Okay, here's a story about my ds, now 16 and planning to take Calculus next fall, scoring A's in preCalc, and thinking about a career in engineering, design, computers or digital media, planning to attend college in that vein. He's been an incredible math thinker since a young age: when he was 3 he told me that 4, 9 and 16 were square numbers. But while he had some interest in math games that I offered him, and the math 'discovery lab activities' that I occasionally introduced him to via Miquon Math, he wasn't interested in any systematic learning of math. He's super bright, but has a fierce streak of perfectionism. So much so that he easily becomes paralyzed, afraid to try things that he might not be able to do instantly and well. I was cool with his unschooled math learning. He seemed cool with it too.
Then at age 7.5 or so he asked for a math workbook because he wanted to improve his computational skills. He wanted something more systematic and book-work focused than Miquon. We purchased Singapore Primary Math at the appropriate level. He tried it a few times and it was okay, but somehow he didn't ever really dive in. He seemed discouraged that he didn't necessarily always know for sure what the correct answer was, that he would occasionally make an error, or have to puzzle away at something. He'd cry and quit. It was enough to reduce his motivation to negligible levels.
A couple of months before his 10th birthday he realized that his "level" in Singapore (where he had left off) was below his grade-for-age, meaning that according to him he was now 'behind.' And at the same time his younger sister began moving towards the same level in the curriculum that he had given up on. He started loudly voicing negative feelings about math: I hate it, I suck at it, math is stupid, that sort of thing. When this happened he hadn't really worked away at math in either a happy or an unhappy way in over a year, so it seemed to me that this was his lack of confidence speaking, and a way of trying to diminish his sister's success and enthusiasm which he felt threatened by. It created a fair bit of stress for his sister as well.
He and I talked a lot about the issues. We talked about his perfectionism, his learning style, his clear mathematical aptitude, his discouragement, his lashing out at "math" and how that was affecting his sister, and so on. He said that he was really mad at himself for not consistently using the Singapore workbooks we'd got a couple of years ago. He said he wished he was still 'advanced' in math. He wanted me to help him progress. I pointed out all the ways that his conceptual understanding of math was advanced, but that wasn't enough for him. We talked about numerous ways to help him master the arithmetical stuff, but it kept coming back to him wanting help sticking to Singapore. He asked me for that help. We talked about exactly what that would look like. I knew he was prone to perfectionistic meltdowns every time he made a mistake or got stuck in something. If he was miserable, if he was crying, should we give up for the day, or for a few days? No, he said. Make me do it, three to five days a week. For how long? I asked. This whole year, he said. I suggested we commit to a month, and reassess at the end of that time to decide whether to carry on.
And for that first month I think he cried almost every time -- more than half the time anyway. It was fear that he wasn't smart enough, and it would shut him down almost before he tried anything. I'd let him sit there sniffing and keep helping him. I always asked him to give "three good tries" before we set something aside for another day. So if he said "I don't get it!" or "This is too hard!" I'd say "Okay, that's your first try. Let me show you a different way, and then you can give it your second try." Or I'd say "Remember the steps we talked about ... " and guide him through it, and count that as the first try. I was trying to help him understand at a visceral level that you can't always do everything right the first time, and trying something difficult three times and then taking a break is reasonable. He knew this intellectually, but when it came time to grapple with something difficult, his anxiety would well up and he'd give up. So I redirected him a lot ("let's do something from the geometry section!" or "Let's do a puzzle!"), and we kept the kleenex nearby.
At the end of a month we talked things over. He had progressed, but he had experienced a lot of misery. I had supported him creatively and consistently, but I felt awful about it. I asked him if this was really how he wanted to be doing things. I really expected him to quit. But incredibly he said that he wanted to keep going.
Somewhere around months 2 and 3 he got over the hump. I suddenly realized that there hadn't been tears in weeks. The "three good tries" thing had become automatic for him. He was progressing -- quickly now! -- and the anxiety was so much less. He could see that he was good at math. That confidence spurred him forward. And then there was a huge breakthrough: after five months he had finished three years' worth of the Singapore program and was now a year or more "ahead" of his age grade. I asked if that was enough, but he decided to keep working and finish out the 6th grade books in the program.
Never again has he suffered math anxiety or lack of confidence. His interest in systematic study of math has waxed and waned, but never due to fear or lack of confidence, and he has always returned to it with enthusiasm when it suited him. He's also proved himself very capable of self-structuring as he's gained a bit of maturity and applied what he learned through his experience with Primary Math to other areas of his life.
So I don't know, it seemed to work. Before I structured that "math recovery" year for him, he seemed to be in a downward spiral of anxiety and loss of confidence, and it was spilling over into the rest of his life and into his relationship with his sister. After I structured that year, those problems were essentially solved. Could I have structured things in a gentler way that would have been as effective? Maybe; I'm not sure. Could I have left it and simply continued to express confidence that he would figure out how to self-motivate and self-structure, modelling my own self-structuring? Yes, and who's to know whether he might have accomplished what he needed in order to recover his confidence. We can't live life over again trying a different approach. But I suppose that's why the scenario I mentioned at the top of this thread piqued my interest so much: I was willing to play the math heavy with a kid who asked me to do so, and the outcome had seemed pretty positive.