Some Progress in Math, Subtraction

The first photo is a recent example of addition problems that Samuel did. It turned out a little messy because I had to "fix" the fours. The touch points for four don't work on one with a closed top. Careless preparation on my part, oh well. Samuel can do these problems without the sentence at the top of the page "I see a plus sign....", I'm just putting it there for right now to make it consistent with getting him to think about the kind of problem he is looking at.

I have been trying to teach Samuel subtraction for several months now. The first attempts I made at teaching him were using word problems in which he crossed out the items being subtracted. This worked pretty good. He seemed to understand that the number he ended up with was the answer to the problem and he knew where to write it. I only had to prompt him how to do this a few times. However, when I removed the sentence with the problem and just put images for him to cross off he couldn't seem to get it.

The next step was top use touch points on the numbers. Samuel learned to add at school with touch points and he had this system down quite well. Using touch points for addition is simply adding the dots that are on the numerals and the total is the answer. For subtraction you teach by starting on the top number and then counting backwards on the touch points of the lower number that is being subtracted. It has taken Samuel a while to understand this but we are starting to make some progress! I have been using more physical prompts (hand over hand placing his finger on the numbers or the touch points) and I try to minimize the verbal prompting. I started putting two problems at the top of the page and folding the paper in half. When Samuel did those problems I prompted him. Then, after he finished them I flipped the paper to the bottom half and told him, "Okay, this time you do them yourself." At first he couldn't and I had to prompt him again, though usually less. Eventually, he was able to do the problems on the bottom half of the page without prompting.

What was really exciting recently was when I put both addition and subtraction problems on the same page. The only "prompt" he had was the words saying that it was an addition problem or subtraction problem. I did not have to prompt him at all to do the problems after that! The next step will be to remove the words from the page.

This photo shows how there are problems at the top of the page, which I had to prompt him to do at first. The page was folded in half and when he finished these problems I turned it to the bottom of the page and he did these with less prompting, eventually no prompting.

This photo is an example of getting Samuel to differentiate between addition and subtraction problems. Eventually the only directions on the page will be words to the effect, "Solve these problems."