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Has anyone used Beast Academy as their *only* math curriculum?


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On 5/25/2021 at 6:15 PM, GracieJane said:

Thank you so much for the responses! If I can add on a question: if you went on to AOPS (we have the pre-algebra book on deck), which math curriculum did you love for the basics? My DS is roughly mid-grade 3 if it helps.

Considering BA is new, all original AoPS students took their courses wo having used those texts. 🙂  FWIW, my ds didn't jump into AoPS until the intermediate alg book (when I first learned about them).  He had taken regular ol' math courses (Horizons for elementary, Foersters for alg 1 and 2).  He loved AoPS and thrived in the courses he took (intermediate alg, precal, cal and C&P).  Equally, I have a dd who was just as good at math as he was.  He tried to convince her to switch to AoPS.  She took their alg 1 course and didn't like it all.  She did fine with it; she just didn't care for the approach. It wasn't for her.  

Pt being, I wouldn't worry about how to get to AoPS.  I would just focus on building a strong mathematical foundation.  

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6 hours ago, stripe said:

I felt like the program was directing students towards math competitions, or some other setting where finding some way to deal with an apparently nightmarish scenario is important, and thus the practice problems were overly specific. As an example, how often do you REALLY need to figure out a “clever” / “shorter” way to calculate 101*99?

I think things like that are not so much about teaching the specific trick as about developing number sense and grasping WHY the trick works. And then of course you can build from that (the example you gave) to difference of squares: 101*99=(100+1)(100-1)=(100^2)-(1^2). (a+b)(a-b)=(a^2)-(b^2).

Insert obligatory disclaimer that I'm not saying BA/AOPS is for all students. No single curriculum is for all students. This one works well for my kids.

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9 hours ago, Not_a_Number said:

Part of the reason I'm posting here, though, is to point out that DD8 is a VERY MATHY kid who doesn't particularly enjoy BA. Sometimes I get the sense that people think that if BA doesn't work, that's because the kid is not in the intended audience -- they aren't mathy enough. That's simply not the case. DD8 has never, ever asked to do a page of BA instead of the normal math she does, and yet she's more than a little mathy -- she's extremely mathematically talented. I can give some examples of the work she's currently doing if anyone wants to see what I mean about that, but I'm not bragging (especially since her talents aren't my doing, anyway) -- I'm simply explaining that it's possible to both be very mathy and very uninterested in a puzzle-based curriculum. 

Yes!!! This is so true. And in my case I would go a step further and confess that my pride was bound up in it. I thought of BA as the best, and the only true "problem solving"  curriculum as opposed to the "just learn the algorithm" approach. And if course that's not true, there are many great programs that teach conceptually. I just really wanted to think of him as a puzzle solver when he wasn't, though he has many gifts and math is his favorite subject. You just have the kid you have! That's why the forum for curriculum says "let's remember no one curriculum fits all kids"! 🙂

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Posted (edited)
24 minutes ago, Emily ZL said:

Yes!!! This is so true. And in my case I would go a step further and confess that my pride was bound up in it. I thought of BA as the best, and the only true "problem solving"  curriculum as opposed to the "just learn the algorithm" approach. And if course that's not true, there are many great programs that teach conceptually. I just really wanted to think of him as a puzzle solver when he wasn't, though he has many gifts and math is his favorite subject. You just have the kid you have! That's why the forum for curriculum says "let's remember no one curriculum fits all kids"! 🙂

Exactly. Honestly, since I'm such a puzzle-solver myself, I kind of assumed DD8 wouldn't be mathy when she wasn't into puzzles at all. And then that turned out to be totally false! 

 

2 hours ago, stripe said:

Yes, I wondered if that was their idea of what it would build, but in some cases I didn’t feel it did.

I feel like building a good solid sense of the distributive property is a better idea than working on corner cases like "difference of squares," anyway. Most kids I've worked with manage to memorize difference of squares, because it's appealingly symmetric. And yet most kids I've worked with also have trouble with distributing...

Edited by Not_a_Number
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I can’t figure out exactly where they presented this. Or if it was what I said, even. But my kids didn’t find it hard (I managed to find one of my kid’s practice books and see several starred problems marked by one kid as “easy”), just sort of… interesting but forgettable/useless. I also firmly believe 3B should be before 3A. I think this section on Clever Computations is for the contest-lovers or mental math whizzes. 

Here is a sample from 3B (p52 and p 93)

 

4D564B92-1B35-4CA2-99DD-C49437D90C3C.jpeg

5EC9BF7B-3C11-4402-B691-A5F35770AB85.jpeg

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3 minutes ago, stripe said:

I can’t figure out exactly where they presented this. Or if it was what I said, even. But my kids didn’t find it hard (I managed to find one of my kid’s practice books and see several starred problems marked by one kid as “easy”), just sort of… interesting but forgettable/useless. I also firmly believe 3B should be before 3A. I think this section on Clever Computations is for the contest-lovers or mental math whizzes. 

Here is a sample from 3B (p52 and p 93)

 

4D564B92-1B35-4CA2-99DD-C49437D90C3C.jpeg

5EC9BF7B-3C11-4402-B691-A5F35770AB85.jpeg

See my kids thought visual proofs were amazing. They still talk about the squaring chapter.

same with truth teller puzzles. 

 I think distributive property exercises are excellent to make sure kids conceptually understand them. 
i see both of those examples as conceptual reinforcements. 
 

Also my youngest (now in 8th) wouldn’t/couldn’t do long division algorithm until he saw it in beast. He says that’s how he always did it mentally and still uses their method. 
 

I wish all levels were out when my kids were younger. We used some of them and absolutely loved them, but I credit SM (our primary math) for strong foundation. 

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17 minutes ago, stripe said:

I can’t figure out exactly where they presented this. Or if it was what I said, even. But my kids didn’t find it hard (I managed to find one of my kid’s practice books and see several starred problems marked by one kid as “easy”), just sort of… interesting but forgettable/useless. I also firmly believe 3B should be before 3A. I think this section on Clever Computations is for the contest-lovers or mental math whizzes. 

Here is a sample from 3B (p52 and p 93)

 

 

 

The only other program I've seen do that in elementary was Gattegno book 5, so if they like that I can look up the page numbers for you so they can practice how it goes further into determining squares (and then cubes) of any number by developing a formula based on already known squares (and cubes). 

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Posted (edited)
1 hour ago, stripe said:

I can’t figure out exactly where they presented this. Or if it was what I said, even. But my kids didn’t find it hard (I managed to find one of my kid’s practice books and see several starred problems marked by one kid as “easy”), just sort of… interesting but forgettable/useless. I also firmly believe 3B should be before 3A. I think this section on Clever Computations is for the contest-lovers or mental math whizzes. 

Here is a sample from 3B (p52 and p 93)

 

4D564B92-1B35-4CA2-99DD-C49437D90C3C.jpeg

5EC9BF7B-3C11-4402-B691-A5F35770AB85.jpeg

So again, this is just me personally... but I don't give questions like those starred questions until a kid is REALLY firm in all the properties of multiplication. The reason for that being that if you don't have a solid picture of what's happening, it's really easy to just apply a bunch of rules and forget about them. 

I'm sure I could give those to DD8 now and she'd blast through them. But it's just not what I do near the beginning of multiplication.

I do keep wondering if part of what happens with BA is that the kids who succeed at it mostly have already fully internalized the concepts (with or without a program, perhaps through free reading and conversations?) Like, I have a kid in my Zoom math class who is about to start out on Beast Academy 3A. In my class, she's been calculating things like 13*28 without a ton of trouble 😂. Occasionally, she gets lost in all the calculations or forgets a fact, but that's the level. 

I'm sure she'll enjoy Beast 3A, because she doesn't NEED conceptual help with any of it. And I'm glad they are doing it, since it'll deepen her understanding. But it's also not fair to say that BA is really teaching her to multiply, you know? She's already multiplying very well... 

Edited by Not_a_Number
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45 minutes ago, HomeAgain said:

The only other program I've seen do that in elementary was Gattegno book 5, so if they like that I can look up the page numbers for you so they can practice how it goes further into determining squares (and then cubes) of any number by developing a formula based on already known squares (and cubes). 

Thanks for the offer. My kids who used BA are now in high school (that’s why I have a pretty good idea about what has stuck with them) so I probably don’t need this, but it sounds cool. 

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2 hours ago, Not_a_Number said:

So again, this is just me personally... but I don't give questions like those starred questions until a kid is REALLY firm in all the properties of multiplication. The reason for that being that if you don't have a solid picture of what's happening, it's really easy to just apply a bunch of rules and forget about them. 

I'm sure I could give those to DD8 now and she'd blast through them. But it's just not what I do near the beginning of multiplication.

I do keep wondering if part of what happens with BA is that the kids who succeed at it mostly have already fully internalized the concepts (with or without a program, perhaps through free reading and conversations?) Like, I have a kid in my Zoom math class who is about to start out on Beast Academy 3A. In my class, she's been calculating things like 13*28 without a ton of trouble 😂. Occasionally, she gets lost in all the calculations or forgets a fact, but that's the level. 

I'm sure she'll enjoy Beast 3A, because she doesn't NEED conceptual help with any of it. And I'm glad they are doing it, since it'll deepen her understanding. But it's also not fair to say that BA is really teaching her to multiply, you know? She's already multiplying very well... 

I think the Perfect Squares chapter is the most ill-placed out of all the BA chapters.  Kids have just been introduced to multiplication, then it gets into this.  After watching my oldest DS struggle a bit with this one and not really retain it at the time (and keep in mind, he was 7 when he was doing this -- I think the summer between 1st and 2nd grade), I decided it fit much better right before the next multiplication chapter, which I think is in 4A.  So both DS12 and DS9 skipped the perfect squares chapter when it first appeared and came back to it right before starting 4A.  The timing was much better as their multiplication skills had time to percolate a bit first, and it was a great warm up before doing the next full chapter on multiplication in level 4.

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Indeed -- in 3A, the student is supposed to memorize the times tables. Then in 3B, we've got long and weird multiplications. I compare this with MEP -- which introduced multiplication earlier, but stays focused on smaller numbers for significantly longer, much like Singapore does (both programs confine themselves to 0-20 almost entirely in grade 1, as I recall). I just think it's confusing. I think MEP has very, very careful scaffolding, with a very logical presentation method, and I think it was designed to make clear mathematical reasoning accessible to students of all levels.

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16 hours ago, Not_a_Number said:

Part of the reason I'm posting here, though, is to point out that DD8 is a VERY MATHY kid who doesn't particularly enjoy BA. Sometimes I get the sense that people think that if BA doesn't work, that's because the kid is not in the intended audience -- they aren't mathy enough. That's simply not the case. DD8 has never, ever asked to do a page of BA instead of the normal math she does, and yet she's more than a little mathy -- she's extremely mathematically talented. I can give some examples of the work she's currently doing if anyone wants to see what I mean about that, but I'm not bragging (especially since her talents aren't my doing, anyway) -- I'm simply explaining that it's possible to both be very mathy and very uninterested in a puzzle-based curriculum. 

I think this is an extension of a particularly American idea that one is either "good at math" or "not good at math."  Whereas the Eastern idea is you are either "good at math" or "need to study more."  

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7 hours ago, Emily ZL said:

Yes!!! This is so true. And in my case I would go a step further and confess that my pride was bound up in it. I thought of BA as the best, and the only true "problem solving"  curriculum as opposed to the "just learn the algorithm" approach. And if course that's not true, there are many great programs that teach conceptually. I just really wanted to think of him as a puzzle solver when he wasn't, though he has many gifts and math is his favorite subject. You just have the kid you have! That's why the forum for curriculum says "let's remember no one curriculum fits all kids"! 🙂

For example, Singapore Math does explain the standard algorithms in detail, if BA doesn't suit.  

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9 minutes ago, stripe said:

Indeed -- in 3A, the student is supposed to memorize the times tables. Then in 3B, we've got long and weird multiplications. I compare this with MEP -- which introduced multiplication earlier, but stays focused on smaller numbers for significantly longer, much like Singapore does (both programs confine themselves to 0-20 almost entirely in grade 1, as I recall). I just think it's confusing. I think MEP has very, very careful scaffolding, with a very logical presentation method, and I think it was designed to make clear mathematical reasoning accessible to students of all levels.

I personally introduce multiplication as soon as addition, subtraction and place value are understood well (technically, one doesn't need subtraction, but that's my order), and I tend to do things like 3*15 or 2*42 or whatnot -- a small number of copies of a big number. Then we work on multiplication at the same time as we're doing addition and place value and it all gets integrated. 

I did multiplication without memorization for something like 1.5 years with DD8, I think. By the end of that time, she could explain ALL the properties in full generality, because she had spent a very long time using them and making them her own. Having worked with a lot of kids, that level of understanding is actually quite unusual. And she didn't lose any time by it, either -- for us, it was time very well spent, and it keeps helping her now that we're firmly into algebra. I've never seen her multiply out polynomials incorrectly, for example... it just doesn't happen. 

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Posted (edited)
1 minute ago, daijobu said:

For example, Singapore Math does explain the standard algorithms in detail, if BA doesn't suit.  

For the record, I taught DD8 all the standard algorithms. They are highly efficient! Why not? 

Of course, by the time we got to them, she could already do everything perfectly either on paper or in her head. I think addition took 1 day to learn to mastery, subtraction 2 days, multiplication 1 day, and long division a whole week. (I did space them out so she didn't get overwhelmed.) 

Edited by Not_a_Number
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15 hours ago, stripe said:

I felt like the program was directing students towards math competitions, or some other setting where finding some way to deal with an apparently nightmarish scenario is important, and thus the practice problems were overly specific. As an example, how often do you REALLY need to figure out a “clever” / “shorter” way to calculate 101*99?

I guess I don't really think about this as one particular trick that can only be used with these 2 numbers.  I feel like it's a part of exercising the brain to think about these shortcuts and why they work.  And reinforce the idea of place value.   

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6 minutes ago, daijobu said:

I guess I don't really think about this as one particular trick that can only be used with these 2 numbers.  I feel like it's a part of exercising the brain to think about these shortcuts and why they work.  And reinforce the idea of place value.   

This might just be me personally, but I far prefer this trick written in variable format. I feel like it actually really clarifies it. (But then I do not think of this trick visually. I can prove it visually, but I kind of don't see the point. The whole idea of algebra is to allow us to get away from visual tricks and make things easy and rote when needed.) 

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Posted (edited)

Looking over these books this morning, I maintain that some topics weren’t presented in a way that I personally thought was very valuable or clear, and I don’t think some of these calculations come up in the wild very often as they are taught there, but my daughter apparently found a lot of them very easy. I’m all for thinking and becoming flexible without just memorizing things. My daughter is amazed by how much other kids want some equation to just stick things into.

Also, we only used the first two books of year 3, so I really can’t speak to the whole series. I bought a few others later but never used them, and my youngest doesn’t seem interested in most of the puzzle book. 

I feel like I derailed this thread. My point was that when they came out, plenty of people tried and then some didn’t like them particularly, but now one could get the impression  that everyone loves Beast Academy across the board.

Edited by stripe
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2 minutes ago, stripe said:

I feel like I derailed this thread. My point was that when they came out, plenty of people tried and then some didn’t like them particularly, but now one could get the impression  that everyone loves Beast Academy across the board.

I think we fixed that issue pretty thoroughly, lol.

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1 hour ago, stripe said:

My point was that when they came out, plenty of people tried and then some didn’t like them particularly, but now one could get the impression  that everyone loves Beast Academy across the board.

That's funny. Every time BA comes up, I feel like I end up having to defend the idea that actually, it really IS a good program for some kids. 

BA, just like Saxon or Singapore or whatever else, is a math program that will be a good fit for some kids/parents and a poor fit for others. They all have strengths and weaknesses. 

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I was thinking about this the other day. From one perspective, yes, it's our only math curriculum for the kids using it right now. Except we added in Multiplication Facts that Stick. And the kids play Prodigy for fun. And they play games that use math naturally. And they read books with math in them. And they quiz each other for fun. And... I think that the creators of Beast Academy assume that kids do those things kind of naturally. My kids would get frustrated with a program that took too much of their time and kept them from doing all the fun learning they do, so Beast Academy works very well for them. Sometimes I see people on Facebook asking whether they should do Beast Academy or Teaching Textbooks. I assume they are looking for an online program that their kids can do without them, and I generally guess that those aren't the families who steep themselves in math naturally (though I may be wrong). In those cases I neither recommend one or the other but suggest that most kids do learn best with a human teacher or facilitator and they should look at which programs they'd do best teaching.

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7 hours ago, Not_a_Number said:

So again, this is just me personally... but I don't give questions like those starred questions until a kid is REALLY firm in all the properties of multiplication. The reason for that being that if you don't have a solid picture of what's happening, it's really easy to just apply a bunch of rules and forget about them. 

I'm sure I could give those to DD8 now and she'd blast through them. But it's just not what I do near the beginning of multiplication.

I do keep wondering if part of what happens with BA is that the kids who succeed at it mostly have already fully internalized the concepts (with or without a program, perhaps through free reading and conversations?) Like, I have a kid in my Zoom math class who is about to start out on Beast Academy 3A. In my class, she's been calculating things like 13*28 without a ton of trouble 😂. Occasionally, she gets lost in all the calculations or forgets a fact, but that's the level. 

I'm sure she'll enjoy Beast 3A, because she doesn't NEED conceptual help with any of it. And I'm glad they are doing it, since it'll deepen her understanding. But it's also not fair to say that BA is really teaching her to multiply, you know? She's already multiplying very well... 

yes but I feel like this is a comment on AOPS generally no? It’s mostly an enrichment program for kids who are learning “normal” math by daytime...

I’m shocked my DD doesn’t have more trouble with Beast. But then again, she’s doing a normal program concurrently. 

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9 minutes ago, madteaparty said:

yes but I feel like this is a comment on AOPS generally no? It’s mostly an enrichment program for kids who are learning “normal” math by daytime...

That's not how people mostly use it as homeschoolers, though. And I do think they try to sell the program as complete, whereas I'd agree with you that it works best as enrichment. 

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1 minute ago, Not_a_Number said:

That's not how people mostly use it as homeschoolers, though. And I do think they try to sell the program as complete, whereas I'd agree with you that it works best as enrichment. 

So of the small sample of homeschoolers I know of that use AOPS (which must be a very small subset of total  AOPS users) they either do the books followed by the same-content class, and/or use a tutor or some other sort of adult help with it. And I’m sure someone with a PhD in math (not you, lol) will tell me that books are written to the student and just by sleeping with the AOPS book under their pillow the content flowed. I think that’s the exception. 

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Just now, madteaparty said:

So of the small sample of homeschoolers I know of that use AOPS (which must be a very small subset of total  AOPS users) they either do the books followed by the same-content class, and/or use a tutor or some other sort of adult help with it. And I’m sure someone with a PhD in math (not you, lol) will tell me that books are written to the student and just by sleeping with the AOPS book under their pillow the content flowed. I think that’s the exception. 

I think it worked like that for @lewelma's older boy. I would guess it would have worked fine for me, but then I could learn from basically any textbook (or frankly lack thereof) like that, because I really really wanted to figure out how things worked. 

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Just now, Not_a_Number said:

I think it worked like that for @lewelma's older boy. I would guess it would have worked fine for me, but then I could learn from basically any textbook (or frankly lack thereof) like that, because I really really wanted to figure out how things worked. 

I think you’re proving my point 😉 

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3 minutes ago, madteaparty said:

I think you’re proving my point 😉 

The point being that someone will say it worked for them? I do think it works in some very exceptional cases 🙂 . I just hesitate to suggest it for people who don't totally love math.

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1 hour ago, Not_a_Number said:

I think it worked like that for @lewelma's older boy. 

It took my son at least 2 full years to be able to learn at speed from reading the AoPS textbooks. He did start young (age 9 with IntroA), but don't expect a child with no experience reading math textbooks to be able to teach themselves immediately.  

And yes, the AoPS books are written to be self teaching. This is why they are so wordy. They say in writing what a teacher would verbally say.

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On 5/29/2021 at 10:08 AM, HomeAgain said:

The only other program I've seen do that in elementary was Gattegno book 5, so if they like that I can look up the page numbers for you so they can practice how it goes further into determining squares (and then cubes) of any number by developing a formula based on already known squares (and cubes). 

I’d like to take a look, if you don’t mind! DS was doing a puzzle with squares today (a year & a half after BA 3B) & was able to recall / use this approach, so it seems to have made an impression! 

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For my older kid, it's been his only curriculum, but really a supplement to absorbing math from the ether. He's only done bits and pieces from a handful of BA/AOPS books, skipping lots of levels, but he hasn't done anything from any other book either. I bought some of the books because hard/puzzly/proof type problems have always been the only kind my kid was willing to do, and it takes more time for me to come up with that kind of problem than for him to do one (especially as he gets older). It seemed helpful that someone had gone ahead and made lots of puzzles in a useful variety of topics with written explanations of the solutions. Of the books he's used, he's mostly  just skipped around looking for interesting problems, and left the rest.

My younger kid did well with BA (parts of level 3 and 4) before deciding to go to public school. She needed to go through the sections and do more of the simpler practice problems to get it, but the concept introduction in the books worked fine for her. Certainly she was well prepared for the (very simple) public school 4th grade math.

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Posted (edited)

Perhaps a good test of whether the concepts worked or not would be to check whether a kid can do combinatorics after having used BA. Because most of the other concepts are ones that mathy kids see so often that they don't NEED BA to figure it out, anyway. 

ETA: and perhaps binary as well, if I remember that it's included correctly? But binary is much easier. 

Edited by Not_a_Number
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20 minutes ago, Not_a_Number said:

Perhaps a good test of whether the concepts worked or not would be to check whether a kid can do combinatorics after having used BA. Because most of the other concepts are ones that mathy kids see so often that they don't NEED BA to figure it out, anyway. 

ETA: and perhaps binary as well, if I remember that it's included correctly? But binary is much easier. 

Yes, BA introduces both binary (4A) & basic combinatorics (4B) like Fence Post Problems, Tree Diagrams, & Venn Diagrams. 

Those were some of DS’ favorite topics - right up there with the Logic chapter (4B) which had him doing Truth Tellers & Liars puzzles & playing Minesweeper 😅

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26 minutes ago, Shoes+Ships+SealingWax said:

Yes, BA introduces both binary (4A) & basic combinatorics (4B) like Fence Post Problems, Tree Diagrams, & Venn Diagrams. 

Those were some of DS’ favorite topics - right up there with the Logic chapter (4B) which had him doing Truth Tellers & Liars puzzles & playing Minesweeper 😅

Right. I know it introduces it, because I'm currently tutoring a kiddo who seems to have absorbed a very minimal amount from the combinatorics section 😉 . 

See, when I teach combinatorics, I figure the important thing is the multiplication principle and when it applies. If you get the multiplication principle, you're well on your way to understanding combinatorics. But almost every time I see people teach this, they blow past the multiplication principle really quickly as if there's nothing to see there... 

That's how I feel about "conceptual" programs in a nutshell. They may be conceptual, but part of what that means is that they think the concepts are easy and don't require much effort. 

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I'd say combinatorics can come from the ether for mathy kids as well. BA 4 weren't books my mathy kid ever used, but he's certainly used factorials, and probability calculations come up all the time in regular geeky kid life (role playing, board games, etc...). Binary and alternate base math come up too. Not sure how his skills compare to those of a kid who'd seen that in a book, but think it'd be hard to find a concept in any math curriculum you'd be sure couldn't have come from life/conversation/youtube, especially for anything in elementary math.

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Posted (edited)
54 minutes ago, Not_a_Number said:

Right. I know it introduces it, because I'm currently tutoring a kiddo who seems to have absorbed a very minimal amount from the combinatorics section 😉 . 

Sorry if that was unclear, I meant to quote only the ETA regarding binary (confirming that you were, in fact, correct).

I mentioned the coverage of combinatorics simply because I know you personally haven’t used the upper levels of BA, & I wasn’t sure whether what was covered there was what you would have expected to be covered or not (either more or less).

ETA: I will say that combinatorics are not, to my knowledge, one of the topics that is continually reinforced throughout later levels in the same way that some other topics are. If that student ever only worked through that one section & never touched on the topic again I’m not surprised that they don’t recall much. 

Edited by Shoes+Ships+SealingWax
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36 minutes ago, mckittre said:

I'd say combinatorics can come from the ether for mathy kids as well. BA 4 weren't books my mathy kid ever used, but he's certainly used factorials, and probability calculations come up all the time in regular geeky kid life (role playing, board games, etc...). Binary and alternate base math come up too. Not sure how his skills compare to those of a kid who'd seen that in a book, but think it'd be hard to find a concept in any math curriculum you'd be sure couldn't have come from life/conversation/youtube, especially for anything in elementary math.

If you’re the kind of kid who just ponders explanations until they make sense, anything works. The problem is that it’d be great for the other 98% of kids (some of whom are actually very mathy, just less motivated!) to be educated well, too.

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30 minutes ago, Shoes+Ships+SealingWax said:

Sorry if that was unclear, I meant to quote only the ETA regarding binary (confirming that you were, in fact, correct).

I mentioned the coverage of combinatorics simply because I know you personally haven’t used the upper levels of BA, & I wasn’t sure whether what was covered there was what you would have expected to be covered or not (either more or less).

ETA: I will say that combinatorics are not, to my knowledge, one of the topics that is continually reinforced throughout later levels in the same way that some other topics are. If that student ever only worked through that one section & never touched on the topic again I’m not surprised that they don’t recall much. 

You’re right that it’s not reinforced much and that this is the issue. Honestly, that’s the thing — elementary math, especially if you don’t try terribly hard to connect it to algebra by generalizing it, only has a small number of concepts. Most things one can do with kids who pick up the concepts easily will work.

But the reason I talk about actually being mindful of mental models is that this approach winds up backfiring pretty badly by higher math. There aren’t going to BE 6 years of reinforcement for most concepts like there are for place value, addition, and subtraction. You can’t treat all concepts like they don’t require time and integration into one’s thinking and hope for good results...

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I’m afraid that I have to disagree with your comment that “anything will work” for a kid who enjoys playing with & pondering mathematical concepts. What drove us to find BA is that other programs (good, solid, well-respected programs) were not working for him. It didn’t matter how much I accelerated or condensed them, they just weren’t interesting.

He went from being good at, but “meh” about, math to LOVING it with the right fit. He didn’t always play with concepts the way he does now or seek out other resources. That came after finding BA. It got him excited in a way nothing else had been able to.

I think that’s what many who sing BA’s praises are reacting to. Not that it’s the best thing out there for every kid, or every mathy kid, or whatever. But that for some kids it changes the game entirely. 

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10 minutes ago, Not_a_Number said:

If you’re the kind of kid who just ponders explanations until they make sense, anything works. The problem is that it’d be great for the other 98% of kids (some of whom are actually very mathy, just less motivated!) to be educated well, too.

Of course. My example doesn't contradict the point. I was just saying that it's nearly impossible to point to any curriculum as the sole factor in understanding or lack of understanding a concept, since most important concepts come up in many places without specific study. Especially for elementary school math. So you never know if anything works in any curriculum, since you can only tell when a kid doesn't understand something. You'd need some kind of valid random sample of kids who'd used different curriculums (thoroughly and as designed) to look for gaps.  Lacking that, all we have is a zillion anecdotes of individual kids that are thoroughly contaminated by casual outside-of-curriculum exposure.

Even my less mathy kid found public school 4th grade math quite easy (it does seem much easier than BA) without doing much more curriculum in her life than a couple of the BA3 books and part of one BA4 book. Also, some kids are incredibly boredom averse (I was like this, so is my older more-mathy kid), and asking them to do anything that seems easy or straightforward for the sake of practice is a battle not worth fighting. I suspect the authors of those books were kids like that.

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5 minutes ago, Shoes+Ships+SealingWax said:

I’m afraid that I have to disagree with your comment that “anything will work” for a kid who enjoys playing with & pondering mathematical concepts. What drove us to find BA is that other programs (good, solid, well-respected programs) were not working for him. It didn’t matter how much I accelerated or condensed them, they just weren’t interesting.

He went from being good at, but “meh” about, math to LOVING it with the right fit. He didn’t always play with concepts the way he does now or seek out other resources. That came after finding BA. It got him excited in a way nothing else had been able to.

I think that’s what many who sing BA’s praises are reacting to. Not that it’s the best thing out there for every kid, or every mathy kid, or whatever. But that for some kids it changes the game entirely. 

That approach would have helped me as a kid, especially as a teenager. I was always good at math, but stopped after calculus in college, because I found it an easy A, but mind-numbingly boring. Learn algorithm, plug in numbers, learn next algorithm, etc...

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18 minutes ago, Shoes+Ships+SealingWax said:

I’m afraid that I have to disagree with your comment that “anything will work” for a kid who enjoys playing with & pondering mathematical concepts. What drove us to find BA is that other programs (good, solid, well-respected programs) were not working for him. It didn’t matter how much I accelerated or condensed them, they just weren’t interesting.

He went from being good at, but “meh” about, math to LOVING it with the right fit. He didn’t always play with concepts the way he does now or seek out other resources. That came after finding BA. It got him excited in a way nothing else had been able to.

I think that’s what many who sing BA’s praises are reacting to. Not that it’s the best thing out there for every kid, or every mathy kid, or whatever. But that for some kids it changes the game entirely. 

 

12 minutes ago, mckittre said:

That approach would have helped me as a kid, especially as a teenager. I was always good at math, but stopped after calculus in college, because I found it an easy A, but mind-numbingly boring. Learn algorithm, plug in numbers, learn next algorithm, etc...

 

Right. That's fair. It's true that as a former math contest kid who LOVED puzzles and was brought up on Martin Gardiner's books, I do think that puzzles and things like that make math more interesting and more fun for mathy kids. Maybe it's mostly that I feel like that's a much easier problem -- if you give mathy kids fun, challenging problems that require deep thought, they'll enjoy math a lot more. I've always known that. 

I'm somehow more interested in how to educate everyone else, because it seems trickier. And I'm also interested in how to communicate that math is a way of thinking about the world to people, because as you say, @mckittre, lots of people seem to think of it as a collection of algorithms, which is just... not the point. 

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I think I'm also thinking about this from my personal perspective -- I wound with a pair of highly mathematically gifted kids who are NOT excited by random puzzles in the least. They aren't like me in this way, and yet their ceiling for math achievement is very high. So I've had to think about how to educate them to live up to their potential WITHOUT counting on them spending time on math on their own time -- that they won't do. 

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43 minutes ago, Not_a_Number said:

I've had to think about how to educate them to live up to their potential WITHOUT counting on them spending time on math on their own time -- that they won't do. 

I wonder if you’re expecting a bit too much ownership of the exploration for their ages. Mathy games / puzzles / art projects / novels, are things we do together. Aside from initiating mathy conversations, he doesn’t just do this stuff independently.

If I didn’t provide the materials & invite him to join me, the play largely wouldn’t happen. He isn’t that driven. He genuinely enjoys it while we’re doing it, asks to continue the novels once we’ve begun them, is disappointed if I try to schedule a “break” from BA, etc... but he’s still 8. Left entirely to his own devices he’d spend all day playing video games & chasing his friends with Nerf guns 😆  

The same goes for his interest in poetics. He loves word play. We read poems every day & he balks if I try to exclude them. He quotes Carroll with some regularity & is slowly memorizing The Walrus & the Carpenter. He enjoys literary devices - especially puns & alliteration. But he isn’t reading books of poetry (or writing works of his own) in his free time.

If you set up a math game, present a logic puzzles to solve together, leave an interesting problem up on a white board, etc... do they enjoy that? Do they like working on the math you have curated for them, or could they take it or leave it? 

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46 minutes ago, Shoes+Ships+SealingWax said:

If you set up a math game, present a logic puzzles to solve together, leave an interesting problem up on a white board, etc... do they enjoy that? Do they like working on the math you have curated for them, or could they take it or leave it?

No, they don’t like it that much. They get a sense of accomplishment when they succeed (I’ve frankly found that most kids do), but if I left a puzzle on a board, it wouldn’t get done unless I pushed. DD8 asked to play Prime Climb a few times, I guess? That may be as far as it goes. They just aren’t all that into games or into puzzles — this includes non-mathy games and jigsaw puzzles.

I wasn’t at all like this as a kid, so I am making a real distinction. And yet my kids are very, very capable mathematical learners... so then there’s the question of how to educate kids who will not make conceptual progress outside of class time but whose ceiling is very high. And personally, I find that a fascinating question. 

 

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