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Hello all. Long story short. Two kids, ages 6 and 8. We recently stopped Singapore math because honestly, it was going at too fast a pace for us the kids were not getting enough time to master a concept before going on.
We're back to working on simple subtraction a skill my 8yearold seemed to forget how to do during Singapore math. Every day, every single worksheet I hear how HARD it is. 82? Gah! How am I supposed to know? This is so HARRRRRRDDDDD, I can't do it. I can't use my fingers. I can't use my abacus.
I always sit patiently with her...even long after the 6yearold is finished. Even with all the complaining and moaning, I'm guessing she gets at least 80% correct. (Usually.) Sometimes she does much worse...but we all have off days.
This hour long complain fest is really getting old. I'm not a natural at math, so I'm definitely sympathetic to the situation. I just can't decide if math is really that hard for her or if she's just using the drama as an excuse.
But....she has to learn it. Should I just deal with the whining and keep working at it? Use some kind of chart? Hire a high voodoo priestess?
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Ooooh. I hear you!
My year old has a really rough time with math, and I have a rough time understanding her rough time, because seriously...she says she "can't" count on her fingers either. She can't subtract or add simple numbers that most kids could just say without thinking. BUT...it's gotten a little better since I sucked it up and put her back into 1st grade math. I just figured it was better for us to start from scratch. Some of the concepts are too easy and she breezes through them (and that makes her feel smart, which is nice for a change...when it comes to MATH!!) but others are really hard for her. We use Time4Learning  it's online, but they have a worksheet or two available to print for most lessons. Anyway, works for my dd who loves to be online ;)
Good luck!
Is it the remembering of the arithmetic facts that she's finding so hard? Maybe she could learn them more easily with games of all kinds, either handson or computer, or maybe she'd at least find it less painful. You might browse through my page of links to articles and websites that offer ideas  Go Figure! I wouldn't click on any till you've browsed through all the titles, because you might find just what you need lower in the list.
Several math enthusiasts I've known over the years have been adamant that children learn math better and have a better appreciation of it if they learn it with handson activities and games outside of a program until they're in higher levels  and that proved quite true with their own. When my son, who hadn't used a program, was 9 or 10, I took him to a math tutoring center to get evaluated, and the head of the center said he understood real math in a way that children don't tend to arrive at through endless worksheets. She said she spends most of her time trying to undo the damage that's been done through all the worksheets children do in school. We did use the Keys To workbooks for a while, though  they're bone simple and don't have a lot of worksheets.
Lillian


Can you just leave math alone for a while? I mean, yeahthey have to learn it... eventually. There have been several studies showing that pushing it on them early can actually backfire in their math achievement longterm (although the study I'm thinking of was specifically looking at early elementary/Kindy). There are several countries that kick our arses in math that don't even bother with academics until the kids are 8yo.
When she's ready, she will pick it up quicker and more fluently than trying to fight with her. Can you, in the meantime, just work on the math that comes naturally through life? Cooking, shopping, building stuff...? Maybe it is the drama. Maybe she truly has a hard time (I seriously cannot do subtraction with my fingers at 40yo and I'm a math geekit just completely stumps me because I don't know if I count THIS finger or start with the NEXT finger... GAH!!!)
If you're not okay with letting it go, have you tried Life of Fred? We've been using them and they are light on practice but strong on teaching the concepts in a way that kids seem to grasp pretty well. They just published the "under 5th grade" series last year. We're about to finish it. We have friend with an artistic daughter who only wants to learn Calculus to find out what becomes of Fred.
Heather  Wife
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We just checked out Anno's Math Games books from the library. The last time we had them was over a year ago, and this time dd1 could nearly get through everything, even though we hadn't done any real math work that entire time. I think it's true that with young brains, time alone can make a huge difference.
One chapter in Anno's math Games II teaches addition and subtraction using the story of a magic box. It also shows pictures of real things that get more and more abstract until finally they are just circles. It also teaches place value (tens), all without using any math more sophisticated than counting (and many puzzles you don't even need to count.)
What I like about this set of books is that I've been able to gauge dd's readiness for moving forward with actual algorithms. She does these a little and enjoys them, homemade math "tests" dh gives her now and then. In the meantime, she keeps herself busy with the occasional Sudoku puzzles and other games.
I am all for the games at this age. Battleship teaches coordinates and graphing. Monopoly teaches simple addition (di) and more complex addition as well. I definitely count origami as math.
Regular, weekly allowance is teaching them several math skills, not just counting and monetary value but fractions as well ("quarter" refers to it being 1/4th of a dollar, "dime" is 1/10, "cent" is 1/100, etc.) They don't understand these concepts yet really, but they are being introduced to it in a meaningful way. One of these years, telling them about sales tax offers them a chance to learn about percentages (for now, I let the sales tax slide on most things).
As they get older, then I'll start keeping wellwritten math books around and start exploring math more academically. At these ages (my girls are nearly8 and 6) there are so many places to teach math that doesn't induce stress the same way as worksheets. (Also, my girls really do love worksheets, but they are rare in this house and no one ever has to actually complete them. Recently I reproduced a secret code puzzle using a number/letter graph but I made up the answers myself, like "HORSES ARE MY FAVORITE FARM ANIMAL". They did 3 of these homemade puzzles in one day, then they don't ask for anything for weeks.
I definitely am a learntheconceptsbehindthemath advocate. What I dislike about formal math is not just the method, but that it is presented in a certain order, and in my brief experience as a parent and HSing parent I've discovered that this order is, at it's best, irrelevant and at its worst a real obstruction to progress. I learned this very quickly when dd1 understood multiplication 3 days after she understood addition, but subtraction took at least another year to sink in. Most math quickly introduces subtraction after addition (being opposites, that's understandable), yet many kids would do better just to jump to multiplication.
heatherdeg, I would love to know some of the troubles that your friend had to work through and how to avoid them.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
I completely agree with the importance of conceptual learning, the efficiency of learning through life and play, the necessity of quiescent periods in children's mathematical learning, the arbitrary nature of much of what passes for "scope and sequence" in many math programs, and the benefits of delaying or slowing down formal math instruction in the early years. My ds was introduced to Singapore Primary Math at about age 6, but he disliked it, despite having many of the concepts and skills well internalized for practical application in real life. On paper, though, it was intimidating and confusing. As an unschooling parent I was comfortable doing nothing other than continue to model math as a delightful part of real life. At age almost10, he decided to dive into the very same program he had balked at 3 years earlier. He was ready for Primary Math 3A, despite having not done any of the earlier levels, and he finished 6B six months later. He went from being (apparently) two years "behind" to being three years "ahead" in the space of 6 months. Awaiting readiness and motivation was definitely the right approach for us.
Having said that, I don't think Savoir Faire is at all unschooly in style, so I'm guessing she won't be comfortable taking math off the table for a while. So my suggestion would be to look at RightStart Math, because my impression is that it presents math in a handson playful way, but is systematic and structured and gives one the satisfying sense of "doing math every day" and progressing through an organized course of study. It is built to allow much more repetition than Singapore's consumable workbooks, and caters to a different learning style than the basic Singapore Primary program.
Miranda
Mountain mama to one great kid and three great grownups
I also heard, many years ago, that the Japanese students use an abacus until they can use an imaginary one!
All that said, I struggle with getting my son to do math. He just doesn't see a need for all te memorization. He has the ability, but refuses to put in the effort. It started with the multiplication tables.
My only advise is keep calm, try not to worry. Using an abacus would not be a stumbling block for me. Many adults use a calculator, so why should it bw different for children. Good luck to you.
I reread my post but I didn't see where I noted a friend that had troubles to work through...? Are you referring to my statement about my friend with the artistic daughter? I just meant that she enjoys art and hates math, but is enthused to get to (and through) to the Calculus book in the Life of Fred series at some point because she's just THAT interested in the story line. She doesn't actually need to learn calc and her mother wouldn't push her to do so, but it's quite a statement that a kid that doesn't love math finds a set of teaching storybooks on a subject she hates enough to want to go past what is required of her... kwim?
If you're referring to something else, lemme know!
Heather  Wife
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No, that was Lillian. I wrote that long post and then some details slipped out the other end and I never went back to fix it. Sorry.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
SweetSilver clarified what she was asking about  it was what problems the tutor had been trying to work with. What the tutor was referring to was the deadening of all those kids to math  making them think that stuff is math, and making them think they hate math. What she was so excited about with my son was that he hadn't had that experience, or at least not since his last year of school in 1st grade. We played around with math thinking, and avoided anything that would give him the idea it was something to dread. In fact, I got him Hands On Equations, the prealgebra program, when he was 8  it's actually created for kids that age and up  so that he could get the idea that algebra was a fun thing to look forward to. He never came to love math, but he also never learned to hate or dread or fear it. When he needed to get ready for the SAT for college entrance, he took a sample test, got a lot of good books, and worked with a math tutor to fill in missing pieces, and he did well on the test. If math were going to play an important role in what he wanted to do with his life, he said he'd have to study it more formally, but that isn't going to be the case.  Lillian
Play games with it: dominoes, chess, snakes & ladders, poker, cribbage, monopoly, yahtzee, UNO.
Build things with it: K'nex, Lego, wooden blocks, buckyballs, pattern blocks.
Craft things with it: weaving looms, knitting, crocheting, woodworking, origami, hand and machinesewing.
Cut and glue things with it: Kirigami, snowflakes, hexaflexagons, fortunetellers, scrapbooking.
Cook and bake things with it: Muffins, cookies, squares, breadbaking, suppercooking.
Make art with it: Mandalas, golden ratios, tesselations, geometric doodles, fractals.
Buy stuff with it: Give your child control over a small part of the family budget ($10 in groceries each week?), consider granting an allowance, make a loan on Kiva and watch the returns trickle in until you can reloan.
Marvel at it: Play with RGB and CMYK codes for colours in a computer paint program, watch Vi Hart videos, explore compound interest using a computer app.
Read about it: "The Number Devil," "Anno's Mysterious Multiplying Jar," "The Man Who Counted," "Penrose the Mathematical Cat," "G is for Googol," "How Much is a Million."
Puzzle over it: Sudoku puzzles, number guessing games, imagine infinity, talk about whether "half of infinity" has any meaning.
Measure with it: Keep track of the height of a bean plant day by day, the temperature outside, your child's weight, how much electricity your family uses. Record, tabulate and graph the results. Get to now some spreadsheet software. See how you can manipulate your data.
If these sorts of mathy things are part of a child's life, very little formal study of math is needed to bring a child up to a high school level.
Miranda
Mountain mama to one great kid and three great grownups
Spirograph! Found an old set.... still trying to find pens to use with it.
Bicycles can also teach some basics about ratios (and work, but then that's onto sciencenot that that's a bad thing).
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
i'm using teaching textbooks with both of my kids this year (after years of using only CLE). my 8 year old son is using the 3rd grade level and it definitely starts at the beginning reviewing the basics. it was pricey imo, so i would recommend buying it used if you can find it. they have sample lesson on their website. my kids did the sample lessons before i bought it. anyway. it has been a godsend this year for us. to fill in any state standard gaps (as TT is written for homeschoolers), we play games online for the FCAT test preparation. anyway i felt it was worth mentioning. i've been very pleased with it.
ETA  oh...life of fred is good too. i was fortunate to borrow the books, and the apples book and other elementary series go nicely with TT3 (or as a stand alone or supplement to any math curricula).
homeschooling mama to DD 10 & DS 7
Here's some good reading on that:
From Boring to Board Games: Math Really Can Be Fun!
Crazy for Calculating  Making Math Fun
Home Education Magazine  Taking a Closer Look at Math
Lillian
This has absolutely been our experience as well.
DS informally explored much of the stuff mentioned in previous posts (with the addition of musicreading, which I believe was really useful to him in learning how to add and subtract fractions, but again this was an informal sideeffect of learning to play a musical instrument, and not something he did "to learn fractions").
Math, integrated naturally as a useful and relevant aspect of DS' everyday life, gave him by age 10 the equivalent of what the average adult uses on a daytoday basis. Because he'd been able to reflect, on his own terms, about numbers and how they worked, he'd acquired a much more profound understanding of fundamental math concepts, with none of the accompanying mathphobia that so many adults seem to have as a result of their early math drills and worksheets (which encourage memorization/procedure rather than understanding).
If DS' math exploration had stopped there, he'd have had enough math to function smoothly through most of life's transactions, and I was okay with that. Honestly, there are many, many worthy paths in life that don't require algebra, let alone calculus.
However, six months ago, at age 13, DS decided he wanted to do high school math (he loves chemistry, and we'd discussed what the university requirements are for that). He plunged into Teaching Textbooks Algebra I without trouble, having done basically no formal math up to that point. The only gap he needed to fill was the multiplication and division of fractions, which he proceeded to learn in a day of worksheets we found online for free. He'd learned everything else he needed for algebra through everyday living math.
He's been acing the Algebra I program and will soon be moving onto Algebra II. Though he finds it easy, he does it out of necessity, not love for the material. But he continues to be selfmotivated probably because, in addition to not having any of that mathphobia, he's now old enough to view math as a personal means to an end (chemistry).
I know it's become a tired cliché about homeschoolers being able to learn what they need through "living math", but our experience at the prealgebra level has completely supported that. In our case, I think the key was to have DS view math as a meaningful and nonthreatening part of his everyday life in the younger years, and then, once he was old enough, to engage him through an ageappropriate dialogue about what math he might need in his future.
Here's a link to a thoughtprovoking essay on the current state of math education: Lockhart's Lament
ETA a disclaimer really. First my computer is playing up a bit and I think I might only have read the first page of replies. Second, I am absolutely not trying to override the unschooling approach, I'm just explaining what has worked for us, which has been a more structured approach. For all I know, the unschooling approach would have been as effective, its just that my personal hang ups don't allow me to leave math in the slightest to chance!
Just to add, we are a family where math is important, as parents we are a mathematician and a scientistintraining and I do feel rather strongly about the importance of teaching mathto my kids. My experience was that despite coming from a mathsy family, despite going to a freerange school, I never really understood math and developed a strong self image of myself as someone who could not do it. I was actually borderline phobic about math for a long time, and selfidentified as a nonmath, arty/languages person. I've sorted this out now and am midway through a part time science degree but my god it is HARD to do it this way. I needed, when i was eight, for someone to sit me down and say, don't be silly, of course you can do this stuff, now what is actually the problem, lets sort it out. So I'm coming at this one as someone who strongly believes in the importance of early, good, inspired math teaching, especially for any kid who selfidentifies as bad at math. I have to say, I'm especially on the look out for this with my girls because I'm aware of society telling them constantly that math, like heavy lifting, is something you get a man to do. I'm also married to a mathematician who is also (despite it not being his job) a really, really good teacher of maths and science.
I'm not pushing this approach, but if, as I understand it, you are, like us, reasonably structured, you might find our experience helpful. Or not!
Soooo what I have learnt so far (my kids are 9, 7 and 4, I'm aware I have an awful lot more to learn!).
First, I really do believe in the importance of play til around age 7. Both my older kids went straight from an early childhood of play to being slightly ahead in math (we use a computer program which happens to track them according to grade levelnot my favourite feature).
Second, I believe in using manipulatives for absolutely as long as they need them. My just 9 year old is doing decimal and fraction work right now, and we absolutely still use manipulatives to explain the concepts, for him to use as long as he needs. We also use things like number boards, hundreds charts and so on. To be honest, even with the university level math courses I now do, if need be I use manipulatives for complex ideas. We have a good range of manipulatives, including coins for decimal/place value work. My rule is to ALWAYS start out visual then move to abstract only when kids can certainly cope.
In terms of textbooks, my absolute favourite program is Miquon. Miquon is wonderful, the epitomy of a the hands on approach. We have never used it as a textbook though, sometimes we just used it as a a jumping off point for work. There is a teacher's manual with lots of great further activities, although for many of them you can easily work out how to supplement. When they had thoroughly finished Miquon we reluctantly moved to Singapore. But we did Miquon very thoroughly first, plus loads of maths games, real life maths, etc. I think if I had a mathreluctant child I'd actually just work with Miquon for a while, even if parts are too easy. I actually think you could probably go on til around 9 or 10 with Miquon, though mine moved on before than. It would certainly be my curriculum of choice if, say, I were teaching a mathphobic older learner.
There are other good books with a more structured approach, but I think what a mathreluctant child probably needs is a boost to their selfconfidence in math (and every child is a mathematician, IMO) and Miquon is wonderful for that.
oh eta2. Don't use fingers, they are no good. You need something that can be put in one place to mean its already counted, IYSWIM. Even just coins are fine and better than fingers. Marks on paper. Anything.
The ideas people have posted are fantastic, but if you're still wanting another outside resource, I highly recommend Life of Fred. Here's the website: http://www.stanleyschmidt.com/FredGauss/index2.html
It's a great combination of a real approach to math and just plain fun.
DD 7/07 DS 1/11
For all I know, the unschooling approach would have been as effective, its just that my personal hang ups don't allow me to leave math in the slightest to chance!
Just to add, we are a family where math is important, as parents we are a mathematician and a scientistintraining and I do feel rather strongly about the importance of teaching mathto my kids. My experience was that despite coming from a mathsy family, despite going to a freerange school, I never really understood math and developed a strong self image of myself as someone who could not do it. I was actually borderline phobic about math for a long time, and selfidentified as a nonmath, arty/languages person. I've sorted this out now and am midway through a part time science degree but my god it is HARD to do it this way. I needed, when i was eight, for someone to sit me down and say, don't be silly, of course you can do this stuff, now what is actually the problem, lets sort it out. So I'm coming at this one as someone who strongly believes in the importance of early, good, inspired math teaching, especially for any kid who selfidentifies as bad at math. I have to say, I'm especially on the look out for this with my girls because I'm aware of society telling them constantly that math, like heavy lifting, is something you get a man to do. I'm also married to a mathematician who is also (despite it not being his job) a really, really good teacher of maths and science.
I know this thread is not about unschooling, so my comment here is a bit OT, but I have to agree with you that even unschooling parents would be wise, if children this age seem to be actively avoiding anything "mathsy", to look deeper into why so that they won't inadvertently mistake lack of readiness and meaningfulness for avoidance for just the reasons you are describing.
Sometimes I think my daughter pushes things aside from perfectionism when she sees others do it so much better, or "getting it" so much faster than her. I made the mistake of making some tangramstyle shapes by folding paper to get a precise square and triangle, etc while she was just cutting the shapes in her own way. I was blissfully charging along, explaining how to get just the right shapes, completely ignoring her own efforts and I could see her deflate. Too late to stop myself. PHLBBBTTT!! Just like that. She had so much enthusiasm at first. I should have waited and watched and let her have her notsoperfect shapes and had *fun*. Sigh! I get so caught up I forget to let her have her own discoveries and get through her struggles without someone peering over her shoulder. (And let her enjoy something despite its lack of geometric perfection. Was that even necessary? I don't think so!)
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
I'm trying to read through (while doing about 500 other things) but wanted to answer this before I forget.
We are the most backtobasics you could get without being unschooly. (Though I like unschooly.) The kids basically have to do math and Explode the Code plus a little bit of a spelling worksheet each day.3045 minutes tops. We don't really fall into any camps we aren't school at home though sometimes we will trail off into unschool for awhile and then go back to the other side. Our goals have always been to teach them the very basics (Three Rs) and the rest will go from there.
Now...off to continue reading....
To update and answer questions:
I don't think that my daughter does not KNOW the material...I think she's just really, really good at convincing herself she doesn't. Kids had same page today. She got about 2/3 through and started in on her song and dance. I can't DOOOOO this. Its too HARRRRRRRD. HELP ME HELP ME SHOW ME HELP ME. I show her. I explain a different way to do it. It could literally have been 1+1 (Actually, I think it was 98) and she would complain how in agony she is.
Finally, she finished the page. Missed just 3 (and 2 of those were because she did not understand something simple). Actually did better than her brother. So, I think she knows enough that we shouldn't have this every single day.
I'm willing to do games and other things, but I still want to see her writing down answers, too.
I'm honestly and truly getting tired of things not working for us. We tried Right Start but I had troubles understanding the material. (I have ADD and if my brain isn't in it forget it.) Singapore was okay until all of a sudden I felt on a 90 to nothing train. I just want stability...and I'm having trouble finding it.
Do you talk with them about the results? Or do you keep that to yourself? I think this can make a huge difference. Some kids might dread the judgment at the of the task, and knowing that she missed 3 might be enough to make her feel that she isn't getting it, that it's hard, even when neither are true. My daughter is like this with many things.
I'm sorry I'm not suggesting a solution so much as wondering if this isn't causing some of the problems.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
hmmm. Personally, if a child did that I would get out the manipulatives and show them, physically, what 9 buttons take away 8 buttons looked like. Regardless of what the underlying motive was.
This is all conjecture without seeing your daughter of course but I do think that this is fairly common where kids have learnt "how to" do math but not "why". They memorize a lot of tricks and techniques, but the problem with that is that if they then forget, say, how to do long multiplication, even something relatively small like which side to start multiplying from, there is no way back and they are panicked. This is one advantage IME of using multiple techniques for this stuff, appealing to as many senses as possible. Simply put, the more different ways something is encountered the more complete picture kids build up. Another thing I always do is to relate things back to life, eg by turning "98" into "your brother has baked 9 cakes. If you eat 8 of them, how many does he have left?". Sorry if these are obvious ideas, but its taken me a while to get into the swing of teaching math!
Would you consider using a computer program? We've used mathswhizz with a lot of success. It does track kids, so you do get a sense of where they "are" if you are that way inclined, if it matters to you. Its very fun, it teaches as it goes. We've used it sporadically to get over math hills, to make math a bit fun again. But also, we've used it to separate out writing from math, which I think can be really important for kids who are still struggling with writing stuff down.
If you think she knows the material, then insisting on going over the same ground in the same pencilandpaper way day after day is quite pointless, I think. It's just an exercise in whining and resistance, entrenching those behavioural patterns and negative associations. Your instincts that she knows the material and has the skills are likely correct, and I doubt she's really "convincing herself she doesn't." Instead I'm guessing that she's feeling something else about the math work that she doesn't know how to articulate, and it's coming out as a sort of indiscriminate whining. The real message beneath the resistance is likely something like "this isn't how I learn." I think I would really really start thinking outside the box for ways that aren't pencilandpaper to carry her math learning forward. At least in the mediumterm, to try to get a better handle on her learning style and to try to break the negative association with math.
I agree with SweetSilver that the approach of having a child do assigned work and then checking it for correctness can be very toxic to some children. They feel like it's all about judgement, and every error is a failure. For my kids it helped to do the work on a whiteboard, rather than on paper, and to have me help them with any problems they began to go astray with. With prompts and redirection they were always able to get the correct answer. Then we'd wipe the board and go onto the next problem. Using the white board got rid of a lot of that implication that they were creating a tangible record of their lack of perfection, and also the implication that doing math was about completing worksheets. I wanted them to know that doing math was about learning. At the end of a session, there was no record of work done, only the knowledge we both had that they were able to solve certain types of mathematical problems logically and accurately.
I could tell the extent of their mastery by how much help they needed to get to the correct answer. If they wanted to work entirely independently I'd give them an answer key. They could work the question, and check that their solution matched the answer. If they couldn't figure out how to arrive at the given solution, they could come to me for help. Again, we both knew that it was about learning, about understanding, not completing problems.
If I could tell they were struggling with something, I would address that area at the beginning of the next session, not as a correction or remediation after the current session. The message was therefore "I have an idea that I think might help you move forward" rather than "You did this wrong today and we need to fix it."
My whiteboard example is still very much about working problems with written symbols. For the time being I think it would be worth discarding that model with your daughter and taking a much more wideranging, playful, experimental approach to math. Play guessing games: Ask her "how old were you five years ago?" And "How long ago was 2008?" And "Here's a really tricky one: What's a number between twenty and thirty, and when you subtract the one digit from the other, the answer is six?" Or play Snakes and Ladders, but allow her to move forward or backwards (adding or subtracting) to get the most advantageous move. Teach her how to use an abacus counting frame to add and subtract. Play "store" with pennies and dimes, selling each other pencils for 5 cents each and pens for 7 cents. Make change for the dimes you pay each other with. Learn cribbage. Build a spinner from a paper plate and create a board game together with adding and subtracting along a numberline gameboard. Build a 20minute "math lab" into your day in the same way that you currently have worksheets or whatever. Use those activities and experiences to build your understanding of what your dd understands about math, and of what grabs her interest and gets past her resistance most easily.
Am I correct in understanding that she has a younger brother who is almost as adept, or perhaps more adept, at the worksheet type stuff? That can be very very difficult for an older siblings. Her resistance may be her way of saying "I am afraid I am stupid, and therefore unloveable, because my little brother learns better than me. If I finish this work, that provides more fodder for comparison, and I'm afraid I will be the loser." If you suspect any of that sort of emotional overlay, your main priority will need to be making her feel smart. Tell her that there are snatches of absolute brilliance that you see in her mathematical reasoning, and you haven't yet discovered how to really turn all that brilliance on, but you know it is possible because you've seen that it's there. So you're going to mix things up a bit and figure out how to help her learn math *her way*.
John Mighton, author of a fabulous book called "The Myth of Ability" and founder of the charitable tutoring organization called JUMP (Junior Undiscovered Math Prodigies) has some amazing advice about unlocking belief in the sense of math, and belief in one's ability to understand that sense, and the absolutely transformative results on children. The secret is to give the child success, and encourage her to believe that she is brilliant because of that success. And by success, Mighton means steps as small as fingercounting. He starts out by moving ahead into new skills well ahead of where the child is, and teaches them the smallest step at a time. For instance, you could teach your dd division by showing her how to count up groups on her fingers. Divide 12 by 3? Every time you hold up a finger, count up three numbers. Stop when you get to twelve. "123 ... 456... 789.... 101112." Four fingers standing, so 12 ÷ 3 = 4. Have her do this. Is she successful? Did she get four fingers standing up? She can do division! She's brilliant. Try 12 divided by 2. That means saying two numbers every time you hold up a finger. Whoa! Six fingers!
I would do this independently with her, without her brother around. Let her feel smarter than him in that she is learning division, and he is not. Give her something that she can do mathematically that makes her feel brilliant, and then begin to build on that.
Good luck!
Miranda
Mountain mama to one great kid and three great grownups
What about computer games? That way she is still "writing down answers" without having to actually sit and write down answers.
Ds plays dreambox learning. I really like the way a lot of the concepts are shown.You can get a free trial. It tracks where the kid is and gives (albeit sometimes odd) suggestions of ways to work on the concepts in daily life.
One of the benefits of things like computer programs for math (and I'm a very handson, low screen time kinda person) is the immediate feedback (e.g. the question is 98 and you select 3 and it says something like "98 is less than 3 try again" or then moves immediately to an illustration of 9 things  8 things etc).
If some of the emotional stuff that Miranda was talking about is in play then she can play a math game with headphones on so it is "private" and no one can hear where she is struggling.
Interesting article which reminded me of this thread:
http://www.digitaltrends.com/lifestyle/thankssciencemathphobiacanliterallycausebrainpain/
The following excerpt seemed particularly interesting, given that the OP stated that she herself wasn't "a natural at math" and so was sympathetic to her daughter's situation:
"The study, supported by the National Science Foundation and the Department of Education, also stated that the math phobia can begin as early as first grade. Additionally, female elementary school teachers can transmit their math anxiety to their female students, influencing them to hate math just as much as they do. The research concludes that since the problem lies to the fear of doing math, an integral school subject, more must be done to help student feel more comfortable about math rather than piling on homework to make them theoretically better at it."
Jumping in a bit late here (haven't been on MDC for a while) but I wanted to share a program that has been working for my kids. We were very unschooly but lately have switched to a more eclectic approach. I got a subscription to the online Math program DreamBox and it is going really really well. The first thing I love about it is that it is very visual and my kids are definitely visual learners. They teach addition and subtraction using various "tools" that show different ways to visualize numbers. So if you think your kid isn't into worksheets and might prefer manipulatives this is a great program. The second thing I love about it is that it breaks math down into different categories and keeps track of where your kid is for each one and adjusts for that level. So they may be great at getting place numbers but not so good at addition: they will move forward with one and not the other. The program sends me a report each time the kids use it (although I sit and watch them  they prefer that!) which is great for reporting for our homeschool program.
Anyways, my 10 year old DD had gotten quite Math phobic, and as a result had been deliberately avoiding math until it became apparent that she was years behind in some basic areas and I think this was contributing to her phobia. She seems to quite like this program (though she won't admit it, but often asks to work on it, lol) and I'm thrilled with the results so far. They offer a free 14day trial and you can pay for your subscription monthly which helps with the cost (I think it's about $12/kid per month).
Homeschooling, Homesteading Mama to DD ('02) and DS ('04)
Also jumping in late...
We keep a few "coffee table" math books out, and also read one on occasion before bed. They're fun enough that it makes the math fun. They don't constitute a curriculum by any means, but anything that makes math part of everyday life and always available is a good idea, in my opinion.
From http://nerdybookclub.wordpress.com/2012/11/24/toptenfunmathbooksbysuevanhattum/
You Can Count on Monsters, by Richard Evan Schwartz
(any age)
Each number from 1 to 100 is a monster, and each one gets its picture on its own page. All of the numbers (except poor 1) are made up from their prime parts. The pictures are colorful, full of intriguing detail, and amusing. The pages in the front and back that explain prime factorization are unassuming, waiting for the reader to decide it’s time to find out more. This and Powers of Ten would both make great coffee table books, to peruse over and over.
Euclid in the Rainforest, by Joseph Mazur
(12 to adult)
Logic, infinity and probability are the topics. Adventures in Venezuela, Greece, and New York furnish the background. Mazur has wideranging interests, and skillfully brings the math to life.
Powers of Ten, by Philip and Phylis Morrison
(ages 6 to adult)
The first photo shows a couple having a picnic. It’s shot from one meter above them. The next is from 10 meters, then 100. After we’ve traveled to the edge of the universe, we come back to the couple, and zoom in. Each page has one large photo, and explanatory text about what can be seen at that level.
The Number Devil, by Hans Magnus Enzensberger
(ages 7 to adult)
The Number Devil visits Robert in his dreams, and gets him thinking about the strangest things! Rutabaga numbers and prima donnas (roots and primes) are just the beginning. Anyone who’d like a gentle introduction to lots of interesting math topics will enjoy this one.
The Man Who Counted, by Malba Tahan
(ages 6 to adult)
Written in Brazil, set in the Middle East, these stories follow the adventures of Beremiz, an accomplished mathematical problemsolver. He uses math to settle disputes, solve riddles and mysteries, and entertain his hosts. The series of 34 adventures, each with a math puzzle, is reminiscent of the Arabian Nights. If you read one chapter a night, your audience will be begging for more – and isn’t that the way it should be?
Cat in Numberland, by Ivar Ekeland
(ages 5 to adult)
The story starts when Zero knocks on the door of the Hotel Infinity. He’d like a room, but they’re all full (with the number One in Room One, and so on). Turns out that’s no problem. The cat who lives in the lobby gets confused – if the hotel is full, how can the numbers make room for zero just by all moving up one room? Things get worse when the fractions come to visit. This story is charming enough to entertain young children, and deep enough to intrigue anyone. Are you ready to learn about infinity with your 5 yearold?
I agree about keeping the focus positive.
(But mostly I am responding just to say: Piglet68, what a treat to see you on here! My first vivid MDC memory was the days of waiting for your daughter to be born... back when there were, like, 40 of us on MDC per day, lol! And here we are homeschooling nearly adolescent daughters. Wowza. Hope you and the family are all doing well. )
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