Tell me how all these math options fit together please!

[4KookieKids]

So I understand that *most* folks use one of: Singapore, Miquon, MEP, Saxon, etc. (all those "normal" curricula). And I understand that BA is sometimes used as a stand-alone and sometimes as the primary curriculum. And I understand that AoPS is what often comes after those are done. But I don't understand where everything else fits in! So what is usually done with stuff like Penrose, Zaccaro, Borac, Moems, Hard Math, etc.? Is it used in addition to everything else? And if so, is the content substantially different from everything else? Is it used to slow kids down so they're not hit with AoPS before they're mature enough to handle it? I guess I'm just not really understanding how it all comes together and I'd love to learn more! :)

 

Right now I have a kiddo who's an average reader but loves math and I'm trying to find something more "fun" for him. I'd love something that covered things like sequences and series, tilings/tesselations, graph theory, combinatorics, number theory, etc. in a way that he could read and enjoy. He's almost 8 and uses BA as his bedtime reading (he's only in the 3D practice book, but reads the guides through 5D an awful lot. lol). He's also finishing up Singapore 4B soon. I considered Zaccaro, but it doesn't really seem like it has much "fun" or new stuff for him to enjoy, once you cover sequences. I considered Hard Math, but after reading ElmerRex's review of it, decided it was not of an appropriate rigor to let ds read on his own.

 

Of course, having a phd in math means that I can cover pretty much anything I want with him, any time he wants. So recently he sat down to figure out all the primes 1-100 and see how many there were. Then he decided to see if there were the same number from 101-200, which led him to also consider 201-300. We ended up in a conversation about the prime number theorem and the twin prime conjecture. We've also covered (on the fly, whenever it came up) some graph theory, coding theory, and cryptography, with a basic explanation of modular arithmetic (enough to discuss cryptography, at least). But I'd really like something that he could just read on his own for fun as well, and I don't want to waste a bunch of our money in the process of trying to find the right fit.

 

I don't really want fun ways to do the same standard curriculum - I really want things that aren't even in the standard curriculum (but done well and rigorously - I don't mind things that are somewhat incomplete, but I can't handle anything being incorrect).Any ideas?

ETA: LoF did not hold his interest much past Dogs.

Edited June 7, 2017 by deanna1ynne

[Mike in SA]

If he is devouring BA, you probably don't need a whole lot of extras.  When he finishes BA5, he's probably ready for AoPS Prealgebra.  You can take it as slow as is needed.

 

We're also a math family, so I guess we shouldn't be surprised that both boys are pretty good at math.  With the older one, we took him through multiple programs for each course, because he races through and then comes back for mastery (big picture to details).  However, we just stuck with college texts and a sprinkling of high school texts.  He's headed to 10th grade, and planning on Calc III + Linear Algebra through a college next year.

 

For the younger one - who started to teach himself algebra at 6 - we've taken a different approach.  He works until he understands a topic, so we don't have to repeat topics very often.  Instead, we have layered in a geometry/pure track (Jurgensen Geometry/Kiselev Planimetry/Kiselev Stereometry/Mathematics of Relativity; Vector Space Geometry next year) and an analysis track (AoPS algebras; AoPS precalculus next year) simultaneously.  We will add in Gelfand's trigonometry next year for extra depth.  This has worked well for him since he wants to study cosmology.

 

If you have a patient kid who is willing to experiment, and you don't mind a little challenge, I highly recommend layering in Kiselev and possibly Gelfand.  Otherwise, just BA/AoPS is fine. 

 

There's no race, but no need to forcibly slow a kid, either.  Let him be happy with his pace, and you'll be happy, too.

[Jackie]

When my daughter was younger and still in RightStart, we did things like Penrose and Zaccaro and similar in addition to add depth, challenge, and complexity to RS.

 

When Beast ended up being too much to dive into when we left RS behind, we spent most of a year doing only the supplementary-type stuff you listed above. Plus a lot of math games.

 

Now that Beast is her "full time" math, we take breaks to work on the other stuff purely for variety. Beast has enough of the challenge and out-of-the-box thinking that I no longer feel the *need* to add in all the rest of it. However, if we hit a topic that is making DD bang her head against the desk, we take a break from it and pull out one of the other options on the shelf. She also just plain likes variety, so sometimes we'll grab one of the other books because she wants a break from one way of thinking. Or sometimes we hit the end of a chapter a week before we mean to take a vacation, and I'd rather not start a chapter and then take a big break in the middle, so we pull another option off the shelf.

 

There is sometimes repetition. We don't do the repetition, unless it's something DD specifically needs more practice on. This does mean half-finished things cluttering up the shelves.

[Arcadia]

So recently he sat down to figure out all the primes 1-100 and see how many there were. Then he decided to see if there were the same number from 101-200, which led him to also consider 201-300.

That is in Chapter 2 of Introduction to Number Theory exercise question 2.3.1 and question 2.6.

It is in Chapter 3 of Prealgebra as well.

 

For reading for fun, we just check out the living math books at Barnes & Noble then use Link+/ILL to get the book from our local library. My kids browse through all the Zaccaro books at B&N and didn't like his style of writing.

 

Some math loving kids like Ian Stewart books but no one in my family did.

Edited June 7, 2017 by Arcadia

[wendyroo]

I don't really want fun ways to do the same standard curriculum - I really want things that aren't even in the standard curriculum (but done well and rigorously - I don't mind things that are somewhat incomplete, but I can't handle anything being incorrect).Any ideas?

 

We like G Is for Googol: A Math Alphabet Book.  It covers some very interesting topics.  It obviously isn't a whole curriculum, and my mathy son blew through it pretty quickly, but it sparked a lot of interesting discussions and he keeps going back to reread it.

 

Wendy

[4KookieKids]

 Beast has enough of the challenge and out-of-the-box thinking that I no longer feel the *need* to add in all the rest of it. However, if we hit a topic that is making DD bang her head against the desk, we take a break from it and pull out one of the other options on the shelf.

 

Yes, I'm not so much concerned about "needing" to supplement, and more just interested in giving him interesting reading material that will expose him to a wider variety of math fields than are usually covered in the standard sequence.

 

 

That is in Chapter 2 of Introduction to Number Theory exercise question 2.3.1 and question 2.6.

It is in Chapter 3 of Prealgebra as well.

 

For reading for fun, we just check out the living math books at Barnes & Noble then use Link+/ILL to get the book from our local library. My kids browse through all the Zaccaro books at B&N and didn't like his style of writing.

 

Some math loving kids like Ian Stewart books but no one in my family did.

 

Thanks! Does B&N actually have a section on living math books? I've never seen such a thing! lol.

 

We like G Is for Googol: A Math Alphabet Book.  It covers some very interesting topics.  It obviously isn't a whole curriculum, and my mathy son blew through it pretty quickly, but it sparked a lot of interesting discussions and he keeps going back to reread it.

 

Wendy

 

Our library has this! Thanks for the idea! :)

[Arcadia]

Does B&N actually have a section on living math books? I've never seen such a thing! lol.

They are just mixed in with the other math books on the science shelves which is usually next to the technology shelves here.

[slackermom]

One resource we liked at that age is Mathematics, a Human Endeavor, by Jacobs.

 

https://www.amazon.com/Mathematics-Endeavor-Harold-R-Jacobs/dp/071672426X

[Mike in SA]

Ah - if you want to enhance exposure to new topics, I would make a different suggestion.

 

Look for a theory of arithmetic book that discusses alternative mathematical systems used in the past (Egyptian, Babylonian, Mayan, etc al). It is very enlightening for a child to see how "invented" all of mathematics is.

 

A simple intro to group theory is also fantastic, for the same reasons.

 

I have found that most children can handle these topics as soon as they understand multiplication.

[Jackie]

Yes, I'm not so much concerned about "needing" to supplement, and more just interested in giving him interesting reading material that will expose him to a wider variety of math fields than are usually covered in the standard sequence.

For that purpose, my daughter's go-to resource lately has been the Murderous Maths series. Fun and engaging, with a wide range of topics. She's not a kid who will look at a textbook for fun, but she'll take these to bed with her!

[wendyroo]

For that purpose, my daughter's go-to resource lately has been the Murderous Maths series. Fun and engaging, with a wide range of topics. She's not a kid who will look at a textbook for fun, but she'll take these to bed with her!

 

:iagree:  :iagree:  :iagree:

 

My oldest reads these over and over.  He is constantly telling me different fascinating math tidbits.  My 5 year old frequently requests them for bedtime reading....they are a slog to read aloud, and they largely go over his head, but he loves them and the exposure is very valuable.

 

I'm planning to get the set of Horrible Science books for DS for Christmas.

 

Wendy

[sunnyday]

I think a lot depends on the kind of learner you have. My son is a "don't teach me, let me dive in" kind of guy. He'd probably thrive on a meandering multi-stream path like what quark has described through the years: http://forums.welltrainedmind.com/topic/320275-designing-a-non-traditional-math-course-for-a-math-loving-structure-hating-child/?p=3272174

My daughter prefers structure (as far as I can tell) and would probably do well just working straight through BA. I think if I kept her home I'd consider doing math M-Th and taking Fridays to be a "mess around with different topics and approaches" kind of day, which would be a time for pulling out the competition math and such, or programming, exploring in Khan, whatever.

For now though, all those "extra" resources have basically just served as stopgaps to keep my public schooled kids from imploding on a steady diet of school math. ;) We use them on occasional weekends and breaks to make sure the kids know that there's a beautiful science of mathematics out there, quite apart from the drudgery of school workbooks. :lol: It's sort of a "slow them down" concept, but also kind of a "feed their need while we figure out where we're going with all this" concept.

[Guest]

Its enrichment. Basically needed because of small print size in more advanced books they would enjoy. We diverted into Gamemaker and math club problem sets, bc the print size and page layout worked.

[seaben]

Its not a book or a whole curriculum but I really enjoy the numberphile videos and you can do alot of side explorations off the various topics discussed. What's nice about it as well is a chance to see various practicing mathematicians and get a sense of math as a living field of research.

[epi]

A simple intro to group theory is also fantastic, for the same reasons.

 

 

Any suggestions for this, in particular, for a kid who's finishing up the AoPS Intro level, and good at math, but not necessarily ready for higher level abstraction. (We've got several Graduate Text in Math books on our shelf. -- They're definitely not suitable.)

 

[daijobu]

I scheduled the old MOEMS and Penrose and other fun math stuff on Wednesdays and the rest of the week was regular Singapore Math.

[Mike in SA]

Any suggestions for this, in particular, for a kid who's finishing up the AoPS Intro level, and good at math, but not necessarily ready for higher level abstraction. (We've got several Graduate Text in Math books on our shelf. -- They're definitely not suitable.)

 

 

Don't underestimate a kid's ability to abstract.  They are far more capable than most adults.  I wouldn't expect them to read a college text or solve proofs, but the concepts can be learned quite adeptly by a young child.

 

I've used my college abstract algebra book as a resource (for myself) in leading 6-7 year olds.  I led them through sets, operations, groups, relations, functions, and on down the line.  One of the tricks was to throw in physical activity to describe commutativity, association, etc. A tile floor allows them to create their own 1- and 2-dimensional systems and unique operations, and test the results of the operations experimentally.  Those same kids look at arithmetic very differently when they learn it later.

 

It's definitely enrichment, and not a course.  I don't know of a suitable book, so a teacher would be needed for young kids.

[4KookieKids]

Thanks all! I ordered murderous math and found a few others at the library and we're going to start there! :)

[SanDiegoMom]

For enrichment my son loved Penrose the Mathematical Cat (and Further Adventures I think?), The Number Devil, Go Figure, Why Pi, and Murderous Maths (though now at 11 he says they were too violent and won't read them anymore).  

 

Now his favorites have been Here's Looking at Euclid, The Grapes of Math (not the picture book but the one by Alex Bellos) and he loves Vi Hart Videos and Numberphile Videos.  

[4KookieKids]

For enrichment my son loved Penrose the Mathematical Cat (and Further Adventures I think?), The Number Devil, Go Figure, Why Pi, and Murderous Maths (though now at 11 he says they were too violent and won't read them anymore).  

 

 

Uh oh... I thought, based on reviews, that the violence was more of a joke. I guess I better pre-read them! I have some very sensitive kiddos. We may be re-selling them! Dang it. :(