"Does McDonalds Sell Cheeseburgers?"...grrrrr

[Halcyon]

This is the mnemonic that my half-sister's gifted public school is using to teach her long division (4th grade). It stands for "divide, multiply, subtract, carrydown". Does she understand the why's and how's. Of long division? Er...no. But she does do page after page of division problems to "cement" this mnemonic in her head.

 

My son has been studying long division over the last week or so, and we've spent a lot of time learning WHY exactly one subtracts, why exactly one "drops down"....so that if he does forget,he can really think about what to do next. It's slow going but I really feel strongly about this, and to be honest, I feel irrationally annoyed that my half-sister's "gifted" class is teaching her no more than a silly procedural mnemonic when she certainly has the capacity to understand it on a deeper level.

[Halcyon]

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[Halcyon]

Eta: I can't seem to edit my post, but re-reading it, I sound a little snotty. I don't mean to imply that the way singapore teaches math is the be-all-end-all. I just remember reading Liping Ma's book and thinking "wow, is that how elemntary math is really taught in this country?" Now that I see it in reality, to my own sibling, I guess I just feel a bit more...incensed. Yes, I'm a math dork :)

[Guest aquiverfull]

I understand how you feel. With my public school education, I always struggled in Math. I still don't really get it. I wish I had been taught how to think instead of how to plug in a formula. Since traditional was all I knew, that's what I went with for my oldest homeschooled student and now sadly, she's in the same boat as I am. The bad thing is that I don't know enough myself to teach her those whys. I'm currently trying to resolve our math woes and get her on the right track.

[michelle l]

Soooo....why DO we divide, mulitply, subtract, and carrydown?:blink:

[NicksMama-Zack's Mama Too]

Soooo....why DO we divide, mulitply, subtract, and carrydown?:blink:

 

"Think of division as repeated subtraction...."

 

Here's a helpful site

 

http://www.homeschoolmath.net/teaching/md/long_division.php

[Snickerdoodle]

Soooo....why DO we divide, mulitply, subtract, and carrydown?:blink:

Basically we are comparing a multiple of the divisor to the dividend.

[Tenaj]

 

My son has been studying long division over the last week or so, and we've spent a lot of time learning WHY exactly one subtracts, why exactly one "drops down"....so that if he does forget,he can really think about what to do next..

 

I guess I'm not sure I understand what the problem with learning the memonic. You are teaching the reasons why so that your son can remember the steps ; they are teaching the memonic so that the kids can remember the steps. I think in the end, you are going to end up with the same result - kids that can do long division easily.

 

There was a discussion some time back here on the boards about the grammar vs. dialetic stage regarding math and it made me wonder if our little grammar stage kids really benefit from all those "whys" we try to teach in math. It makes sense to me that the "whys" may come along later in the logic stage.

 

I have some kidlets who love the "why" explanations but I also have two (at least) that get cross-eyed when thinking about the "whys" and just want the facts. Both kinds of kids eventually end up at the same point, they just take different paths. One of my "just the facts" kids loves math so much as a senior that he's probably going to end up majoring in math at college. He's figured out the "why's" as he's gotten older, but he would have loved having a memonic to memorize in elementary school for the steps of long division.

 

Just my 2 cents . . .

[mom31257]

Do you know for sure that when division was taught the teacher didn't cover the "why's" of the process? If not, I think you are assuming that a mnemonic means the school is only teaching the steps.

 

I've looked at several public school elementary math textbooks in the last couple of years. All the ones I've seen always teach the why along with the how.

 

I think the problem is that in a public school classroom a teacher is not going to have time to sit with every student and make sure they understand the "why" before moving on; therefore, the teacher covers the why and gives lots of practice in the steps hoping that the students will "get it" through the practice. Well, at least get it enough to be able to do it come standardized test time since a lot of people in this country want their jobs to depend on it.

[Cranberry]

I went to public school and the "divide, multiply, subtract, check" thing was definitely drilled. I learned it quickly and was also taught the WHY behind what I was doing. I can actually remember the worksheets that showed us why we were subtracting. But the steps were drilled by memory as well. I was always very good at Math in school and college and frankly I think it was one thing the PS did well...at least for me.

 

I do think that just because you see someone teaching a mnemonic, it's not a fair assumption to make that they aren't teaching the why as well.

 

We have all sorts of memory work for my kids. When we teach it, I teach the why and the reasons and all that, but the memory work cements the learning and helps them recall the why.

 

Now, the choice of the mnemonic....about mcDs cheeseburgers? REally? :lol:

[Hedgehogs4]

i thought the the frustration was going to be about them giving free advertisement for mcdonald's. bleh!

 

i have no problem with a mnemonic as long as they are understanding.

[Soror]

Well, I thought it was funny. I do hope as well that they are teaching the whys as well.

[Sahamamama]

Eta: I can't seem to edit my post, but re-reading it, I sound a little snotty. I don't mean to imply that the way singapore teaches math is the be-all-end-all. I just remember reading Liping Ma's book and thinking "wow, is that how elemntary math is really taught in this country?" Now that I see it in reality, to my own sibling, I guess I just feel a bit more...incensed. Yes, I'm a math dork :)

 

:grouphug: I don't think you sound snotty at all. I think you sound ticked off! And rightly so.

 

What's the point of simply teaching the "steps" to children who can learn more? I don't think there's a problem with using a mnemonic -- not sure I like the Cheeseburger one :tongue_smilie: (surely the teacher could come up with something better?) -- but using a mnemonic is a time-tested way of ensuring learning. What I DO object to doing is leaving it at that.

 

Does McDonald's Sell Cheeseburgers is not doing math. It's advertising. :tongue_smilie:

[Pamela H in Texas]

*I* think that when you have 30 kids, you cover things several different ways. So you go through a page like the one linked above to make the points and then you teach the mnemonic. The teacher probably did a handful of other things also. Her job is to make sure ALL 30 kids can do it and do it well, especially something like this which is a life skill. No doubt, she was doing informal assessments of what the kids were picking up the whole week to adjust her teaching also. And so maybe THIS child really jumped on teh mnemonic while another child jumped on something else. And seriously, this teacher is going to go on about this for weeks this year and other years other teachers will chime in. Maybe this child is at the McD's level right now and will pick up on another level another week or year. Thankfully, the teacher is determined that all children (again, she has 30, not 1) will have the skill when certain aspects may be more individual.

 

Of course, I'm HOPING that they will step up and give them full understanding in time. It would stink to settle for the skill. Unfortunately, that is probably more about the individual teacher. Maybe give her a copy of Teach Like a Champion or Teaching as Leadership?

[Halcyon]

I want to clarify: in my opinion, the teacher did not explain the 'why' of long division well to my sibling. My sibling can't really explain why she's doing each step. To those of you who think "who cares?" Whether she knows the "why", my guess is you haven't read Liping Ma's book LOL.

 

I have no problem with the mnemonic if the mechanics are understood. But understanding the why is, imo, key. (Well, as an anti-corporate vegetarian I DO have a problem with this particular mnemonic......;)

[kewb]

Now I feel guilty for using it with my dd. We explained the whys, the steps, the everything and she just couldn't get it until I gave her that phrase.

 

Of course, what really cemented it was relating it to toys. The toys cost $5,539 and you have $36. How many toys can you buy.

[oldskool]

"Think of division as repeated subtraction...."

 

Here's a helpful site

 

http://www.homeschoolmath.net/teaching/md/long_division.php

 

 

This was really helpful. I never knew "why". My math background is not good, but I have done my best teaching my kids. We use Saxon and I don't remember it going over the why of long division, although I remember them learning the steps.

 

I am reading Liping Ma's book right now and have found it very interesting.

 

 

Lesley

[Mandy in TN]

i thought the the frustration was going to be about them giving free advertisement for mcdonald's. bleh!

 

i have no problem with a mnemonic as long as they are understanding.

:lol::lol::lol: That is too funny, because that was exactly what crossed my mind when I read the title.

 

And :iagree:as long as they have also taught the whys, I have no problem with using mnemonics as a memory device.

 

In the teacher's defense maybe she did explain the why and your sister just isn't remembering the explanation. If you explained the whys once to your ds on a board while he was sitting in a group of 25 and then handed him a sheet of long division problems with the snappy little mnemonic at the top, what are the odds that he would remember the explanantion.

 

There are plenty of kids who go to traditional classroom schools who are still participating in parent led education for this exact reason: you just can't beat one-on-one tutoring!

 

Cut the teacher some slack and explain it to her again. ;)

Mandy

[prairie rose]

I want to clarify: in my opinion, the teacher did not explain the 'why' of long division well to my sibling. My sibling can't really explain why she's doing each step. To those of you who think "who cares?" Whether she knows the "why", my guess is you haven't read Liping Ma's book LOL.

 

Wow. Just wow. I have read Liping Ma. But I've also taught 3 children up to this point to divide. Yes, children should be taught the "why" behind what they are doing and not just the rote memorization of the steps but there will always be a child who looks at you with a deer in the headlights look when you explain mathematical concepts. No matter how long and hard you talk yourself blue in the face trying to explain it in a way that makes sense to them, they don't get the why of what they are doing. But they still need to know how to divide like everyone else. One day, when they are ready they might see the same explanation and the light bulb will come on and they will say "oh now I get it" but until then, they still need to know how to divide. I should know, I was that child. I was classified as gifted or above average intelligence in school but no matter how hard I tried, trying to understand the whys behind math was beyond my grasp until late high school and college. Not all gifted children are gifted in every academic area. I also have one child who, just like me, cannot seem to grasp the why right now. For now, just knowing how is enough until she is ready to understand, IMO. If it's important to you that your half sister understand the why, then teach her yourself. You wouldn't be the first person to do such a thing.

 

As a side note, I've tutored many public school children. Just because they cannot explain it doesn't mean it wasn't taught. It could simply mean that the child simply has not absorbed it and internalized it yet. Could it mean it was not taught or was only breezed over quickly? Sure. But without sitting in on the class or asking the teacher, it's assuming a bit much to say it was not taught because the child cannot explain it.

 

 

Well, as an anti-corporate vegetarian I DO have a problem with this particular mnemonic......;)

 

Well, that's why you homeschool isn't it? Your view is not mainstream. The majority of public school children can identify with mnemonic thus making it easy for them to remember. I seriously doubt the teacher has time to come up with a different mnemonic for each child that fits with their family's views so he/she has to "play to the middle". Most children, especially public school children, recognize McD's and like cheeseburgers. Even if they are vegetarians, they've more than likely at least heard of McD's. Like it or not, it's effective with public school students. You don't agree, so you choose to homeschool your children and teach them as you see fit. Some homeschoolers choose to teach the same mnemonic to their children because it's how they see fit to teach their children. I didn't teach my children a mnemonic for division. I just didn't find it necessary. In my opinion, if they can memorize "Does McDonalds Sell Cheeseburgers?", "Dad, Mom, Sister, Brother" or whatever other mnemonic floats your boat, they can just as easily memorize "Divide, Multiply, Subtract, Bring down". Just my personal preference.

 

Just my 2 cents FWIW.

[maryanne]

Some how I managed to get through an electrical engineering degree (summa cum laude, no less) without understanding the why's of long division. It wasn't until I was teaching my son long division that I really got the why's. Here's the really ironic part; you know which curriculum I was using to teach him Saxon.

 

Forgive me if I don't get what all the fuss about conceptual math is all about. I also don't get the accusations that Saxon doesn't teach concepts either. Math is very painful to do if you understand the concept but have no speed or fluency with the procedures. Certainly you can re-derive everything, but that's a long,slow, painful way to get math done.

[Spy Car]

Makes my head want to explode :D

 

Bill

[Mandy in TN]

Forgive me if I don't get what all the fuss about conceptual math is all about. I also don't get the accusations that Saxon doesn't teach concepts either. Math is very painful to do if you understand the concept but have no speed or fluency with the procedures. Certainly you can re-derive everything, but that's a long,slow, painful way to get math done.

:iagree::iagree::iagree:

 

Wow. I could have written that post.

 

I have read Laping Ma's book, used Miquon (only book 1) and Singapore PM (1-6). I have also used Saxon and Kumon. Saxon does present concepts. Drill does achieve immediacy.

 

Of course a child should be presented the concept, but those young Asian students don't forego practice and just look at concepts all day. You must work with the material presented. Some children simply will not get the concept. This doesn't mean that it shouldn't be presented, but dawdling over it can likely bring about confusion and contempt.

 

Find the balance.

Mandy

[2cents]

Well, as someone who has nothing against a big greasy McD cheeseburger, I kinda like that mnemonic. Even better, I'd teach the mnemonic and the whys behind the process while eating a cheeseburger and fries. ;)

[mom31257]

Well, as someone who has nothing against a big greasy McD cheeseburger, I kinda like that mnemonic. Even better, I'd teach the mnemonic and the whys behind the process while eating a cheeseburger and fries. ;)

 

:iagree:

[Tutor]

I loved math in school and did well at it. Until I started teaching my own children, I didn't realize how little I actually knew. I am now the mother of a child who despises math... it just doesn't click. I've explained the whys (as I understand them, now that I do understand them) but I also taught her a mnemonic (this very one, actually) so that she could remember all the steps and move on. If I had not, my 8th grade dd would still be in 4th grade math. I just have to trust that one day she'll have an "ah-ha" moment like I did when it comes to math.

[anneofalamo]

just a note on jiggles,

 

I grew up with the original School House Rocks, and I was horrible at GRammar!! I knew all the words to each jingle and remember everyone in school being excited when the "new" jingle came out!

Easy Grammar grade 3 opened my eyes, to what a conjuction, interjection, lolly lolly adverb and adjectives really were!

 

but..............

that being said, I have taught the whys to math...

and

wish I had this mnemonic for my kids last year, I think it would have helped them!

[catholicmommy]

Some how I managed to get through an electrical engineering degree (summa cum laude, no less) without understanding the why's of long division. It wasn't until I was teaching my son long division that I really got the why's. Here's the really ironic part; you know which curriculum I was using to teach him Saxon.

 

:lol::lol::lol::lol::lol:

 

For some reason, this just cracked me up !! Thanks for the chuckle.

Forgive me if I don't get what all the fuss about conceptual math is all about. I also don't get the accusations that Saxon doesn't teach concepts either. Math is very painful to do if you understand the concept but have no speed or fluency with the procedures. Certainly you can re-derive everything, but that's a long,slow, painful way to get math done.

:iagree:

I haven't read 'the book' so I don't know what to think about this whole debate thats been going on, but I myself have done very well learning math my whole life without understanding the why of it either. I don't think I was ready to conceptually understand some of those ideas. I have watched my kids learn math through the elementary years and realized that some, who are more spatial, seem to 'get it' and internalize an understanding.. and others who are less spatial and more like me, seem to do just fine learning the 'steps' without a deep understanding. It is just the grammar stage and there is time for their brains to develop and go back and understand the beauty of math, isn't there?

[catholicmommy]

Well, as someone who has nothing against a big greasy McD cheeseburger, I kinda like that mnemonic. Even better, I'd teach the mnemonic and the whys behind the process while eating a cheeseburger and fries. ;)

 

:tongue_smilie: mmmmmmm.... french Fries!! (and more importantly, for my sad gluten free self, they are some of the only fast food variety of fries that I can eat!) Now I want to go get some!!

[Halcyon]

Makes my head want to explode :D

 

Bill

 

Well, at least I've got you on my side, Bill. That's something.:D

[Halcyon]

I loved math in school and did well at it. Until I started teaching my own children, I didn't realize how little I actually knew. I am now the mother of a child who despises math... it just doesn't click. I've explained the whys (as I understand them, now that I do understand them) but I also taught her a mnemonic (this very one, actually) so that she could remember all the steps and move on. If I had not, my 8th grade dd would still be in 4th grade math. I just have to trust that one day she'll have an "ah-ha" moment like I did when it comes to math.

 

 

I have no problem with mnemonics, even if I wouldn't have chosen that particular one ;). My issue is that according to my sibling, the teacher did not explain the rationale behind the process. Of course, my sibling could be mistaken. She could have been in the bathroom when the teacher explained it, she could have been giggling in the back row (although I doubt it LOL). Or perhaps, just perhaps, it doesn't stick out in her mind because her teacher actually didn't emphasize it. What the teacher does seem to have emphasized is procedural math. Hence the memorable mnemonic.

 

Personally, I feel _understanding_ the WHY of math is just as important, if not more important, than understanding the _how_ of math. Mandy in TN wrote "some children simply will not get the concept. This doesn't mean that it shouldn't be presented, but dawdling over it can likely bring about confusion and contempt." I politely, but strongly, disagree with this statement. To state that the act of explaining the rationale behind a procedure can actually confuse a child more (perhaps, in the short term, that may be true) and thus, one should simply move along to the procedure because, after all, that's what matters, is a bit mind-boggling to me. Perhaps the explanation itself was inadequate, not the child's understanding. I do think most PS teachers are concerned more about whether a child will get the right answer (and that's obviously not their fault--the emphasis on test scores is ridiculous) than whether a child understands why one, for example, "carries down" the next digit in the number.

 

I have always loved math and done well at it myself. But it wasn't until I sat down and learned the process of math that I truly understood the beauty, the versatility, the potential of math. And if anyone should be conveying that beauty to children, it's the teachers. I think overall, our nation would be far more competitive in engineering, science, and other math-based disciplines if the WHY of math, the beauty of math, were brought more front and center.

 

Of course, many will argue "who has time for that?" and "most kids don't care about that" and "teachers can't teach 30 kids about the beauty of math--they need to teach them how to get the answer". I would argue that that is specifically what is wrong with mathematics education in this country.

 

Okay, off my soapbox.:tongue_smilie:

[Spy Car]

Well, at least I've got you on my side, Bill. That's something.:D

 

I'm (almost) speechless :D

 

Bill (who is tempered to blame junk-food :tongue_smilie:)

[catholicmommy]

To state that the act of explaining the rationale behind a procedure can actually confuse a child more (perhaps, in the short term, that may be true) and thus, one should simply move along to the procedure because, after all, that's what matters, is a bit mind-boggling to me. Perhaps the explanation itself was inadequate, not the child's understanding. I do think most PS teachers are concerned more about whether a child will get the right answer (and that's obviously not their fault--the emphasis on test scores is ridiculous) than whether a child understands why one, for example, "carries down" the next digit in the number.

 

I have always loved math and done well at it myself. But it wasn't until I sat down and learned the process of math that I truly understood the beauty, the versatility, the potential of math. And if anyone should be conveying that beauty to children, it's the teachers. I think overall, our nation would be far more competitive in engineering, science, and other math-based disciplines if the WHY of math, the beauty of math, were brought more front and center.

 

 

 

I am no expert in these issues and I haven't read 'the book', but I do have some questions about this... What if a child's brain isn't actually mature enough to 'get' some of these concepts yet? I've heard on these boards many times about homeschool moms who have had those 'aha' moments in math while teaching their own children (and thus are encouraged to teach the understanding to their own children)... but you had this aha moment as an adult when you have so much more maturity and growth in your brains.

 

Could it be true that just as some kids are slower for reading to 'click' that conceptual math skills will also be slower? Just because you don't teach it in the early years doesn't mean you can't teach it though the logic stage or older. I love learning the why of math now.. but I have the basic skills that allow me to hang that understanding somewhere in my brain.

 

Not trying to argue.. just wondering about child development.... and thinking about things like why we don't start logic until later etc...

[Gwenhwyfar]

my daughter fell behind in math because of so much time spent trying to get her to UNDERSTAND what she was doing as opposed to just following the rules.

 

she got confused. i got confused. we both ended up lost & frustrated and hating math more than we did in the first place.

 

we've gone back to the rules.

 

different people, different things work. ;)

[Mandy in TN]

I am no expert in these issues and I haven't read 'the book', but I do have some questions about this... What if a child's brain isn't actually mature enough to 'get' some of these concepts yet? I've heard on these boards many times about homeschool moms who have had those 'aha' moments in math while teaching their own children (and thus are encouraged to teach the understanding to their own children)... but you had this aha moment as an adult when you have so much more maturity and growth in your brains.

 

Could it be true that just as some kids are slower for reading to 'click' that conceptual math skills will also be slower? Just because you don't teach it in the early years doesn't mean you can't teach it though the logic stage or older. I love learning the why of math now.. but I have the basic skills that allow me to hang that understanding somewhere in my brain.

 

Not trying to argue.. just wondering about child development.... and thinking about things like why we don't start logic until later etc...

This is indeed true of some children. They just are not ready yet.

 

Still- present the concepts, because that aha moment may come when they are working through the problems. IOW, some kids just need to work with the concept to get it. Others you may present the concept- you may even try beating them over the head with the concept- but they just are not yet developmentally ready to understand. Does this mean that you shouldn't let them do the problems? Well, that would be throwing out the baby with the bath water. Let them do the problems and (thanks to the one on one that homeschooling affords) periodically repeat some conceptual dialog.

 

HTH-

Mandy

[catholicmommy]

Does this mean that you shouldn't let them do the problems? Well, that would be throwing out the baby with the bath water. Let them do the problems and (thanks to the one on one that homeschooling affords) periodically repeat some conceptual dialog.

 

HTH-

Mandy

 

Thanks Mandy.. this does help. What of the parents who don't have the understanding themselves :-) ? I have had aha moments in many math concepts, now as an adult, but in some things I'm clueless. Maybe it's just the program (horizons) that i'm using (because it doesn't seem to spend a whole lot of time explaining concepts, and I find the TM confusing to use). Does this Lipping Ma book explain some of the whys? I'm fascinated by the spinoff discussion on they why of long division! I never knew division was just fast subtracting. Of course it should have occurred to me, since I knew that multiplication was fast adding :blush:.

 

I don't want to switch at this point to Singapore. We are in grade 5 and so close to being done the elementary math sequence and it hurts my brain to think of learning a new way of math. :001_huh: You people scare me with these asian math threads... I CAN'T get sucked in HAHAHAH.. I already got sucked into AAS from you crazy people.

[Mandy in TN]

I politely, but strongly, disagree with this statement. To state that the act of explaining the rationale behind a procedure can actually confuse a child more (perhaps, in the short term, that may be true) and thus, one should simply move along to the procedure because, after all, that's what matters, is a bit mind-boggling to me.

Yes, in fact some children are not ready to understand the concept behind what is being taught. Yes, indeed these children should be allowed to move on to actually doing the problems, because they may develop understanding during practice. OTOH- they may not understand the concept until much later. Either way, a child should be shown both- the concept and the procedure. I didn't mean to imply that the process was all that matters. That is why I said that there must be balance.

 

 

my daughter fell behind in math because of so much time spent trying to get her to UNDERSTAND what she was doing as opposed to just following the rules.

 

she got confused. i got confused. we both ended up lost & frustrated and hating math more than we did in the first place.

 

we've gone back to the rules.

 

different people, different things work. ;)

Thanks for the example. Sorry your child fell behind while beating yourselves with the concepts.

 

Mandy

Edited October 7, 2010 by Mandy in TN

[Violet Crown]

Ah, brings back memories of how I learned to divide.

 

Missed several days of school due to illness. Came back and was handed a sheet of division problems. Had no idea how I was supposed to do them, having missed the crucial lessons.

 

When I raised my hand for help, the teacher's aide came over, and when I said I couldn't do these problems, helpfully showed me how to type the problems into my calculator.

 

When I reached a problem for which the calculator gave me a decimal ending (there being a remainder), I asked the girl next to me what those numbers were; she said it was the remainder, and I dutifully wrote in the numbers at "R.__" on the page.

 

Then I got the page back the next day with most of the problems marked wrong, and a big fat "F." No help or comments from the teacher; and no apparent curiosity about why an A student got nearly every problem wrong. No idea on my part what I'd done wrong. I brought the page home in shame, and my engineer mom showed me the technique for long division.

 

And, pace our dear Bill and his dislike of public school horror stories, this was supposed to be a really good school district. I'm sure there was lots of good teaching, too.

[Mandy in TN]

Thanks Mandy.. this does help.

 

You're welcome.

 

What of the parents who don't have the understanding themselves :-) ? I have had aha moments in many math concepts, now as an adult, but in some things I'm clueless. Maybe it's just the program (horizons) that i'm using (because it doesn't seem to spend a whole lot of time explaining concepts, and I find the TM confusing to use). Does this Lipping Ma book explain some of the whys? I'm fascinated by the spinoff discussion on they why of long division! I never knew division was just fast subtracting. Of course it should have occurred to me, since I knew that multiplication was fast adding :blush:.

 

Her book is not a full instructional guide to all of elementary math, but a comparison of how a few key topics were taught by a few teachers in the US versus China. While I must admit that I was appalled by the American teachers interviewed in the book, I sincerely hope that it is not representative of our nation's elementary math teachers. (The public shool in Bill's area seems impressive. ;)) If you do not have a handle on the topics discussed in the book, you will when you finish reading it.

 

HTH-

Mandy

[Spy Car]

I am no expert in these issues and I haven't read 'the book', but I do have some questions about this... What if a child's brain isn't actually mature enough to 'get' some of these concepts yet?

 

The key is you teach them in ways at are appropriate to their intellectual development.

 

For example, when my son was playing with Cuisenaire Rods as an (early) 4 year old he "discovered" that a 3 Rod and a 2 rod was the same value as a 2 rod and a 3 rods. So we talked about that, and I told him what he had discovered was called the "Commutative Law." And we talked about that.

 

From then on, and to this day, when presented with back to back questions like 3+2 and 2+3, he will laugh and say: "That's the Commutative Law."

 

When we started with multiplication he immediately got that the Commutative Law work in this operation as well. 5-Threes is the same as 3-Fives. He could "prove it with rods. Not difficult. Not esoteric. In ways like these the mathematical axioms are ingrained in the education from the beginning in an age-appropriate and meaningful way.

 

We've done the same with the Distributive Law and the Associative Law. All learned using simple concrete means. And the understanding of these Laws is put into practice in problem solving. My son is 6.

 

I've heard on these boards many times about homeschool moms who have had those 'aha' moments in math while teaching their own children (and thus are encouraged to teach the understanding to their own children)... but you had this aha moment as an adult when you have so much more maturity and growth in your brains.

 

Better late than never, however not gaining these skills in childhood rather truncates a child's life opportunities.

 

Could it be true that just as some kids are slower for reading to 'click' that conceptual math skills will also be slower?

 

To some slight degree, but so what? One still teaches the slower child to read, no? There are the few (homeschooling) parents who, when faced with a child who is very slow picking up phonics ditch that method for memorizing sight words, but those are the exceptions not the rule.

 

The amount of time we spent going over introductory math could have been cut drastically if all I wanted was for my son to parrot back "math facts." It would have been too easy. But I know the difference when he can explain the mathematical reasoning of everything he is doing in clear terms, which he can.

 

Just because you don't teach it in the early years doesn't mean you can't teach it though the logic stage or older. I love learning the why of math now.. but I have the basic skills that allow me to hang that understanding somewhere in my brain.

 

But there are other things to learn later. And there is fundamental knowledge than builds upon the mastery of earlier prerequisite understandings. One may be able to "fake it" when given a formula and numbers to plug in, but that is not understanding.

 

It is better to build a foundation on rock than on sand (hoping you can shore up the building later).

 

Not trying to argue.. just wondering about child development.... and thinking about things like why we don't start logic until later etc...

 

Thinking about child development is a good idea. One needs to ask themselves how to teach children the things they will need to know using means that fit their intellectual development at the moment. But trust me, there are ways to begin teaching math a very early age that address a deep understanding of how our number system works, and how mathematical laws function in ways that make math fun and engaging.

 

Math is usually a painful subject when "you don't get it." But when the early math education is all about making sure the child does "get it" math is fun and meaningful.

 

Bill

Edited October 7, 2010 by Spy Car

[Daisy]

my daughter fell behind in math because of so much time spent trying to get her to UNDERSTAND what she was doing as opposed to just following the rules.

 

she got confused. i got confused. we both ended up lost & frustrated and hating math more than we did in the first place.

 

we've gone back to the rules.

 

different people, different things work. ;)

 

I totally agree. I wasted two years trying to use Singapore math. My kids could do the problems and then promptly forget how to do them because even though we had taught the concept they just didn't GET IT. (Yes, I used the HIG. Yes, I did everything the way it was written). I sometimes think math works better when you start with rote memorization and then explain the whys.

 

Though I personally loathe McDonalds :D, I have no problem with using memory devices to speed math along.

[Spy Car]

Others you may present the concept- you may even try beating them over the head with the concept- but they just are not yet developmentally ready to understand.

 

More likely the means of teaching the concept are developmentally inappropriate and the methods need to change to meet the needs of the student rather than waiting for the student to mature sufficiently to understand the (formerly) inappropriate means of teaching the concepts.

 

You meet the child where they are. It is not that difficult.

 

Bill

[Spy Car]

And, pace our dear Bill and his dislike of public school horror stories, this was supposed to be a really good school district. I'm sure there was lots of good teaching, too.

 

If I were under the illusion that the public school system was going to give my son the kind of math education I feel is sufficient I would not have spent the time and effort I have on that aspect of his education.

 

Still, I'm dismayed that many home educators who have the gift of being able to set their own standards and choose their own ways to teach would chose to replicate the worst methods of the public school systems and give their children a procedurally based math education with the idea they can figure out the "concepts" at some later date. I'm astounded by this attitude.

 

Bill

[Daisy]

More likely the means of teaching the concept are developmentally inappropriate and the methods need to change to meet the needs of the student rather than waiting for the student to mature sufficiently to understand the (formerly) inappropriate means of teaching the concepts.

 

You meet the child where they are. It is not that difficult.

 

Bill

 

Guess I'm too dumb to teach my kids the concepts the right way. Seriously. It wouldn't be the first time that was the case. I'm definitely better at doing math than I am at teaching it. But since the tutors weren't doing any better, we switched maths. Eventually, you run out of options. I need Bill to come teach my kids math. That would be awesome! :D

[Mandy in TN]

I need Bill to come teach my kids math. That would be awesome! :D

That's not a bad idea. I'm always open to new ways to present a concept.

Mandy

[Daisy]

That's not a bad idea. I'm always open to new ways to present a concept.

Mandy

 

He could do Youtube clips for all of us.

[Corraleno]

I find it really bizarre that math is the one subject where people think it's fine if students don't understand it. I never see anyone write that their child totally doesn't understand the "concepts" of history, so it's OK for them to just memorize a bunch of names and dates and forget about understanding the "why" of it. Or "My child doesn't understand biology at all, so he's just going to memorize some vocabulary and diagrams, that's all that really matters anyway." :confused:

 

I think the idea that young kids (or at least some kids) simply aren't capable of understanding the "why" of math does them a great disservice. If the teacher or parent hasn't explained the concepts in a way the child understands, it's blamed on the student, rather than being seen as a problem with the explanation. My son was doing remedial 3rd grade math in 4th grade PS, and had been convinced by the teacher that he was stupid because he didn't understand the way she explained things. In fact, she was further confusing him with her explanations, as a PP mention — not because he was incapable of understanding math concepts, but because she was incapable of explaining them in a way that he understood. (In fact, she was an art major and had a very poor understanding of math herself.)

 

Within a year (of homeschooling) he'd moved up 2 grade levels, using a strong conceptual math program, and I've never written off any math concept as just being "beyond him." For example, we spent several weeks on the concept of rounding, which for some reason was a big sticking point for him, and when I was finally able to explain it to him in a way he understood he said "Oh! Why didn't you explain it that way to begin with!" :lol:

 

I would really urge anyone who thinks that their child "just isn't the conceptual type" to read Liping Ma's book, and to keep trying to find the conceptual explanations that they can understand, instead of assuming that if they don't get the one explanation in the textbook, then they're just not capable of undertanding math concepts.

 

Jackie

[Guest Dulcimeramy]

He could do Youtube clips for all of us.

 

*Endorse*

 

And not just for five-year-olds, either. I would be very interested in math lessons from Bill for grades 8 and up.

[Spy Car]

Guess I'm too dumb to teach my kids the concepts the right way. Seriously. It wouldn't be the first time that was the case.

 

No, but you are not. Few of us (me included) were raised with a conceptual understanding of basic mathematics. We didn't learn it because the teachers didn't have such an understanding themselves (most still don't) and they (and the school textbooks) didn't/couldn't do much beyond teaching procedural math.

 

So many of us (even bright intelligent ones who like learning most other subjects) felt like "math dummies." Or if not "dummies" (because we could plug numbers into formulas well and get As) either found math boring or somewhere deep inside understood we really didn't get a bigger picture.

 

That is not your fault. That is the way math has been taught here.

 

The good news is there are other means. The bad news is that a parent/teacher has to break a little sweat re-educating themselves. I certainly did. The Liping Ma book that is often referee to on this forum I read when my son was in utero. It crystalized what I knew was wrong with my own math education, and I had a "Scarlett in Gone With the Wind moment." :tongue_smilie:

 

Home educators have an array of amazing options for teaching math to young children. It is a luxury of riches.

 

I'm definitely better at doing math than I am at teaching it. But since the tutors weren't doing any better, we switched maths. Eventually, you run out of options. I need Bill to come teach my kids math. That would be awesome! :D

 

If I can do it you can do it. You are a highly intelligent woman and all you have to decide is if you are willing to apply yourself to learning some of the things that can help make you a better math teacher. Thinking about what your child needs to know in order to understand what he or she is doing, and how you can make that comprehensible of a child of that age.

 

Bill

Edited October 7, 2010 by Spy Car

[Mandy in TN]

I find it really bizarre that math is the one subject where people think it's fine if students don't understand it. I never see anyone write that their child totally doesn't understand the "concepts" of history, so it's OK for them to just memorize a bunch of names and dates and forget about understanding the "why" of it. Or "My child doesn't understand biology at all, so he's just going to memorize some vocabulary and diagrams, that's all that really matters anyway." :confused:

 

I think the idea that young kids (or at least some kids) simply aren't capable of understanding the "why" of math does them a great disservice. If the teacher or parent hasn't explained the concepts in a way the child understands, it's blamed on the student, rather than being seen as a problem with the explanation. My son was doing remedial 3rd grade math in 4th grade PS, and had been convinced by the teacher that he was stupid because he didn't understand the way she explained things. In fact, she was further confusing him with her explanations, as a PP mention — not because he was incapable of understanding math concepts, but because she was incapable of explaining them in a way that he understood. (In fact, she was an art major and had a very poor understanding of math herself.)

 

Within a year (of homeschooling) he'd moved up 2 grade levels, using a strong conceptual math program, and I've never written off any math concept as just being "beyond him." For example, we spent several weeks on the concept of rounding, which for some reason was a big sticking point for him, and when I was finally able to explain it to him in a way he understood he said "Oh! Why didn't you explain it that way to begin with!" :lol:

 

I would really urge anyone who thinks that their child "just isn't the conceptual type" to read Liping Ma's book, and to keep trying to find the conceptual explanations that they can understand, instead of assuming that if they don't get the one explanation in the textbook, then they're just not capable of undertanding math concepts.

 

Jackie

I disagree.

 

"I never see anyone write that their child totally doesn't understand the "concepts" of history, so it's OK for them to just memorize a bunch of names and dates and forget about understanding the "why" of it."

 

This is exactly what we do with history. When they are young, we tell them history stories (SOTW) and memorize some info. We don't sit around and explain the indepth whys of history to young children.

 

With life science we expose young children to the various kingdoms, but we don't spend a lot of time explaining the processes of biology. For example, we may discuss reproduction, but we don't usually get into the details the first time around.

 

We may introduce grammar through memorization and a little diagraming or parsing, but we do it again year after year. We don't expect young children to understand it all at once and never need to practice with the material.

 

Much of what we do in the elementary grades is fire lighting and peg hanging.

Mandy

[Halcyon]

Ah, but Mandy, the difference is that a child rarely "revisits" addition in later years. It is assumed to be understood, and later mathematical material is built upon that foundation. With history, or science, children often _do_ revisit the very same material, adding new layers of complexity and understanding throughout the years. If an 8 yo child simply learns the procedure of multiplication, for example, it is unlikely in later grades that straightforward multiplication is revisited, and deeper understanding gained. That groundwork is already laid, presumably. That is why, as Bill stated, those foundational underpinnings, that core understanding, needs to be so strong.