On Language and Logic

For a few last afternoons, Robert was pasting pictures in  the order determined  by the three sentences printed above the four empty rectangles.

We worked on problems presented on pages of a thin workbook Cut, Paste, & Color. Logic, Grade Level 1-2 by Remedia Publication.

X is first.

Y is not the last.

W is behind Z.

It was not our first attempt to do so.  Using copies of the pages from that book, we worked on those tasks a few  times in the previous  three or four years.   We had to work together as Robert needed a lot of support and was not able to complete the tasks  independently.

The reason was that Robert had problems with understanding negation. After reading, ” Gorilla is not the oldest.” he, not surprisingly,  placed the picture of the ape above the word “oldest”. To remedy that, we returned to the old set of cards from Super Duper School Company.  Despite Robert becoming very good in understanding negation in this context (cards), whenever we returned to the Logic workbook, the errors resurfaced. Consequently, we brought back the cards, returned to the workbook , practiced with cards, and ….gave up.

For the last few days, I have been trying a different approach.  Simpler one and more… logical.  After reading, for instance, the sentence, “Gorilla is not the oldest” I ask Robert to write, “No gorilla.”  in the space above the word “oldest”.  I think, it would work better.

The error I made during the  previous teaching attempts, was caused by not addressing the problem in the context of the activity, but practicing it in different setting (with cards). Nothing wrong with the cards as long as they are used as a SUPPORT of the main activity.  When used separately, they become a goal in itself and do not apply to anything else.  I made a mistake of not using Robert’s ability to understand (?) negation in one context to solve more complex problems  in a different setting. Consequently, Robert did not recognize a new problem as a variation of the old one.

Lack of a full understanding of this language concept -negation-  resulted in failing to complete exercises in logical thinking.

Negation, unfortunately, is not the only concept Robert has not grasped yet.  Many “simple” words still manage to confuse Robert.  While he understands “north,south, or southwest”, he still has difficulties with “top and bottom. ”

That might suggest that Robert  understands the idea of “top and bottom”  (when presented as “north and south”) but doesn’t understand the language concepts as the names for those ideas.





On Pictures and on Words

Many children with autism go through programs of matching pictures.  They might match identical photographs or the different photographs of the same concept (for instance pictures of different chairs).  They can match objects by the categories to which they belong.  They can match part to the whole thing.  They can match by the same color, shape , or … function.  Matching, as simple  as it seems, is the  great introduction to complex language concepts even for those who seem not to have language.

Robert did a lot of matching in his first years of ABA at the private school.  He also did a lot of matching with me, although in a different format.  I used many toddler level workbooks to provide opportunity for more “natural” matching by connecting pictures by lines or by placing stickers in proper places.  Although Robert completed each of the book twice or three times (Yes, I bought a few copies of each workbook), working on those simple exercises allowed Robert to flexibly move from one kind of matching to another.  On one page he matched body parts of different animals to the animals, on the other he matched animals to their habitats, and so on.

A few years later, I introduced Robert to simple (?) verbal analogies.  Although by that time, he could already read, those analogies were much harder for him to complete than matching pictures. Since picture matching is also a form of analogy, I had difficulties understanding what was a nature of this problem and thus how to address it.  Luckily, I found. through Remedia Publication, a  workbook in which one part of the analogy was presented as a picture and another one as a word.  For instance, Robert had to glue  pictures of a bird, a whale, and a bear in rectangles with words: ocean,  nest, or forest.

I think that this phase helped Robert with understanding of the analogies expressed by words only.

A few days ago, I returned to the same workbook.  I wanted Robert to do something very easy and almost mechanical. Just to make him feel good about his abilities. Oh well, as soon as I observed Robert  completing his tasks without any hesitation, I changed my mind.  I did not want to be mean.

I simply discovered another learning/teaching opportunity and the skill I neglected to practice in this environment: talking.

Because the words do not come easy to Robert, in the past we used them only in a very limited way.  It is not that I was silent through the activity.  I did comment, I think.  I also elicited a few singular words from Robert.

This time, as Robert was placing pictures in proper spaces, he had to say an almost (almost!) complete sentence, ” A fin is a part of a fish.” or

“A beak is a part of a bird.”  Four sentences of similar structure.  If he missed an article, I did not ask for correction.  I repeated after him without an error.  (I think.) If he missed any other word, he was encouraged to repeat.

I wanted Robert to practice talking in sentences, but I also wanted Robert to understand the nature of analogy by describing it with a word. Thus, in this case,  the emphasis on “IS A  PART”  of each sentence.

In other exercises the emphasis was on “IS THE OPPOSITE OFF”   (Happy is the OPPOSITE of sad. Back is the OPPOSITE  of front.  ) or “LIVES IN”  (A whale LIVES in the ocean. A boy LIVES in the house.

As I am working with Robert, I  am often not exactly sure what I am teaching and what I am missing.  That is why I am returning to the same exercises we have completed in the past, because at different times they offer  opportunities to learn something entirely different.

In the past, Robert learned that words represent objects (or the concepts).  He learned that those concepts are in different relations with each other.  Now he was learning words representing RELATIONS  between words… and/ or objects.

Finding a Piece of a Puzzle

I don’t mean THE PIECE that is the ultimate solution to the problem.  I mean “a piece” that fills some minor void without claiming the right to answering all the questions or even to completing the picture. 

For a very long time, Robert was able to answer only very simple questions and not capable of asking any.

The questions had to be concrete and relate to  visible  objects or their pictures. “What is it?”, “What color is it?” Or  later,”Where are they? ” “What are they doing?” He was unable to answer reliably any question about himself.  He also could not answer any question as it related to the simple sentence, he had just read.

I was baffled by that fact and felt powerless.   Today, I believe that Robert didn’t have an idea of the “question”.  Fifteen or twelve years ago, I was not aware of that fact.   Yet  unknowingly, I  introduced the concept of the question to Robert. I did that with the help of an old Schaffer’s Publisher workbook for kindergarten or first grade level reading.  I don’t have this workbook anymore.  I tried without success to find it on multiple websites. I don’t even remember its title.

To make up for this lack of concrete information, I will try to recreate its method of developing the idea of question as I remember it.

On the right side of each page, there was a small picture.  On the left side, there were three very simple and short sentences printed in large letters.  Below the text, there the same sentences were written.  Each sentence was copied twice or even three times.  Each copy  had one empty space replacing one of the words.

For instance:

The cat sleeps under a chair.

The ……………sleeps under a chair.

The cat sleeps ………………..a chair.

The cat …………………..under a chair.

At first, I wanted to skip this part of the workbook and move to the part where “WH” questions were asked.  I noticed, however, that Robert had difficulties even with those simplest (?) of tasks.  I concluded, that the practice was in order to help Robert better attend to the text.  So we did work on filling voids in the sentences before moving to questions in the next part of the same workbook.

It did not occur to me then, that by writing missing words, Robert was learning the concepts of questions and answers much more precisely than when he was answering the questions I described in the first part of this post, in the context of a concrete picture.

The question is nothing more than a  the missing information, thus missing word.  To  answer is to  provide that information and thus to fill the void.

With the support  of a Schaffer’s workbook (I doubt if it has been reissued during the rule of Common Core Standards) I helped Robert understand the concept of the “question”  and place a small piece of the puzzle in the right place.

I did not realize that ten or twelve years ago.  For me, those were  only exercises in paying attention.  Had I understood this mechanism better, maybe I could teach better.  But then, maybe not.

Increasing the Pace to Connect the Dots

In  my old post Teaching out of Autism, I wrote about my “discovery” that “simple” activity of stringing beads was, in fact, a complex one.  I found out that it was composed of a few steps which had to be taught separately.  In that post, I listed those steps, described Robert’s strong resistance to learning, and concluded  that mastering the skill , despite previous vehement opposition,  was  reinforcing in the end.

At that time, I was not aware of the existence of ABA  with its  concept of a reinforcer as a tool that entices learning.  Thus my struggles to keep Robert seated, and bruises on my chin.  Nonetheless, when I look back on that experience and compare it with later teaching through ABA, I have to make those important observations.

1. Robert learned stringing beads very quickly when compared to  gross motor imitation introduced through discrete trials.

2. Robert did not receive any reinforcers during learning to string beads, but the activity itself became reinforcing later.

Since placing beads on a yarn is a complex activity comparing to touching a nose or clapping  why there is  such a difference in learning times?

Of course, the partial explanation would involve the fact that in the first activity he had to look at objects, in the second he had to look at a person in front of him and copy her movements.

The first activity had a clear result at the end of the of chain of actions.  The bead was on a thread.  Repeating the activity lead to the string getting longer and thus looking  better and better.  In the second activity, after completing the movement, there was no visible change.  After touching nose, Robert was back to touching nose, and then again to touching nose with pieces of M&Ms in between.

Today, almost 18 years later, I have the feeling that we missed some important variables, and were too slow to connect the beads.

Discovering the Path of Microsteps

The skills were  simple. Basic really.  There was nothing to them.  They were so simple that the very idea that they should be taught seemed ridiculous.   The children either had  inborn potentials to demonstrate those abilities at some point of their development or did not.  If they did not,  nothing could be done.  Although the teaching would help a child to go over some rough surfaces, or climb a few steps up, at least the path for teaching and learning was already cleared. Everybody more or less knew  what to expect on the developmental curve.

I did not.

When Robert was two and three years old, I couldn’t “teach” him even one hand movement from any of  the children’s songs and finger plays.  I dutifully learned them all and tried to pass my knowledge to Robert.  I sat on a chair, he sat on a table.  We faced each other.  It had to be this way as in any other arrangement, Robert would run away after  the first few notes.  Somehow, he did not even try to escape from this position. He appreciated my singing and  all the silly movements of my fingers, hands, and arms.   He smiled all the time.  He was happy to participate but only as long as I kept moving his hands.  He repeated neither a syllable nor a gesture. He kept placing his hands in mine expecting  me to move them accordingly, but he did not move them himself.  He smiled  while I led his hands  through the steps taken by Eensy Weensy Spider.

I used the same  tricks that the generations of mothers and  nannies created and mastered over the ages  to help their charges appropriate new abilities easier and quicker:   I went faster.  I went slower.  I stopped in the middle of the song, as if I  needed help remembering next word and next gesture.  I stopped just before the last word and the last movement so Robert had an opportunity to fill the blanks. I exaggerated.  I whispered.  I changed the pitch.  Robert, still smiling, did not show any inclination to initiate, continue, or finish the finger play.

It was after the first application of  Applied Behavioral Analysis methodology in its most rigid and plain form – discrete trials – when Robert for the first time learned to imitate my singular gestures such as clapping, spreading arms out, touching nose.

Each skill was taught separately and with heavy reinforcement.

Saying,”Do this”, followed by a gesture to be replicated by Robert.

Helping Robert to copy the movement with some level of prompting.

Reinforcing him with a piece of candy and words, “Good boy.”

Repeating the same procedure again.  And again,  And again

Of course, there were small variations in regards to delays, level of prompting, schedule of reinforcements, but the idea was the same:  to teach the most simple, singular skill.  Not a skill in connection with other skills, not a skill that changes depending on circumstance but one that is clearly presented, easy to follow, and doesn’t depend on anything else but demand, “Do this” accompanied by a model.

Our goal was not to bushwhack through wilderness.  Our goal was to carve a new trail. To do so, we had to slow down and work on finding  ground for every step our feet would have  to take.

1.In one of the previous posts, I had already made a distinction between TEACHING IMITATION  and TEACHING SEPARATE  GESTURES . I cannot stress it enough that the purpose of teaching clapping, touching nose, tapping on the table is mainly to provide a repertoire of tasks to choose from while teaching imitation.  That mean that the child has to attend to the stimuli, and differentiate between the demonstrated movements imitating only what was shown, and not the whole bank of learned gestures.

2. Although I consider discrete trials crucially  important, I also believe that when overdone, over-repeated, and not subjected to regular check up (Something different from collecting all the data), they can have a stifling effect on overall development. Discrete trials are  powerful tools, but only when applied smartly.

On Changing Units and Methods

Yesterday I worked with Robert on changing customary units of length:inches, feet, yards, and miles.  It was not Robert’s first encounter with requests to switch from inches to feet or yards and vice versa.  He also heard before that a mile had 1760 yards or 5280 feet.  He heard but vaguely remembered.  Not once I prepared for Robert worksheets of the form:

1 foot = …………..inches

1 yard= ……………feet

4 feet =……………inches

……………feet=    36 inches


………..yards= 15 feet

Those exercises went rather smoothly, although sometimes Robert needed a short reminder of what to do before he started answering questions.

Yesterday, however, I used not my worksheets but pages from 4th grade Spectrum Math workbook.  Those pages presented similar problems but with a huge range of numbers.

For instance:


………..feet= 180 inches

132 yards= ……………….feet

132 feet=   …………………yards

Robert was lost.  As before he had to either multiply or divide, except previous operations he did easily in his head, almost automatically. Now, he had to do a chosen operation on paper.  Somehow choosing the operation became much more confusing.

I realized that without being specifically taught Robert solve “easy” problem by comparing two sets of equations:

1 foot=12 inches

X feet= 48 inches

He made an easy proportion.

When the number became large, they, somehow complicated everything:

1foot = 12 inches

X feet= 192 inches

Now, Robert needed a method, an algorithm that would  withstand menacing character of big numbers.  The simple method that would replace confusion about which operation to choose with clear step by step process.

Yesterday, I did not think about such method.  I was observing as  Robert was  half guessing, half understanding the choice between multiplication and division. I was trying to understand why Robert seemed to almost “intuitively” solve problems with simple numbers and could not do the same with larger ones.

I think that Robert knows those smaller numbers much better.  When he sees 60 he also sees 12 times 5 behind.  On the other hand, in the number 192, he doesn’t see 12 times 16.

Two things struck me yesterday:

What looks like almost intuitive ability to solve easy problem might be the results of very well-practiced/mastered  skills.

Ability to solve easy problems “without” consciously applying any algorithm might not help Robert in understanding the mechanism behind finding solution.

As I stated before, last evening, I did not use any new strategies to extend Robert’s skills to larger numbers.  Today, I will attempt to practice solving proportions, and later introduce them as a way to help with changing units.  I  worry, however, that doing so, would make the whole process more abstract and artificial.  In the end, it might lead Robert to loosing his present understanding of units of lengths and the way they change into each other.