great Conversation does require an understanding of grammar, including the grammar of math. Unfortunately, even the upper divisions of math as taught in this country are still often "procedural." Many students of upper-level math (from what I gather) still really don't understand what they are doing, and can't problem-solve unless given a formula into which they can plug numbers. It is a shame. And this starts at the beginning of our approach to math education.

 

Bill

[Spy Car]

The single most important book I've read on educating my child mathematically ever. Hands down. I've read it several times and it always recenters my math teaching.

 

Without a doubt, everyone on these boards who wants their child to have a strong math education needs to read it.

 

I should be so succinct :D

 

Bill

[SophiaH]

Teaching a conceptual understanding of mathematics is important, and Ma's book can help you understand how a good teacher of mathematics will do that. And that China seems to have more of those good teachers than we do!

 

But having a good conceptual knowledge doesn't mean that you don't teach math facts. Students with a good conceptual knowledge will also know their math facts. IMO, you can't have a good conceptual knowledge and not know the basic math facts. And I think that in reading Ma's example problems, it is pretty clear that knowledge of math facts is foundational. You can't even talk about place value issues and division of fractions if you can't do basic addition, subtraction, multiplication, and division.

 

If the goal of the parent or teacher is only to get the basic facts and algorithms mastered, the child's math education will be lacking the conceptual understanding that will make him/her truly math literate. But you also can't have true mathematical literacy without mastering those elements. I think it's okay to post those math fact threads, and I'll optimistically submit that the posters know there is more to math than just facts. But in order to take part in the "Great Conversation" of mathematics--to be able to grapple with the ideas in algebra or trig or beyond, you do need to be able to "speak the language" and have the math facts down.

 

Good points. I'm right now reading an article by the afore-mentioned Dr. Wu entitled, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education." He makes some brilliant points about the need for children to be fluent in basic algorithms before being able to move on to more complex concepts. I like how he says that "deep understanding of mathematics ultimately lies within the skills."

 

Towards the end of the article, he gives a nod to Knowing and Teaching Mathematics by Liping Ma. He agrees with her that "the problem of rote learning then lies with inadequate professional development and not with the algorithm."

 

I think conceptual understanding is good; I think memorizing math facts is good. *I* prefer to have the basic conceptual understanding first, then memorize math facts, then introduce algorithms for the more complex problems. But maybe we should be careful not to create an automatic blacklist against terms such as "memorize," "math facts," "algorithm" or even "rote learning."

[Spy Car]

Good points. I'm right now reading an article by the afore-mentioned Dr. Wu entitled, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education."

 

I think the idea that those who want their children to fully understand the conceptual understanding of mathematical operations don't want their children to have good basic still is the real "bogus dichotomy." It is an absurd suggestion, and a "straw-man fallacy."

 

On a pretty diverse forum (understatement of the year :D) I doubt you'll find a many (any?) people who are attempting to teaFch along the lines of those outlined by Dr Ma as "conceptual math" who don't want their children to have good math skills, including the low-level cognitive skill of a quick recall of their math facts. Memorizing those as "the means" of learning the math might be another issue, just as one (to beat the analogy to death) enjoys hearing there child reading fluently after they have suffered listening them decode Bob Books, but they've done so rather than resort to memorizing sight-words as the method.

 

Everyone wants fluency, including fluency with "math facts", but we should want fluency with the phonics and grammar of math as well, and that kind of math education is something we can provide, if we have the will.

 

Bill

Edited May 18, 2010 by Spy Car

[Corraleno]

Students with a good conceptual knowledge will also know their math facts. IMO, you can't have a good conceptual knowledge and not know the basic math facts.

I disagree with this. Quick recall of math facts certainly makes doing math much faster and easier, but conceptual understanding is a separate issue from memorization of facts. Benoit Mandelbrot never learned his times tables above 5, but that didn't prevent him from becoming the "father of fractal geometry." My DH can (and does!) do calculus and linear algebra in his sleep, but he's terrible at simple mental arithmetic, and my DS's conceptual understanding of math has always far outstripped his memorization of facts.

 

I certainly agree that memorizing math facts is an important skill, but it's quite possible to have a deep conceptual understanding of math without having memorized all your math facts ~ I suspect this may actually be quite common among visual/spatial thinkers.

 

Jackie

[SophiaH]

I think the idea that those who want their children to fully understand the conceptual understanding of mathematical operations don't want their children to have good basic still is the real "bogus dichotomy." It is an absurd suggestion, and a "straw-man fallacy."

 

One a pretty diverse forum (understatement of the year :D) I doubt you'll find a many (any?) people who are attempting to teach along the lines of those outlined by Dr Ma as "conceptual math" who don't want their children to have good math skills, including the low-level cognitive skill of a quick recall of their math facts. Memorizing those as "the means" of learning the math might be another issue, just as one (to beat the analogy to death) enjoys hearing there child reading fluently after they have suffered listening them decode Bob Books, but they've done so rather than resort to memorizing sight-words as the method.

 

Everyone wants fluency, including fluency with "math facts", but we should want fluency with the phonics and grammar of math as well, and that kind of math education is something we can provide, if we have the will.

 

Bill

 

Bill,

 

:confused: Did you take my post as aimed at you? It's hard to tell through writing, but it sounds like you are offended? I wasn't trying to suggest at all what you (seem to) accuse me of above. I was merely passing along some thoughts from a very thought-provoking (for me) article. (Maybe I should have said "I" instead of "we" in the last sentence.)

[Spy Car]

I disagree with this. Quick recall of math facts certainly makes doing math much faster and easier, but conceptual understanding is a separate issue from memorization of facts. Benoit Mandelbrot never learned his times tables above 5, but that didn't prevent him from becoming the "father of fractal geometry." My DH can (and does!) do calculus and linear algebra in his sleep, but he's terrible at simple mental arithmetic, and my DS's conceptual understanding of math has always far outstripped his memorization of facts.

 

I certainly agree that memorizing math facts is an important skill, but it's quite possible to have a deep conceptual understanding of math without having memorized all your math facts ~ I suspect this may actually be quite common among visual/spatial thinkers.

 

Jackie

 

The Nobel Prize winning physicist Richard Feynman spoke about this in his memoir Surely You're Joking, Mr. Feynman! (a great read BTW). He mentioned how he, and many of the mathematicians working on the A-bomb project during WWII were quite bad at basic arithmetic.

 

Feynman also publicly excoriated the powers-that-be in the Brazilian math academies (where he was a guest professor) for having students in upper level math and physics that had no idea what they were doing once problems moved beyond solving problems with a provided formula. He was brutal!

 

I'm not suggesting a poor grounding in math fact retention is the road to greatness in mathematics, but learning math by memorizing math facts (absent real understanding) is a short-cut than can have negative repercussions.

 

Bill

[fractalgal]

Good points. I'm right now reading an article by the afore-mentioned Dr. Wu entitled, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education." He makes some brilliant points about the need for children to be fluent in basic algorithms before being able to move on to more complex concepts. I like how he says that "deep understanding of mathematics ultimately lies within the skills."

 

Towards the end of the article, he gives a nod to Knowing and Teaching Mathematics by Liping Ma. He agrees with her that "the problem of rote learning then lies with inadequate professional development and not with the algorithm."

 

I think conceptual understanding is good; I think memorizing math facts is good. *I* prefer to have the basic conceptual understanding first, then memorize math facts, then introduce algorithms for the more complex problems. But maybe we should be careful not to create an automatic blacklist against terms such as "memorize," "math facts," "algorithm" or even "rote learning."

 

In every math class I've ever taken the concept is introduced and explained first before a student is encouraged to memorize a formula.

 

When we learn what the number 5 means, we learn it by seeing 5 units of something and making the connection that that is what 5 is. We see this over and over in different ways until we have memorized what 5 means.

 

A math concept should be taught before a formula is memorized. Memorization, however, is not the enemy. It seems to me that the enemy to understanding math has more to do with poor instruction or lack of understanding in the communicating of a concept. How well a concept is taught has to do with how well the teacher understands and conveys the subject and also how well the student understands what that teacher is saying.

[Spy Car]

Bill,

 

:confused: Did you take my post as aimed at you? It's hard to tell through writing, but it sounds like you are offended? I wasn't trying to suggest at all what you (seem to) accuse me of above. I was merely passing along some thoughts from a very thought-provoking (for me) article. (Maybe I should have said "I" instead of "we" in the last sentence.)

 

No. No. Sorry, not offended. I know we see things (more or less) the same way.

 

Sorry. I was jumping off there a little, I didn't mean to make it seem directed at you. I should have been more careful. Please forgive me.

 

I've just read this article by Wu (whose writings I respect generally) previously and I think he presents a "false dichotomy" (one I've heard on the board as well) that proponents of conceptual math are somehow antagonists of "math skills." And that is absurd. And I get fired up sometimes :tongue_smilie:

 

Please forgive me.

 

Bill

[SophiaH]

A math concept should be taught before a formula is memorized. Memorization, however, is not the enemy. It seems to me that the enemy to understanding math has more to do with poor instruction or lack of understanding in the communicating of a concept. How well a concept is taught has to do with how well the teacher understands and conveys the subject and also how well the student understands what that teacher is saying.

 

Good grief! You said what I was trying to say, but so much better! :) Thank you.

[ScoutTN]

I had a poor math education (despite being in elite prep schools my whole life!) and though a diligent student, I stalled out at Algebra because I just didn't understand it.

 

Discussions here and reading this book have encouraged me to believe that giving my children a real understanding of math, the grammar of it, as Bill has so aptly said, is something that DH and I can do. This is exciting to me! I have a different and clearer goal than I would have even a few months ago.

 

I am not sure how to do teach in ways which help my kids to develop this conceptual understanding of math. Not right now, since we are just beginning our hs journey. But certainly the goal affects what materials and methods we will choose. And what "teacher enrichment" opportunities we will pursue.

 

And though certainly not a how to book, I have learned a few things about methods just from the first two chapters - the role of discussion about whys and hows of the problem solving steps for one. And the importance of terminology and precise terms for another.

 

Thanks again to all who have posted about this! I am sure the discussions will continue....:)

 

Spy Car - I do think that changes are possible, even in traditional school settings. Persevere!

[SophiaH]

No. No. Sorry, not offended. I know we see things (more or less) the same way.

 

Sorry. I was jumping off there a little, I didn't mean to make it seem directed at you. I should have been more careful. Please forgive me.

 

I've just read this article by Wu (whose writings I respect generally) previously and I think he presents a "false dichotomy" (one I've heard on the board as well) that proponents of conceptual math are somehow antagonists of "math skills." And that is absurd. And I get fired up sometimes :tongue_smilie:

 

Please forgive me.

 

Bill

 

Oh, okay. Apology accepted. :)

 

That's not quite what I took away from his article, but I can see how different points he made would stand out to each of us differently. The article was actually very encouraging to me with where we are in our math journey right now; I feel like I'm maybe on the right track to right some of those wrongs we're talking about. :)

[stripe]

In every math class I've ever taken the concept is introduced and explained first before a student is encouraged to memorize a formula.

Really? It wasn't until I read a Mathematician's Lament that I actually thought to even wonder why the area of a triangle is 1/2 b * h.

 

I would consider myself a fairly mathy person.

[Doubleblessings]

The Nobel Prize winning physicist Richard Feynman spoke about this in his memoir Surely You're Joking, Mr. Feynman! (a great read BTW).

 

We really enjoyed it. Although, it was a bit dijointed. A warning however to others...if you are reading it aloud to your spouse in the car with your children present, you may need to edit a bit. :blushing: However, many parts my kids enjoyed.

[fractalgal]

 

I'm not suggesting a poor grounding in math fact retention is the road to greatness in mathematics, but learning math by memorizing math facts (absent real understanding) is a short-cut than can have negative repercussions.

 

 

:iagree:

[Spy Car]

I had a poor math education (despite being in elite prep schools my whole life!) and though a diligent student, I stalled out at Algebra because I just didn't understand it.

 

Discussions here and reading this book have encouraged me to believe that giving my children a real understanding of math, the grammar of it, as Bill has so aptly said, is something that DH and I can do. This is exciting to me! I have a different and clearer goal than I would have even a few months ago.

 

The good news is, I can promise you, is that it will stay exciting. When you can actually teach your children using means they understand, and they really *get it* and YOU (speaking of me too) really get it, it's like, WOW!

 

Fun stuff. And they go off boldly using the things they have learned. It is exciting!

 

I am not sure how to do teach in ways which help my kids to develop this conceptual understanding of math. Not right now, since we are just beginning our hs journey. But certainly the goal affects what materials and methods we will choose. And what "teacher enrichment" opportunities we will pursue.

 

And though certainly not a how to book, I have learned a few things about methods just from the first two chapters - the role of discussion about whys and hows of the problem solving steps for one. And the importance of terminology and precise terms for another.

 

Thanks again to all who have posted about this! I am sure the discussions will continue....:)

 

Best wishes on this journey. There is a good support system here, and an embarrassment of riches in terms of the math programs and resources now available to help meet your goals.

 

Spy Car - I do think that changes are possible, even in traditional school settings. Persevere!

 

Together. We will persevere together. My hope? Someone reads this thread many years from now, and realizes how much thing have changed from the time we are having this discussion. I do think that will happen (the change that is, who knows about old threads being found :D).

 

Let your sprits soar, and thank you for starting such a positive thread (except for the parts where I get "rant-y" :tongue_smilie:)

 

Bill

[Spy Car]

We really enjoyed it. Although, it was a bit dijointed. A warning however to others...if you are reading it aloud to your spouse in the car with your children present, you may need to edit a bit. :blushing: However, many parts my kids enjoyed.

 

Oh yes, that's true. Dr Feynman was not immune to the charms of women :D

 

It's hard for me to fault him for that :tongue_smilie:

 

Bill

[fractalgal]

Really? It wasn't until I read a Mathematician's Lament that I actually thought to even wonder why the area of a triangle is 1/2 b * h.

 

I would consider myself a fairly mathy person.

 

I was fortunate to have had very good teachers. I also drew pictures of concepts when I didn't understand what was going on because I learn best visually.

[TracyR]

In every math class I've ever taken the concept is introduced and explained first before a student is encouraged to memorize a formula.

 

When we learn what the number 5 means, we learn it by seeing 5 units of something and making the connection that that is what 5 is. We see this over and over in different ways until we have memorized what 5 means.

 

A math concept should be taught before a formula is memorized. Memorization, however, is not the enemy. It seems to me that the enemy to understanding math has more to do with poor instruction or lack of understanding in the communicating of a concept. How well a concept is taught has to do with how well the teacher understands and conveys the subject and also how well the student understands what that teacher is saying.

 

 

I absolutely agree with this. I couldn't tell you how many times growing up where I had a teacher that spoke above my head. I never understood math. There are also some children that no matter how simplified you explain the subject though they just don't get it.

 

My oldest is very good with math. She gets it , understands it. I had read many a post before homeschooling on the type of math that should be taught. So naturally I started out with Bob Jones math with my daughter. She loved this program and really got quite a bit out of it. Sometimes even though I didn't understand where the concept was going while I was teaching it she understood it just fine. She made teaching math very simple for me.

 

Then my 2nd daughter came along. Naturally I would use the same math method with her. Since it was considered the 'superior' way to teach math. Unfortunately her brain did not function that way. No matter what I did to show her or try to get her to understand it lead to tears and the " I don't understand. I don't get it." Even using manipulatives and drawing pictures didn't seem to help. I figured I would draw on her strength of being visual but she just did not see it that way. Through the years I've continued to push and push conceptual math programs in hopes that it would eventually click. Guess what? It really hasn't. The only thing she has gotten out of it is that if 5+4=9 then 4+5= 9. That's about it. If I throw to many different ways to solve a problem at her she just cries and tells me she doesn't understand. So naturally I get out things to show her and I still get " I don't get it." It got so bad that it finally got to a point that she told me she was stupid in math. So Saxon it became and Saxon is what she is doing much better in math in. So not all children are wired for learning conceputual math at a young age. Sometimes it comes later on. I have found that to be true for me as an adult. So I expect that this understanding will come later for her. When I don't know.

 

My third daughter is sort of in the middle. She understands conceptual math but needs tons of review. Since there isn't a math program like that out there I just use Saxon math that gives her the review and throw in the conceptual math with her K12 math I have at the moment. This combo seems to be working and it only took me almost the full year of 1st grade to figure it out. :lol:

 

I don't think that all parents want their children to have a poor math education. I don't think even some want their children to have a poor math education. I think all parents want their children to have a good math education. This isn't about those select parents who want their children to have a good math education. But you have to look at the true facts. One maybe a good speaker about math, and tote the facts about what a good math education is. But if you aren't able to get those facts across to your child at any given point in their life it doesn't make you a failure. It just says that they don't understand at this point in their life. Not every person does everything or understands everything at the same time in their life.

 

I can't tell you how many times I've read good literature about how to teach a subject. What you have read has been proven and tried and true yet you have that one child that defies that tried and true method. I have finally come to the conclusion that I am not failing my daughter by using a program like Saxon. I am helping her get to her goal. Just using a different road to eventually lead her to the road she needs to get to eventually.

 

But then I'm one of those moms who use both phonics and sight method to teach my girls how to read. To bad they've become excellent readers.

[Greta]

In every math class I've ever taken the concept is introduced and explained first before a student is encouraged to memorize a formula.

 

Then you have taken some much better math classes than I did! You are very fortunate. The memory of third grade math can still make me cringe - timed drills where we had to spit out what seemed to me to be random sequences of numbers that had no connection or meaning whatsoever, more popularly known as "times tables". I hadn't the faintest idea what multiplication meant, I just had to memorize it. Unfortunately, that basic pattern continued throughout my ps experience. In high school I remember plugging numbers into formulas and churning out answers without any real concept of what I was doing.

 

Always knowing that I wasn't truly "getting it" made me hate math, and convinced me that I didn't have the ability to get a degree in a field involving math, though I very much wanted to study astronomy. I want VERY MUCH to do better by my daughter. I have Dr. Ma's book sitting unread on my shelf. Shame on me! I'm going to start it this evening.

 

I used RightStart with my dd for the first three years, and I think that is a wonderful program. We're now using MEP and Math on the Level. I'm happy with my curriculum choices, but I still think I would benefit tremendously from that book. I'm grateful for this thread and everyone who has contributed!

[EKS]

I've just read this article by Wu (whose writings I respect generally) previously and I think he presents a "false dichotomy" (one I've heard on the board as well) that proponents of conceptual math are somehow antagonists of "math skills." And that is absurd.

 

 

 

I always thought that Dr Wu's article was about reform math (TERC Investigations and the like) vs traditional math as it plays out in schools. Programs like Investigations leave out (or at least they did in their original forms) the drill that ensures fluency. I don't think he was including what we think of as conceptual math on this forum.

[fractalgal]

Then you have taken some much better math classes than I did! You are very fortunate. The memory of third grade math can still make me cringe - timed drills where we had to spit out what seemed to me to be random sequences of numbers that had no connection or meaning whatsoever, more popularly known as "times tables". I hadn't the faintest idea what multiplication meant, I just had to memorize it. Unfortunately, that basic pattern continued throughout my ps experience. In high school I remember plugging numbers into formulas and churning out answers without any real concept of what I was doing.

 

Always knowing that I wasn't truly "getting it" made me hate math, and convinced me that I didn't have the ability to get a degree in a field involving math, though I very much wanted to study astronomy. I want VERY MUCH to do better by my daughter. I have Dr. Ma's book sitting unread on my shelf. Shame on me! I'm going to start it this evening.

 

I used RightStart with my dd for the first three years, and I think that is a wonderful program. We're now using MEP and Math on the Level. I'm happy with my curriculum choices, but I still think I would benefit tremendously from that book. I'm grateful for this thread and everyone who has contributed!

 

I think you should read Ma's book. If I remember correctly (it's been over a year since I read it) she noticed in her book than many American teachers that she observed had a poor understanding of some of the most basic concepts of math. Unfortunately, this weakness gets transferred to the next generation they teach. She points out something on the line of how can you teach a concept you don't understand?

 

Another problem with learning math in a classroom setting is that even if you have a teacher who understands the concepts they are teaching, they may not catch it when a student does not get it. That is one of the things that makes homeschooling beneficial. The personal attention from a parent can help catch these little problems before they become big problems.

 

I also think that when we become teachers, our motivation to learn a subject goes up. I learned math in much more depth when I had to teach it at university; I had to be prepared for any question about math from any student.

 

I like MEP, too. My problem is that I could spend hours on math because I find so many math programs I like. I have to limit my curricula if I plan to get through any of them. :D

 

I'm sorry you had a bad experience when learning math. There are so many people who can relate, and it is really sad. I'm glad you are getting it now and enjoying it more.

Edited May 18, 2010 by fractalgal

[stripe]

I think you should read Ma's book. If I remember correctly (it's been over a year since I read it) she noticed in her book than many American teachers that she observed had a poor understanding of some of the most basic concepts of math. Unfortunately, this weakness gets transferred to the next generation they teach. She points out something on the line of how can you teach a concept you don't understand?

 

Yes.... one teacher -- who teaches the same grade math year after year, couldn't remember how to find the perimeter of a rectangle. He said he had to look it up. This was the topic they were covering in class at the time. He got the perimeter and area formulas mixed up and couldn't even wing it, to figure out the formula in his head. Stories like this in the book are frightening but entirely believable.

 

Speaking of which, my math teacher in high school -- who'd taken the most math in college of all the teachers in my school -- was a theater major in college.

[Greta]

I think you should read Ma's book. If I remember correctly (it's been over a year since I read it) she noticed in her book than many American teachers that she observed had a poor understanding of some of the most basic concepts of math. Unfortunately, this weakness gets transferred to the next generation they teach. She points out something on the line of how can you teach a concept you don't understand?

 

Right, I have been concerned about how to teach my daughter a skill/subject that I was never very good at myself. That's one of the reasons I chose RightStart - it really does the "teaching" for you. In fact, it's embarrassing to admit how much a Kindergarten through 2nd grade math curriculum helped ME! But it honestly did. By using it to teach her, things about basic arithmetic clicked for my like they had not before. I think that using the abacus really helped me see numbers in my head in a new way that made arithmetic easier.

 

Though I never felt competent in math, I did get A's in my math classes (and I took the highest math that was offered at my high school - Algebra, Geometry, and Trig). I did learn how to plug numbers into an algorithm, just like they wanted us to. So I got by. But I still remember the excitement and awe that came with one moment of genuine understanding. In college physics, after we had been working with the equations for rectilinear motion for quite some time, one day out of the blue I suddenly understood them! They weren't just a thing that you plugged numbers into to get a correct answer on a test, they were an eloquent and meaningful statement about the nature of motion, a description of a natural phenomenon, not in words, but a clear, concise, and accurate description all the same. That was such an exciting feeling, to grasp the idea that an equation was expressing, rather than just how to use it to finish the homework or whatever. The sad part was that this was well into the semester, and I think my fellow students who had all had the opportunity to take calculus in high school had grasped that from day one!!! :lol:

 

I'm sorry you had a bad experience when learning math. There are so many people who can relate, and it is really sad. I'm glad you are getting it now and enjoying it more.

 

Thank you! Slowly, but surely, I am understanding it better and definitely enjoying it more. My daughter was really frustrated with the way RightStart introduced division (which is why we switched). But she's fine with that now, and that's the only math frustration she has known so far. I try to make it both fun and meaningful for her, with lots of manipulatives, games, and puzzles. I'm not trying to say I'm a super math teacher, but I think I've done alright so far. And dh (PhD in physics) plans to take over with Algebra in 8th grade, so I'll be off the hook then. :D

[TracyP]

So not all children are wired for learning conceputual math at a young age.

 

 

 

 

I just wanted to point out that the book is not about making sure all kids learn conceptual math at a young age. Dr. Ma probably is an advocate of that but that is not where she puts the emphasis. Her emphasis is on the teacher having a strong conceptual understanding. How can a teacher who does not understand math expect their students to understand math?(not at all aimed at anyone) I do not know if some children will still not "get it" - I am still too early in this to say. I just think that if I (as the teacher) don't "get it" than my kids don't have a chance. Really, this book was an eye opener.

[tennismomkelly]

This thread has made for a very interesting read! Thanks for posting. :D The comment comparing math instruction to phonics instruction really hit home with me. I just ordered a copy of this book from my library. I'm looking forward to diving into it!

[SophiaH]

Though I never felt competent in math, I did get A's in my math classes (and I took the highest math that was offered at my high school - Algebra, Geometry, and Trig). I did learn how to plug numbers into an algorithm, just like they wanted us to. So I got by. But I still remember the excitement and awe that came with one moment of genuine understanding. In college physics, after we had been working with the equations for rectilinear motion for quite some time, one day out of the blue I suddenly understood them! They weren't just a thing that you plugged numbers into to get a correct answer on a test, they were an eloquent and meaningful statement about the nature of motion, a description of a natural phenomenon, not in words, but a clear, concise, and accurate description all the same. That was such an exciting feeling, to grasp the idea that an equation was expressing, rather than just how to use it to finish the homework or whatever.

 

 

Wow, I wish I had had this experience just ONCE! I have always enjoyed math. But when I got to Geometry, I absolutely fell in love with proofs:001_wub:...love, love, love proofs! Math really made sense that year. Then I took Trig, then Pre-Calculus, and was completely lost from the first Sin and Cosine. I knew the order to punch things in a calculator but that was it. I still enjoyed it, and continued on into college, taking Calculus I and II. I would have LOVED to have had that moment you are talking about! The whole time I felt as if I were in a fog. Like the concept was just out of reach, and my brain just.could.not.figure.it.out. Oh, what frustration! I worked SO hard, and never ever had even a glimpse of understanding. I made a B and A respectively, though. :glare:

 

All that to say, I hope that all is not lost for me! I, too, understood more through RightStart B and C (so many lightbulb moments!) than I remember ever understanding in school (besides the beloved Geometry year). I *love* it that my daughter can do double-digit addition in her head faster than I can! I love it that she can use all these strategies for quick mental calculations, while I'm over with pencil and paper using my "touch math." :001_rolleyes: But I intend to rectify this. I'm already doing better on my mental calculations, so that's getting the old brain warmed up for bigger and better things. ;) Through a mixture of old 60s math textbooks (using the proofs that I love) and LOF that I am taking myself through, I am determined to finally understand what has eluded me for so long! I AM going to figure out what the heck sin and cosine really mean (and hopefully a lot more)! :lol:

[TracyR]

Ahh, I see. I hope in time I can understand math in a different way. I find a little bit at a time I am learning. I'll have to read the book.

[Corraleno]

I just wanted to point out that the book is not about making sure all kids learn conceptual math at a young age. Dr. Ma probably is an advocate of that but that is not where she puts the emphasis. Her emphasis is on the teacher having a strong conceptual understanding. How can a teacher who does not understand math expect their students to understand math? (not at all aimed at anyone) I do not know if some children will still not "get it" - I am still too early in this to say. I just think that if I (as the teacher) don't "get it" than my kids don't have a chance. Really, this book was an eye opener.

My son's 4th grade teacher was an art major who hated math and had NO CLUE how to teach it. She would get extremely annoyed with any child (often DS) who asked questions, saying "This is really very simple, I don't understand how anyone could not get this" and then repeat the same incomprehensible "explanation" she had just said. This same teacher also believed it was pointless to teach spelling and grammar, so she did a paragraph of dictation every week ~ using paragraphs she wrote herself, which were full of grammar & punctuation errors! But in order to get 100% on the test, the student had to replicate her errors. :rolleyes:

 

I'm half-way through Ma's book now, and it's very enlightening ~ but sadly not surprising.

 

Jackie

[Greta]

Wow, I wish I had had this experience just ONCE!

 

Hey, if it could happen to me, it could happen to ANYONE! Trust me! :D And if you already love math, that puts you one big step ahead of where I was at the time!

 

 

I have always enjoyed math. But when I got to Geometry, I absolutely fell in love with proofs:001_wub:...love, love, love proofs!

 

Oh, how funny. Even though I ranged from hating math to enduring it, Geometry proofs was the one thing I LOVED! To me, they didn't "feel" so much like math as like a logic puzzle, and I thought they were one of the most fun and interesting things I did in my entire four years of high school. It was kind of funny because my best friend, who always did better in math than I did, hated proofs. In fact, I think everybody else in my class hated them! But I thought they were the best thing since sliced bread. I was so disappointed when we moved on to other topics!!!

 

Math really made sense that year. Then I took Trig, then Pre-Calculus, and was completely lost from the first Sin and Cosine. I knew the order to punch things in a calculator but that was it. I still enjoyed it, and continued on into college, taking Calculus I and II. I would have LOVED to have had that moment you are talking about! The whole time I felt as if I were in a fog. Like the concept was just out of reach, and my brain just.could.not.figure.it.out. Oh, what frustration! I worked SO hard, and never ever had even a glimpse of understanding. I made a B and A respectively, though. :glare:

 

I did fine in Calc I but bombed Calc II. Calc II was the class that really drove it home to me that I simply did not have the ability to become an astronomer, my math skills were just not there. I, too, spent that entire semester feeling like I was in a fog. I just totally did not get it. I shed many tears. And then I changed my major to biology, so that I could still do science, but not have to deal with calculus! . . . and lived happily ever after. :D

 

I *love* it that my daughter can do double-digit addition in her head faster than I can! I love it that she can use all these strategies for quick mental calculations, while I'm over with pencil and paper using my "touch math." :001_rolleyes:

 

Me too! The first time my daughter beat me at mental math (and it didn't take long!) I felt like maybe I could successfully teach her, even though I wasn't so strong with it myself. I was so proud of her!

 

Good luck on your math journey! Is it really awful of me to confess that I don't even want to try to conquer those integrals that kicked my butt all those years ago? If I knew I was going to be responsible for dd's math education all the way through high school, that would be different. But knowing that her very capable father is going to handle it, I'm content to let him! And I think I'd rather channel my own (limited) brain power into learning Latin. Excuses, excuses. :lol: But I'm proud of you and sincerely wish you the best!

[SophiaH]

Good luck on your math journey! Is it really awful of me to confess that I don't even want to try to conquer those integrals that kicked my butt all those years ago? If I knew I was going to be responsible for dd's math education all the way through high school, that would be different. But knowing that her very capable father is going to handle it, I'm content to let him! And I think I'd rather channel my own (limited) brain power into learning Latin. Excuses, excuses. :lol: But I'm proud of you and sincerely wish you the best!

 

Thanks, GretaLynne for the encouragement! If I ever get into too much trouble trying to teach her, or if she catches up with my studies (very likely), then I'll also just pass the duty over to dh, who teaches high school math and has a natural math brain (even though I made a better grade than him in the Calc II class we took together...oh, the irony :rolleyes:). Maybe I can get through Calculus by the time my 3yo is a senior. :lol: Plus, I'm learning Latin, too, and hoping to add Greek in another year or so. I hope I don't find the limits of brain power anytime soon 'cause I'm gonna need all I can get! :tongue_smilie:

[Aludlam]

Can anyone speak of the differences between the old edition and the new edition of the book? I'm looking to get a used copy.

 

thanks so much

Angela

[PinkInTheBlue]

Ok, I've read this book discussed so many times on this board for years. I see it's available in a Kindle edition. Is there any reason I would NOT want it on my Kindle instead of book form?