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Æthelthryth the Texan

Can someone please explain whole to part, parts to whole learning

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Can someone please explain whole to part vs parts to whole learning in context as far as typical homeschooling subjects, hopefully with curriculum examples? And why it really matter or what the differences mean? I am struggling to wrap my head around this one after hearing a discussion on it that was unfortunately not well articulated. I get it as far as learning to read- that sight word/whole language reading instruction is the whole to (maybe) part, where as phonics would be parts to whole. But other than reading, I'm not really understanding how it translates as far as other subjects. 

I vaguely remember something on it possibly from one of Cynthia Tobias's books years ago, but I no longer have those books so I'm unable to look it up- assuming I'm even correct that it was her and Google did not illuminate matters at all, LOL. 

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I think if it must clearly I terms of Latin. I think GSWL is parts to whole because it demonstrates individually each conjugation of a verb, summarizes them into a table and then shows how that can be applied to each verb. Similarly, it teaches you the standard noun parts (nom. similar, gen. singular) and the gender, even right you don't use some of that until later. Minimus, on the other hand, dios you right into an immersive text and is much less explicit at pointing out the patterns in verbs and nouns.

Similarly in writing, WWS breaks out steps for all the assignments, even the independent assignments, and has demonstrated examples for each step. Some other programs I've looked at are new vague, discussing a paper or essay or argument approach and then the assignment us to wrote a similar paper on a topic of your choosing.

My bias is that any vagueness gives me hives. I need it all spelled out for me. People who can just "do" these things or apply inferences more broadly amaze me.

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Maybe the problem is that you're trying to buy into a debunked theory? Most "learning styles" mess has been debunked and not stood up to scrutiny. You even have what Kbutton charmingly calls "toilet bowl" learners, people who swirl around and swirl around, going whole to parts to whole again.

I think the more interesting question is whether the dc *can* make the inferences and *can* pull it together into a whole when given the parts or whether he's the type to *miss* the forest for the trees. To me you're just responding to what it takes to help the dc see the patterns, see the bigger picture, make the inferences. And I think that has to do with brain structure (theories on gestalt learning, etc.) more than personality or mysterious learning styles.

If your kid gets the parts and can't see the whole, then you'll need to teach him the whole/big picture more explicitly. If he sees the big picture easily and revels in learning more parts, you'll feed him more parts. And if your kid has another way of framing the world than what the curriculum says (like maybe relating everything in life to planes), then you're going to frame everything in terms of the structure they can understand.

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11 minutes ago, PeterPan said:

Maybe the problem is that you're trying to buy into a debunked theory? Most "learning styles" mess has been debunked and not stood up to scrutiny. You even have what Kbutton charmingly calls "toilet bowl" learners, people who swirl around and swirl around, going whole to parts to whole again.

I think the more interesting question is whether the dc *can* make the inferences and *can* pull it together into a whole when given the parts or whether he's the type to *miss* the forest for the trees. To me you're just responding to what it takes to help the dc see the patterns, see the bigger picture, make the inferences. And I think that has to do with brain structure (theories on gestalt learning, etc.) more than personality or mysterious learning styles.

If your kid gets the parts and can't see the whole, then you'll need to teach him the whole/big picture more explicitly. If he sees the big picture easily and revels in learning more parts, you'll feed him more parts. And if your kid has another way of framing the world than what the curriculum says (like maybe relating everything in life to planes), then you're going to frame everything in terms of the structure they can understand.

Okay, that makes sense. 

What spawned this is I bought ds7 Saxon math recently which dropped some jaws when talking about what we were using curriculum wise with some other homeschoolers. An acquaintance said something to the effect of,  "well that's a parts to whole program which is a really bad fit for your son imo since he's so STEM oriented."  Apparently I missed the memo there......and I'll just shut up or Ill get snarky over math snobbery. 

FTR, I don't really care what she thinks about what fits my ds- I'm the one teaching him, and the one who has shelled out a zillion dollars for math for this kid to find a fit,  and it's not like I just fell off the turnip truck yesterday as far as homeschooling......but anyway, it did make me go :huh: as far as figuring out how the heck you'd have whole to parts math for elementary anyway. Then my brain spun to other things like history etc. trying to figure out exactly what the heck she was talking about, although I do get what SusanC said about Latin. That part makes sense. 

I really like the toilet bowl analogy. That cracked me up. 

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12 minutes ago, Æthelthryth the Texan said:

"well that's a parts to whole program which is a really bad fit for your son imo since he's so STEM oriented."

Yeah, sometimes not responding to such brilliance is the only path. I mean that's just dumb. It's incremental, hello. Normal, developmentally typical children learn parts to whole and all lessons in mastery-based curricula are still structured parts to whole. They'll include a brief overview, but then they teach the parts and build them into a whole. Now a discovery-based method could be whole to parts, sure. But incremental instruction is a totally different issue.

14 minutes ago, Æthelthryth the Texan said:

I'll just shut up or Ill get snarky over math snobbery. 

Yeah, you'll find engineers who learned just fine with Saxon, Teaching Textbooks, MUS, and all sorts of things people say aren't good enough. I personally find that the difference is the dc and the dc's ability to apply simple things to more complex, novel situations. If the dc has that ability, they're going to succeed with almost any curriculum. If the dc is struggling, putting him in a curriculum that is too hard doesn't help. 

16 minutes ago, Æthelthryth the Texan said:

I'm the one teaching him, and the one who has shelled out a zillion dollars for math for this kid to find a fit,

Absolutely!!! Math is the hardest to get the right fit for. It sounds like you've made a ton of effort and have reasons for why you're doing what you're doing.

17 minutes ago, Æthelthryth the Texan said:

I really like the toilet bowl analogy. That cracked me up. 

Good, I didn't want to bowl you away, hahaha. 

A dc can have issues with generalization, like being able to use the skill in the next setting, not only in the particular workbook particular, particular types of problems. A dc can have trouble with the language of math or with applying computation to word problems and knowing when to use what. But you know I think most people on this board are highly cognizant of that and bringing in resources if they think it's an issue for their dc. We can also check it by doing standardized testing, in which case you just shut them up by saying his scores are great. 

Sometimes what we think of as pulling things into a whole, seeing how the parts fit, etc. gets hit in our reading or writing curriculum. Remember, it's also reading comprehension. And when we work on narration and later on outlining, we're doing the same thing, making sure they see how the parts fit together into a whole or how the whole is built from a flow of parts. But it's not necessarily *taught* in the academic content area but might be taught over in your reading or writing curriculum. Then you verify they think that way by having them outline, learn to take notes on the subject area, etc.

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Well, to defend the other mom, she probably used the wrong terminology but was trying to convey something valid. Saxon is both incremental and spiral. It breaks concepts down into tiny parts and introduces them veslowly. For kids who grasp concepts quickly, its approach can be akin to torture. 🤣 Saxon would make my kids want to poke their eyes out. 😉 That isn't a dig at Saxon's outcomes; it is an emphasis at just how poor of a fit it would be for my kids.

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3 minutes ago, 8FillTheHeart said:

Well, to defend the other mom, she probably used the wrong terminology but was trying to convey something valid. Saxon is both incremental and spiral. It breaks concepts down into tiny parts and introduces them veslowly. For kids who grasp concepts quickly, its approach can be akin to torture. 🤣 Saxon would make my kids want to poke their eyes out. 😉 That isn't a dig at Saxon's outcomes; it is an emphasis at just how poor of a fit it would be for my kids.

I had used it before with dd16 when we first came home and it did make her cry- but for different reasons that being too slow. It went completely off my radar after that, so believe me, this is not what I saw myself getting. But,  I am surprisingly a fan (so far and it's early)  and it's working as far as getting it done and not being a burden on either of us. So I am taking it. 

I went through the entire Saxon 3 text before committing and it seems to be a good fit for him at this point. I'm not married to anything curriculum wise with this kid- but I had to find something that I could open, do, and move on and not piece everything together daily, worrying we were missing something. I want to enjoy dd's senior year. 😀 I sort of feel like she's gotten the shaft the last 18-24 months since the dynamic duo started "real" school as far as my time investment. And wonder of wonders, after pouring through, or even trying, every elementary math program in my path, we found this so I'm going to ride this wave until it crashes, LOL. 

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I actually think Saxon might be a good fit for my granddaughter. My ds, her dad, detested Saxon when we briefly tried it, so it will be a tough sell. The goal should be learning. If that is happening in a good way......success. 

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6 minutes ago, Æthelthryth the Texan said:

we found this so I'm going to ride this wave until it crashes, LOL. 

Yup, it's not like you can't tell when your kid is bored stiff. I've known some very intelligent people who used/like Saxon. Even saying STEM=smart=hate Saxon isn't reasonable. 

Besides, you could just as easily bring in something that totally rocks his math world in other ways. It's not like using something LIMITS you to using ONLY that, mercy.

I taught my dd with RightStart and then BJU (after some forays into other things), so I had a certain amount of snob cred. So when ds came along, I decided to teach him with the Saxon K5, just to be able to say I did, haha. It was fun, adorable, and those early years written by Nancy Larson (yes??) are WAY more interesting than the later stuff. At least that was my take. I think the Saxon 3 is still Nancy Larson. I don't see the issue. 

You gotta flush people who give you a hard time. They aren't worth it. It's none of their business.

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2 minutes ago, 8FillTheHeart said:

I actually think Saxon might be a good fit for my granddaughter.

How old is she? The K5 is ADORABLE. We had so much fun lining up teddy bears and putting them on the bus...

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2 minutes ago, PeterPan said:

Yup, it's not like you can't tell when your kid is bored stiff. I've known some very intelligent people who used/like Saxon. Even saying STEM=smart=hate Saxon isn't reasonable. 

Besides, you could just as easily bring in something that totally rocks his math world in other ways. It's not like using something LIMITS you to using ONLY that, mercy.

I taught my dd with RightStart and then BJU (after some forays into other things), so I had a certain amount of snob cred. So when ds came along, I decided to teach him with the Saxon K5, just to be able to say I did, haha. It was fun, adorable, and those early years written by Nancy Larson (yes??) are WAY more interesting than the later stuff. At least that was my take. I think the Saxon 3 is still Nancy Larson. I don't see the issue. 

You gotta flush people who give you a hard time. They aren't worth it. It's none of their business.

Yep, this is Nancy Larson. I haven't looked at the higher levels- or well not since dd did 8/7 and I think I've blocked that out, LOL. 

It just seems well put together and almost sneaky how it ramps up. We like the Meeting. It reminds me of the beginning of RS lessons, only less random. Actually, a lot of it reminds me of RS, but it has the drill that I felt like RS lacked after a point. So we'll see where it goes after this. We're just starting back up after weeks off, so I'm not ready to think that far yet!!

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2 hours ago, Æthelthryth the Texan said:

An acquaintance said something to the effect of,  "well that's a parts to whole program which is a really bad fit for your son imo since he's so STEM oriented."  Apparently I missed the memo there......and I'll just shut up or Ill get snarky over math snobbery. 

 

Well, if I am in the mood to be snarky, Basis public charter schools use Saxon math 🤨 Besides I don’t agree with pigeonholing kids, especially a 7 year old.

As for math, DS13 learns better with an overview, then the parts, then review (kind of like cake baking, he has to see how the cake would look like first, then get the ingredients, then put it all together). DS14 learns wide and deep so his is a mixture of whole and parts. Regardless of which curriculum my kids use, we use a lot of pencil and paper discussions that are outside the curriculum, lots of YouTube videos, lots of library books. 

DS13 works better with applied before conceptual. That’s why word problems were great for him in elementary math and sciences (Chemistry and Physics) are great for him in higher maths. He learns his calculus from physics which is why we switch the sequence and did AP physics C first before calculus BC.

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23 hours ago, Æthelthryth the Texan said:

...

What spawned this is I bought ds7 Saxon math recently which dropped some jaws when talking about what we were using curriculum wise with some other homeschoolers. An acquaintance said something to the effect of,  "well that's a parts to whole program which is a really bad fit for your son imo since he's so STEM oriented."  Apparently I missed the memo there......and I'll just shut up or Ill get snarky over math snobbery. 

...

Where is the old-board "running away" icon when I need it???  Here's my Deep Dark Secret: math-gifted DS13 is using Math U See.  Even people on this board think that is horrid!

(full disclosure -- we toss in other stuff, too, but MUS is spine a program that DS learns from & it doesn't make him cry & I like a lot of it, which is a rare package deal)

21 hours ago, Arcadia said:

 

...

DS13 works better with applied before conceptual. That’s why word problems were great for him in elementary math and sciences (Chemistry and Physics) are great for him in higher maths. He learns his calculus from physics which is why we switch the sequence and did AP physics C first before calculus BC.

This is just brilliant, and crystallizes stuff that's been banging around in the back of my mind.  Just a terrific option: thanks. 

Edited by serendipitous journey
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On 6/23/2019 at 2:01 PM, PeterPan said:

Yeah, you'll find engineers who learned just fine with Saxon, Teaching Textbooks, MUS, and all sorts of things people say aren't good enough. I personally find that the difference is the dc and the dc's ability to apply simple things to more complex, novel situations. If the dc has that ability, they're going to succeed with almost any curriculum. If the dc is struggling, putting him in a curriculum that is too hard doesn't help. 

I think this is really key.

I also don't see how whole to part and parts to whole relate to at least primary math.  In language yes, but in math?  I mean, sure you can provide an overview of something first or have the child do investigative/discovery work but even when doing something totally discovery or proofs based the student is still manipulating the parts within a whole and they need knowledge of both for full understanding.  I hope I'm describing that accurately/clearly but I really have trouble seeing how even something like Miquon is "whole-to-parts" and not "parts-to-whole."  And a "whole-to-parts" learner might need to see the end goal before getting bogged down in the details (I'm like that) but the "parts" are still needed, it's not like they can just be skipped, kwim?

That's why I prefer to speak of incremental/intuitive vs. parts/whole for math.  A particular child might need very incremental presentation or he might be able to make conceptual leaps from seeing a few details and maybe a bigger picture presented simultaneously.  At the end of the day we go without curriculum for most things at the primary level because the same child might need incremental teaching for one topic and grasp another one in two seconds flat just from seeing "the big picture" all within the same day and I have trouble tweaking curriculum: either I follow it as written or I don't do it at all (I don't think I have OCD, lol).  I'm over my own anti-Saxon prejudice these days but I still dropped 5/4 with DD10 because I couldn't teach it effectively and it was taking too long as written.  I'm not getting rid of it yet though and actually bought the next two sets in the series when I found them at a great price because who knows what the future will bring: maybe I'll burn out and cycle back to the Robinson Curriculum again one of these days, lol.

The longer I home school the more I realize that home schooling is hard (please don't laugh at me, I was pretty naive when I started).  I thought if I just found the right philosophy/approach/text things would just run on autopilot and we'd go along swimmingly.  I should have known better and all of you with older kids than mine will probably roll your eyes but it is finally starting to sink in on more than just a surface level how much a particular child and a particular parent brings to the equation.

OP, I hope Saxon works great for your kiddo!  The comment that you got IRL makes little sense to me in the context of hearing Saxon recommended around these parts IRL for future engineers (it's only on here that I ever hear Saxon criticized) and my dad, who taught math and physics here and in the former USSR for 30 years claimed that Saxon was the best English-language textbook that he had ever encountered (though nothing for him compared to Russian math, of course, and he passed away before I could show him AOPS 😢).

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6 hours ago, serendipitous journey said:

Where is the old-board "running away" icon when I need it???  Here's my Deep Dark Secret: math-gifted DS13 is using Math U See.  Even people on this board think that is horrid!

(full disclosure -- we toss in other stuff, too, but MUS is spine a program that DS learns from & it doesn't make him cry & I like a lot of it, which is a rare package deal)

This is just brilliant, and crystallizes stuff that's been banging around in the back of my mind.  Just a terrific option: thanks. 

Ds really likes MUS! So that is my back up plan to go back to if Saxon turns into a fail. He just needs more reinforcement on the previous lessons because we skipped ahead pretty fast and then I was cobbling review and MUS etc. etc.  He doesn't have the patience right now for straight up mastery- he wants to dabble. But MUS saved math for my Saxon hater and we are huge Mr. Demme fans. 🙂

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2 hours ago, mms said:

 

I think this is really key.

I also don't see how whole to part and parts to whole relate to at least primary math.  In language yes, but in math?  I mean, sure you can provide an overview of something first or have the child do investigative/discovery work but even when doing something totally discovery or proofs based the student is still manipulating the parts within a whole and they need knowledge of both for full understanding.  I hope I'm describing that accurately/clearly but I really have trouble seeing how even something like Miquon is "whole-to-parts" and not "parts-to-whole."  And a "whole-to-parts" learner might need to see the end goal before getting bogged down in the details (I'm like that) but the "parts" are still needed, it's not like they can just be skipped, kwim?

That's why I prefer to speak of incremental/intuitive vs. parts/whole for math.  A particular child might need very incremental presentation or he might be able to make conceptual leaps from seeing a few details and maybe a bigger picture presented simultaneously.  At the end of the day we go without curriculum for most things at the primary level because the same child might need incremental teaching for one topic and grasp another one in two seconds flat just from seeing "the big picture" all within the same day and I have trouble tweaking curriculum: either I follow it as written or I don't do it at all (I don't think I have OCD, lol).  I'm over my own anti-Saxon prejudice these days but I still dropped 5/4 with DD10 because I couldn't teach it effectively and it was taking too long as written.  I'm not getting rid of it yet though and actually bought the next two sets in the series when I found them at a great price because who knows what the future will bring: maybe I'll burn out and cycle back to the Robinson Curriculum again one of these days, lol.

The longer I home school the more I realize that home schooling is hard (please don't laugh at me, I was pretty naive when I started).  I thought if I just found the right philosophy/approach/text things would just run on autopilot and we'd go along swimmingly.  I should have known better and all of you with older kids than mine will probably roll your eyes but it is finally starting to sink in on more than just a surface level how much a particular child and a particular parent brings to the equation.

OP, I hope Saxon works great for your kiddo!  The comment that you got IRL makes little sense to me in the context of hearing Saxon recommended around these parts IRL for future engineers (it's only on here that I ever hear Saxon criticized) and my dad, who taught math and physics here and in the former USSR for 30 years claimed that Saxon was the best English-language textbook that he had ever encountered (though nothing for him compared to Russian math, of course, and he passed away before I could show him AOPS 😢).

Thank you. And that's interesting about your Dad and good to hear! (Sorry for your loss though. :sad:). 

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For me it means I am never going to remember small details of a subject until and unless I understand the bigger picture. So, although technically all biology is chemistry, I NEED to understand biology before I understand or grasp the chemistry. So, if I know about cells, and cell membranes, THEN I will much better be able to grasp ions and ion exchange in chemistry, if you tell me it is like what happens across a cell membrane. I'm tired, that analogy may be terrible, lol. 

Or, tell me what the civil war was about, the big picture, before telling me about the major battles. 

Give me the broad concept, or the big arial view, then bring me in deeper/closer a bit at a time. 

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Also, more than parts to whole, i often need/want to know WHY before I know HOW. Otherwise it is in one ear and out the other. I need context, bare facts fall right out of my head but give me some context and I'll remember FOREVER. (why living books/historical fiction/documentaries are my personal best learning method)

I cannot STAND the show "how it's made" on Netflix, where they make stuff and you watch, because it doesn't say WHY they do it that way or what the machine or whatever is for, etc etc. Like, fine, you use machine X to make part Y, but what does part Y do...why do you need it to be that shape, etc etc. Meanwhile my husband and DD LOVE that show. They never even ask why. They just like knowing how it is made. For me, without the why, I have zero interest in the how. 

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9 hours ago, Ktgrok said:

For me it means I am never going to remember small details of a subject until and unless I understand the bigger picture. So, although technically all biology is chemistry, I NEED to understand biology before I understand or grasp the chemistry. So, if I know about cells, and cell membranes, THEN I will much better be able to grasp ions and ion exchange in chemistry, if you tell me it is like what happens across a cell membrane. I'm tired, that analogy may be terrible, lol. 

Or, tell me what the civil war was about, the big picture, before telling me about the major battles. 

Give me the broad concept, or the big arial view, then bring me in deeper/closer a bit at a time. 

 

Yes, completely. Though I think this is often related to maturity. I think more teens and adults are like this than are children.

I think presenting the big picture is just part of good teaching. As the teaching parent I often find myself presenting the big picture and the “why”. The curriculum itself doesn’t have to do this to be effective, and I don’t really expect it to, because even understanding the big picture, at some level learning has to be broken down into smaller parts. The only time I’ve had trouble with this in homeschooling has been with Latin, because it was something I didn’t know. At first, I struggled with helping my kids learn in even the beginning Latin programs, because I didn’t understand how the language was put together as a whole. 

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I understood it as whole to parts = someone who needs to see the big picture or they feel bogged down in the details. 

Parts to whole = big picture is overwhelming, give me the details and when I get to the big picture it will all make sense. 

I tend towards the former myself, I need to get my head around 'where is this going?' Or I'm likely to bail!

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I had never heard of this whole/parts expression before this thread.  But when I read it, I immediately thought of BFSU, because I thought it had a nice forest/trees balance.  In fact, you are never allowed to get too much focused on a tree without a reminder that this is part of a larger forest.  For example:

He teaches ionic and covalent bonds like every other middle school chemistry text.  But then, he goes all forest on you.  What does a covalent bond mean for LIFE?  Life means chemical reactions, that is, atoms being exchanged between molecules constantly.  You can only really do that with covalent bonds where they can easily be broken and reformed over and over.  Ionic bonds by contrast are pretty much formed and stay there with incredible force.  While you will find ionic bonds in living systems, we usually think of ionic bonds in things like rocks, which change very little over time.  

Over and over again he does this.  I think science curricula gets too bogged down into the parts, and doesn't spend enough time looking at the whole forest, especially for the younger ones who might need more context.  

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I think the parent definitely misspoke.  I expect she meant that Saxon was spiral and not a mastery based math program.

With homeschooling, the parts-to-whole methodology made me immediately think of IEW.  I don’t know if I’m being fair to IEW because DS used a writing tutor that heavily pushed process and no invention  The method ran completely contrary to my thinking about writing because of the hyper focus on style. Once I understood the method (not saying I liked it), a light bulb went off and I was able to conceptualize the program better.

Edited by Heathermomster
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On 6/23/2019 at 10:39 AM, Æthelthryth the Texan said:

An acquaintance said something to the effect of,  "well that's a parts to whole program which is a really bad fit for your son imo since he's so STEM oriented."  

I would definitely characterize Saxon as parts to whole.  In fact, that was one reason we ditched it halfway through 7/6.  My son apparently thought that every little thing he learned in Saxon was completely different from every other little thing he learned, so rather than building a castle, all of the bricks were just lined up side by side.

That said, I think that to a great extent *all* arithmetic programs are parts to whole. 

I also don't think that one size fits all when it comes to nurturing STEM-focused kiddos.

Edited by EKS
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4 hours ago, EKS said:

I would definitely characterize Saxon as parts to whole.  In fact, that was one reason we ditched it halfway through 7/6.  My son apparently thought that every little thing he learned in Saxon was completely different from every other little thing he learned, so rather than building a castle, all of the bricks were just lined up side by side.

That said, I think that to a great extent *all* arithmetic programs are parts to whole. 

I also don't think that one size fits all when it comes to nurturing STEM-focused kiddos.

See, that's what I thought on the bolded and part of why I was really confused. 

My ds is pretty quick at getting the gist, so to speak, on the general "overall concept". For that I do think he's a big picture/whole type kid. But he still needs work on refining the details, because in his ego filled head, he's buffing his nails on his shirt thinking "I got this...." and then he rushes, doesn't pay attention to the signs or something stupid and it's more "Nope. You don't." And he also has things fly right out of his head if we don't circle back reasonably soon, so although he loved MUS, I was still needing to supplement to keep up those facts and order of ops etc.-- which I assume is pretty normal for 7.

I will say so far it seems like Saxon 3 has a totally different feel that what I remember from Saxon dd used in 7th grade, which I guess it would since it's different authors. But I haven't picked up on the whole life sucking vibe so far I see on older posts when anyone mentioned Saxon. I wish I still had 7/8 laying around to compare the layout. It's hard to tell on web samples and I've completely forgotten anything about it except the timed tests from that long ago! 

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4 minutes ago, Æthelthryth the Texan said:

I will say so far it seems like Saxon 3 has a totally different feel that what I remember from Saxon dd used in 7th grade, which I guess it would since it's different authors. But I haven't picked up on the whole life sucking vibe so far I see on older posts when anyone mentioned Saxon. I wish I still had 7/8 laying around to compare the layout. It's hard to tell on web samples and I've completely forgotten anything about it except the timed tests from that long ago! 

See, that's the other thing that I found funny about the other lady's comment: you don't have to commit to Saxon for the long haul just because you're using it when he's 7.  Elementary Saxon is very different from the rest of the series in format and style, far more interactive between teacher/student with manipulatives, etc.  As far as I can tell the only things similar are the "incremental" and "spiral."

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On 6/24/2019 at 10:11 AM, serendipitous journey said:

This is just brilliant, and crystallizes stuff that's been banging around in the back of my mind.  Just a terrific option: thanks. 

 

DS13 pulled through for AP Physics C Mechanics as well as AP Physics C Electricity and Magnetism. This kid 🤣

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Whole to part math is an idea from the Constructivist  Ed philosophy  which was very popular in the ‘80’s-‘90’s until standardized tests took over. If you’ve used any of the Marilyn Burns books, that would be an example. Basically, you give the kids a situation to explore and figure out, and then teach the formal math after they have had a chance to explore it and draw some conclusions. Miquon is a good examp,e for younger students. Life of Fred is an example, where the situations Fred encounters in a chapter are the whole, and then broken down into parts. AoPS also does this. Mathematicians tend to love constructivist style math because it is the way they think-find a problem, then create the math to solve it. And, the whole is important. Real world problems usually don’t come clear cut as to what to do as problems in math classes. 

In my experience, it works very well for very young children and informally, and indeed, is how preschoolers learn, where they explore concepts and later, get the labels. It also works well, in a more formal sense, once kids have basic tools to use, where they can solve the problem, but there is a simpler way to do it (calculus to explain physics is a prime example). It does not work well if the concept that is to be discovered is one that the child does not yet have the tools or language to solve/explain, and I’ve seen a lot of 1st-3rd grade kids really struggle due to the language component. They can explore with blocks or whatever and discover the idea, but be unable to articulate it, and feel like a total failure at math. 

And, regardless, the part is important. It takes practice to cement the how, even if you figured out the why. A big failure of the constructivist movement in the early 1990’s was that it tended to not have enough practice of discrete skills. Similarly, just memorizing facts and algorithms also is not likely to be effective without application. 

FWIW, the meeting  component of the younger Saxon books actually includes decent amount of the whole, as well as a lot of parts. 

 

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