Counting Invisible Blocks

hidden_blockMarch 2, 2014
One of the first skills introduced to Robert when he was 3 or 4 was block imitation. Robert should copy the presented 3D model. I don’t remember the maximum number of blocks Robert was supposed to use. I don’t remember how well or bad he was doing. I don’t think he had ever progressed from imitating 3D models to making a structures based on 2D pictures. That was done at his private school. At home, Robert played often with Lego and built structures based on sequences of pictures. I always assisted him more or less. And of course, he usually built everything only once, so there was never any opportunity to reach mastery and being completely independent.

For the last few days, Robert was counting volumes of different 3D shapes based on their pictures in the workbook from Singapore Math, grade 3. He counted all the blocks except those he couldn’t see, as they were behind or under other blocks. I asked him to build those structures. He began but soon became confused. He saw the block in the second layer, but didn’t see the block that should be underneath it. Robert’s hand held the block in the air. That was the right position according to the picture, except it was impossible to leave the block there without the support of another block that was NOT visible in the picture.
Robert’s hesitation was priceless. The discord between the picture and the reality forced him to doubt himself.

In the last few days, he mostly build rectangular prisms. He could easily assemble them, layer by layer, based on the drawing. Although he made them without difficulties, he still had trouble finding their volumes based only on the pictures.
His first response, when presented with the drawing of the solid, was to count what he saw in the picture and not using his mind to count the invisible cubes.
Many times, after he erected the prism, I separated all the layers taking them down one by one, and then I restock them hoping Robert would remember those invisible blocks covered by the subsequent layers. Robert seemed to find the proper value of volume.
Unfortunately,with the next rectangular prism, he proceeded in the same manner, making all the same errors. He looked at the picture not to make a mental model in his mind, but to count the blocks on the visible surfaces. He was able, however, to build the rectangular prisms based on their pictures, and then count their volumes.
Today, he had difficulties with constructing more complicated models. That is why he held the block in the air and felt that something was amiss. This moment of hesitation was much more important factor in understanding the importance of invisible blocks, than the automatic recreation of the rectangular prisms.
The few seconds during which Robert’s hand hung over the space where something should be but wasn’t, provided priceless opportunity for an analytical insight. The confusion Robert felt could be the first step to recognizing the problem, and thus thinking…
I regret that I didn’t realize how important the block imitation could be, much earlier. In ABA format block imitation became rather mechanical and boring task. It was repeated over and over until given model has been replicated with 80% accuracy. There are of course good reason for that – working on attending skills could be one of them. What I haven’t realized then was that copying even simple picture might have helped Robert to replace his reliance on what is visible in the drawing to what makes sense in his mind. That the mind can fill the gap left by imperfect images.

Bacon, HIs and Mine

This post was a part of another one I wrote on March 31. After close reading, I decided, that it should stand on its own as this is a separate and important topic. Moreover, today, on April 2nd, another trip to the supermarket brought a nice, calm solution to the described problem.

Just before the lunch, we went to Stop and Shop to buy Robert’s favorite Tyson chicken. At the beginning, everything went very well, as it always goes. Robert tried to buy his favorite Thai Chips, but I gave him a choice of chips or chicken. He put chips away and found Hot and Spicy Tyson Chicken instead.
But then, I chose two packages of Farmland bacon, because they were on sale: two for 4.99. Robert removed them from the shopping cart and put two packages of Oscar Mayer instead. He must have been convinced that I made a mistake and he attempted to correct it. After all I always buy Oscar Mayer. When I tried to explain to Robert why this time I wanted to buy Farmland, he didn’t accept my explanation about higher and lower prices. I don’t blame him. Rarely during our shopping, I asked him to choose cheaper item. I don’t think Robert understands that concept yet. Anyway, when I asked Robert to switch back, he became agitated, protesting rather loud. I stood my ground and told him that since we disagreed, we would not buy any bacon that day. Although unhappy, Robert put Oscar Mayer bacon back. Of course, I could easily predict that this would happen and plan for this situation. But life does not always let us prepare for the unexpected thus managing one’s reaction to such event is a true challenge.
The entire “discussion” lasted maybe half a minute but it was a loud exchange and I considered it a setback. Because, I was loud too. Being stern and using a full voice served two purposes. For once, if I whispered, it would give Robert the wrong impression of my weakness caused by the embarrassment. Secondly, I did not want anybody, who witnessed this exchange to consider me the victim of someone out of control. The image of people with autism being out of control has been already installed with too many bystanders. Robert is not out of control, even though his behavior was problematic.
Despite the appearance, I was pretty shaken, as this was the first problem in the grocery store since 2006. In eight years of going to the store, we didn’t have any problems. Robert could find anything and was never insistent on buying something I told him not to, because we had it at home or because it was not good for him (like cheese in a can).
While, I understood that the reason Robert wanted to switch one Farmland bacon for Oscar Mayer’s, I didn’t anticipated such a strong reaction. Was it because he is much more stressed by staying home and resulting from that his sleepless night?
Yes, I appreciate the fact that Robert has been so wonderful in stores in the past. I appreciate that he agreed to leave Oscar Mayer bacon in the store and leave the issue unresolved until later. I appreciate the fact that the rest of our shopping trip went smoothly as Robert demonstrated much more independence using self register – scanning the items and even entering the codes for tomatoes and apples.
I appreciate all of that, but I still worry.
Robert does too. He hates confrontations. He is exhausted and slightly depressed after they happened. Yesterday, he was sad too. Luckily, he had his last cooking class in the session. He was among his peers. He was busy. He was happy.
Today, April 2nd, after a morning session of learning, Robert and I drove to the Stop and Shop Supermarket. Before we left, I asked Robert, ” Could we buy one Oscar Mayer bacon for you and one Farmland bacon for me?”
“OK”, he said.
Still, I wasn’t sure. But at the store, he chose one his, and I chose one mine kind of bacon. It was that simple.

Journal, Page 8

March 31, 2014

Robert woke up late. I did not try to wake him earlier, as he couldn’t fell asleep last night. He was up, until almost 2 AM. We studied together using Let’s Predictcards. Robert had to tell what was happening in the picture and then predict what would happen next. We also worked with Changing statements to questions cards. Robert continued building structures using cubes and counting their volumes. He was doing much better in copying the structure from the picture. Since, he still had difficulties predicting the volumes of rectangular prisms based on the drawing, he had to build them layer by layer.
I remember that in the past, when we for the first time approach this topic, I didn’t notice that Robert didn’t understand the word “layer” and thus my explanations about counting area of one layer and multiplying it by the number of layers was lost on him.
Yet again that was an example of a teacher (me) using language that confuses instead of clarifying.
Now, Robert understands the word “layer”, but he still has a tendency to counting only the cubes visible in the picture instead of using deduction to “notice” those cubes that are hidden under or behind other blocks.
We read the next story from Third grade Spectrum Reading and Robert with my help answered five WH and one HOW questions about it. “Who, when, and where” are almost independent, but “what, why and how” require assistance. And of course we went on with Saxon math grade 4, lesson 133. Robert for the first time independently drew a picture for a multiplication word problem and then solved it. Later, he also counted the price of two large drinks and three small hamburgers. This problem required multiplying decimals and adding them in a proper order.