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how my 2nd grader (who is dyslexic) struggles with solving 12-7 on her homework worksheet but can answer 16x8 in her head for fun, just because.

When DD9 picks up a pencil, her brain freezes. At least, that is how she describes it to me. With dysgraphia and stealth dyslexia, both just recently diagnosed, she developed an intense fear of making mistakes. To this day, she has such anxiety when she has to write anything that she is sometimes paralyzed by the easiest of tasks. Math is especially hard for her, because not only does she struggle to make the numbers correctly but she also has to keep her columns straight. Add in ADHD that prevents her from concentrating well enough to make it through an entire math problem on her own and she pretty much just gives up before she starts.

BUT... ask her how to do the work out loud and she will blow you away with her reasoning skills. So frustrating for them.

DD9 always has been able to do math in her head. When she was in first grade doing second grade math, she always got messed up on the "show your work" part. If you asked her, she could tell you that 93 + 28 = 121. If you asked her to use a number line or "sticks and dots" to show how she "got the answer," she would mess up -- making extra jumps on the number line or miscounting her messy sticks and dots. Using the methods mandated by the teacher, she often got the wrong answer. This would make her doubt the correct answer that she would get if she just did it in her head. Talk about frustrating.

Sometimes, turning the paper sideways (so the lines act as column guides) or using graph paper can help somewhat with this.

If she has access to a computer for assignments, math symbol software like the program at the link might be helpful for setting problems up.

ETA: There is a very good pdf on choosing math assistive technology here.

We have had problems with "show your work," too, and DD is not dysgraphic at all. She just gets bored drawing all the little dots or sticks or what have you when she already knew the answer just by looking at it.

DD9 says she hates math and can't do it, etc. etc. etc but then spends time figuring out how many minutes are in a year and how many minutes a trip will take if we have 150 miles to go and are traveling at 75 mph!
She too got stuck on the show your work stuff when it was simple arithematic, and even now is more accurate in her head than on paper. I wish I could figure out a way to increase her confidence in math and then I think her ability to write down her reasoning would increase because she doesn't like to get things wrong, so she doesn't want to show her work.

You could consider trying to do some Kumon workbooks at home. We do one page a day and it has greatly increased my kids' accuracy and confidence. More than that is boring, but there is something to be said for a little repetition to get the basics right. My older son would also refuse to show his work and would occasionally miss things due to silly carrying errors, but the Kumon workbook finally got him in the habit of showing his work.

DS9 hates to do his math homework, but spends hours writing page after page of cubed numbers for no apparent reason. He doesn't want to do a report, but cuts the weather reports out of the paper and glues them into a notebook for no apparent reason.

They're crazy!