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Asking this here because I'm interested in a childledlearning perspective.
I was never planning to give my kid worksheets. Not when he's learning so much without them. Especially not at his age: notquite 5 years old. I was sure he wouldn't have the patience to write numbers yet, in any case. But he was recently introduced to "number puzzles" somehow at grandma's, loved them, and wanted me to print more out. So I found a few free puzzles of various types online. And, though I told them they were "puzzles", they were also labeled as 1st and 2nd grade math worksheets! Eek. (I don't think he's that advanced  the puzzles he did didn't require anything more than addition and logic).
From a parent's perspective, these have one huge advantage over baking stuff and math games  he can do them by himself. Without 3 yr old sister messing things up, while I cook, etc... But I don't want to make things too formal too early.
Would it make more sense to just tackle that interest headon and get some kind of sensible math curriculum he could use if he wanted? Continue with random internet worksheets? Or hope it'll peter out soon and lead him away from that stuff for another few years?
He's the oldest in his peer group, so none of them are in school. Therefore there's really nothing external driving this one way or another. He'll think math is whatever I say it is.
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Has he tried Sudoku?
How about games like Dominoes, battleship, checkers, etc .., I can't remember if 5 is too young for that.
There are also puzzlelike books published by Kumon.
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... dd is going on 12 (!) how was I to know there was a homeschool going on?
I don't think it's too early for your particular kid. Not at all.
It's entirely in keeping with how K is and how he thinks and how he approaches new information that he's interested in.
E has been doing mathseeds online, and is also getting really excited about numbers. I've been looking around at various approaches and philosophies about math, to see if we want to go down the road of formal curriculum or not.
Not, so far. But I am going to look at the khan academy stuff online to start with.
I was going to be all about delayed academics, but that has not panned out. E's pursuit of information and the desire to aquire the knowledge HERSELF and not always imparted/managed/facilitated by me is strong. Hence learning to read.
So while a lot of her project work about viruses and pathology is helped along by me (the books/sites she wants to explore are written for postsecondary, typically), she spends a lot of her time pursuing the information herself.
Thanks for the mention of sukoku, rumi! My kid loves that kind of thing.
Not real games or puzzles, but ones on a 2dimensional grid, especially (word searches, crosswords, that kind of thing.)
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We make up little "math tests" for the girls. And yes, we also called them "puzzles". Math is very much a puzzle for them, and because of that they still love it at 7 and 9. All we did was write down a few equations for them to puzzle through on plain paper. At first it was very basic, only about 5 problems (I hate that word for mathwhat are my options here? Is "equation" correct, or does that refer to the finished "2+2=4"?)
As they advanced and we did this more often (though still very infrequently) I would try to include problems that were easy for them, ones I figured were just about right, and one or two a little further ahead to gauge what they were ready for. Last August, I printed out some Singapore sample pages, which they enjoyed.
We also do math games in the car. Very simple ones, since I am not mathematically clever enough to come up something trickier. We simply take turns throwing problems at each other. Both my girls are very good at mental math because most of the math they do is mental. I'm not so great at it, but helping my girls puzzle through it has helped me immensely. You could do the same in the kitchen or while walking or folding laundry.
Doing math off the paper is something I value greatly, most especially in the early years. My 9yo still prefers it, even while she advances into addition with carrying and 3digit numbers. Even when I write it down on paper, she uses the paper merely as a starting point for her mental calculations. She understands that the special notation can allow her to add insanely huge numbers, but she's not interested in that yet.
Sudoku is funit is mathematics but the numbers are incidental, as you can play it with pictures or colors. I would stick with that, homemade worksheets, printed worksheets and puzzles, not necessarily curriculum at first. We've really enjoyed just playing with cuisenaire rodswe have the wooden ones and I should have purchased the bucketsize. Those lead to all kinds of mathematical discoveries and are fun to play with by themselves. Solitaire card games can help internalize number sequence and logic (I have 3 games I've showed them). Wooden pattern blocks for making pictures, illustrating the relationship between shapes and just being gorgeous. For computer time, we've recently been playing with bbcbitesize, on the Scottish KS1 (KS1 has mostly the same material, but I find the Scottish level easier to understand, accentwise, across the board.)
I've stuck with suggesting things he can do on his own. I have a slew of other suggestions that he can do with others that have helped with our mathematical explorations.
ETA: we found that Khan academy, while fun and it does have basic math there, simply isn't geared towards the younger set. My girls failed to be be engaged by it, though I had lots of fun with it as an adult.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
HEXAFLEXAGONS would be PERFECT for K! It would combine his mad origami skills with mathy sorts of sensibilities!
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Formal math has already been introduced to him in the sense of the formal logic of math: that which is rendered abstractly using numerical symbols in the form of equations. But you haven't crossed any huge divide giving him access to that. I don't think that math equations on paper need to be viewed as anything categorically different from, say, sudoku or crossword puzzles. If they're not being assigned as part of a schoollike regimen, they're just an interesting intellectual diversion that happens to take place on paper, the sort of thing a person might enjoy challenging his brain with, gaining a sense of accomplishment from it just like any other selfled pursuit. I think that obviously at this age you don't want symbolic math to make up the whole of his mathematical education, but of course you're not suggesting that it would. I'm sure you're still assuming he'll get lots of handson, intheflowoflife learning about math whether by helping in the kitchen, measuring things, playing games, messing about with manipulatives, asking questions, noticing numbers and shapes and their relationships and so on. Some kids have a real affinity for numerals, or for the act of working out "answers" on paper. I don't think there's any harm in allowing that to continue.
You could stick with giving him random worksheets off the internet, continuing to look at this as a sort of crosswordpuzzlelike diversionary activity, but really just keeping the Math of Life as the main approach. I think the risk with this is a loss of interest as the worksheets become unchallenging and repetitive, don't build on each other in interesting ways, or build on each other without the necessary conceptual learning being nurtured along. On the other hand you could move into formal guided study of math, in the form of a traditional curriculum: a sequential curriculum that he is encouraged to work through systematically. I think the main risk here is in the way children can get boxed into the curriculumwriter's sequence and way of approaching things, and can lose the curiosity and delight that comes from childled exploration and discovery.
I've faced this dilemma, especially with my two youngest kids who really wanted to be doing mathonpaper like their older siblings and seemed to be asking for something systematic. I decided to try to find a middle path between childledwithrandomworksheetsforentertainment and curriculumledsystematicteaching. We used Miquon Math, a program that is designed to be very openended and creative. It has workbooks, and sometimes my kids were able to use workbook pages independently. But largely it's a parentandchild process of exploring manipulatives, operations and relationships using an approach that's called "guided discovery." The heart of the approach is in the math lab activities that you do together. So it's not nearly as convenient for the parent as just sticking with traditional printed worksheets. However, I think it fed that interest in formal math in a developmentally appropriate way that built a strong conceptual foundation. As a side benefit it provided enough of the "math on paper" to feed my kids' wants in that respect. It worked well for us, and might be worth looking into for you. There are other manipulativebased programs that are good for kids at this stage, but they're either much more expensive, or much more scripted and sequential that Miquon.
By the way, I think that facility with symbolic basic addition prior to age 5 is advanced! And the interest in doing so on paper is definitely unusual in a 4yearold boy. If you've got an advanced mathkeen unschooled kid, I think it's good to feed that interest and ability. If a child is blissfully ignorant of the fact that math bookwork falls into the category normally referred to as "schooling" I think as parents we should avoid projecting our own dichotomous thinking on our kids by worrying that this type of learning should be offlimits. Our kids have no such assumptions. To them solving an addition equation on paper isn't categorically different from solving the puzzle of a twoway jacket zipper. It's all just interestled learning.
Miranda
Mountain mama to two great kids and two great grownups
Oh, and about "how early"....
My eldest started with Miquon around her 5th birthday, dabbled on and off for a year, then got busier with it. My second child was similar. My third and fourth kids started at notquite4.5. All four of my kids have all done really well with math, even most artsminded among them, though the older three hit a bit of a wall around age 9, where they had moved quickly through elementary and middle school skills but weren't yet developmentally ready for high school content. So they just ditched curriculum for a while and did other things. A couple of years later they were ready to roll again and they moved easily through high school courses ahead of schedule. My most mathy kid (number 4) didn't hit the same wall and is currently finishing up a Grade 9 math course at school at age 10 with no difficulty at all. This is just to point out that the early start didn't create any kind of burnout or faulty learning in our case.
Miranda
Mountain mama to two great kids and two great grownups
My girls started doing the homemade worksheets when dd1 was 5.5. While she would have enjoyed the *math* of a curriculum like Miquon, she was not interested in what I had to offer her. She rarely wanted to be in a position where *she* felt I was teaching her anything (whether that was my intention or not). Mathematically, she was ready.
ETA: Her discomfort with writing at that young age played a big role in how much she enjoyed working on paper.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
Thanks everyone for the thoughts. Glad to know I don't seem like a crazy hothouse mom. :)
Of course we do plenty of mathinlife, and will continue to. Though not really in cooking, since I never use recipes. And only rarely in games, because the 3 yr old wants so desperately to play and usually messes them up. But I swear my son folds origami for at least half his waking athome hours, and we talk about numbers a lot. The number guessing game Miranda suggested in another thread I started has been great. And Starling, he loved the hexaflexagons.
I'll skip the computer sites for now  the kids seem to have forgotten about the existence of computer games, and more competition for mom and dad's work computers isn't needed. Also, I think part of me figures that learning apps have so many bells and whistles  if he likes math in black and white he must really actually LIKE it, and not just be looking for a chance to use the computer.
Maybe I'll just go ahead and print him a bunch of worksheets and see what he does with them. Somehow, it's easy to see him doing the more puzzlelike ones (kid sudoku, some kid versions of magic square things) and think "hey, that's cool." Harder when he seems equally excited by a page of simple addition problems. But that's my projection of what's "too academic" and really has nothing to do with him. He's a very focused kid and I suppose puzzling through basic math problems is the same to him as puzzling through the complicated arrows and folds in all his origami diagrams (lots of adults get confused by those).
And perhaps I'll add one of those Miquon books to my Amazon list to have in my toolkit if his interest keeps up. I see that orange is the first one, but can't tell how easy/hard it is from their web page (sample pages look easy, though). Miranda: How narrow are the levels? You say your kids started at a similar age to mine, I imagine at the first book? If I get it and don't end up using it right away, will it still be useful later? Or would I likely just need to skip to the next one?
Miquon levels are pretty wide. <edit> The first book First grade </edit> introduces all four operations within the first two books, and much about the exercises is designed to build facility and numbers sense in ways that incorporate the cuisenaire rods. It's suggested that even kids coming to Miquon at older ages, having done a year or two of 'regular' math, start with the first book because there's so much depth in there. Somewhere in the first book are questions like x  5 = 10 (albeit not using the 'x' but instead an empty box) and (2 * 3) + 4 = ___. So the first couple of dozen pages are dropdead simple, but the conceptual learning starts accruing before you know it.
The only thing about Miquon is that it's not really about the workbooks. They're a place to symbolically represent the learning that comes through the guided discovery exercises. To use the program as it's intended you need the cuisenaire rods and the Lab Sheet Annotations book. I'm not one to normally purchase the teachers' manuals that go with curricula, but in this case I think it's really necessary. So it doesn't really work as a "oh, we'll try a bit of this" resource: it's best as a program that you understand thoroughly and feel good about making use of whenever your child wants to explore a new concept. Perhaps you could find somewhere to borrow the Annotations book to look over (library? homeschool support group?), and that might give you a better feel for whether it's worth spending the $75 or so that it would cost you to buy cuisenaires, the Annotations book and the first workbook or two. After that, adding subsequent workbooks is very inexpensive.
I think the Singapore Math workbooks are pretty solid too and they stand alone better; my ds used a couple of the K5 workbooks back when he was little and wanted to have a math book like his older sister but wasn't exactly all that driven to learn math. I don't think he learned much from them (they were pretty easy for him) but they kept him busy and maybe they solidified some symbolic math stuff for him in a decent conceptual way. I think they covered addition and subtraction up to 20, and a bunch of ancillary learning (measuring, grouping tens, recognizing numberwords, comparisons). Gosh ... that boy is writing a preCalc exam today: it's been a while! They were called Early Bird back then, but nowadays I think there are a number of other Singaporean K4 and K5 books out there. Generally I like emphasis of the Singaporean syllabus on concepts, number relationships and such, though I preferred the more childguided handson approach of Miquon for that first real foray into primary math learning.
Miranda
Mountain mama to two great kids and two great grownups
Miranda: Thanks, that's very helpful. He does have some of the rods already since I thought he might enjoy playing with them and understands a little bit how to use them (ran over to get them after dinner one night and came back excitedly saying that he'd eaten 9 pieces of sushi, because 3 3s is 9). But I wouldn't have thought about the teachers book. I suspect my teeny tiny town library will have neither Miquon nor Singapore books to look in, but I will check. Both me and my husband are geeks who would certainly quite enjoy exploring math with him, but it does sound like more of a time/energy/money commitment, especially if he doesn't end up being interested.
Miranda, if I were to order the Miquon books, would I have to order 2 workbooks for my girls? Or can I order one set? These have been on my list for a while, but finances are tight and we need to wait a bit, even though the cost is reasonable. I would have no problem purchasing a set each, if there was any advantage to each having their own.
Sorry to sidetrack the thread slightly, but you've answered some of the questions regarding Miquon that have been on my mind.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
Miranda
Mountain mama to two great kids and two great grownups
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Hi,
There is a math workbook series by Dr. George Saad that allows kids to learn math from basics to algebra all on their own. It's a sort of look and follow me approach. My son (who reads a lot but couldn't add much) started and he likes to do a few pages a day or something like that and now he is on substraction. He is 8.5 though. Book 1 starts with writing numbers. It's a very simple book, with somewhat mature illustrations i.e. no aliens :) and really simple clean pages that advance quite slowly.
Update: I did end up getting the Miquon books, because I decided having something to go to when he felt interested in doing some 'math puzzles' seemed simpler than starting from a Google search for worksheets every time.
So far, he likes them. He likes the numbering system of the pages  that he can flip around in both books and find something he likes to do, but use the letter and number to tell what kind of puzzle it is, and how difficult. He often picks something too difficult, does a little, then flips back to do an easier one. He enjoys some of the red book ones, and finds some in the orange book too hard, so I'm glad we have both for him to flip through.
The lack of words is nice, since he can't read yet. But he finds the boxes too small to write in easily. He's willing to attempt to write any number if he has lots of space, but in the little frames, he asks me to do all the ones with "curvy parts." So, a lot of parental involvement still required. Though he'll do the "draw the lines to connect stuff" ones by himself if I explain the sheet at the beginning.
You could consider getting a set of number stamps for him if he's frustrated by the necessity of having you do some of the writing. Scrapbooking places usually have such stamps. But Miquon really shouldn't be about the workbooks, and there should be lots of parentguided activities with rods and other manipulatives, rather than just going through the workbook, so it's best if you're pretty heavily involved anyway.
Crayola used to make ministampers with numbers on them, but I haven't seen them in a few years.
Miranda
Mountain mama to two great kids and two great grownups
This is where he and I disagree. :) So far, the process goes like this: He eagerly finds a workbook page and asks me to tell him what the 'rules' are about how to do it. I bring out the rods, and start trying to do the interesting visualizations, games, etc... "I don't have to, right?" "No, you can do whatever you want with it." So I sit there next to him and play with the rods myself, and write in the curvy numbers for him until he gets stuck. Then maybe he'll start using the rods himself, and/or let me show him some sort of trick. Or not. He asked what the times symbol was the other day, but only wanted a 2 second explanation before diving into the problems. He's totally fine with me writing numbers for him, but not so eager for the adultguided activities.
So for now, he really does love the workbook aspect, and maybe I should have gotten something different, but he's having fun, and using the rods a little bit when he's stuck, and has lots and lots of time to learn all this. Any tips on a different method of working with it would be great if you have them, though!
My kids also don't like the guided activities when I try to do them at the same time as the book. So, I just stay ahead of them, and continually introduce new things through games, conversation, etc. Then, when they get to it in the book, they don't need my help, or very little.
Yes, this is a good strategy. Once they're fixated on doing a particular task like a workbook page or whatever, my kids didn't like running aground, or getting pulled up short by the need for preliminaries. So I'd just do some playful conceptual explorations with them at other times. I would often leap way ahead of where they were at in the workbooks, so that the groundwork was laid. Prime numbers, factoring, long division, fractions, place value, whatever.
We used our rods a lot for 3D constructions, and for patternbuilding, and for games. I think all of that was very useful. It didn't take my kids long before they could just "think" the rods in their heads when they needed a manipulativebased approach.
Miranda
Mountain mama to two great kids and two great grownups
So far, she's more interested in the rods, which I have way more fun with, and am perhaps more enthusiastic about.
With the rods, she's been exploring adding, subtracting, multiplying and dividing in a really holistic way, or so it seems to me. I like that she's getting to know each value she plays with in and out, without the restrictions of socalled 'ageappropriate curriculum.'
She was getting a bit anxious about the workbooks (you know how E is ...), so I didn't bring them with us for our 5 weeks in Mexico.
We've been using the rods exclusively, and she's been dictating her equations to me. That's been great!
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The idea of separating the visualizations/games from the books is a good one. Last night I got out the rods and started fooling around with them, and my son came over and invented a mathy sort of game with dice and the rods that he was super excited to play for a long time. And then decided to put them all away in multiples of ten.
I don't have any page protectors, but that might be an especially good idea for my 3yo, who would absolutely love to do something exactly the same as big brother is doing, but is nowhere near ready to do any more math than counting.
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