On Feedback
For example, Larry and I were recently working together on his mastering short division. At least we were supposed to be working together on that. It quickly became apparent, however, as we sat at the dining room table in his home, that I was working on it much more than he was, at least in the beginning. I knew it because of the feedback available in the situation, some of which is revealed in the following narrative. We began by my placing an orange rod end-to-end with a light green one. I looked at him and waited, expecting that he would show the hand sign for “thirteen.” Instead, he looked at me blankly and did not move. Now, that could mean many things: perhaps he was waiting for me to go on, or he thought it was silly for him to show that he knew what I already knew he knew, or he was pulling my leg, or he was distracted, or he was confused or he did not want to be bothered with it, etc., etc. So, because I did not yet really have a clue as to what was going on inside him, I waited a bit longer, assuming that by now (after perhaps 30 hours of working together) he understood that my sitting back and waiting was often an indication that I expected him to do something. Still, he took no initiative in that direction. At this point, I took a sheet of ruled paper, wrote on the uppermost line the numeral “13,” and then underlined it. I looked at Larry, who shrugged and nodded simultaneously. Since I only very rarely asked him to be engaged in something which was not worth his time, I wondered at his apparent detachment and felt very definitely his reluctance to begin working with me. Alerted to and keeping in mind his reserved state, I made sure that my next request for his cooperation involved his doing something new but also immediately accessible if he watched. I formed, just below and touching the orange and light green train of rods, a second train, equivalent in length but composed of six red rods and a white one. Then I wrote, on the second line on the sheet of paper, “6 twos + 1.” I looked at Larry, who stared blankly at the rods. Watching him, I touched with my pen the first train of rods and then the numeral “13,” pausing there. Still no response. I then touched the second train, and 6