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Any non-conceptual mathers out there?


toddandleah
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Guest Alte Veste Academy

I fear this might be like people admitting they favor whole language over phonics here at the WTM forums. :lol:

 

Funnily enough, I am working on conceptual math with Miquon and SM/MM but realizing more and more (much to my chagrin) that ds7 loves arithmetic tricks and doesn't really care if he understands, only that he is right in the end. Still, we plug away with concepts and I let DH teach him tricks in the off-hours. :D

 

Saxon maybe? I've heard it swings the other way.

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I fear this might be like people admitting they favor whole language over phonics here at the WTM forums. :lol:

 

 

 

:iagree::lol:

 

Non-conceptual math is quite like non-phonetic reading. The balance is likely different from family to family (and maybe even from child to child), but I would be surprised to find someone here who simply relied on rote memory at the exclusion of actually teaching the concepts behind the math.

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I fear this might be like people admitting they favor whole language over phonics here at the WTM forums. :lol:

 

 

 

I'm not so sure. I think the WTM encourages memorization, and the learning of facts during the grammar stage, so it depends on what age you are talking about. I don't think the phonics vs. whole language comparison works even though I've heard others bring that up before. I would compare learning the phonograms to learning the math facts and algorithms. Then, in the later years, when reading and math skills are strong, you read the classics and move onto higher, abstract math.

 

We use R&S Math which is a more traditional math program that moves along at developmentally appropriate pace. It is not a conceptual program. :001_smile:

 

Lisa

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But surely there's a range isn't there? Otherwise people wouldn't suggest supplementing with drill sheets to practice math facts.

We're working Math Mammoth right now, and I'm finding my son is having trouble seeing (after a slew of lessons on regrouping) that borrowing and carrying is just regrouping. if that makes sense. Arg! Anyway, I've got to decide on what we're going to do - he'll be starting 3rd grade in January, and there's no way he's ready for multiplication.

 

Help!

Leah

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I do both.

 

I love Saxon (I know many people hate it), and don't want to give it up because of some elements I really like. Saxon teaches a bit of the concept, but really hammers home the memorization.

 

I'm supplementing with Math Mammoth, which is conceptual/Asian style math. It is a cheap and easy addition to our hs curriculum.

 

Dd seems to like both approaches, so we're going with these two as long as it works for us.

 

(And I must confess, we're doing both in reading too. I'm hitting the phonics hard, but dd seems to learn best with whole language.)

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I don't think the phonics vs. whole language comparison works even though I've heard others bring that up before. I would compare learning the phonograms to learning the math facts and algorithms. Then, in the later years, when reading and math skills are strong, you read the classics and move onto higher, abstract math.

 

 

 

I had this question before. If we're supposed to be cutting with the grain- and kiddos are super-good at memorizing now and are more worried about the why's of things later, why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on? I've heard tons of folks say, Oh after we taught through RightStart or Singapore or whatever - I finally understood math. Yeah, but we're all older now, our brains have matured we should be able to understand more abstract concepts as 20, 30, 40 year olds. Am I missing something?

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We're working Math Mammoth right now, and I'm finding my son is having trouble seeing (after a slew of lessons on regrouping) that borrowing and carrying is just regrouping. if that makes sense.

 

Get yourself an AL Abacus and the Activities for the AL Abacus workbook. You don't need to invest in the full Right Start program but do take the time to learn how to use the abacus.

 

Also, I STRONGLY recommend reading Knowing and Teaching Elementary Mathematics by Dr. Liping Ma and paying special attention to chapter 1.

 

Will your child be okay if you choose a traditional approach to math rather than one based on the Asian approach? Probably. But to my mind it's like the formula vs. nursing choice- why settle for just okay when with a little bit of effort you can do what is optimal?

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If we're supposed to be cutting with the grain- and kiddos are super-good at memorizing now and are more worried about the why's of things later, why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on?... Am I missing something?

 

Yes. The conceptual math programs start with the very concrete and only move on to the conceptual once the child thoroughly understands it using the manipulatives. They also teach the traditional algorithms and include plenty of practice doing pencil & paper calculations.

 

It sounds to me like you're trying to move too quickly- sometimes you will need to "park" on a concept for a while. You may also need to try using several different manipulatives before the child "gets" it. Don't just use Base 10 blocks/cards- also try the AL Abacus, bundles of popsicle sticks, dimes and pennies, Digi-Blocks, etc.

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Guest Alte Veste Academy
I'm not so sure. I think the WTM encourages memorization, and the learning of facts during the grammar stage, so it depends on what age you are talking about. I don't think the phonics vs. whole language comparison works even though I've heard others bring that up before. I would compare learning the phonograms to learning the math facts and algorithms. Then, in the later years, when reading and math skills are strong, you read the classics and move onto higher, abstract math.

 

Well, that was kind of a joke, as indicated by the :lol:. The joke was more in reference to the admission rather than a comment on the efficacy of different methodologies.

 

I do think that kids are capable of understanding the concepts and of memorizing the facts. We do both. SM and MM both include drill and encourage having the facts down cold (SM HIGs and MM worksheets incorporate quite a bit of it).

 

I had this question before. If we're supposed to be cutting with the grain- and kiddos are super-good at memorizing now and are more worried about the why's of things later, why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on? I've heard tons of folks say, Oh after we taught through RightStart or Singapore or whatever - I finally understood math. Yeah, but we're all older now, our brains have matured we should be able to understand more abstract concepts as 20, 30, 40 year olds. Am I missing something?

 

Yes, reading Ma and going through these conceptual programs with my kids have given me many "aha" moments but that's because the instruction I received was poor, not because my brain couldn't have accommodated the information at a young age.

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Guest Alte Veste Academy
Yes. The conceptual math programs start with the very concrete and only move on to the conceptual once the child thoroughly understands it using the manipulatives. They also teach the traditional algorithms and include plenty of practice doing pencil & paper calculations.

 

This is an excellent point! Many people (myself included, unfortunately) refer to some of these programs as conceptual (synonymous with abstract) when, in fact, they begin with the very concrete, pictorial illustrations. There is nothing abstract about the way they begin. I think we wrongly say they're conceptual because they teach how numbers actually work rather than simply (but injuriously) expecting only memorization of how to do the math. Procedural and conceptual understanding need to go hand-in-hand. There is nothing developmentally inappropriate about that.

Edited by Alte Veste Academy
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I'm not so sure. I think the WTM encourages memorization, and the learning of facts during the grammar stage, so it depends on what age you are talking about. I don't think the phonics vs. whole language comparison works even though I've heard others bring that up before. I would compare learning the phonograms to learning the math facts and algorithms. Then, in the later years, when reading and math skills are strong, you read the classics and move onto higher, abstract math.

:iagree:

 

Also, I STRONGLY recommend reading Knowing and Teaching Elementary Mathematics by Dr. Liping Ma and paying special attention to chapter 1.

FWIW- I have read Teaching Elementary Math. I do not feel that there is anything in her book that would discourage me from teaching math facts. It is about balance. Sure, it is wonderful to present concepts, but most children need practice to achieve mastery.

 

You can discuss parallel parking. You can discover the hows and whys of parallel parking by playing with matchbox cars. At the end of the day you may totally understand the concept of parallel parking, but most people need to do it many. many times to achieve mastery.;)

 

I had this question before. If we're supposed to be cutting with the grain- and kiddos are super-good at memorizing now and are more worried about the why's of things later, why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on?

:iagree: to an extent. You should definitely present and explain the concept, but then follow up with practice. The child may not grasp the concept initially, but after practice. It will make sense. The while may be a while. If that is the case, simply present the concept again once the child is doing the problems well.

 

My youngest is using Saxon and Kumon.

 

HTH-

Mandy

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Yes. The conceptual math programs start with the very concrete and only move on to the conceptual once the child thoroughly understands it using the manipulatives. They also teach the traditional algorithms and include plenty of practice doing pencil & paper calculations.

 

It sounds to me like you're trying to move too quickly- sometimes you will need to "park" on a concept for a while. You may also need to try using several different manipulatives before the child "gets" it. Don't just use Base 10 blocks/cards- also try the AL Abacus, bundles of popsicle sticks, dimes and pennies, Digi-Blocks, etc.

:iagree:You posted while I was typing. Thanks for expanding.

Mandy

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I had this question before. If we're supposed to be cutting with the grain- and kiddos are super-good at memorizing now and are more worried about the why's of things later, why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on? I've heard tons of folks say, Oh after we taught through RightStart or Singapore or whatever - I finally understood math. Yeah, but we're all older now, our brains have matured we should be able to understand more abstract concepts as 20, 30, 40 year olds. Am I missing something?

 

I think it is a grammar-stage kid's "forte" to memorize. The content for memorization shouldn't be "because Mommy told you so" imHo.

 

I expect my dc to memorize the math facts. I expect them to understand the concepts of adding, subtracting, multiplying and dividing as the *foundation* for holding all of those facts in their brains.

 

All dc are different, but my ds7 canNOT simply attach info to thin air. He memorized his add/subt facts by going through several 1st grade currics that taught from different angles and at various levels of challenge. RS games helped too. Multiplication facts are going the same way at the present...actually working with the numbers makes them stick.

 

I don't think it's "Classical" to skip the understanding to merely memorize. I think the "grammar" of math *is* +-x/. Understanding them completely (being able to parrot back facts is not the same understanding) is the foundation of the logic stage and beyond.

Edited by 3blessingmom
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Guest Alte Veste Academy
Will your child be okay if you choose a traditional approach to math rather than one based on the Asian approach? Probably. But to my mind it's like the formula vs. nursing choice- why settle for just okay when with a little bit of effort you can do what is optimal?

 

FWIW- I have read Teaching Elementary Math. I do not feel that there is anything in her book that would discourage me from teaching math facts. It is about balance. Sure, it is wonderful to present concepts, but most children need practice to achieve mastery.

 

You can discuss parallel parking. You can discover the hows and whys of parallel parking by playing with matchbox cars. At the end of the day you may totally understand the concept of parallel parking, but most people need to do it many. many times to achieve mastery.;)

 

 

:iagree: to an extent. You should definitely present and explain the concept, but then follow up with practice. The child may not grasp the concept initially, but after practice. It will make sense. The while may be a while. If that is the case, simply present the concept again once the child is doing the problems well.

 

My youngest is using Saxon and Kumon.

 

HTH-

Mandy

 

Well, to follow up Crimson Wife's formula v. breastfeeding analogy... With either, you still burp the baby (aka drill the facts). :tongue_smilie:

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Dd10 was NOT ready until now for conceptual. Not for me not trying-we did Miquon, THREE levels of RS, etc. She HATED math and couldn't get the conceptual. We had all along been doing CLE (more non-conceptual) too, so we finally dropped everything and just used that. NOW that she is entering logic stage, she is more ready for the MM we have started. But just now and just barely.

 

Believe me, I tried to keep doing conceptual all along the way. I have read Ma's book, have many of the Singapore HIGs and read them for fun, etc. I did all I could to teach it to her. She was NOT ready. So maybe there is something to the progression of stages for some dc in some subjects?

 

Now, this same dc was reading at 3, writing three paragraph reports in K, with great spelling, etc. She is practically gifted (if not gifted) in everything else but math.

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If we're supposed to be cutting with the grain- and kiddos are super-good at memorizing now and are more worried about the why's of things later, why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on? I've heard tons of folks say, Oh after we taught through RightStart or Singapore or whatever - I finally understood math. Yeah, but we're all older now, our brains have matured we should be able to understand more abstract concepts as 20, 30, 40 year olds. Am I missing something?

 

I've had the same thoughts as you over the years. I'm not a math guru, so I always feel a little insecure about my choice of R&S for math, yet I loved how it taught the math facts, and how thorough it seems to be. There are explanations in it that have helped me to understand things *I* missed in school, but from what I read about conceptual programs here, I don't think R&S measures up on the conceptual side of things. Which makes me somewhat nervous. And yet, I go through spurts of checking math books out of the library, for math activities and games, and I always feel like, if we've done an activity or a series of activities, my kids "got" the concept. They don't want to be beaten over the head with the same concept in a million different ways. So, what someone else wrote above about getting the concept but then needing to practice it, makes sense to me. I'm sticking with R&S til the end (book 8), and then going with a high school sequence that seems to explain things to that more-mature-brained part of me, that my kids will probably start to enter into in high school? I hope. It's the 1960s Dolciani sequence that is talked about a lot on the high school board. I have student books of each course, and the explanations of things are very understandable to me - much better than whatever I had in high school. I might actually understand math after all this.

 

Dd10 was NOT ready until now for conceptual.

 

She was NOT ready. So maybe there is something to the progression of stages for some dc in some subjects?

 

Very interesting. I think my dd10 is the same way. My ds12 has always adored math concepts and ideas, but dd doesn't really care. I did various games and activities with her a year or two ago to help her understand borrowing and carrying, and I think she had fun, and she may have understood the concept at the time, but when it came time to do her math work, all she really wanted was for me to show her how to work the problem. Then I read about conceptual math for elementary students here, and I worry a bit. I was the same way in school - just show me how to work the problem and let me get my good grade on my homework. But I think that bombed out by high school, and if I'd had something like Dolciani for high school, I wouldn't have carried on with the "show me how to do the problem to get my good grade" mentality that eventually caused me to give up because I just couldn't understand the math (high school) anymore.

 

So, I'm thinking there is something to this theory that we should go with the stages - memorize in early grades, learn to work the problems while playing with the concepts periodically, and get more into the concepts starting in logic stage? At least, I hope this is how it will work for dd.

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Colleen-I could have written your post! That's how I learned math, and I was determined dd would learn conceptual. But she got very confused if I tried to explain the "why" behind things or show different solving strategies. It was tears every. single. day. during that time, just awful.

 

Over this spring and summer it was like something clicked, like she got her feet under her and now understands more when I explain strategies. I give the time of just using CLE the credit for letting her approach math her own way and gain the confidence she needed. I'm glad I backed off of forcing the conceptual on her and waited until she was ready. I think maybe some kids are just wired more readily to getting math concepts than others. I think they all can eventually get it, but maybe a different approach is needed with children like our dd's.

 

Toddandleah-I love CLE. In fact, I am using it with younger ds too, even though he is very mathy, just because I love the foundation it lays and the spiral review it gives. (I also use other more conceptual math with him because he "gets" it with no problem.)

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:

FWIW- I have read Teaching Elementary Math. I do not feel that there is anything in her book that would discourage me from teaching math facts. It is about balance. Sure, it is wonderful to present concepts, but most children need practice to achieve mastery.

 

You can discuss parallel parking. You can discover the hows and whys of parallel parking by playing with matchbox cars. At the end of the day you may totally understand the concept of parallel parking, but most people need to do it many. many times to achieve mastery.;)

 

 

:iagree: I purchased & read Ma's book. To be honest, I don't get the "it is going to change your life, you must read this book" sentiment.

 

I am doing some ACT math-prep work with an older student. She likes math, but she doesn't "get" math. She's working through Saxon Advanced Math and is very frustrated with the lack of explanation for the algebraic & geometric topics introduced. She pointed out that she wanted to know how sine/cosine/tangent worked, not just how to use the formula. I replied that Saxon is probably not a good program for learning the "why"s. Her mom just wants her to learn the material (quickly) without understanding. She replied that she will understand better if you explain why. (Ma's point being China's teachers understand the whys and therefore are better teachers for just this sort of thing, yes?)

 

I think it is important for teachers to understand the whys so they can better explain the how tos. I'm not sure the little kids need to understand the whys at every corner unless they aren't getting it, ask the question, or learn best that way.

 

Sorry for the hijack!

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?... why doesn't it make sense that we fill their heads with the "grammar" of math (facts and procedures) and explore the why's (concepts) later on?

 

The concepts are the "grammar." Math facts and procedural based math absent understanding the conceptual grammar of math is a very incomplete education. You will build a foundation on sand.

 

Bill

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Math facts and procedural based math absent understanding the conceptual grammar of math is a very incomplete education. You will build a foundation on sand.

 

Bill

 

Excellent way of putting it, Bill. If the child doesn't understand *why* the algorithm works, he/she is vulnerable to misremembering it and getting the problem wrong.

 

That's what happened to the American math teachers in Dr. Ma's sample when they were asked to solve a simple dividing by a fraction problem. More than half of them got the problem wrong because they couldn't remember how to do it. By contrast every single Chinese teacher got the problem correct because they actually understood the underlying concepts.

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Guest Alte Veste Academy
That's what happened to the American math teachers in Dr. Ma's sample when they were asked to solve a simple dividing by a fraction problem. More than half of them got the problem wrong because they couldn't remember how to do it. By contrast every single Chinese teacher got the problem correct because they actually understood the underlying concepts.

 

Right! Then, perhaps even more importantly, they used that understanding to discern where their students were having trouble so they could correct their thinking.

 

I loved when both sets of teachers were asked how they would deal with kids who had a problem with 3 digit multiplication. The American teachers gave their answers (don't remember those...probably wrong anyway :tongue_smilie:) and the Chinese teachers responded that their kids wouldn't have a problem with 3 digit multiplication because those problems would have been spotted and dealt with back when they were doing 2 digit multiplication. Priceless. :lol:

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