In my previous post, https://krymarh.wordpress.com/2012/03/31/looking-for-variables/, I described how I helped Robert to learn adding numbers up to 20 despite his issues with short memory,.

In a different post https://krymarh.wordpress.com/2012/12/11/take-it-to-your-brain/, I wrote about teaching Robert to use algorithm for rounding numbers. In both instances, solving problems on paper was only an introduction that was supposed to help Robert to solve problems mentally.

I have just realized, that too often, I didn’t practice switching from finding results on paper, to finding it mentally. Consequently, Robert has not learned those methods, I though he had mastered.

Almost two years ago, Robert was learning to write large numbers switching from words to digits and vice versa. But as we were, recently, practicing changing kilometers into meters, kilograms into grams, and liters into millilitres, Robert kept making errors alerting me to the fact, that his grasp on decimal system was not as solid as I believed it to be. He could write 2387, 2031, or 2008 using words, but he had problems switching from words to digits such numbers as two thousand thirty-one or three thousand nine. When either tens or hundreds were missing, Robert forgot to put zero in the right place. We had to return to Robert placing digits in each of the four columns. While he was placing digits in appropriate columns for ones, tens, hundreds, and thousands, he appropriately put zeros when hundreds or tens were missing. Now, before he has to switch from words to digits, I tell Robert, “Help Yourself”, and he draws those four column by himself and completes the tasks without error.

Now, is just one more step in learning. Step, which I used before. Once successfully while teaching basic addition up to 20 and once not so, while introducing an algorithm for rounding numbers. This step calls for using the same support mentally, without writing. To write the number three thousand seventy-four in digits, we would start with drawing and naming the columns, BUT, in that phase, I would not let Robert write down the digit. I would ask him to imagine, that he does so, and then write the 3074 on the side. Next, I would cover those four columns with my hand and ask Robert to imagine in what space under my hand he would write the digits.

The similar trick we used just this week, to help Robert count minutes until full hour, that is to subtract mentally two digit numbers from 60.

At the beginning, Robert practiced by subtracting first tens then ones. 60- 24= 60-20-4=40-4= 36. except he wrote the first difference above the first subtraction. After practicing that for a few days (It was easy for Robert, because that part we did before.), I wrote only, “60-24” and Robert did both operations in his head. He first said, “forty” and follow quickly with “thirty-six.” However, he was still looking at the numbers in front of him. So, in the next step, I wrote “60-35”, let Robert take a quick look, then I covered the subtraction with my hand and waited for Robert to answer. Finally, I just asked, “How much is 60-18?”. We practiced during car rides, not just with subtracting from 60 but all other full tens: 20,30, 40…and so on. Robert kept doing the same thing. For 60-15 he first said “50” to quickly follow with “45”. But, I didn’t mind.

After all, he took the method to his brain.