Tracey over at Inside the Mommyvan has some really great tips on teaching when your child seems stuck on a concept. And I have to be honest, when my kids have to do this, we're screwed. I have no idea what she is talking about. Give me sine and cosine any day over this!
Last fall, one of my young students began to struggle with a particular math concept. In his case it was adding numbers with sums just beyond the next ten, like 8+7 or 43+9, and doing similar subtractions "across a ten.". i put that away for a bit and moved on to some different math topics, thinking maybe we just weren't quite ready to tackle that. The "Asian math" curriculum we've been using as our primary is known for being fairly rigorous and fast-paced.
When i revisited it in December, the results were no better; if anything it was worse. i tried every teaching method i could think up or read about, but nothing seemed to stick with this child. ALL of the manipulatives came out: the unit blocks, the base-ten set, the abacus, the ten frames. i drew pictures and diagrams. I explained with words and we counted on our fingers. We used online programs and iPad apps to make it more interesting. I offered bribes and made dire threats. He could get to the correct answer by brute force (and, interestingly, he had many of the sums between 10 and 20 already memorized) but i could tell that he just wasn't getting the key concept.
(That concept, for those interested, is that the "ones" being added are split into two parts. First enough are "given" to the other addend's ones digit to complete "the next ten" and then the remainder become the ones digit of the sum. 28+5 becomes, first physically with blocks or abacus and then on paper with little tens-and-ones pictures and finally with numerals, (28 + 2) + 3, and on to 30 + 3, and finally 33. That they learn this before the old "carry the one" vertical addition algorithm is critical to developing strong mental math skills.)
We'd hit a brick wall. This child was going nowhere, and I had exhausted all of the topics with which I could work around this one. If we were going to progress, I had to find a way to get this idea into his brain. My patience was wearing thin at this point, and i was about ready to throw in the towel and... i don't even know. We even tried an outside enrichment program, to no avail (it wasn't a very good one).
Finally, I took a leap and purchased another popular math curriculum. I'd previously shied away from it because it seemed to have a lot of busywork, drill questions which looked like duplicates of work we were doing online. it wasn't cheap for something i wasn't even sure we'd use, but i was desperate. It devotes a couple dozen pages to slowly building this particular topic up, step by tiny step. Surely the kids would be bored before we were halfway through, going over and over the same material.
I pulled every page relevant to our trouble topic out of both the main text/workbook and the supplement. i reviewed the first baby step with our manipulatives. I took a deep breath, and set the first page in front of him. He breezed through it! We tried two more pages the next day... same result. I could see the light bulb flickering to life! Before long, he'd made it through the entire section. Best of all, he's gotten a taste of success where previously there had been only frustration, and he's enjoying it! He is now doing sums in his head that he could previously do only with base ten blocks and lots of coaching.
Often, a failure in the classroom - even a homeschool classroom - is unilaterally placed on the student's shoulders. It's inattention, carelessness, laziness or willful obstinance, even a learning disability. For some students this is accurate, but before slapping one of those labels on we need to be sure it's not instead a failure of the teaching. As homeschoolers, we have the luxury of slowing down, even backing up to try a different teaching method or curriculum, but we must remember to take advantage to that and not be slaves to the checkboxes in our lesson planners. In our case, a simple change from one math book to another was the ladder we needed to hop right over that brick wall we'd slammed into a few months back.