View Full Version : Teaching Long Division

sunshinet

12-17-2013, 08:47 AM

Do you teach the 'standard' or partial quotients algorithm for long division? Or something else?

I've demonstrated standard long division in the past and my ds8 looked at me like I was doing a magic trick. Divide, multiply, subtract, bring down, divide, multiply, one that he doesn't think he can learn. He is doing Beast Academy and just arrived at the Division chapter. It is a whole lot different that what my husband and I learned.. So I'm learning along. But then I started doubting..... Is partial quotients enough?

-T

CatInTheSun

12-17-2013, 11:55 AM

I think the key is to teach division thoroughly as an idea, a REAL concrete practical idea, before teaching an ALGORITHM or procedure. In that sense I never teach either "algorithm" and yet my 10yo knows both.

The standard method teaches a procedure for finding how many X are in Y. The partial quotients algorithm tries to replace this with just a different algorithm by having the kids guess that is smaller than the correct answer then use the standard procedure, then repeat the procedure and then finally add up all these partial answers, so X = x1+x2+.... In *principal* this is easier since they are building up their answer using easier math facts and their problem progressively gets easier. For me the problem is it is STILL an algorithm but there is no guidance for how to choose those pesky xi's. You can also spend a lot of time and do lots of little problems if you pick badly.

I still recall being taught the partial method in 3rd grade and I was a kid that HATED it. Because I was indecisive and I didn't know how to chose a GUESS. I always rather calculate than estimate as well! I would say estimation comes from experience, not guessing, too. I preferred to play with the standard method working backwards and forwards until I understood what was happening. Other kids will benefit from breaking a problem into parts.

My point is just use whatever works best, but the point is not to teach your child to calculate division, but to understand AND calculate. Understanding means they can walk away years and pick it up and still do it when needed.

atomicgirl

12-17-2013, 12:52 PM

I don't know the partial quotients method, but when my daughter learned long division the school used a unique method that had me doubting in the beginning. It's a method where the kids start by "building the problem" with blocks and then doing an operation on the blocks to solve the problem. Once they've mastered this very concrete and highly visual approach they move to the symbolic algorithm that we think of as long division (with some differences that I still don't quite get. My daughter still looks at me oddly when I do long division on the white board as a part of a solution. She gets the right answer by her method, so I don't ask about it anymore.). I had to go to a 2 hour long class on this approach just to help my kid with homework and I hated it at first. However, it worked. There was something about the process of transitioning from one method to the other that grounded the process and kept long division from seeming like a magical process for her. It answered the "whys" along the way.

Avalon

12-17-2013, 01:18 PM

We used base 10 blocks to demonstrate all the steps of the standard algorithm at the same time as showing it on paper. It took a long time, but my daughter did understand it. If we just did it on paper, she had no idea what we were doing, and it was too many steps to remember, so doing it simultaneously with the blocks worked very well for her.

dbmamaz

12-17-2013, 02:26 PM

First of all, I would totally trust Beast Academy. I would accept that there is value in learning what they are teaching.

Second of all, I would wait and see if BA (or whatever you use next) covers the standard algorithm - even if its next year - before you go off road and teach him something free-hand.

Now, to be honest, I did teach it 'off road' but only because we were not using a curriculum. And fwiw, teaching it was PAINFUL! My son catches on to most things quickly, but long division took weeks.

farrarwilliams

12-17-2013, 02:31 PM

I agree that the conceptual why over just the process of the algorithm is what you're aiming for. Partial quotients is sort of an algorithm, though unlike the standard algorithm, there are often multiple ways to solve the problem. I think it serves as an excellent introduction for most kids. I think it relies on experience and really seeing the number relationships.

Just as a note, I'm pretty sure BA does the standard algorithm in the fourth grade set. We really liked the method introduced in BA, but it's similar to how Miquon introduces it so it was actually mostly review for ds.

Solong

12-17-2013, 05:39 PM

We waldorfed it:

2162

It is the standard method, with storytelling. "Three knocks on the door of 54... how many threes fit on each floor... etc" . The stories just stick with my kid. She had the 'how' in five minutes and hasn't forgotten it yet.

Then we had to work on the 'why'. We use the soroban abacus in place of base 10. You can line the thing up right under a long division problem, and voila!

I can't believe how well waldorfing the soroban has worked out so far. Trippy Tiger Math.

sunshinet

12-18-2013, 10:34 AM

I'm pretty certain that he totally gets the concept of division. If I give a simple word problem that requires division he can do it. When he is doing the problems in the workbook he just looks at it and basically estimates the answer. "It's gonna be about 43.. no 44." He's usually close, in his head he divides fine, but he doesn't care about remainders. When I prompt him to work the long division on paper he just gets stuck in the middle, throwing out random numbers for the answer. We've hit a wall.

dbmamaz- BA has been fantastic for us ,, so I should probably just stick with it, yes.

atomicgirl- I'm trying to wrap my brain around building the problem... and do I need blocks or not? Can it be done on paper..

AnonyMs- He was in Montessori last year and they knock-knocked & jump-jumped for addition and subtraction, and it caused a lot of confusion

Yesterday was terrible,, if today is the same.. I think I'm giving it a rest until January.

farrarwilliams

12-18-2013, 12:03 PM

That Waldorf picture, while it might help kids remember the order of the steps in the algorithm, is one of the sorts of things that really concerns me about getting something conceptually because it doesn't support the concepts at all. It reminds me of in Knowing and Teaching Elementary Mathematics, the American teachers who put an apple or a little picture instead of a zero when multiplying larger numbers and told kids it was just "to hold the place" or "to help you remember to skip that space." But that's really misleading... there's a reason we put a zero there and if kids don't get it, then they're missing something about why they're doing what they're doing. It's sort of like being able to sound out the word versus having memorized the word to me.

SunshineT, you say he gets division, but part of getting it at this stage, is getting the why behind the algorithm as well. So whether you're using the standard algorithm or the partial quotients one, then he needs to get why he's doing it that way. So why do you break up the dividend and divide each part and then add the quotients? And, actually, when you do the standard algorithm, you are still breaking up the dividend, just in a more proscribed way.

I assume you're in 3C? I say get through the problems and then just hold on for 4B, which will be out in February anyway and which I'm like 99% sure will present the standard algorithm.

farrarwilliams

12-18-2013, 12:05 PM

And one more resource, if you have C-rods, Education Unboxed's long division videos are really good:

Education Unboxed - Multiplication and Division with Large Numbers - Math Videos (http://www.educationunboxed.com/multiplication_and_division_with_large_numbers.htm l)

CatInTheSun

12-18-2013, 12:54 PM

That Waldorf picture, while it might help kids remember the order of the steps in the algorithm, is one of the sorts of things that really concerns me about getting something conceptually because it doesn't support the concepts at all. It reminds me of in Knowing and Teaching Elementary Mathematics, the American teachers who put an apple or a little picture instead of a zero when multiplying larger numbers and told kids it was just "to hold the place" or "to help you remember to skip that space." But that's really misleading... there's a reason we put a zero there and if kids don't get it, then they're missing something about why they're doing what they're doing. It's sort of like being able to sound out the word versus having memorized the word to me.

Farrar, I understand your concern, but storytelling in Waldorf math isn't just nemonic devices slapped together or cutesy bits here and there, they are a pervasive "whole child" engagement philosophy.

Me, I'm math-y and would have found the stories distracting. My eldest, enjoys the tales but I had taught her from a math-foundations with "bunny math" as her own touchstone. My 8yo dd THRIVES on OMs version of Waldorf math. I've tried other math styles, from MM, SO, BA, PIM -- but this kid lives and breathes stories and imagination. Every. single. math problem has to be a story problem! Twelve elves invited fourteen frogs to tea and they each wanted three cookies, how many do they need? She's happy as a lark! She can DO it without, but she starts shutting down. When I explain carrying straight or with groups of blocks...she tunes out. Use the Waldorf gnomes and houses can only be so big and blah-blah -- she's got it!

Originally I thought all the gnomes/fairies/etc was a big distraction and BS, but now I see that at least for SOME kids it just engages them on all cylinders and they see the math vividly, and yes, they do understand it conceptually through the story. Power of myth? For others, it is just a cute story they remember, maybe a bit of a nemonic. For others I am sure it is irritating as all get out. haha I'm sure as a kid I would have been wondering what the heck my teacher was talking about and whether she had been sniffing the glue.

Different kids, different approaches, but always good to remember to think about what we are teaching, how and WHY. :D

FWIW, I ALWAYS come back and revisit "basic" math skills from different perspectives after my kids have well mastered them. For example, my 10yo mastered long division 4 years ago, but I just showed her Kahn academy's video on the partial method and we discussed what they were doing, pros and cons. Compared it to different ways one could do long division (make a table on the side, guess and test, etc). I think that sort of layering helps kids make deeper connections and make the skills their own rather than just "the algorithm they learned".

farrarwilliams

12-18-2013, 01:21 PM

When I've seen Waldorf story problems I get that. And the idea that some kids do better with everything if there's a story makes sense - story problems, stories to help remember. Though I admit it's not my style, I think I get it. But in this particular case, what does the chimney and the house have to do with the reason that you follow the steps of the algorithm? If this is the main thrust of the teaching, then it feels like kids will be missing something. But, of course, if there's more and this is just to help remember... I dunno... I'm still cautious about that sort of thing because I think the best way to remember is to bring the why together with the steps, but not all kids do well that way. I do think it's optimal to teach kids why you do something first (this, I think, is the reason for using partial quotients before the standard algorithm) and then learn the steps, but some kids do better by doing and then seeing the reasoning. Okay, now I'm just meandering, but basically I don't get this particular thing at all.

sunshinet

12-18-2013, 02:31 PM

Farrar, yes, we are on 3C. Today went better, we reread part of the chapter and he did one practice page. Anon- We will definitely step back move at a slower pace. To be honest, I'm not really sure how to assess if he is getting the why.

So why do you break up the dividend and divide each part and then add the quotients?

I'm pretty sure he's going to say because I / the book told him to! But I'm going to ask him tomorrow and let you know his reply.

CatInTheSun

12-18-2013, 05:22 PM

Farrar, I think a lot of the storytelling caters to kids who think more visually or concretely and aren't as comfortable with the symbolic structures and space. It also is a whole lot less SCARY to talk about elves and walking down steps and putting remainders in chimneys than to stare down a symbolic long division problem that has been stripped of any physical relevance to the world.

Maybe a part of it is that it provides a scaffolding that makes math more like a warm, comfy blanket rather than an imposing trudge through abstract contrived computations?

One could also argue that given that studies have shown that one of the greatest failings of math education in the US is that we teach only to the analytic brain and not the creative side, which is what they blame the passive hate-of-math developing by 3rd grade and above....could it possibly be that by engaging creativity, even in an only vaguely associated way whether it just keeps the kid happy (my 8yo dd now proclaims she LOVES math when I do it this way) or because it is activating both parts of the brain and encouraging them to internalize math as both an analytic and creative pursuit?

farrarwilliams

12-18-2013, 06:07 PM

But do we teach only to the analytic side? The studies I've seen blame poor explanations and overly spiral programs more than any other factors. I appreciate that using storytelling as a mnemonic device is useful for some kids, but the mnemonic isn't connected to the meaning, so it's just a parlor trick - it's not math any more than "My Very Eager Mother Just Served Us Noodles" is astronomy, as useful a trick as it is. As such, it can't be the central part of the teaching if you're really aiming for understanding.

And to me, things like that or the chimney and house thing are markedly different from something like dividing up decorations for cookies or pencils for kids in a classroom or whatever. Dividing actual things is just connecting the math to concrete things. Or having a story about a character who has to divide a lot of stuff up, that's actual math, that's not adding an extra layer about apples instead of zeros or a house instead of knowing how you're breaking up the dividend.

If you're going to do something creative, optimally, shouldn't it reflect the math, not a tacked on story? Shouldn't it be like finding number patterns yourself or looking for creative connections a la Vi Hart or something more on those lines? Or having complex problems to solve? Or using manipulatives more? Or doing math labs or playing more math games? Or reading more living math books where you see how math is used to solve problems like in the animal babies math books. I don't think math should be flat and dull, but I feel like an approach where everything in concrete, or where manipulatives are used more, or where there's a discovery based approach, or where art and music are tied in more are going to be more successful because they don't require the addition of a story that is unrelated to math. Math is really creative in and of itself - it shouldn't need to become something it isn't.

I actually think Beast Academy is brilliant at presenting fun, creative puzzles for kids that require real math and reflect that math. Of course, BA's style of creativity isn't going to be the right one for every kid.

But I do agree that you have to do what works for you kid... And the why can come after if it must, though it shouldn't be just an afterthought...

farrarwilliams

12-18-2013, 06:09 PM

And I'm appreciating this discussion, by the way. Feel free to keep disagreeing with me. :)

dbmamaz

12-18-2013, 06:18 PM

From the perspective of someone who has always had an intuitive grasp of math, and whose kids have as well, it occurs to me that if it makes her enjoy math, it probably increases the chance that, in middle school, she will develop a deeper understanding for math than she would if she hated it. I think for people who are not logical thinkers, any approach that pulls them in is a good one. And just as Raven is able to process language more and more appropriately as he matures, hopefully these kids will be able to make more and more sense of logical math as they mature.

Solong

12-18-2013, 06:49 PM

Yep, Cara. That's me too. I hated math until I needed it, and then I loved what it could do for me.

For my dd it is also an issue of anxiety. She hates to get things 'wrong', do things 'wrong'. Discussing concepts of math were anxiety-producing, because she knew that the problems were coming up. She couldn't pay attention to what I was saying. Using a waldorfy-soroban-manipulative-project-fibonacci approach (we've tried it all) to get her moving through the methods successfully first just worked. Once she is confident in a skill, I can say "Look what you are doing! Why does that work? How can we apply it to this situation?"

The waldorf approach is in no way detrimental that I can see. It can be confusing or irritating, in which case I'd skip it too. Dd's made many, many connections between waldorf and soroban or waldorf and fibonacci. Connections I frankly didn't see on my own. When doing the waldorf count-by stars last year, she pointed out that the stars which are "big friends" (bridging #s) in soroban are also the same shape, ie they share a pattern of progession in the ones place value. Uh, I can assure you that I did not do that on purpose. Not in the lesson plan.

Creating the story is just an introduction to the method, not the full shebang. LOF is another example of a program that people either love or hate. I chuckled. Dd rolled her eyes and asked to just skip ahead to the point. We're sticking with what works. I can't fight her over math for the next eight years. I'd rather fight to find quirky approaches that fit my kid's quirks.

CatInTheSun

12-19-2013, 01:07 AM

But do we teach only to the analytic side? The studies I've seen blame poor explanations and overly spiral programs more than any other factors. I appreciate that using storytelling as a mnemonic device is useful for some kids, but the mnemonic isn't connected to the meaning, so it's just a parlor trick - it's not math any more than "My Very Eager Mother Just Served Us Noodles" is astronomy, as useful a trick as it is. As such, it can't be the central part of the teaching if you're really aiming for understanding.

And to me, things like that or the chimney and house thing are markedly different from something like dividing up decorations for cookies or pencils for kids in a classroom or whatever. Dividing actual things is just connecting the math to concrete things. Or having a story about a character who has to divide a lot of stuff up, that's actual math, that's not adding an extra layer about apples instead of zeros or a house instead of knowing how you're breaking up the dividend.

I think the most chilling indictment of math education as NOT teaching the whole brain came from a NOVA special I saw some years ago as they showed how preK kids spent 80-90% of their time doing "math" (sorting, comparing, counting, etc) as PLAY and fun yet by a couple years of form education the majority disliked math. PET scans showed nearly no activation of the creative side of the brain during math assignments or lessons. My personal theory is that we all have our own internal way of thinking math. To effectively teach math you need to teach someone how to convert it into their own internal native brain language. Instead math is taught in a top-down "THINK THE WAY I TELL YOU" manner that shuts down the brain. I am a intuitive learner who always excelled at math -- mainly because I learned how to tun out my instructors as soon as I got the jist of the content. Then I just wanted them to shut up so I could go play in the new sand box and learn. As early as 3rd grade I would literally turn in my desk or plug my ears to block them out. Out of frustration I once told a teacher who was scolding me, "Could you please just be quiet; I'm trying to learn!" And yes, I got in a lot of trouble for it. By middle school I learned to tune out more subtly.

Waldorf math stories ALWAYS have their reasons. From the beginning they introduce the four processes (operations) and teach place value with ideas like houses. As in some houses can only have people come and go 10 at a time, 10x10 at a time, etc. Each floor of the long division house represents a different place value, each step down towards the basement is a decrease of a factor of 10x. The remainder is the bits so small you can't make a whole number, so perhaps that is why you burn them and send them up the chimney? I don't know all the details of that tale, but I'm sure there is reason (and math) behind all of the symbolism.

As AnonyMs said, all these different styles often illuminate each other or hitch together in unexpected ways.

Ultimately, for dd8, MEP or MM or other things would be a drudge I can MAKE her do, but she drags her heels and lagged. When I use Waldorf stories and methods, she LOVES math, excels at her work, and is quickly working at a high level of math understanding. If it gets her through the next few years without hating math that in itself would be worth it.

Beyond that, I think it can be, for kids like her, just good solid math. Not saying it's the best math for everybody. ;) I guess I was surprised myself since I originally felt I was making a concession switching to it since dd8 is actually quite gifted in math, but that's when I started seeing that ability plus a great program isn't enough if it isn't nurturing the right parts of the kid. Some kids will self-nurture enough or tough it out through any gaps, but others will shut down, get intimidated, or just opt to fail. Finding the right match matters.

I'm not a touchy-feely type, and I'm eclectic, not a Waldorf-phile, BUT I do have to say some of the "whole child" principles have grown on me (though not lots of the other Waldorf principles).

You make good points about the many other ways of bringing math to life -- I just think that it should be the bulk rather than the supplement until a child is comfortable. Some programs do this, and it is easier to manage in an hs environ. [ETA: I also tried many of these with dd8 -- she loved the supplements, for a while, but still hated the main work; her affection for Waldorf math stories has been enduring since the first! I can't tell you why beyond that they are intrinsic.]

In ps it is very difficult and rarely done since it is much easier to jump to symbolic math which can be assigned and graded. The fact that so many kids have difficulty with word problems is a sign to me that we have weaned them from "real" problems to abstract/symbolic math (usually for the purpose of teaching math facts) too soon. Kids should never lose the connection!

Farrar, I appreciate the discussion as well. I will continue to seek points of contention. haha Though honestly I think we mainly agree, but just are knocking around the details. Personally, that's the kind of "disagreements" that I tend to learn the most from!

farrarwilliams

12-19-2013, 10:58 AM

Cat, thank you for the explanation of the house. If it's built up over time as a structure for place value, that makes so much more sense than just as a mnemonic type story for remembering the steps of the standard algorithm for long division. By itself, I was like, this is just a random, disconnected story.

The brain thing is interesting. I guess I have the idea from seeing ps math programs that a lot of them have this false creativity to them - and that was/is my fear about the Waldorf stuff. It's tacked on creativity that isn't really about math. So then when you go to do the math, of course you're not really creatively engaged, because it was just that the math book had pretty pictures or that it told you little stories and then when you go to do the math, you're still just analytically following the steps. I'd be very curious to see, for example, kids doing math with problems like SM's CWP or BA's wacky puzzles or the Waldorf story problems to see if they were creatively engaged while doing math. Do adult mathematicians show that they're using their creative brains when they do math?

I think the best math programs - like MEP and Singapore and Math Mammoth and Beast Academy - all push kids to do a lot of story problems. Singapore's began to grate on me and we dropped them, but I see what you're saying about symbolic versus "real" problems. Both my kids struggled with MEP's purposeful unevenness in the problems, but that also intrigues me, how MEP throws in unsolvable problems because that always seems like it should engage creative thinking. The symbolic should always be grounded in a real concept otherwise it's useless. One of my go to strategies as a kid (and, um, still occasionally) if I forgot the algorithm for something was always to picture a real situation for the math, sometimes with simpler numbers for clarity (Ed Zaccaro talks about the simpler numbers thing - the "2 and 10" method is what he calls it). This is part of why I have trouble getting at it from the other side - teaching the algorithm first and then the reasoning. Because if you forget the algorithm, then you never had to derive it or learn it from scratch, how will you remember it? Though, again, I get that some kids need to practice the skill first, before they learn it.

But that makes me think of art. Usually when we do art programs at the museums, the order is that the kids visit the museum art and discuss it then make their own art with some project. However, we once went to an art day at the Corcoran where the doing part ended up coming first. The exhibit was about the Washington Color School so we went through and did all these art projects like dying strips of color and icing cookies with colors and making collages with colors. And then, after that, we saw the real Color School art. And it was a totally different experience. Anyway, there's no right way, right? The concepts first or the algorithms first, as long as they come together for the kid in the end.

crunchynerd

12-20-2013, 12:34 AM

Whatever works, though I agree with those who feel the gnomes and fairies bit does not help anyone learn math except as some elaborate non-math-based emotional/verbal rote soliloquy that may happen to arrive at correct answers without a clue as to the how and why.

MY mother fell prey to that in public school in the early 1950's. She couldn't make heads or tails of the way elementary arithmetic was taught, so she made up little stories in her head about the numbers beingcharacters, and having personalities, and interacting. It did not help her. She remained weak on logic, numeracy, basically anything not verbal. I see the gnomes-and-fairies stuff as something similar, where in place of real conceptualization, you put elaborate stories to make the disconnected facts stick, but never develop the thinking skills necessary to go on to deep understanding.

I went with research, plus my own intuition and memories of what did not work well for me in school, and a determination not to visit that on my kids, and started them with Nurture Minds soroban abacus curriculum. Recently, I discovered "Speed Mathematics Simplified" by Edward Stoddard (Dover Books) which takes the soroban logic of complementary numbers, and applies it to left-to-right calculations common in Russia at the time and certain parts of Europe, and the result is, an intuitive habit of left-to-right mental arithmetic that is fast and accurate, that does NOT require years of grueling soroban training to develop "Flash Anzan" or "mental soroban" ability (wherein the brain actually builds a virtual soroban and the person accesses their spatial centers directly to calculate at dazzling speed).

There are soroban schools sprouting up in progressive cities across the US, and none within driving distance of me, and I am not prepared to become a one-woman flash anzan school. Awesome as that ability is, hours a day on just that one skill, isn't for us.

But in a few weeks of intermittently reading and applying that Stoddard book, along with having already become aware of complementary numbers on the soroban from helping my kids, I went on Khan Academy and found I could do mental arithmetic that once froze my brain over even attempting it. Now I am able to teach that to my kids. I only wish I had been taught that way in school because it totally supports intuitive numeracy, whereas I agree with Stoddard, that turning a number like 4,535 into 5,3,5,4 in your head so as to calculate right-to-left as we were all taught in school, works against intuitive numeracy and slows mental math down to a crawl. In fact, mental math never reverses things like that, and yes, even long multiplication and division can be done mentally, using the methods taught in that book.

So I'm so glad I discovered it in conjuction with learning a bit about adding with complements of 10 instead of calculating or attempting to memorize beyond 10. At 40, it has revolutionized my relationship with arithmetic, which had been so bad all my life growing up, that it seriously hobbled my intuitive math abilities. At least my kids don't have to start out fettered!

Anyway, that's my 2 cents' worth on what really helped us, and is making my daughter able to apply mathematical reasoning fearlessly, without getting "deer in headlights" over arithmetic calculations or mental math.

dbmamaz

12-20-2013, 11:05 AM

Crunchy, while I am glad you've found a method that works well for you and yours, I find your dismissal of Waldorf math as useless stories similar to ones your mother made up for herself as a child - uh, i find that offensive and I dont even like waldorf. Its a math program developed by adults who cared about educating children. You are assuming that something you know nothing about is hogwash. I mean, she said that they teach powers of 10 by saying you can only fit 10 people in the house - this is not random stories, it is giving meaning to the logic of math.

RachelC

12-20-2013, 11:28 AM

I admit I am not familiar with Waldorf, but from what was written here, I agree with Farrar and Crunchy's sentiments. It reminds me a bit of how Math-U-See teaches place value: there's a neighborhood, and the houses can only fit so many people, etc. What house can only fit ten people? Why not twelve people? I find it silly and somewhat misleading, and extra work to memorize (like Math-U-See's obsession with memorizing the colors of the different bars. Why? Five is not always purple, or whatever).

These sorts of devices may help some children in the very early stages of math, because it draws them in. They seem to learn the math by default, as they are actually focusing on the story and extras. But how long can that work? As the math gets more advanced, the stories and devices would have to get more convoluted and complicated.

I have seen this plenty firsthand with reading. Lots of stories and songs (not that I am against these things, but it really depends on how they are used and WHAT they are teaching) to help kids remember letter sounds, blends, etc. Trying to remember which character and color and story goes with which letter- it takes so much memory, and the point, the actual letter sound, gets lost. But the kid is having fun and not objecting to learning, so those involved feel it's working.

ikslo

12-20-2013, 01:31 PM

How long does it work? Until it doesn't,

I got the feeling what they were trying to say is it builds a shaky foundation making it harder to switch to something that does work later on. Kind of like teaching a med student to put a tourniquet on someone's severed arm to stop the bleeding. A temporary fix that works, but doesn't really solve the long-term problem.

RachelC

12-20-2013, 02:04 PM

Kind of a thin line between expressing skepticism and critiquing, though.

I was not trying to bash Waldorf. I just enjoy discussing and speculating about different methods. I am sorry if it felt like at attack on your choices.

CatInTheSun

12-20-2013, 05:27 PM

Whatever works, though I agree with those who feel the gnomes and fairies bit does not help anyone learn math except as some elaborate non-math-based emotional/verbal rote soliloquy that may happen to arrive at correct answers without a clue as to the how and why.

Crunchy, I'm not sure why what you have against word problems or stories that relate base-10, etc. That isn't the same as hobbled together stories by the math illiterate to get by (your mom) or tacked on to existing curricula (ps) or sugar to make bad tasting medicine go down. Up until the last couple centuries math was written out in paragraphs, not equations. Einstein developed his theories in stories, then developed the equations to back it up. The stories were math, too.

As to some of the concerns about "when it stops working" by some.. I assure you Waldorf and such programs doing get to calculus with, "and then the fairies wanted to integrate the pixies over the domain of 2*pi...." Waldorf starts by teaching to the "heart" and transitions to the "head" gently, so as topics get more abstract the stories aren't as necessary because the kids don't need it. It is no different that learning to count with your fingers, then moving on when it is no longer convenient, or using blocks or other manipulatives (which Waldorf also does) and then no longer using because you are too fast without them.

10s blocks just provide a physical representation of our 10-base system. A story of houses or floors that can only hold 10s and 10s of 10s of elves does the same. So Waldorf has kids draw pictures of the houses. So what?

With my eldest, before I'd even heard of Waldorf, I used stuffed animals and we did math with lego "carrots" she divided. Was that somehow less "real math" than if I had made her just work symbolic problems with official math rods? She's 10yo in her second year of algebra -- have I somehow scarred her for life by giving her a weak foundation of bunny math?? :rolleyes:

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