value in sequential learning?

[earthmama369]

I have an asynchronous learner who falls somewhere on the gifted end of things. She's 5 years old and we're homeschooling (more on the eclectic unschooling end of the spectrum). She's been playing with addition, subtraction, and multiplication concepts on a basic level since she turned 2. We haven't pushed any drilling or worksheets and are only just getting into sight reading and writing numbers on a fairly regular basis. Right now she can easily count past 100 but only sight reads through 10 with any confidence. She likes to write her numbers backward, often in mirror writing, and still needs reminders on how to write a couple numbers below 10.

But she's doing multiplication up to 9s, completely on her own and in her head or by counting on her fingers. She's just gotten interested in workbooks and any time there's something like a number path, she'll figure it out in multiplication terms. One of her grade 1 workbooks has activities like "Find the number 3 path and follow it to the bunnies" and it will have a path marked with 1s, another with 2s, and another with 3s. So she'll draw the line down the path and then say, "Mama, nine 3s is 27."

So it seems like there's a lot going on in her head, even though she's really not very interested in writing or reading on a functional level yet and is fairly resistant to guidance on how to form letters and numbers on paper. She does know mathematical symbols and can do a sheet of addition and subtraction up to 10, including the zero concept, without any errors, pretty quickly (if you ignore some backwards numbers and mirror writing).

Is there a strong value in pushing a child to go through mathematical skills sequentially? I'm wondering if I should just get into multiplication with her now, and answer all her questions and give her some workbooks with the opportunity to practice multiplication skills, since she's so interested in it, even though we really haven't gotten into higher order addition and subtraction yet, or sight reading of numbers, etc.

[TEAK's Mom]

I think that there is a time in mathematics when sequential learning is important. Differential equations would be difficult without some understanding of calculus, but that is a long way off for your dd (I'm guessing anyway ). Arithmetic is all interconnected, but there are countless different sequences for learning it.

While she is learning so effectively through play and exploration, I would not mess with it. Help her when she gets stuck, have cool resources around about non-arithmetic math, and let her go to town. As she gets older, she may want a sequential program, but for now, she's doing brilliantly.

[no5no5]

Originally Posted by TEAK's Mom

Arithmetic is all interconnected, but there are countless different sequences for learning it.

While she is learning so effectively through play and exploration, I would not mess with it. Help her when she gets stuck, have cool resources around about non-arithmetic math, and let her go to town. As she gets older, she may want a sequential program, but for now, she's doing brilliantly.

ITA. I don't see any value at all for pushing a child like this to learn arithmetic in a more traditional way, and I think there is potential for serious harm if you try it.

[Marissamom]

with arithmetic, teach in the sequence that's working for her and you'll be able to fill in other stuff as you go. Some educators even strongly believe in teaching algebra alongside arithmetic, it's not until after that that sequence is somewhat important (but only to some extent, which is why if you look at a couple higher level mathbooks, they won't tackle everything in the same order), just build skills in what seems a natural order for her.

[Roar]

Working in the way that makes sense to the child and not worrying about the sequence worked very well for us. So, I say - enjoy it and don't worry. Our child really enjoyed Miquon and that teaches all four math operations at the same time. It promotes a really wonderful development of the sense of numbers and the relationships between the four operations.

[Delicateflower]

Just do what she enjoys. It would be tragic if you held her back from the fun of division and probability and geometry because she couldn't write a 5 well yet. There is a lot more to math than arithmetic.

[Marissamom]

Originally Posted by Roar

Working in the way that makes sense to the child and not worrying about the sequence worked very well for us. So, I say - enjoy it and don't worry. Our child really enjoyed Miquon and that teaches all four math operations at the same time. It promotes a really wonderful development of the sense of numbers and the relationships between the four operations.

I was trying to remember the name of the Miquon series. my mom used it with my younger sister who didn't learn arithmetic in the "proper order" well, and my sister really did well with it. my sis was also one that could do everything really easily in her head. she refused to learn how to write carrying and borrowing out because it was easier and faster just to do it in her head. she also taught herself multiplication when she was about 6.

[earthmama369]

Thank you for the confidence boost! I generally follow my kids' lead, but every once in a while I start to wonder if I'm missing something that I'm "supposed" to be doing. And while I'm competent with general math skills and some higher order math (algebra, calc, etc.), it's not something that comes naturally to me, so I don't have an innate sense of whether or not I'm approaching it in a practical way.

And thanks for the Miquon recommendation. I'll definitely check that out. She's rocking out on the Kumon workbooks right now, but she's going through them so fast now that she's gotten into the whole workbook thing. They're about 70 pages long and she's finishing them in 2-3 days. She reminds me so much of her father in that respect -- an intense interest in something for as long as the obsession lasts, and then onto something else with the same intensity. It can be hard to keep up!

[Bird Girl]

My five-year-old is mathy, and we're doing Miquon. (We homeschool, too.) Miquon is organized by level (orange is the first) and then each activity page has a color code that responds to the strand of mathematics it addresses. If you buy Miquon, and the four workbooks aren't expensive, you may wish to consider buying the Lab Annotations book, which shows various ways to use the activity pages. We're in a homeschooling charter school, so as my son is officially a Kindergartener, and has to produce work samples, I make sure he completes one activity page per day. He can choose to do more, if he wishes. Other math work is done at his request.

As far has the handwriting aspect goes, I do believe in introducing children to the proper formation of letters and numerals, so we use the Handwriting Without Tears series to practice that skill. I consider it fine motor work, rather than mathematics.

At some point, I'll switch over to Singapore math, which is what I use for my DD, who's a 3rd grader. We have no problem, in our house, with a small amount of assigned, sequential work, and since we homeschool, that leaves plenty of time for child-led learning, math games, and free exploration of ideas. I do about an hour-per-grade of assigned work, and so far, we haven't had any loss of enthusiasm for learning on any topic.

I hope that's a helpful response.