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Using AoPS with average math students


lewelma
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GASP.:001_huh:

 

Please tell me you are kidding.

 

Absolutely NOT kidding. Do a search on Myrtle.

 

Good grief. I stopped browsing the "I'm doing SM my way" threads a looooong time ago. I told the first 20 or so posters over the years to please not destroy the magic of SM by totally undoing all the good things in it . . . and explained why/how/what/when . . . and then, after the many years of banging my head on that wall . . . I just try to not even open SM math threads b/c they make me so sad.

 

Interesting.

 

Soon, I'll probably be that way about MCT and AoPS too. I'm sure someone will soon be talking about how great AoPS works when, instead of allowing their child to do the PROBLEM SOLVING, instead, they carefully extract all the rules, formulas, tricks, and such, and spoon feed each concept to their child before overwhelming the child with the oh-so-scary problems that they, GASP, have not yet been taught how to solve. Ohhh, I am sure there will soon be advocates of it. There will be one or two who post over and over about how great it is, and bring many others down their cheery lane . . . and somehow believing that by "modifying" the program in such a way, their child is getting the amazing benefits of the true curriculum which others had noticed and explained . . . (when it is used properly). Mark my words, I will not duke it out again. I will not. I will not. I will not. I will avoid the threads. I might ignore the frequent posters.

 

Myrtle is a math legend on these boards. As is her husband, Charon. Myrtle's retired blog: Drat These Greeks!.

 

If it's good enough for Myrtle, it's good enough for me.

 

I tend to follow materials as presented by the author/expert. But I won't criticize parents for giving it their own twist. The math police won't bang down the door on folks who tweak their math program.

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I happen to be able to appreciate the incredible amount of insight and expertise that goes into a good math curriculum. I believe that in this case "mom knows best" is true for very few moms who are qualified to modify a math curriculum while retaining the logic, sequence, didactic value and mathematical rigor. (Of course one can always modify and create an inferior product.) Altering a math curriculum is, in fact, a very difficult task which requires a much higher level of mathematical knowledge than what the curriculum is teaching.

Much more difficult than altering a history or literature curriculum - because in math you can not omit anything, nor can you teach things in the wrong order.

:iagree: with you. Who determines the definition of 'altering' as it relates to this conversation? Is it simple tweaking? Not following the TM? Odds/evens? Calculator or no?

 

I'm not debating the math experts here. (That would be ridiculous of me to try.) I'm just chiming in to say that I enthusiastically disagree with the sentiment below:

 

I often think the kids would be better served if the parent chose a lower level of the program or simply a less challenging program. It seems ego-driven when a parent chooses a higher level of a gifted program and then modifies it beyond recognition . . . instead of simply choosing a more appropriate level and/or program. Everyone loses, IMHO.

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:iagree: with you. Who determines the definition of 'altering' as it relates to this conversation? Is it simple tweaking? Not following the TM? Odds/evens? Calculator or no?

 

I'm not debating the math experts here. (That would be ridiculous of me to try.) I'm just chiming in to say that I enthusiastically disagree with the sentiment below:

 

 

I think it depends what modifications we're talking about.

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I think it depends what modifications we're talking about.

 

:iagree:

 

I know you're looking at aops for your ds. I hope you don't feel like you need to follow it line by line as written. That is a great text for picking and choosing topics, imho. Modification is OK. Isn't that why we homeschool? We aren't cookie-cutter parents. We choose to blaze our own path and give our dc the education that is uniquely suited for them -- as individuals.

 

On days like this I miss KarenAnne and Jackie. I love this subject. Outside-the-box thinking is always good. I am thankful they exposed me to that option. It's freeing.

 

Dd is doing a modified lesson from NEM (grade 8) this morning with Rachna. Dd is learning a ton. Yay, homeschool. :)

 

For example...

 

(x-post from another thread -- a glimpse into Abi's class this morning)

Find the value of r so that the line passing through (8,r) and (4,5) has a slope of -4.

 

Find the slope of a line that passes through points at (2,3) and (-8,-2).

 

Abi solved them and Rachna said (in her adorable Indian accent), "Great job! You handle those questions very well. How do you like this topic?

 

Abi said, "I think it's fun."

 

R just showed her a graph and asked A, "Which line has a zero slope and how can you justify your answer?"

Edited by Beth in SW WA
typo
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:iagree:

 

I know you're looking at aops for your ds. I hope you don't feel like you need to follow it line by line as written. That is a great text for picking and choosing topics, imho. Modification is OK. Isn't that why we homeschool? We aren't cookie-cutter parents. We choose to blaze our own path and give our dc the education that is uniquely suited for them -- as individuals.

 

On days like this I miss KarenAnne and Jackie. I love this subject. Outside-the-box thinking is always good. I am thankful they exposed me to that option. It's freeing.

 

Dd is doing a modified lesson from NEM (grade 8) this morning with Rachna. Dd is learning a ton. Yay, homeschool. :)

 

For example...

 

(x-post from another thread -- a glimpse into Abi's class this morning)

Find the value of r so that the line passing through (8,r) and (4,5) has a slope of -4.

 

Find the slope of a line that passes through points at (2,3) and (-8,-2).

 

Abi solved them and Rachna said (in her adorable Indian accent), "Great job! You handle those questions very well. How do you like this topic?

 

Abi said, "I think it's fun."

 

R just showed her a graph and asked A, "Which line has a zero slope and how can you justify your answer?"

 

 

:iagree: I miss their input here too.

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I would not use AoPS with an average math student.

In my eyes, high school math is a *general education* subject, and AoPS takes things way PAST the "general" part (plus some parts of it are essentially competition math). It is a very worthwhile intellectual effort on its own, but in the context of general education, the amount of time, effort, and a certain intensity it requires may be too high of a cost for the ultimate benefit. I might use it with an average student with high inclinations towards math-heavy fields, who is willing to pay that price, but basically, I would only use it with a fraction of children who truly enjoy the subject, "click" with it easily, and want to do it.

 

Likewise, I would not have a child read complete works of Cicero and Virgil in Latin - that is beyond the scope of general education. A child who wants it, bring it on, but general Latin is something else, and even a GOOD general education Latin is something else (and I do not have low standards in this camp LOL). A child who wants to go further, or a family with a particular cultural emphasis on some things - bring it on - but I would not consider it a "standard" situation.

AoPS is a less extreme example, but still, I think loosely along these lines.

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Much more difficult than altering a history or literature curriculum - because in math you can not omit anything, nor can you teach things in the wrong order.

 

I'd like to hear more about this viewpoint regarding math needing to be taught in order. I'll start a new thread on this :001_smile:

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I'd like to hear more about this viewpoint regarding math needing to be taught in order. I'll start a new thread on this :001_smile:

Literature and history, when done "properly" are also very far away from "do it as you please and mix and match as you please", LOL. I am always amused with the perception that these fields are somehow easier to tweak. They probably are if you are not interested in the big interconnected picture, but only in taking bits as regards your interests, but if you are... not so easy. There is still some order and some connections which must be made.

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Literature and history, when done "properly" are also very far away from "do it as you please and mix and match as you please", LOL. I am always amused with the perception that these fields are somehow easier to tweak. They probably are if you are not interested in the big interconnected picture, but only in taking bits as regards your interests, but if you are... not so easy. There is still some order and some connections which must be made.

 

Yes, but even with a systematic approach, you can select focus areas of study, and you can select literary works. It is utterly impossible to cover ALL of literature, so any curriculum will involve selecting works...and for a student who simply can not get into Antigone I might substitute another Greek tragedy, and instead of Rome and Juliet and Othello I can study Hamlet and Macbeth, and I can choose which Dickens novel to read.

I can focus on art history OR on military history and do a rigorous, systematic course for either.

 

In math, however, the canon of things is more prescribed and no substitutions possible. Algebra must come before calculus. Linear equations must come before systems of equations and quadratics. You can not choose to omit either, nor can you select a focus - the student must master every single topic in order to advance. A hole in math has immediate dire consequences: a student with lack of algebra will fail precalculus, whereas a student with gaps in medieval history might do reasonably well in Modern history.

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Yes, but even with a systematic approach, you can select focus areas of study, and you can select literary works. It is utterly impossible to cover ALL of literature, so any curriculum will involve selecting works...and for a student who simply can not get into Antigone I might substitute another Greek tragedy, and instead of Rome and Juliet and Othello I can study Hamlet and Macbeth, and I can choose which Dickens novel to read.

I get what you mean ;), and you are right, but there actually are non-negotiables... it is just that the "logic" behind it is more subtle and more culture-bound than in fields in which there is a direct progession. But I *cannot* skip Antigone even if my student does not really get into it, for example, because I *need* it for some connections I want to establish. There is a whole lot of works I cannot skip, or if I can, I can maybe skip one or two of those works off that list, but I definitely cannot alter it drastically or I lose those connections.

 

Even in classical languages where I more often work with fragments than with whole works, it is not random at all which fragments I choose.

 

Flexibility potential is somewhere about 10-20% (assuming normal school focus and normal progression - with advanced children and particularly interested it is slightly different).

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because in math you can not omit anything, nor can you teach things in the wrong order.

I tend to agree with you on many things, but I am not sure I agree with this. I was taught that at some point in time, it was possible for the mathematical student to learn the entire body of math. That is no longer possible. However, I suppose it is still possible for the realm of HS level math, as opposed to the entirety of the field. It seems to me, for example, some countries place more emphasis on different things, for example, I noticed a more geometrical bent (pardon the pun) in Japanese books. But I don't know that there is always a certain order to things. I am not saying you are wrong, I am saying (perhaps you can tell I just read "A Tree Grows in Brooklyn"), "I wonder."

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I tend to agree with you on many things, but I am not sure I agree with this. I was taught that at some point in time, it was possible for the mathematical student to learn the entire body of math. That is no longer possible. However, I suppose it is still possible for the realm of HS level math, as opposed to the entirety of the field. It seems to me, for example, some countries place more emphasis on different things, for example, I noticed a more geometrical bent (pardon the pun) in Japanese books. But I don't know that there is always a certain order to things. I am not saying you are wrong, I am saying (perhaps you can tell I just read "A Tree Grows in Brooklyn"), "I wonder."

 

Depends on what you mean by order. I tried to explain this in more detail in the other thread.

Of course you can focus on geometry. And of course you can study many geometry aspects before finishing algebra - the compartmentalized nature of math education in the US drives me nuts and is very contrary to how math is taught in my home country.

What I mean is:

you can not solve systems of linear equations before you can solve a single linear equation.

You can not solve quadratic equations before you can solve a linear equation.

You can not do complex trigonometry before learning arithmetic with complex numbers and trigonometry with real numbers.

You can not learn multivariable calculus before single-variable calculus.

Does that make sense?

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Does that make sense?

Of course, but one could also excel at say, real analysis while being only average in geometry; the compartmentalization extends into the advanced fields, which is part of what made Wiles atypical and thus able to bridge the gap to prove Fermat's Theorem in such an unexpected way.

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We aren't cookie-cutter parents. We choose to blaze our own path and give our dc the education that is uniquely suited for them -- as individuals.

 

On days like this I miss KarenAnne and Jackie. I love this subject. Outside-the-box thinking is always good. I am thankful they exposed me to that option. It's freeing.

 

Well said. I joined these boards only recently and have missed many of KA's and Jackie's responses but the few I've seen have been inspirational to me. I suppose the fact that not everyone feels this just goes to show where each of us are at any given time on the out-of-the-box continuum. :001_smile:

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Of course, but one could also excel at say, real analysis while being only average in geometry; the compartmentalization extends into the advanced fields, which is part of what made Wiles atypical and thus able to bridge the gap to prove Fermat's Theorem in such an unexpected way.

 

You just had to mention Wiles, didn't you? :001_smile: (be still my thumping heart).

 

I wonder if all this argument is moot if one can surmise that what works for someone who does math for math's sake will not work for one who does math for some other end.

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:iagree:

 

I know you're looking at aops for your ds. I hope you don't feel like you need to follow it line by line as written. That is a great text for picking and choosing topics, imho. Modification is OK. Isn't that why we homeschool? We aren't cookie-cutter parents. We choose to blaze our own path and give our dc the education that is uniquely suited for them -- as individuals.

[/color]

 

 

 

Thanks, Beth :) I am just listening, and absorbing what I can from those who have walked this path before. We will see what happens once DS starts Pre-A this fall. I am more than willing to change gears if AoPS doesn't work for him. And I hear you on "picking and choosing". It really does depend on how AoPS works for my older.

 

What I am not understanding here is why, for some, using AoPS (or any other math curriculum) in a way that might suit your child is verboten? Assuming you are using a good spine and not "missing" key math concepts, I mean. Is it because you believe that AoPS is only valuable if used exactly as presented by the publishers? (And assumedly, for those users, it would lose its value if used as a supplement).

 

As homeschoolers, isn't tweaking just part of our job? Are you saying that homeschool parents shouldn't tweak a curriculum like AoPS because its value lies in particular and solely in its approach? And so to approach a discovery-based math like AoPS in any way other than exactly as laid out by the authors is to completely devalue the curriculum as a whole? What if you use the discovery-based approach for certain lessons, and a more linear approach for others?

Edited by Halcyon
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What if you use the discovery-based approach for certain lessons, and a more linear approach for others?

 

Just be aware that for me using a discovery text for direct instruction is really really annoying. I am relearning algebra with my ds but fast tracking a bit myself by not using the discovery method. And Wow is the AoPS text wordy if you are just reading it and not using the discovery method. Really annoying for me personally. I just keep thinking "get to the point."

 

But my ds(11) loves it and has never even mentioned the length of the explanations. Just a non-issue for him.

 

Ruth in NZ

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What I am not understanding here is why, for some, using AoPS (or any other math curriculum) in a way that might suit your child is verboten? Assuming you are using a good spine and not "missing" key math concepts, I mean. Is it because you believe that AoPS is only valuable if used exactly as presented by the publishers? (And assumedly, for those users, it would lose its value if used as a supplement).

 

As homeschoolers, isn't tweaking just part of our job? Are you saying that homeschool parents shouldn't tweak a curriculum like AoPS because its value lies in particular and solely in its approach? And so to approach a discovery-based math like AoPS in any way other than exactly as laid out by the authors is to completely devalue the curriculum as a whole? What if you use the discovery-based approach for certain lessons, and a more linear approach for others?

This was probably not directed at me, but I wanted to take a stab at it anyway.

 

One may, within the legally imposed limits based on where they live and which may mandate covering some areas, do whatever the heck they wish. Your homeschool, your rules. :) The reason why most people do not emphasize it in every discussion of these issues, I believe, is because it goes without saying. Ultimately, you can do however you please and whatever you find the best for your DC, whether is it sticking to a prepackaged curriculum by the book, or improvizing it all, or something in between with lots of mixing and matching. So, nothing is really verboten.

 

The thing, though, is that sometimes one gets the optimum of the program by actually following it, and some programs are designed the way that they are harder to rip to pieces and mix and match with other things as you please than other programs. It still does not mean that using a curriculum outside of its "intended metholody" is verboten, but it does mean that the calculated optimum will probably not be accomplished that way. AoPS, in particular, is one of those programs which I would actually not alter, because while it may work, I think the optimal way to use it, for us, is to use it the way it is. On the other hand, the optimal way to use SOTW for us has been davka by supplementing, mixing, matching, using additional resources and eliminating activities and even large parts of the text itself - because I felt I could offer more, and better, by not using it as a stand-alone thing and by not using it perfectly the way it was "intended" (albeit it is a flexible example). With AoPS, however, I simply do not find that I have enough background knowledge to make that estimate and go "against" such an excellent curriculum with my own ideas which most likely stem from half-ignorance far more than out of a deep familiarity with the discipline. So, in that respect, I feel like I might have lost that optimum had I gone against the current. My daughter does tweak it minimally in the process, but she, neither, has done anything drastic to it.

 

People, of course, have a full right to decide that what they personally want out of something is not what the intended methodology proposes. I do think, however, that it takes knowledge of the discipline to know what exactly you want out of it and how you are going to tweak it to meet those goals.

 

The art of tweaking is like being a good painter, or a good cook. It is not only about mixing the ingredients and some benevolent joy in improvization. It is also about knowing when to STOP your hand lest you overpass the optimum. And here is where I, personally, like to seek advice from people who have not only BTDT, but also have a background in the discipline, because I believe I can profit very much from their recommendation as to when to STOP.

 

It still does not mean blindly following the instructions.

It still does not mean having the curriculum own you rather than you owning it.

It still does not mean stifling the child's soul into a box.

Nor does any radical tweaking automatically imply a courageous step out of the box.

And sometimes, to step out of the box the way you meet your optimum, means knowing the box backwards and forwards first, rather than stepping out of it "blindly", which would have been the case with me and AoPS. To go against something, you must know it first. You must know the content, then it is easy to improvize. Otherwise the tweaking becomes the cooking of an amateur chef - and while it may allow for much joy and surprises and good solutions along the way, it may also lead up to burning the kitchen and ending up with barely edible dishes. The balance is tricky to get. But, at the end of the day, we are all free to cook as we wish, by the feeling or with detailed instructions or anything in between. So sure, we adapt. But even in adapting... there is some wisdom in knowing when to stop adapting, IMO, and just implement some materials in their intended form. AoPS may or may not be one of those materials for you.

Edited by Ester Maria
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Nor does any radical tweaking automatically imply a courageous step out of the box.

 

This is such an interesting point, with regard to AOPS, curricula in general, and, in fact, life. I have often observed (maybe mostly among Americans) that inventing your own way and/or deleting things is both always beneficial and more thoughtful.

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I also think that it can be a case of "the more you know". Having gone through grad school in math ed, I'm well aware of just how well done a GOOD curriculum is (and I won't pick a bad one), and am unwilling to reinvent the wheel. Same with music-having written music curriculum professionally, and knowing what's involved, I'm very unwilling to break what isn't broken by going too far afield. Supplementing, yes. Changing the whole character, no. For example, I cringe when a parent tells a music student to "just write in the notes", because, with a very few exceptions, that's one of the things you can do that slows down music learning dramatically. If a child is struggling with reading music, better for them to learn aurally first, or by studying the piece off the instrument and memorizing-but don't give them an additional visual system to deal with. Having had both HWOT and Singapore Math teacher training, it bothers me when I hear of people leaving off big chunks of those curricula, like just getting the HWOT workbook and claiming to use the program, or not bothering to teach number bonds and just teaching "the way I learned" in SM-because in both cases, you've missed the reason why the program works by doing so. HWOT isn't particularly exceptional as a handwriting workbook, but as a way to use OT techniques for a child with motor skills issues at home, it's great. If you don't teach SM strategies, don't use number bonds, don't use model diagrams, and so on, you're just using SM as another math workbook, and there are many cheaper options available.

 

 

Sonlight, on the other hand....well...I've NEVER managed to do that program as written. The first year we got into the first book on the list, DD didn't want to stop, and the program converted to "Read CHOW and do the map/timeline, while DD reads the rest of the books on her own". This year, we didn't even make it that far-DD had most of the books read before the school year even started, so we've done the spine/timeline/maps, plus other resources, plus a stack of library books. And I feel fine with that because, after all, my goal was for DD to learn history. But I suspect that if I knew as much about SL and WHY it was put together as it was as I know about SM or HWOT, I might well feel differently.

Edited by dmmetler
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This was probably not directed at me, but I wanted to take a stab at it anyway.

 

One may, within the legally imposed limits based on where they live and which may mandate covering some areas, do whatever the heck they wish. Your homeschool, your rules. :) The reason why most people do not emphasize it in every discussion of these issues, I believe, is because it goes without saying. Ultimately, you can do however you please and whatever you find the best for your DC, whether is it sticking to a prepackaged curriculum by the book, or improvizing it all, or something in between with lots of mixing and matching. So, nothing is really verboten.

 

The thing, though, is that sometimes one gets the optimum of the program by actually following it, and some programs are designed the way that they are harder to rip to pieces and mix and match with other things as you please than other programs. It still does not mean that using a curriculum outside of its "intended metholody" is verboten, but it does mean that the calculated optimum will probably not be accomplished that way. AoPS, in particular, is one of those programs which I would actually not alter, because while it may work, I think the optimal way to use it, for us, is to use it the way it is. On the other hand, the optimal way to use SOTW for us has been davka by supplementing, mixing, matching, using additional resources and eliminating activities and even large parts of the text itself - because I felt I could offer more, and better, by not using it as a stand-alone thing and by not using it perfectly the way it was "intended" (albeit it is a flexible example). With AoPS, however, I simply do not find that I have enough background knowledge to make that estimate and go "against" such an excellent curriculum with my own ideas which most likely stem from half-ignorance far more than out of a deep familiarity with the discipline. So, in that respect, I feel like I might have lost that optimum had I gone against the current. My daughter does tweak it minimally in the process, but she, neither, has done anything drastic to it.

 

People, of course, have a full right to decide that what they personally want out of something is not what the intended methodology proposes. I do think, however, that it takes knowledge of the discipline to know what exactly you want out of it and how you are going to tweak it to meet those goals.

 

The art of tweaking is like being a good painter, or a good cook. It is not only about mixing the ingredients and some benevolent joy in improvization. It is also about knowing when to STOP your hand lest you overpass the optimum. And here is where I, personally, like to seek advice from people who have not only BTDT, but also have a background in the discipline, because I believe I can profit very much from their recommendation as to when to STOP.

 

It still does not mean blindly following the instructions.

It still does not mean having the curriculum own you rather than you owning it.

It still does not mean stifling the child's soul into a box.

Nor does any radical tweaking automatically imply a courageous step out of the box.

And sometimes, to step out of the box the way you meet your optimum, means knowing the box backwards and forwards first, rather than stepping out of it "blindly", which would have been the case with me and AoPS. To go against something, you must know it first. You must know the content, then it is easy to improvize. Otherwise the tweaking becomes the cooking of an amateur chef - and while it may allow for much joy and surprises and good solutions along the way, it may also lead up to burning the kitchen and ending up with barely edible dishes. The balance is tricky to get. But, at the end of the day, we are all free to cook as we wish, by the feeling or with detailed instructions or anything in between. So sure, we adapt. But even in adapting... there is some wisdom in knowing when to stop adapting, IMO, and just implement some materials in their intended form. AoPS may or may not be one of those materials for you.

 

 

I need to run out the door to DS' hockey game, but wanted to thank you for this post. Food for thought, and I am going to mull over it today and post later.

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I am sure that there are many "average" kids who could handle it, but I would presume it would take them a lot longer. My 9 yo doing PreAlg in about 4-5 hours a week is a perfect match for PreALg. . . but, I would guess that many kids of similar age and/or math background but without her profound talent and intelligence, would simply need much more hand-feeding of concepts and much more reinforcement. Maybe a "neurotypical" 9 yo, or even 12 yo, might need 6-10 hours a week instead of 5. Would it be worth the time? That's not my call. But, at the end of the day, there are only so many schooling hours available to each child, so I think there is a limit to how many of them should be devoted to math.

 

I have never seen AoPS pre-alg, so I have no way of comparing, but if your children take the online upper level classes, you might want to re-adjust your thinking toward time allotted for math. My ds spends at minimum 10-12 hrs/wk on his AoPS classes (and if you factor in actual class time, add a couple more hours). My ds is no slouch in math, either. I would suspect that those kind of hrs are the norm for kids that are completing the problems and challenge sets.

 

 

This was probably not directed at me, but I wanted to take a stab at it anyway.

 

One may, within the legally imposed limits based on where they live and which may mandate covering some areas, do whatever the heck they wish. Your homeschool, your rules. :) The reason why most people do not emphasize it in every discussion of these issues, I believe, is because it goes without saying. Ultimately, you can do however you please and whatever you find the best for your DC, whether is it sticking to a prepackaged curriculum by the book, or improvizing it all, or something in between with lots of mixing and matching. So, nothing is really verboten.

 

The thing, though, is that sometimes one gets the optimum of the program by actually following it, and some programs are designed the way that they are harder to rip to pieces and mix and match with other things as you please than other programs. It still does not mean that using a curriculum outside of its "intended metholody" is verboten, but it does mean that the calculated optimum will probably not be accomplished that way. AoPS, in particular, is one of those programs which I would actually not alter, because while it may work, I think the optimal way to use it, for us, is to use it the way it is. On the other hand, the optimal way to use SOTW for us has been davka by supplementing, mixing, matching, using additional resources and eliminating activities and even large parts of the text itself - because I felt I could offer more, and better, by not using it as a stand-alone thing and by not using it perfectly the way it was "intended" (albeit it is a flexible example). With AoPS, however, I simply do not find that I have enough background knowledge to make that estimate and go "against" such an excellent curriculum with my own ideas which most likely stem from half-ignorance far more than out of a deep familiarity with the discipline. So, in that respect, I feel like I might have lost that optimum had I gone against the current. My daughter does tweak it minimally in the process, but she, neither, has done anything drastic to it.

 

People, of course, have a full right to decide that what they personally want out of something is not what the intended methodology proposes. I do think, however, that it takes knowledge of the discipline to know what exactly you want out of it and how you are going to tweak it to meet those goals.

 

The art of tweaking is like being a good painter, or a good cook. It is not only about mixing the ingredients and some benevolent joy in improvization. It is also about knowing when to STOP your hand lest you overpass the optimum. And here is where I, personally, like to seek advice from people who have not only BTDT, but also have a background in the discipline, because I believe I can profit very much from their recommendation as to when to STOP.

 

It still does not mean blindly following the instructions.

It still does not mean having the curriculum own you rather than you owning it.

It still does not mean stifling the child's soul into a box.

Nor does any radical tweaking automatically imply a courageous step out of the box.

And sometimes, to step out of the box the way you meet your optimum, means knowing the box backwards and forwards first, rather than stepping out of it "blindly", which would have been the case with me and AoPS. To go against something, you must know it first. You must know the content, then it is easy to improvize. Otherwise the tweaking becomes the cooking of an amateur chef - and while it may allow for much joy and surprises and good solutions along the way, it may also lead up to burning the kitchen and ending up with barely edible dishes. The balance is tricky to get. But, at the end of the day, we are all free to cook as we wish, by the feeling or with detailed instructions or anything in between. So sure, we adapt. But even in adapting... there is some wisdom in knowing when to stop adapting, IMO, and just implement some materials in their intended form. AoPS may or may not be one of those materials for you.

 

EM, I always enjoy reading your posts.

 

I think experience w/material/content allowing for flexibility in teaching/approach is a valid contention. When I first started homeschooling, I was far more likely to "follow the text." After teaching through grade levels and having an understanding of where we were going and the steps required to get there, I gained confidence to focus more on teaching and less on the curriculum.

 

That said, I only take that approach w/certain subjects and only at certain levels. I am only able to do it w/content and approach that I know. That which I don't, I don't adapt. Either I use as is or switch.

 

For example, MCT teaches (at least at the lower levels.....I disagree w/him on the upper levels) very similarly to how I naturally teach. I had never seen his materials until last yr, but when I opened them, there was an affinity of style/thought. I could step right in and use it how I liked and it make it better for my particular child. (writing/grammar are areas that I am confident in teaching even w/o a book). AoPS alg, otoh, I am not. I have taught my older kids far beyond alg 4 times already, so it was not the subject. But, the approach.....no, it does not represent the way I teach math or even think about math. It is not something that I could alter and ultimately know if I were helping or harming. I had to switch back to a text/approach I knew in order to alter the pace/presentation for my dd b/c with that book I knew the big picture of where we were going and what it took to accomplish that text's objectives.

Edited by 8FillTheHeart
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