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Elements of Mathematics: Foundations reviews? (x-posted)


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I'm getting no response over on the Logic/Middle Grade board, and Roadrunner remembered having seen chatter here regarding IMACS in the past, so...

Can anyone give me a recent review of Elements of Mathematics: Foundations?  I've seen a few people reference it recently, but the only in-depth reviews/discussions of it I can find are from 5+ years ago.  As a parent who is floundering to teach AoPS and can't afford the online classes, I am wondering if EMF is a possible alternative--still unique and challenging, but not quite as expensive as AoPS online.  ODS loves math and wants something challenging that requires creative thinking.  His greatest fear is that I'll switch him to something straightforward and math won't be fun anymore (his words).  At the same time, DH is concerned that the Institute for Mathematics and Computer Science (IMACS, the course creator) is for-profit and thus the course is not rigorous or high-quality.  There's got to be SOME middle ground between AoPS and a standard slate of courses.  Right?  Right?  *crickets*

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2 hours ago, eternallytired said:

At the same time, DH is concerned that the Institute for Mathematics and Computer Science (IMACS, the course creator) is for-profit and thus the course is not rigorous or high-quality.  There's got to be SOME middle ground between AoPS and a standard slate of courses.  Right?  Right?  *crickets*

I don't have personal experience with EIMACS, but I'm pretty sure your DH is wrong and they are a legit organization.  I vaguely recall reading positive reviews and hearing praises from friends of mine, but we are AoPS frequent fliers.  

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1 hour ago, Not_a_Number said:

No knowledge of this, but following 🙂 .

 

32 minutes ago, daijobu said:

I don't have personal experience with EIMACS, but I'm pretty sure your DH is wrong and they are a legit organization.  I vaguely recall reading positive reviews and hearing praises from friends of mine, but we are AoPS frequent fliers.  

You two look strangely familiar...  🙂  It's been a looong time since I've been on these boards, and I'd forgotten how fun it is to see the same "faces" from one thread to another.

The frustrating thing for me is that a general Google search seems to only turn up EMF results from the IMACS page (besides the really old WTM threads and one reference to a Florida school system that uses the program).  They are listed on Davidson's, which I thought held some weight, but DH says that if that's the only reference out there, it makes him think there's some promotional deal.  And I do agree that it's fishy, especially given the fact that I can find numerous references to pretty much any other program I ever search for.

I'm hoping that we will have passed our two rough patches for this AoPS book and can continue on in bliss hereafter (with a little help from Not_a_Number on occasion!), but I want to have done some research in case I do end up jumping ship after this year.

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I've read of people using it on various message boards and the feedback has always been positive. I remember that a poster on this board's son used it. I don't think the people running it are in it for the money.

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EMF/ imacs is a legitimate organization. There are other "accelerated" boards where it is more widely discussed. 

EMF is based on the same "new math" curriculum as Project MEGSS, but is online and doesn't require a teacher. 

You start at the beginning and go through the courses. It was still being built when dd was at the typical math level for entrance, so she didn't start EMF until she was otherwise doing Algebra 2. There is a fair amount of discrete math and abstract algebra topics in the "prealgebra" topics. Dd did the first 6 classes or so before moving onto the University Computer Science (which she just started). She liked it, but basically made a choice based on her available hours in the week and wanted the UCS1 class.

As for boring vs regular math, we've always done two maths. We did Singapore/ Foerster/ Holt/ Derek Owens/ Blue Tent + always had a second thread of fun math going.

Dd never liked AoPS, although we've dipped in and out a couple of times and did a short online class. She says she feels like AoPS makes simple concepts tricky on purpose, but imacs makes hard math accessible. To be fair, she can be very frustrated by problems in EMF, too. She's not a speedy math student and likes to go deep. She has a surprising math intuition, and is willing to work hard at it, but it's not her only jam. 

ETA good call tagging me. I haven't been on the Logic Stage Boards in years, and I don't come over here unless something catches my eye in the latest topics. 

Edited by MamaSprout
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16 hours ago, eternallytired said:

I'm getting no response over on the Logic/Middle Grade board, and Roadrunner remembered having seen chatter here regarding IMACS in the past, so...

Can anyone give me a recent review of Elements of Mathematics: Foundations?  I've seen a few people reference it recently, but the only in-depth reviews/discussions of it I can find are from 5+ years ago.  As a parent who is floundering to teach AoPS and can't afford the online classes, I am wondering if EMF is a possible alternative--still unique and challenging, but not quite as expensive as AoPS online.  ODS loves math and wants something challenging that requires creative thinking.  His greatest fear is that I'll switch him to something straightforward and math won't be fun anymore (his words).  At the same time, DH is concerned that the Institute for Mathematics and Computer Science (IMACS, the course creator) is for-profit and thus the course is not rigorous or high-quality.  There's got to be SOME middle ground between AoPS and a standard slate of courses.  Right?  Right?  *crickets*

Also, the first class is free right now because of Covid. They do require a placement test. Dd had done some advanced topics and finished the first course in 2 weeks and second course pretty quickly, too. We had gotten the first course during a summer discount, so I was glad of that.

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1 minute ago, Not_a_Number said:

Yeah, I’ve looked. I can’t tell how deep they go from these descriptions.

Can't help you there. I have an old thread saved somewhere from Tagmax that details AoPS vs. EMF/ MEGSSS, but that was years ago and is not on this computer.

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Here’s the course description for the first course:


”This course covers modular arithmetic using secret codes and online games. Learn about operational systems and their properties (commutativity, associativity, neutral elements, invertibility) by building interactive machines and evaluating non-numeric operations. Get a solid introduction to the concepts of least common multiple and greatest common divisor, as well as to the geometric notions of midpoint and reflection.”

 

It is very hard for me to tell what they do in this class from this! We haven’t done mods at all yet, but we’ve talked about other stuff they mention. I’m also curious whether they scaffold the ideas with intuitions kids have from integers or not, or if it’s presented as totally new and mysterious... 

Basically, I’m having trouble evaluating. It seems neat, but that’s all I can tell.

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7 minutes ago, Not_a_Number said:

Here’s the course description for the first course:


”This course covers modular arithmetic using secret codes and online games. Learn about operational systems and their properties (commutativity, associativity, neutral elements, invertibility) by building interactive machines and evaluating non-numeric operations. Get a solid introduction to the concepts of least common multiple and greatest common divisor, as well as to the geometric notions of midpoint and reflection.”

 

It is very hard for me to tell what they do in this class from this! We haven’t done mods at all yet, but we’ve talked about other stuff they mention. I’m also curious whether they scaffold the ideas with intuitions kids have from integers or not, or if it’s presented as totally new and mysterious... 

Basically, I’m having trouble evaluating. It seems neat, but that’s all I can tell.

It's taught in a pretty hands-on kind of way initially (using clocks and such).

A lot of their stuff is taught in a more concrete transitioning into abstract way, which is why it was probably a good fit for my Singapore kid. She found their method really intuitive for her. They lead with proofs and then kind of back into the concept from there. Not sure if that makes sense? It was completely hands off for me. It needed to be her thing.

 

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3 minutes ago, MamaSprout said:

It's taught in a pretty hands-on kind of way initially (using clocks and such).

A lot of their stuff is taught in a more concrete transitioning into abstract way, which is why it was probably a good fit for my Singapore kid. She found their method really intuitive for her. They lead with proofs and then kind of back into the concept from there. Not sure if that makes sense? It was completely hands off for me. It needed to be her thing.

 

I’ve had good luck with “concrete transitioning to abstract” teaching in general, so that does sound appealing. I’m not quite sure how leading with proofs then back into the concept works, but thanks for explaining what you remember!! 

I’ll have to keep it in mind if we ever want to outsource math more. I use lots of AoPS topics and occasionally their questions but I don’t think I’ll want to use the programs as written except as review....

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If you have something that works for you, then stick with it. AoPS didn't work for us, EMF and imacs does. ~shrug~

 

We're almost a different "generation" of homeschoolers, though. When dd was ready for prealgebra, the AoPS book had just come out, and most of the then current AoPS users didn't like it, so we just went with Derek Owens and some contest books for fun. There was maybe a half of a level of Beast Academy out before dd hit prealgebra. We did a lot of fun math explorations with books nobody talks about anymore. The focus is just different now, and AoPS is what everyone knows. If it works, great. But if it doesn't, that doesn't mean kiddo isn't good at math.

We still live in a place where it is almost impossible to find math contests or activities, and when we do find them, dd is almost always the only girl in room.

We're homeschool dinosaurs, I guess, and that's okay.

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46 minutes ago, MamaSprout said:

If you have something that works for you, then stick with it. AoPS didn't work for us, EMF and imacs does. ~shrug~

We're almost a different "generation" of homeschoolers, though. When dd was ready for prealgebra, the AoPS book had just come out, and most of the then current AoPS users didn't like it, so we just went with Derek Owens and some contest books for fun. There was maybe a half of a level of Beast Academy out before dd hit prealgebra. We did a lot of fun math explorations with books nobody talks about anymore. The focus is just different now, and AoPS is what everyone know. If it works, great. But if it doesn't, that doesn't mean kiddo isn't good at math.

We do our own thing. I’m very familiar with the AoPS books through work, but I don’t think of them as the epitome of rigor or anything. 

Right now, we don’t use any curriculum, and that’s the plan for the foreseeable future. I am always interested in options, though.

 

46 minutes ago, MamaSprout said:

We still live in a place where it is almost impossible to find math contests or activities, and when we do find them, dd is almost always the only girl in room.

Yeah, I was often the only girl in the room in math stuff, and even more so at the highest levels.

 

46 minutes ago, MamaSprout said:

We're homeschool dinosaurs, I guess, and that's okay.

Hah. I sometimes feel like I’d fit in better in a different era of homeschooling, although I really appreciate all the social opportunities that come with it in being mainstream.

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4 hours ago, MamaSprout said:

Also, the first class is free right now because of Covid. They do require a placement test. Dd had done some advanced topics and finished the first course in 2 weeks and second course pretty quickly, too. We had gotten the first course during a summer discount, so I was glad of that.

I noticed that, so I'm really tempted to have him try it and see what he'd think.  But he is SUCH a plodder that I worry that derailing him with a separate curriculum will just mean that we'll just be that much further behind eventually if we continue AoPS.  (He started the BA books two grade levels ahead, but he's slowly lost ground and is now doing AlgA on grade level because he is not a speedy worker.)  I think I need to let go of my mental calendar...

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10 minutes ago, eternallytired said:

I noticed that, so I'm really tempted to have him try it and see what he'd think.  But he is SUCH a plodder that I worry that derailing him with a separate curriculum will just mean that we'll just be that much further behind eventually if we continue AoPS.  (He started the BA books two grade levels ahead, but he's slowly lost ground and is now doing AlgA on grade level because he is not a speedy worker.)  I think I need to let go of my mental calendar...

Yep. Let it go, especially if he's still in middle school. What are your goals for AoPS? For math in general? Let it be fun.

That's one of the reasons we always did two tracks of math. I knew she was solid on the foundational stuff without bunches of repetition, and she still had time to go deep.

We wouldn't be as far along sequentially if EMF or AoPS had been her only math in middle school, but because she wanted to get to calc-based physics, we just kept moving forward. She didn't care that Richard Rusczyk said it was bad. 🙃

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55 minutes ago, MamaSprout said:

We wouldn't be as far along sequentially if EMF or AoPS had been her only math in middle school, but because she wanted to get to calc-based physics, we just kept moving forward. She didn't care that Richard Rusczyk said it was bad. 🙃

I don’t think he said that was bad. Just that not doing more uncommon types of math along the way was a bad idea. It sounds like she did both.

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1 hour ago, eternallytired said:

I noticed that, so I'm really tempted to have him try it and see what he'd think.  But he is SUCH a plodder that I worry that derailing him with a separate curriculum will just mean that we'll just be that much further behind eventually if we continue AoPS.  (He started the BA books two grade levels ahead, but he's slowly lost ground and is now doing AlgA on grade level because he is not a speedy worker.)  I think I need to let go of my mental calendar...

How old is he again?

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2 hours ago, MamaSprout said:

Oh, I've read it, lol. How could I have not?!! 😛 But you must know the kind of student/parent he means!

Richard has a serious following, doesn't he? I have the feeling the company kind of has a mythos around him, too. 

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3 hours ago, Not_a_Number said:

How old is he again?

He's 12.  By age, he'd be a sixth grader.  He started BA3 in first grade after having flown through RS B&C in kindy and requesting "hard" math.  He was doing pretty well at getting through a year of BA in a calendar year (we probably lost six months over the course of BA3-5), but PreA took 18 mos, and he's ten mos into Intro to Alg and still finishing chapter 10.  Since the AoPS classes go so quickly, it makes me feel like we're falling waaay behind.  I'm trying to remind myself that I'm more concerned about mastering the material than speeding ahead, but I'm not always successful at convincing myself that I'm not failing him by not pushing him to move at a more normal clip.  (Can you tell that I overthink pretty much every area of my life?)

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3 minutes ago, eternallytired said:

He's 12.  By age, he'd be a sixth grader.  He started BA3 in first grade after having flown through RS B&C in kindy and requesting "hard" math.  He was doing pretty well at getting through a year of BA in a calendar year (we probably lost six months over the course of BA3-5), but PreA took 18 mos, and he's ten mos into Intro to Alg and still finishing chapter 10.  Since the AoPS classes go so quickly, it makes me feel like we're falling waaay behind.  I'm trying to remind myself that I'm more concerned about mastering the material than speeding ahead, but I'm not always successful at convincing myself that I'm not failing him by not pushing him to move at a more normal clip.  (Can you tell that I overthink pretty much every area of my life?)

OK, there's no way he's way behind if he's by age in 6th grade and working on Intro to Algebra 😉 . In fact, it's possible part of the issue he's having is that on average, kids who take this class are a bit older, and therefore, he might have trouble with some of the "keeping work organized" parts as much as the math parts. 

What I'd probably suggest is going forward even if you can't get a starred problem, but not giving up on those -- come back to them as review, ask me for hints, whatever. That way, you can pick up the pace a bit, and you can also keep working on the hard stuff. 

I will say that letting stuff marinate often really helps your brain figure things out. See if you can get him to think of that not as "giving up" but as "letting your brain work on it while you sleep." 

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3 minutes ago, Not_a_Number said:

OK, there's no way he's way behind if he's by age in 6th grade and working on Intro to Algebra 😉 . In fact, it's possible part of the issue he's having is that on average, kids who take this class are a bit older, and therefore, he might have trouble with some of the "keeping work organized" parts as much as the math parts. 

...

I will say that letting stuff marinate often really helps your brain figure things out. See if you can get him to think of that not as "giving up" but as "letting your brain work on it while you sleep." 

Well, I thought he was doing fine at Intro to Alg in 6th, but according to the AoPS website, that's right on target.  By their schedule, he should be finishing the book this semester (or doing C&P and finishing it next semester).  This is why I stopped going to forums and reading blogs for several years: it just gets me totally stressed out.  (On the other hand, it can also help with suggestions and advice, like now, so...)

Your comment about letting it marinate is actually rather perfect, since my DH (whose brain works similarly to ODS') actually says that works for him.  He's regularly told me that "sleeping on it" often does help him solve things.  For me, it just means I lose sleep...  Thanks for the advice!

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Just now, eternallytired said:

Well, I thought he was doing fine at Intro to Alg in 6th, but according to the AoPS website, that's right on target.  By their schedule, he should be finishing the book this semester (or doing C&P and finishing it next semester).  This is why I stopped going to forums and reading blogs for several years: it just gets me totally stressed out.  (On the other hand, it can also help with suggestions and advice, like now, so...)

Oh, just ignore their schedule 😛 . I've seen kids dutifully go through the motions of finishing their courses without understanding them, and I really don't approve. The important thing is him understanding and retaining the concepts. If we keep in touch on here when you guys get stuck, I promise I'll keep an eye on the standard things that trip kids up 🙂 . 

 

Just now, eternallytired said:

Your comment about letting it marinate is actually rather perfect, since my DH (whose brain works similarly to ODS') actually says that works for him.  He's regularly told me that "sleeping on it" often does help him solve things.  For me, it just means I lose sleep...  Thanks for the advice!

No problem! I'm curious: does it never work for you? I remember solving contest problems as I was falling asleep in high school 😄 

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1 hour ago, eternallytired said:

Well, I thought he was doing fine at Intro to Alg in 6th, but according to the AoPS website, that's right on target.  By their schedule, he should be finishing the book this semester (or doing C&P and finishing it next semester).

There are lots and lots of stories on here of accelerated kids taking 2 years to thoroughly and carefully go through AoPS pre-algebra. I agree with the wise women on here—definitely don’t rush this one.

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16 hours ago, MamaSprout said:

Dd never liked AoPS, although we've dipped in and out a couple of times and did a short online class. She says she feels like AoPS makes simple concepts tricky on purpose, but imacs makes hard math accessible. To be fair, she can be very frustrated by problems in EMF, too. She's not a speedy math student and likes to go deep. She has a surprising math intuition, and is willing to work hard at it, but it's not her only jam. 

I am intrigued by this. I like AoPS a lot, but also really like the idea of making hard math accessible. I love discovery based math, but also have kids who sometimes just do better with direct, clear instruction. I am definitely going to keep an eye on this thread for the future and hope that it gets updated as folks give it a try. 😉 

2 hours ago, eternallytired said:

Your comment about letting it marinate is actually rather perfect, since my DH (whose brain works similarly to ODS') actually says that works for him.  He's regularly told me that "sleeping on it" often does help him solve things.  For me, it just means I lose sleep...  Thanks for the advice!

Ha ha - I definitely kept pen and paper next to my bed during grad school. I'd say that 70% of what I wrote down was pure bull and I looked at it and wondered what I was thinking the next morning. But the other 30% was pure gold and all the biggest results in my dissertation came from those night time wakings to jot down proof ideas. 

31 minutes ago, rzberrymom said:

There are lots and lots of stories on here of accelerated kids taking 2 years to thoroughly and carefully go through AoPS pre-algebra. I agree with the wise women on here—definitely don’t rush this one.

Yes, I just had a kiddo take almost 18 months to work through pre-algebra. He didn't do the book problems because there was no possible way he could've kept work like that organized (major EF challenges) and I have three other 2E kids (so no way *I* could've kept his work organized) -- it was all I could do to make sure he had paper and pencil for scratch work when he sat down for math (and even that was pretty hit or miss...) Instead, he read the entire book on his own, section by section, working through Alcumus, reading every solution, and got all bars blue while set to "insanely hard," which was my version of getting him to do some star level problems. He missed a TON of problems - I think his "percent correct" is something like 60%. But he's a kid that learns from mistakes and from reading solutions, so he'd often do something wrong, wrong, wrong, wrong, wrong, wrong, and then things would start to click and it'd change to right, right, right, you know? Not a great record if I had to go on "total percent correct," but I don't really care how poorly he started off, so long as he's solid by the end... 😄

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9 hours ago, eternallytired said:

Well, I thought he was doing fine at Intro to Alg in 6th, but according to the AoPS website, that's right on target.  By their schedule, he should be finishing the book this semester (or doing C&P and finishing it next semester).  This is why I stopped going to forums and reading blogs for several years: it just gets me totally stressed out.  (On the other hand, it can also help with suggestions and advice, like now, so...)

Your comment about letting it marinate is actually rather perfect, since my DH (whose brain works similarly to ODS') actually says that works for him.  He's regularly told me that "sleeping on it" often does help him solve things.  For me, it just means I lose sleep...  Thanks for the advice!

The ages on the AoPS website are the earliest they recommend using those. NOT recommended ages. Back in the dark ages a lot of students used those books after or alongside whenever they did the regular courses. Math has become this weird arms race, and not how the books were originally intended.

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7 hours ago, 4KookieKids said:

I am intrigued by this. I like AoPS a lot, but also really like the idea of making hard math accessible. I love discovery based math, but also have kids who sometimes just do better with direct, clear instruction. I am definitely going to keep an eye on this thread for the future and hope that it gets updated as folks give it a try. 😉 😄

EMF is probably more discovery-based than AoPS. ETA It's more "concrete" in the sense that they are sometime manipulating physical representations of what they are learning, but dd is still discovering what the names of things are (in Calc BC) that she knows intuitively from the earlier EMF classes. She occasionally misses questions in class because what the teacher is trying teach is just "common sense" to her.

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1 hour ago, MamaSprout said:

EMF is probably more discovery-based than AoPS. ETA It's more "concrete" in the sense that they are sometime manipulating physical representations of what they are learning, but dd is still discovering what the names of things are (in Calc BC) that she knows intuitively from the earlier EMF classes. She occasionally misses questions in class because what the teacher is trying teach is just "common sense" to her.

Oh wow- I will definitely look into it more. My three autistic kiddos definitely do better with concrete first. I wonder why AoPS is the main program I hear about for discovery based, math loving kiddos? Oh well.  Thank you so much!

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43 minutes ago, 4KookieKids said:

Oh wow- I will definitely look into it more. My three autistic kiddos definitely do better with concrete first. I wonder why AoPS is the main program I hear about for discovery based, math loving kiddos? Oh well.  Thank you so much!

imacs/ emf does a really bad job of talking about what they do. I've emailed with them about it, but it just isn't important to them.

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1 hour ago, 4KookieKids said:

Oh wow- I will definitely look into it more. My three autistic kiddos definitely do better with concrete first. I wonder why AoPS is the main program I hear about for discovery based, math loving kiddos? Oh well.  Thank you so much!

Please keep us updated if you try it out! I'd love to hear more detail about WHAT exactly they do. 

I think AoPS is better known just because they are much bigger and because the classes have a teacher component. 

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16 minutes ago, Not_a_Number said:

Please keep us updated if you try it out! I'd love to hear more detail about WHAT exactly they do. 

I think AoPS is better known just because they are much bigger and because the classes have a teacher component. 

Will do. DS is in ch 2 of AoPS Algebra now, plugging along at his own pace. I confess that EMF seems a bit pricey to me, given that I have a math background and can offer an awful lot of help myself (all we pay for with AoPS is the textbook itself)... But I also recognize it's probably about on par (or even less) than many "deeper" options. I'm thinking of giving him the placement just to see where he'd land, but I notice that they say to start at the beginning and work through the whole thing, regardless of background. I'd really love to get him into something that would help him write proofs, because right now, that's an area where he's really struggling and we've made no real headway.

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Just now, 4KookieKids said:

Will do. DS is in ch 2 of AoPS Algebra now, plugging along at his own pace. I confess that EMF seems a bit pricey to me, given that I have a math background and can offer an awful lot of help myself (all we pay for with AoPS is the textbook itself)... But I also recognize it's probably about on par (or even less) than many "deeper" options. I'm thinking of giving him the placement just to see where he'd land, but I notice that they say to start at the beginning and work through the whole thing, regardless of background. I'd really love to get him into something that would help him write proofs, because right now, that's an area where he's really struggling and we've made no real headway.

Need any help with the proof writing? What's he having trouble with? 

(I've always done proofs with DD8, and she slid into them very naturally by herself. So I do know about teaching little kids about proofs.) 

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10 minutes ago, Not_a_Number said:

Need any help with the proof writing? What's he having trouble with? 

(I've always done proofs with DD8, and she slid into them very naturally by herself. So I do know about teaching little kids about proofs.) 

He just can't do it. At all. Like, he has no idea what to write down. When he does write things down, they don't make much sense. Organizing work is horrible (very smart, but autistic and dysgraphic and pretty high on the adhd scales....) Last summer I sat with him 2 hours a day for five weeks straight, with a focus on proofs and write-ups, and I'm not sure he learned anything that entire five weeks. lol. I haven't tried since then, because I've just had no idea how to even try again. lol. 

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21 minutes ago, 4KookieKids said:

Will do. DS is in ch 2 of AoPS Algebra now, plugging along at his own pace. I confess that EMF seems a bit pricey to me, given that I have a math background and can offer an awful lot of help myself (all we pay for with AoPS is the textbook itself)... But I also recognize it's probably about on par (or even less) than many "deeper" options. I'm thinking of giving him the placement just to see where he'd land, but I notice that they say to start at the beginning and work through the whole thing, regardless of background. I'd really love to get him into something that would help him write proofs, because right now, that's an area where he's really struggling and we've made no real headway.

With EMF you have to start at the beginning. The placement test is to see if the program is a good fit. It's really not prealgebra. I wish they wouldn't call it that.

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21 minutes ago, 4KookieKids said:

He just can't do it. At all. Like, he has no idea what to write down. When he does write things down, they don't make much sense. Organizing work is horrible (very smart, but autistic and dysgraphic and pretty high on the adhd scales....) Last summer I sat with him 2 hours a day for five weeks straight, with a focus on proofs and write-ups, and I'm not sure he learned anything that entire five weeks. lol. I haven't tried since then, because I've just had no idea how to even try again. lol. 

I think making one's reasoning linear is hard work. To be honest, that's why I start working on it at age 4. But I know lots of people don't and still figure it out. 

I would skip the written part of this and make him linearize his verbal reasoning first. Make sure he can EXPLAIN the steps in order, even if that's not how he came up with the argument. Make him defend his logic. Poke holes in it. Start with questions that are far too easy for him, so that the frustration level is lower, but make him really work to convince you. That's how we slid easily into proofs with DD8 -- she was so used to explaining things orally that she started writing things down naturally along the way. I wasn't even particularly trying to start proofs with her... I'd just give her questions and she'd write down the kind of airtight argument she's used to giving me verbally, and voila... a proof. 

You know what I've had weirdly good luck with in terms of explaining linear reasoning? Minesweeper. My Zoom class kids requested to play it, and we've been working on marking mines and opening squares... and it's been VERY interesting to watch that DD8 is basically the only kid in the very bright class who understands what it really means to fully justify an argument. A lot of kids argue via the "there's a mine there because look, that square has a 3, and it must have LOTS of mines near it," even thought that's not really a complete argument, not when there are more than 3 squares showing. 

The nice thing about Minesweeper (and programming, and lots of automated things) is that they'll show you that your logic was incomplete without making it feel like it's only wrong because the teacher said so. Another thing that can be useful for that is actually trying to convince other kids. I don't know if you can arrange for that in the context of homeschooling, but by a few games of Minesweeper in, some of the kids are starting to call out bad logic on each other's parts, in the "Wait! You can't be sure there's a mine there! What if the two mines are in other squares? We'll blow up!" kind of way. 

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1 minute ago, 4KookieKids said:

Ha ha, thanks for the minesweeper hint. That sounds like a fun way to practice logic!

I had him take the aptitude test and signed him for the freebie EMF course. I figured it can't hurt and will be interesting to see what happens. 🙂 

Please report back, preferably with screenshots!! 

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7 hours ago, Not_a_Number said:

 

You know what I've had weirdly good luck with in terms of explaining linear reasoning? Minesweeper.  

Wow, I've been on these boards for years, and this is probably the first recommendation for Minesweeper.  But it totally makes sense as a way to train logic and rhetoric when played as a group.  

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1 hour ago, daijobu said:

Wow, I've been on these boards for years, and this is probably the first recommendation for Minesweeper.  But it totally makes sense as a way to train logic and rhetoric when played as a group.  

Honestly, I thought it would be totally useless as a math game!! The kids asked for it, I thought it'd be a fun feat to code a text-based version in Asymptote (I've gone slightly insane and am coding games in Asymptote that we play via screen share, because over my years doing the math class and working at AoPS, I've build up a huge library which is very convenient to use), and I thought it'd be a fun occasional break from "real" math games. 

And then we played it. And I realized it was NOT useless and was in fact the best thing I had ever used for training their logic. I was kind of amazed. 

Edited by Not_a_Number
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7 minutes ago, 4KookieKids said:

Gosh, so ds is about 1/8th of the way through the first EMF course, and he LOVES it so far. Says it's the best "math game" he's ever had. lol. So far, it's all sorts of cryptography and modular arithmetic sort of stuff. 

Oooh. Screenshots, please!! Or just pictures from a phone? 

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1 minute ago, 4KookieKids said:

Ha ha, he forgot my instruction to take them, but I'll grab some tomorrow!

Please! I'm super curious. Mostly so I can steal their ideas as opposed to sign DD8 up (she's already totally proficient at proofs and in fact kind of resists using any formula she can't prove herself), but it sounds like a very interesting program, and I'd love to compare notes and intuitions with it. 

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