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How did reading Liping Ma's book change how you teach math?


Manamana
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For those of you who have read Liping Ma's book, would you tell how this book has changed how you are teaching math in your homeschool? Did you change curriculum after reading the book? Did you pursue a deeper understanding of math concepts yourself? How? Do we assume a basic procedurial understanding of math is enough for students who don't plan to be engineers, computer programmers or math teachers?

 

I'm in the process of reading the book and it has already impacted my teaching of multiplication by the way I talk about place value and exploring real life problems, etc. But it also makes me think that we as homeschool teachers are doing a disservice to our kids by depending on math textbooks to provide a deeper knowledge of the concepts behind 2 digit multiplication or any other topic.

 

I'd like to be a better math teacher at home but I think my view of math, prior to reading the book, is similar to the average American public school teacher represented in the book - "how hard can the basics be"?

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If you haven't already seen these, you might enjoy them:

 

http://www.welltrainedmind.com/forums/showthread.php?t=246544

 

http://www.welltrainedmind.com/forums/showthread.php?t=139839

 

http://www.welltrainedmind.com/forums/showthread.php?t=206235

 

I haven't finished it yet - I tend to finally pick it up when I'm already half asleep. I'll probably have to start from the beginning :tongue_smilie:

Edited by wapiti
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Thanks, wapiti, for the additional posts. I did a tag search after I posted and also found this thread:

 

http://www.welltrainedmind.com/forums/showthread.php?t=178544

 

I read the chapter on dividing fractions this morning and was shocked by the American teachers' lack of knowledge.

 

I also found this additional reading on Prof. Hung-Hsi Wu's webpage:

 

The Mathematics K-12 Teachers Need to Know

Edited by Manamana
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I started out using a program based on the Asian way of teaching math (Right Start) simply because those countries have the best test scores in the world. After reading Dr. Ma's book, I understood *WHY* the test scores are so high and felt it was even more important to teach math from a "conceptual" POV.

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I read it several years ago. I just found myself nodding my head and doing this: :001_huh: a lot. I had already started with Singapore and I understood elementary math. I was :001_huh: and sad (and even a little angry) that SO many of the U.S. teachers in the study did not have a clue when it came to multiplication, division, and fractions.

 

There is nothing so difficult about elementary math that the vast majority of children should not be able to understand arithmetic beyond plugging in the basic algorithms. It's a complete sham that so many people grow up with an education like that.

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There is nothing so difficult about elementary math that the vast majority of children should not be able to understand arithmetic beyond plugging in the basic algorithms. It's a complete sham that so many people grow up with an education like that.

 

I agree. It's how I was taught, and I've always been "good" at math. In fact, years ago, I considered becoming a teacher through Alternative Certification. The first step was to take a state exam (don't remember which one), and I aced the math portion. The recruiter was practically drooling at the prospect of slotting me as a math teacher. We ended up going a different direction in our lives and I didn't pursue it any further, but it makes me feel a bit odd to realize I could have been one of those math teachers- good enough at math to pursue teaching it, but without a real understanding of some of the underlying concepts.

 

As a result, for our homeschooling we switched from the primarily algorithm and memorization based Saxon math to Math Mammoth. My son was only starting Saxon 3, but I started him all the way back at the beginning of MM 1 (moving at an accelerated pace) because of the significantly stronger conceptual focus in MM. We still haven't caught up completely to grade level, and I don't care a whit- I know we'll get there and his understanding

of the WHY of his math facts is exponentially greater.

 

I'm more apt to ask them to explain more than one way to solve a problem and I use composing and decomposing in my teach-talk!

 

Yes, composing and decomposing was one of my biggest take-aways as well. It just makes SO MUCH SENSE, and leaves me highly annoyed that I was not taught this way.

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1. I realized that all the " tricks" I got in trouble for in math class were actually good. They just wanted me to memorize and shut up already.

2. It has kept me persevering with MM and RS w/ my kid along with their preferred CLE. Ibfigure it's like broccoli, good for them Even if I have to encourage the first bite.

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I read this book in college since I am trained as a math teacher. It's been almost a decade but here are some things have stuck with me.

 

I realized how shallow my own conceptual knowledge of the basics were after reading it and worked on that in my classes and training. Especially fractions and division.

 

I also now view math very much as a web with many interconnected topics and not as a linear staircase . I don't rely on texts to teach my kids the basics and am very big on using manipulatives and helping my kids explore and play alot with things that just happen to be math-y.

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There is nothing so difficult about elementary math that the vast majority of children should not be able to understand arithmetic beyond plugging in the basic algorithms. It's a complete sham that so many people grow up with an education like that.

 

It is terrible, and that's exactly how I was taught in school, and I believe it's why I began disliking math so much by middle school. It just didn't make sense to me. Why did I need to put that "place holder" zero there when I was multiplying multi-digit numbers? What was happening when I "borrowed"? I knew how to do it all, but I just didn't get why I was doing it the way I was, and I wasn't stupid. I was always in the gifted programs, had a very high IQ, straight A's, etc., and after using Rightstart with my daughter and reading Ma's book, it's all so simple that I'm embarrassed to admit that I didn't understand it 2 years ago. When I think about it now, I don't even understand how I never figured it out on my own - it's that simple.

 

Quite frankly, I'm ANGRY that my teachers failed to explain something so simple to me. I would've understood it. I was actually very, very interested in a field that would've required a lot of math, and I didn't pursue it because I simply didn't understand math. It's awful that people's lives have been limited over something that would've been so easy to teach, because I surely can't be the only one. How many bright kids are out there who feel inadequate over math, when the real problem is that they just haven't been taught what they need to know? Ugh.

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This book has been in my "Save for Later" pile on Amazon for at least a year. I was hoping it might come down in price, but I just now "sucked it up" and ordered the book.

 

I have always been very good at math, but I now realize that, for the most part, I have been really good at memorizing algorithms.

 

I came up with a (slightly disturbing) way to explain dividing by fractions to my children . . .

 

It involves a man at a carnival giving pies (or portions of pies) to people (or portions of people - I warned you that it was slightly disturbing - I drew 1/4 people with just feet, 1/2 people from the waist down, etc.).

 

So, it starts with carnival guy saying, "I'm giving away 1 pie to every 1 person!" It's easy to figure out how many pies he gives to two people (2), a family of four (4), or that sad little half-person (1/2).

 

Then, I move on to . . . carnival guy is giving 1/2 pie to every 2 people. So how many pies does 1 person get (1/4)? How many pies does the half-person get (1/8)?

 

So then I get on to "the point" of dividing by fractions which is basically to determine how much "pie" would 1 "whole person" get.

 

So now carnival guy (sadly, running out of free pie) is giving 1/5 pie to every 2/3 person. How much pie will 1 whole person get? Well, 1/3 person will get 1/10 of a pie (1/2 of 1/5), so 1 whole person will get 3/10 of a pie. Sure it's easier to say "flip the second fraction and multiply (1/5)/(2/3) = (1/5) *(3/2) = 3/10, but then the kiddos have NO idea why! Plus, drawing fractional zombiesque people eating fractional (BRAIN) pies was fun :lol::glare:.

 

So, yeah, I need to read this book. My pitiful half-stick people and not quite circular pies need to be put out of their misery! Hopefully, I'll find new (and improved and half-people free) inspiration for teaching math.

 

~Tiff

2 girls (13 and 12)

+ 2 boys (10 and 4)

4 ever busy

Edited by Tiffnkids
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I also now view math very much as a web with many interconnected topics and not as a linear staircase . I don't rely on texts to teach my kids the basics and am very big on using manipulatives and helping my kids explore and play alot with things that just happen to be math-y.

 

Allyall, since you have a math teaching background, what resources are you finding helpful to explore topics with your kids? Do you have a mental list of topics you want to cover with them, or a program you plan to use in the future or is it very relaxed/child led?

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I was actually very, very interested in a field that would've required a lot of math, and I didn't pursue it because I simply didn't understand math. .

 

This was true for me too. I got by in K-12 knowing the math procedures and gained some knowledge but in college it became much harder to do well in math classes without a deeper knowledge. So I changed a majors to something less math intensive.

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It didn't really change the way I taught math, but it helped me articulate a philosophy of math education which I already had a sense of. It allowed me to explain with more clarity to my daughters' math teachers why I was pulling my kids out and homeschooling math - and what I felt was missing in their math program (TERC Investigations).

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This is very interesting. My husband has been wanting me to switch up math programs. We have used Saxon 1 this year, but he would prefer our daughter know why she is doing what she is doing- more conceptual math and mental math skills. He really wants her to learn to use an abacus :confused: I have no idea how those work!!!

 

I'm all for it, especially after reading this thread, as I was one who hated math in school too. What curriculums do you all recommend to head more in this direction?

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Do we assume a basic procedurial understanding of math is enough for students who don't plan to be engineers, computer programmers or math teachers?

 

No, it is not enough, because anything where the underlying REASON is not understood will be forgotten. If, OTOH, the student understands the concept behind the procedure, he will always be able to re-derive the procedure for anything, should he need it at some later point. Even decades later.

Really, elementary math is not difficult - most people would have no trouble understanding the concepts if somebody who did explained them well enough. (Of course, teachers who don't understand concepts themselves, can not possibly teach them.)

 

Btw, in higher math the conceptual understanding becomes even more important - otherwise a student would be completely overwhelmed by what he perceives as different situations and cases, each with a different procedure, where really all it is are applications of the same simple basic concept.

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No, it is not enough, because anything where the underlying REASON is not understood will be forgotten. If, OTOH, the student understands the concept behind the procedure, he will always be able to re-derive the procedure for anything, should he need it at some later point. Even decades later.

Really, elementary math is not difficult - most people would have no trouble understanding the concepts if somebody who did explained them well enough. (Of course, teachers who don't understand concepts themselves, can not possibly teach them.)

 

Btw, in higher math the conceptual understanding becomes even more important - otherwise a student would be completely overwhelmed by what he perceives as different situations and cases, each with a different procedure, where really all it is are applications of the same simple basic concept.

 

:iagree:

And, if we don't teach our kids to understand math (as well as arrive at the correct answer :)), even if they don't go into a field which uses math, what about their children? Especially if they decide to homeschool also. How will they help their children understand math....the cycle just continues.

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It didn't really change the way I taught math, but it helped me articulate a philosophy of math education which I already had a sense of.

 

This.

Not that I really know what I'm going to do about it in practical terms. When maths gets to the top of my self ed list, I'm worried that I won't be able to relearn it properly because it will look too familiar and I won't see the difference between "knowing" it and KNOWING it in myself.

 

Luckily I have time to figure it out :)

 

Rosie

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This is very interesting. My husband has been wanting me to switch up math programs. We have used Saxon 1 this year, but he would prefer our daughter know why she is doing what she is doing- more conceptual math and mental math skills. He really wants her to learn to use an abacus :confused: I have no idea how those work!!!

 

I'm all for it, especially after reading this thread, as I was one who hated math in school too. What curriculums do you all recommend to head more in this direction?

 

Singapore is the program most people would point you towards.

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I'm all for it, especially after reading this thread, as I was one who hated math in school too. What curriculums do you all recommend to head more in this direction?

 

There are a number of options,. but the ones that are easiest-to-teach IMHO are Right Start, Math Mammoth, and MEP. RS is a Montessori adaptation Asian math that is very hands-on and has totally scripted lessons. Math Mammoth is similar to Singapore but all-in-one and designed to be self-teaching. It also explains concepts step-by-step-by-step rather than assuming the student can make conceptual leaps like Singapore does. MEP is a free program that takes a "spiral" approach (mix of different types of problems in each lessons) rather than a "mastery" approach like RS, MM, and Singapore (one topic at a time).

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This is very interesting. My husband has been wanting me to switch up math programs. We have used Saxon 1 this year, but he would prefer our daughter know why she is doing what she is doing- more conceptual math and mental math skills. He really wants her to learn to use an abacus :confused: I have no idea how those work!!!

 

I'm all for it, especially after reading this thread, as I was one who hated math in school too. What curriculums do you all recommend to head more in this direction?

 

Look at Rightstart...it's fabulous for teaching conceptual math and using varied strategies. Also uses the abacus!

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I'm more apt to ask them to explain more than one way to solve a problem and I use composing and decomposing in my teach-talk!

 

Would you be willing to give the bullet points for what composing and decomposing are? (Or is this in another thread that I should look up?) :001_smile:

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No, it is not enough, because anything where the underlying REASON is not understood will be forgotten. If, OTOH, the student understands the concept behind the procedure, he will always be able to re-derive the procedure for anything, should he need it at some later point. Even decades later.

Really, elementary math is not difficult - most people would have no trouble understanding the concepts if somebody who did explained them well enough. (Of course, teachers who don't understand concepts themselves, can not possibly teach them.)

 

Btw, in higher math the conceptual understanding becomes even more important - otherwise a student would be completely overwhelmed by what he perceives as different situations and cases, each with a different procedure, where really all it is are applications of the same simple basic concept.

 

I so agree, most especially because everyone would've said that I was someone who wouldn't become an engineer or physicist or whatever. That was BECAUSE they didn't teach me what I needed to know, though!!! If anyone had bothered to explain things to me, math wouldn't have seemed so random and utterly inexplicable to me. By the time I was in 6th grade I already hated it, and although I was perfectly proficient, it made no sense. I made it through high school Geometry and Alg. 2, but I hated it and struggled the whole time. That wouldn't have been the case if I ever knew what it was about. I get so incredibly frustrated when people determine that their 8 or 10yo kids won't ever do anything that involves math and therefore don't need to understand it. You can't set a kid's path in life that early, and if you've never bothered to explain math, perhaps they can't see the beauty in it and they don't understand it, and that's WHY they don't want anything to do with it. (That's all a general 'you' of course.)

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I'm just now reading the book. I have already bought Rightstart for when I start teaching my kids math. I wish I would have learned this way!! By the time I got to 6th grade, math didn't make sense to me. I was still in advanced math, but I spent hours on homework and finally burned out in 7th grade.

 

My husband was put in a gifted program when he was in 2nd grade and learned this way. It wasn't until a couple of months ago that I realized just how differently we approach math. I always assumed it was because he was just plain smarter (hehe), but even if that is the case, I feel cheated that I wasn't taught in a way that made sense. I am however, excited and a little nervous about learning math all over again!

Edited by brendag
I should read before I post! Hehe!
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Thanks so much for the curriculum ideas. I have been looking at Rightstart and it looks so great...it's hard to spend that much money though. Yikes. But, it looks like a lot of it you would only really have to buy once, and then younger siblings would move through it much cheaper. Hmmm.....thanks for the ideas. I know my husband will be easy to convince if he sees the abacus!!! :)

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Would you be willing to give the bullet points for what composing and decomposing are? (Or is this in another thread that I should look up?) :001_smile:

It might be in the other thread, I'm not sure. Basically, it's teaching that we are working towards composing tens (10-unit; 10-tens; etc.) and not "borrowing." It's more like building and breaking down (regrouping). The book can explain it much better than I can with the noise behind me. Good stuff, though! It has encouraged me to break down math and present it to understanding, not just to teach to fill in the blanks.

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Do you think the book would be a good read for 16-17yo who had a traditional upbringing in math? They are finishing up Algebra II and precalc at this point, with another year of math each ahead. I am using a different approach for my younger elementary ones, but am wondering if my older would be able to benefit from reading the book at least.

 

Thoughts? Thank you! :)

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Do you think the book would be a good read for 16-17yo who had a traditional upbringing in math? They are finishing up Algebra II and precalc at this point, with another year of math each ahead. I am using a different approach for my younger elementary ones, but am wondering if my older would be able to benefit from reading the book at least.

 

Thoughts? Thank you! :)

 

If I were them, I'd go off and cry and think nasty things to my teachers for putting me through years of study that wasn't even teaching me properly.

 

Rosie

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I first read it when my now 6.75 year old was in utero. I knew prior to reading Dr Ma's book that I was dissatisfied with the kind of math education I had as a child, and had a "generalized" sense of the problem.

 

Her book crystalized the differences between a "procedural" approach to teaching mathematics and teaching for deep understanding. Dr Ma helped me set an "ideal" for the sort of education I wanted for my son.

 

Her book was only the first step on the journey, but it certainly helped set me in the right direction. I would cal it a *life-changing* read.

 

Bill

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Allyall, since you have a math teaching background, what resources are you finding helpful to explore topics with your kids? Do you have a mental list of topics you want to cover with them, or a program you plan to use in the future or is it very relaxed/child led?

 

I'm sorry it took me so long to respond and I hope you find any of this helpful.

 

Overall I use a child led approach to math. I think a big part of this though is that math is a game to me and there is a very positive environment for math questions in my home. I do pull a lot from my training experiences. I have taken and played many of my games that I learned with a friend's kids and its gone well that they like to "play" math with me now too.

 

I did buy the Miquon work books for my kids to "do" because they kept asking for math homework to do. So I have them choose pages out of those to do and help them as needed. Those match well (in agenda and overall approach) for me with what we do otherwise. They also "play" on Khan academy when they want to for practice. But we have had cuisenaire rods and pattern blocks for them to play with from the time they were 3-4.

 

Beyond that I have a good basic library of elementary stories that have math as topics and a bunch of board games that involve math-y things. Now my definition of math-y is very broad. For example: Battleship is an excellent math game that prepares you for graphing and charting. (and Connect 4 is a great math game pre battleship). Backgammon is a great game for counting and logic. Scrabble has arithmetic practice, etc etc. Favorite math stories: The Number Devil, The Man who Counted, The Greedy Triangle, One Grain of Rice, The Sir Cumference Series, The Dot and the line, One Hundred Hungry Ants, etc... (Great lists and resources here: http://www.livingmath.net/)

 

As far as mental list of topics, I think the NCTM breaks it down into nice broad groups - which are:

Number and Operations

Algebra

Geometry

Measurement

Data Analysis & Probability

Process Standards

 

 

And you can access basic ideas about them here: http://nctm.org/standards/content.aspx?id=4294967312

 

 

I have read thru Texas state standards in Math for different grades, as well as some summaries of skills in books like "What your homeschooler needs to know" and dislike the spiral approach. I prefer to learn deeply about a topic.

 

 

 

For example, My kids wanted to learn about really big numbers before they had mastered all there was to know about 1-10 and such. So we have talked a lot about place value and the names for numbers up as far as there are names for numbers. http://en.wikipedia.org/wiki/Names_of_large_numbers

 

 

 

Anyway, I am impressed with the Math Mammoth from what I've seen, but haven't felt the need for it with the kids I have right now. When they are ready for algebra if I had to choose a book right now, I'd go with the ones by Key Curriculum Press - Discovering Algebra, Discovering Geometry, etc. But we'll see if I still feel that way when we get there! :)

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This book has been in my "Save for Later" pile on Amazon for at least a year. I was hoping it might come down in price, but I just now "sucked it up" and ordered the book.

 

I have always been very good at math, but I now realize that, for the most part, I have been really good at memorizing algorithms.

 

I came up with a (slightly disturbing) way to explain dividing by fractions to my children . . .

 

It involves a man at a carnival giving pies (or portions of pies) to people (or portions of people - I warned you that it was slightly disturbing - I drew 1/4 people with just feet, 1/2 people from the waist down, etc.).

 

So, it starts with carnival guy saying, "I'm giving away 1 pie to every 1 person!" It's easy to figure out how many pies he gives to two people (2), a family of four (4), or that sad little half-person (1/2).

 

Then, I move on to . . . carnival guy is giving 1/2 pie to every 2 people. So how many pies does 1 person get (1/4)? How many pies does the half-person get (1/8)?

 

So then I get on to "the point" of dividing by fractions which is basically to determine how much "pie" would 1 "whole person" get.

 

So now carnival guy (sadly, running out of free pie) is giving 1/5 pie to every 2/3 person. How much pie will 1 whole person get? Well, 1/3 person will get 1/10 of a pie (1/2 of 1/5), so 1 whole person will get 3/10 of a pie. Sure it's easier to say "flip the second fraction and multiply (1/5)/(2/3) = (1/5) *(3/2) = 3/10, but then the kiddos have NO idea why! Plus, drawing fractional zombiesque people eating fractional (BRAIN) pies was fun :lol::glare:.

 

So, yeah, I need to read this book. My pitiful half-stick people and not quite circular pies need to be put out of their misery! Hopefully, I'll find new (and improved and half-people free) inspiration for teaching math.

 

~Tiff

2 girls (13 and 12)

+ 2 boys (10 and 4)

4 ever busy

 

 

I really like your illustration. But, my dd would be too stuck on the fact the 1/2 people don't have mouths to eat with or all of their digestive system, so why give them a pie :lol:. She gets hung up on the details, very legalistic. But I will have to tell dh this. He is not very good at fractions, so this will help him :D.

 

I will have to get this book pronto. I love math from a conceptual understanding vs just "plug & play."

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