1995 PCDI Conference, 17 Years Later

I attended a couple of conferences before December of 1995.  One of them was by Lovaas.  I only vaguely remember it because whatever was said or shown there, I had already learned from Lovaas’ Me-Book. I knew what discrete trials were as I watched them being done with my son and did them myself.  I went there, mainly to see the man, who started it all.   Another conference was  presented by a famous, local speech professor. He told a story about a male student who spent many years unable to communicate at ABA school. As soon, however, as the boy got an assistive technology device (or a computer program ) and learned to use it to communicate,  he typed the  message, “Take me out of here.  They are all crazy.” The crowd laughed approvingly.  Not surprisingly, the audience preferred a miracle over ABA. I did not laugh.  I don’t remember anything else from that conference as nothing what was said there  applied  to Robert’s teaching.

In December of 1995  I signed up for the PCDI conference.  The images from that conference, for better or for worse, are still  imprinted in my brain.

For better, because I learned that there were people who not only knew how to teach children like Robert but were constantly looking for novel ways of teaching.  People, who defined criteria for progress, and were not afraid to change program if it was not sufficiently effective.

For worse, because I wrongly assumed that all Robert’s teachers  would not be much different than presenters.

For better, because I learned a lot and I was able to use many of the ideas to teach Robert.

For worse, because I never was able to pass that information/ideas to my son’s teachers and thus was very often disappointed with the quality of the teaching which never quite measured up to the presentation.

Moreover, since so many people attended the conference I believed that it  would not be long before the tools/concepts presented at the conference became known to every special education teacher in Massachusetts.

The future seemed  open to progress.

But it was not.  The ideas were not a match for moldy, from lack of fresh air, walls of special education classrooms.

At that time, Robert was still not talking.  He approximated a sound for “juice” and maybe for something else. What was more concerning, he did not have any receptive labels.  It was hard to watch a presentation because  so many problems and solutions did not  relate to Robert as he was in December of 1995. His issues were the more basic and more serious.   Since Robert did not acquire language despite six months of ABA, he was one of those children that were doomed to not recover according to results of Lovaas’  experiment. As I listened to Patricia Krantz, Gregory MacDuff,  Edward Fenske, or Lynn McClannahan and watched the students performing different tasks, I wondered if my son would ever be able to get to such levels and learn the skills those students had already mastered.

I watched the students seating at the large table, working on an art project and using sentence strips to “chat” with each other.  In 1995, that was not a possibility for my son.  It  certainly would have been doable and beneficial in 2006.

I listened to criteria for transition to main stream, and I doubted if such transition would ever be possible for Robert.  It was not.  What was possible was to transition from one to one instruction to a group instruction. But again, in Robert’s placement in 2006 there was no one who would plan, monitor,and adjust program to facilitate such transition. Nobody attended the PCDI conference.

I was learning new methods, gaining new tools and yet I did not know  if my son’s development would ever allow me to apply the information I was receiving. Today, I am glad I listened even to those lectures that seemed to address needs of much higher functioning children. For once, some of them became useful later.  Secondly,  I learned not only how to deal with very specific, limited range  issues but, because the range of topics was pretty wide, it was possible to apply similar way of thinking to address problems not mentioned in the conference.  Maybe the word “generalize” would explain better what I mean.

As I watched young man emptying dishwasher with the help of  the picture schedule detailing all micro-steps required, I realized  I could do that with Robert. It took a few days to assist Robert in unloading the dishwasher, before he became completely independent.

As I watched children following picture activity schedules by choosing the puzzles and/or other activities from shelves and later putting them away, I knew that Robert could learn this quickly.  Well, he did and he did not.  His teacher was unable to make  Robert  point to the ONLY picture before reaching for the ONLY puzzle. Since Robert didn’t point, he was not allowed to complete the puzzle.  I, on the other hand,  ignored pointing for as long as it was not a functional gesture (Which it was not, since there was only one picture and one toy just in front of Robert.  Nothing to choose from.)   and let Robert to follow picture schedule of three activities.  Which he did. Meantime his teacher  kept recording failure after failure, day after day, week after week, month after month. Unable to make concession and skip pointing, the teacher stopped this program. Oh, well…

I attended other conferences after PCDI. I left each of them with one or two  tools, which, no matter how small they appeared to others, allowed  me to teach Robert and/or manage his behavior. Nothing, however, compares with this presentation.

Just a few months before this conference, we, the parents, were seating in the hospital office of the psychiatrist considered to be an autism specialist. It was a depressing event.  The psychiatrist gave us  a diagnosis and shared his  conviction that there is nothing to be done about it.  We tried to shake the gloom, but it lingered.  It was this conference that finally dispersed those feelings. I felt energized and capable if not exactly hopeful.

I felt that I not only had tools, but also the ability to make the tools myself.

I still have the binder from that conference . When I looked through its pages, I was surprised by how much of what was said 17 years ago is still valid.

Kathryn. When the Words Heal

Two months ago I posted  Three Rejections about our painful experiences from the spring of 2006.  It seemed that at that time, all the doors were closing in front of Robert (and me).  As we, the parents, tried to enlarge Robert’s world by introducing Robert to new places and new activities, the institutions  that, by definition, should be open to him, expelled him one way or another.  I am not sure how Robert felt about this.   Maybe he was relieved that he did not have to go to the school, he did not like.  Maybe he felt that something was missing from his life. I can’t tell.  I know that I felt anger, confusion, and piercing sadness. 

I was sitting at the large,  oval table in a conference room at the local ARC.  Kathryn, representing ARC was sitting in front of me. Next to her sat the representative of, as it was called then, Department of Mental Retardation.  We were talking about Robert.

-“Why don’t you bring Robert to our program?”  asked Kathryn”

” He is very tense lately, and I never know how difficult he might behave.”  I answered, remembering all those times I was called to school to pick him up, because of the behavior the teacher was not able to control.  “I never know if he will have a melt down or not” .  “I would rather keep him at home than be called to take him home.”  I said knowing from the past year experiences that picking Robert up was never easy.  He was aware that my arrival to school meant that he did something wrong. He certainly did not want to admit that.  So he did not want to leave the school.  I felt I did not have any other option but to keep Robert at home.

But the Kathryn said,
“Please don’t  think that you can bring Robert  only when he is behaving perfectly.  To the contrary, when he has hard day at home he should come here. This is  one more reason to bring him here.  We are capable of working with him through any behavior.  We are here to help.”

I do not remembered exactly, word for word, what Kathryn said in the late spring or early summer of 2006.  She  used fewer words.  They were simpler and calmly radiated with meaningful assurance.  I wish , I recorded her words and listened to them whenever I needed to heal from the wounds caused by others.

Robert attended the program twice a week.  There had  never been a problem with behavior. That shouldn’t be a surprise. Kathryn, who was a director of family support, rather administrative position that did not include hands on care,  almost always was with children taking care of those who, on a given day, had the hardest time in the program. By doing so she was not only supervising young employees and volunteers.  She was giving them an example of how to meaningfully engage and take care of young people with many developmental issues.

Later, I learned that Kathryn’s major was Business Administration.  She moved to California and started working for financial institution.  I miss her a lot, mainly because I have never again been so convincingly reassured that others are able of taking good care of Robert even on his worst days.

Intermezzo. On Logic, and Laughter

Last  Friday evening, Robert and I were sitting at our dining table drawing heights in triangles. I was fidgeting with my pencil, when Robert bent his head down and moved it forward wanting to take a closer look at the vertex and the base of a triangle.  The tip of my pencil touched the top of his head and scratched him. Robert felt pain. He shook his head and, for a second,  closed his eyes. When I tried to comfort him, Robert dropped his pencil, picked up mine, and replayed what had just happened. He placed the pencil’s lead on top of his head and shifted it to one side. That did not feel right. Robert put the pencil away, hesitated for a fraction of a second, picked  the pencil again and  used it the way pencils should be used: begun writing on the top of his head.

Something was still wrong. Robert put the pencil away, looked at me inquisitively, and  did precisely what one was supposed to do with an unwanted and impossible to decipher scribbles written in the wrong place.  He grabbed the eraser and energetically wiped the writing off his scalp and hair.

That should have been the end of this story if I wrote it as a joke for Reader’s Digest .  But that was not the end of the story of Robert.

I giggled.  Surprised, Robert looked at me trying to understand why instead of  feeling sorry for him I laughed at him.  He put down the eraser, took it again,  returned to wiping  invisible words, and… smiled.

He seemed to be telling me, “There is something funny going on.  I  share your amusement but I am not sure exactly why.”
He  picked the eraser again.  As he was wiping off  “doodles” from his head, he burst in laughter.
He got it!

He not only KNEW that he did something hilarious, he FELT it.

Replays

Three days ago, I watched Robert running down the stairs. He slipped on one step, lost balance, regained it without falling, and ended up standing two steps below. Instead of continuing his journey to the basement, he turned back, climbed two steps up, and reenacted his misstep.

Well, not exactly.

He bent his left knee and with the right foot he gently traced his previous movement  leading the foot through the edges of the two steps. He did not risk another slip up.  He had full control of the movements.

It was not the first time, I watched Robert replaying such bumps.  Whenever I observed Robert tripping  over something, I also noticed him repeating the incident in a well controlled manner.

I remember that long ago, when we once bumped our heads as we were reading a book, Robert gently placed his forehead on mine as if he were saying, “This is what has just happened.”  I understood the communicative intent then, because he was talking to me.

On the other hand, when I observed Robert replaying his missteps, I considered that behavior to be a form of magical thinking.  Since nobody was around (I was either behind, or in another room.), Robert was not talking to anybody.

Because I also witnessed Robert repeating the faulty step three times (Slipping on dry leaves in Moose Hill Park .), I suspected that this behavior was a manifestation of obsessive compulsive disorder.

This time, three days ago, I was struck by a realization  that the reenactment was a  way Robert was  telling  himself what  had just happened.  He was communicating with  himself… without words. The fact that in the park, he replayed his slip-up three times, probably meant, that he couldn’t get it right on the first two trials.  He wanted to be exact and to understand the incident correctly.

I have been trying to understand the  ramifications of Robert’s reenactments for the three days now. I am concerned.

The fact that Robert communicates even with himself without words, is not to be taken lightly.

Robert! Robert!! Robert!!!

Since this is my 100th post, I have given myself permission to restate the reasons why I am writing this blog.  I want to understand Robert. Who he is, how he learns,  how he thinks, and how he interacts with his environment. I want others to understand Robert, or at least try. Robert doesn’t explain himself. That is  why he  gets  into trouble even when he means well and when he  is 100 percent right.

The day was 24th, the month was December, the year was, the year …. I don’t remember.  It could be 2002, 2003, or 2004. The year is not important. At least not  in this story. The time of the day was a late evening.  Maybe eight or nine.  The Christmas Eve supper with 12 dishes not counting deserts was over. The presents were distributed, according to Polish customs, soon after the supper.  Now Robert’s three cousins were contemplating their presents – clothes and electronic gadgets.  Aunt and Uncle sang Polish Carols while Amanda accompanied them on the piano.  Robert’s father was serving hot tea and coffee to fight off drowsiness, a consequence of overeating.  Robert couldn’t find place for himself. .  He carried a pile after pile of dirty  dishes to the kitchen but refused to be involved in the impossible task of placing them  all in a  dishwasher. He knew his limits.

He walked around from the kitchen, to the dining room, from the dinning room to the living room, and vice versa…  There was  nothing for him to do. He was not  interested in his presents. After all, they were already unwrapped. He could not talk with his cousins. He could not sing with his Aunt and Uncle. But he didn’t want to go to the den to watch TV either. He wanted to stay with all the members of his  family. Except he did not know HOW TO BE with the family. What was he supposed to do?  Where should he sit?  Next to whom?  He couldn’t figure out what was his role in this situation. So he wandered through all the rooms maybe wondering how to attach himself to something or… somebody.

I looked at Robert from time to time, but did not help him to define his role in a house changed by holiday’s customs and guests.  I did not know how to help.  Besides, I was busy picking up wrapping papers from the floor.

As I was folding empty boxes, I heard, “Robert don’t!” The oldest cousin warned Robert.

“No, Robert, no! ” followed the middle one.

“Stop it , Robert!.” joined the youngest brother.

I looked up.  Robert was  moving the piano away from the wall, while Amanda was still playing. That was such a senseless, mean thing to do! The three cousins and I rushed to avert the disaster which we all had envisioned.

Before we reached the piano, Robert had already bent down and got up.  In his left hand he was holding three white envelops.

“Ah” sighed the three cousin together. Ah, sighed I.

“Thank You Robert”,  said one cousin after another. Each of the them opened his envelope. The good American cash, thoughtful present from grandma, was still there.

I don’t know when the envelopes fell behind the piano.  I don’t know how my continuously  moving son was able to notice that fact.

What I know, however, is that because Robert doesn’t have words, his actions are frequently misinterpreted.  That evening, we all, in the end, understood reasons for moving the piano. But often, Robert is stopped from completing his tasks, because the people around think it is wrong , senseless, or dangerous.  When that happens Robert’s motives never come to light.

Up-Side-Down Teaching

I have never analyzed the ways in which  typical children learn  language concepts.  I suspect that the very young children obtain new words through some sort of an impossible to describe osmosis.  The school age children, on the other hand,  are taught new concepts by connecting a few simple, well understood words into  definitions.  I imagine a pyramid made of layers of words. The most basic and supposedly the easiest ones are placed at the bottom. Their internal connections support more complex words placed on higher levels of the pyramid.  That seemed as logical as Euclidean Geometry. Unfortunately, this sort of logic doesn’t apply to Robert’s learning.

Robert often learns new concepts simultaneously with the words included in their definitions.  I suspect that sometimes  Robert has knowledge of the concept before he understands words which were supposed to explain its meaning. When I say “understands” I mean “has visual representation”.

A few weeks ago, my daughter bought for Robert a set of fifteen educational puzzles, Landforms Match-Ups by Lakeshore Learning.  Each puzzle had three parts: a picture of a landform, its name, and its definition. Left alone, Robert can put all the pieces together in a few minutes just by looking at their shapes. When I join him, the game changes.  Robert spreads all 15 pictures on the table.  I keep smaller puzzle pieces with names and definitions in my hand to make sure  that Robert doesn’t see them.  I read the names, Robert points to appropriate pictures.  I read the definitions, Robert is supposed to point to the correct pictures.  But he does not.

In the set there are picture representations of three unknown to him  landforms: isthmus, archipelago, and river delta.  I have never introduced them to Robert and, I am pretty sure,  nobody else did.  But twelve others landforms and waterways, Robert has  already encountered through two geography folders from Take Me to Your Seat  series.

When I say the landforms names, Robert  hesitates but places ten out of 15 correctly.  Some of his errors are explainable. For instance, for a mountain he points to a valley as it is between two mountains.

When I, however, read  definitions, Robert makes only 5  correct choices. Moreover, I suspect that at least two of them were lucky guesses.

Robert knows what the lake is, but he doesn’t know what is  “a large body of unmoving water that is completely surrounded by land”.

After practicing, Robert “knows” what isthmus is, but not what is “a narrow piece of land that connects two larger land areas”.

Are the sentences too long for Robert to process? Possibly.

Somehow, Robert doesn’t have problems with a wordy definition of delta of the river. This definition contains a phrase “mouth of a river”.  And this is a part that lets Robert make a connection with a picture.  In a definition of the ocean, it is the phrase “salty water” which helps Robert to understand it.  But in many other explanations, Robert cannot find any word or short phrase that would direct him toward a proper picture. The words seem simple to me, but they don’t explain anything to Robert.

The fact that Robert learned which picture represents”isthmus” but he didn’t learn what is “a narrow piece of land that connects two larger land areas” is a result of compounding together only vaguely  understood words and phrases such  as  “piece of land” or “connects”.

I wonder if replacing this definition with something more visual like ” a land bridge” would make a difference.  It is possible that Robert selects from each long expression only two words phrases as meaningful ones, and bases his answers on them.

It is also possible, that typically developing children do the same.

As Robert completes the puzzles with my help (?) , he is not learning just what a  peninsula is, but what the expression, “mostly surrounded by water”  means.

Those, supposedly, more specific and more advanced words like isthmus or peninsula are only tools. They allow me to find the gaps in Robert’s basic vocabulary and fill them with the missing fundamental language concepts.

I wonder…

When the person is  being referred to as the so-called  ” visual learner”  does it  mean that for that person it is easier to make a connection between a picture and its label than between label and wordy definition?

Is “the visual learner”, someone who can relate new words to their visual representations, but not to their verbal descriptions?

If so, more questions surface.  What to do, about such a learner?  Ignore his difficulties and saturate his environment with as many visual representations of concepts as possible?  Such approach would allow “a visual learner” and his care providers to manage certain environments but would not address his/her functioning in the world at large. The world at large is mainly…verbal.

I think, the Landforms Match-Ups game offers a solution.  We can connect all three together and allow the picture to become a bridge between two categories of words: labels and definitions.

Counting Fries, Discounting Blessings


Ten years ago, Robert and I were sitting at McDonald’s.  Robert had Big Kids Happy Meal with six chicken nuggets, multiple fries, two containers of sweet and sour sauce, four tiny paper cups of ketchup and, of course, medium size coke.  As it was our (mine really) habit, I kept dispensing fries by two, three or four and asking Robert to count them together. Sometimes I gave  Robert five or six fries at a time and as he was eating them by twos or threes, I asked how many were left.  I didn’t think I had much hope that this activity would help Robert memorize any addition or subtraction fact.  After all, his teachers were doing the same things using cute bear counters for years  with no success.   I guess that I felt guilty for coming to McDonald’s much too often.   Counting fries allowed me to fool myself into believing that I was not wasting  time but to the contrary I was using it productively.  I was teaching.  What could be more productive than that?   I even convinced myself that counting fries was a more promising method of teaching. The edible counters related to real life had more value for Robert than blocks or bears.

I was engrossed by my teaching  mission when I heard, “Bless you, bless you for your work with THIS child.”  I lifted my head and noticed a middle-aged man glancing at me on a way to his table.  Luckily, he passed me rather quickly relieving me from any obligation to respond.  I would not know what to say. I knew he meant well, but his words felt sticky and stale.

Unfortunately, I heard the same phrase, “Bless you” many times more.  I heard it always in a company of my son.

In 2006 in a hallway of the Medfield Middle School, the teacher, whom I didn’t know said almost exactly the same thing, “Bless you for the work with THOSE children”.  She obviously took me for a special ed teacher.

This summer, as I was buying ticket to Plimouth Village and Robert bounced happily while waiting to visit the place he remembered from prior trips, the clerk at the desk  offered to pray for me.  This time, I responded, “Please, don’t.”

Each and every person who wanted to pray for me or bless me, was inadvertently telling me that she or he perceived my son as a  heavy burden. Nothing more.

I did  mind (a little)  being an object of other people pity, but I minded hundred times more that fact that they were unable to notice my son’s deep humanity. It was easier for THOSE people to discharge blessing on me than to say one friendly word to my son.

That is why I had to reject the blessings and decline prayers.

Kathy Can Stay

Oh, how embarrassed I felt on those Tuesday’s evenings in 1996, when my daughter’s ballet teacher, Kathy, was bringing Amanda home.   At that time it was rather difficult to  pick up Amanda after her dance classes. Waiting until she changes her clothes was not easy  with Robert, who couldn’t stay still even for a fraction of the second. To help us, Kathy drove Amanda home after every  lesson.  I always asked Kathy to stop for a few minutes, and  had a bowl of her favorite, home-made chicken soup ready for her. But Robert did not want Kathy to come in. He let Amanda in, but tried to prevent Kathy from crossing through the door.  The little four years old creature, looking  like two years old toddler, was pushing her outside with his arms and… head.   The first time this happened, Kathy wanted to leave as not to cause any problems.  I begged her not too.  Holding  Robert  I explained that Robert had to learn to tolerate people coming in. ” I know it would be hard for you, but please stay at least for 5 minutes.”  The most important thing was, in my opinion, for Kathy to sit down and pretend Robert’s objections did not bother her.  When Robert was not protesting too strongly, Kathy and I ate the soup together at our kitchen table and  chatted.  When Robert was protesting vehemently, I calmly and slowly filled a plastic container and gave it to Kathy, so she could take the soup home and eat in a calm atmosphere.

Every time Kathy came, she said in her calm, friendly way, “Hi Robert, How are you?”  Maybe sometimes she changed a word or two, but her voice was always friendly and NEVER artificially sweet.  Robert did not respond.  At that time, he knew maybe 5 expressive words and not even one receptive label. I am not sure what he understood.  The best he could do was to turn around, ran to the living room, and let us be.    After generously leaving us alone for 2-3 minutes, he came back and handled Kathy her purse, or (later) her jacket. It was a hint, I asked Kathy to ignore.  She agreed to get up when Robert was NOT “asking” her out.  When in the door, she never forgot to say, “Bye Robert.”

One Tuesday, two or three months later, as soon as he heard the door bell, Robert rushed to the door, which I was just unlocking.   I wanted to pick him up, terrified that the old habit would return and Robert would push Kathy, when I noticed that he was bouncing happily in place, and pulled the door to open it…. wider.  He was happy!  He wanted both Kathy and Amanda to come in.

When they entered, Robert shut the door and  stretching  his arm toward the latch at the top of the door he made clear that he wanted to lock it.  After I closed the latch, Robert bounced happily off to the living room.   Kathy, Amanda, and I ate chicken soup (Robert did not eat that stuff.) and even some ice cream. We chatted  and laughed realizing that Robert demonstrated the same attitudes toward Kathy, he previously expressed toward Louis, the Cat.  Did Robert accepted Kathy and Louis  as extended family members, close family members, or just friends?

We did not know.  Robert did not explain himself.

I am not really sure how many times Kathy came before Robert considered her a very good friend but I know that he certainly appreciated that she ALWAYS addressed him at the beginning and the end of each visit and did not mind that he did not answer. 

The Functions of the Latch

In the fall of 1996, a day after Robert’s opened the door and aiming for the playground ran through the narrow streets and the treacherous parking lot of our apartment complex , my husband installed a latch on top of the door.  Robert quickly understood its function  and sincerely detested it. It was there to prevent  him from going out.  Robert wanted out, out, out.  So a few times a day, he stretched himself along the door’s surface, his head tilted backwards while short, little hands extended dramatically toward the latch.  Sometimes it worked, sometimes it did not.

There were many reasons Robert wanted out.  He wanted to go to the playground, to the swimming pool, to the grocery store to buy more bubbles, and he wanted to admire Louis.

Louis was a black and white cat, living across the street (and the parking lot), who at some point started to spent a lot of time on the steps leading to our townhouse.  It is possible that it was because in the afternoons, the sun warmed up our side of the street.  It is possible. However,  I am convinced that Louis kept coming because he loved Robert and Amanda. He waited for each of them to return from their schools, but he hid between the bushes and the wall of the townhouse  when other children tried to approach him.  Louis  clearly felt pampered and entertained  by Amanda who, pretending to be Isadora Duncan, danced for him with thin shawls twirling around. Louis also accepted gracefully Robert’s dance of appreciation, quick bouncing in place and flapping arms.  So he kept coming to our stairs, and Robert kept going outside.

It was unavoidable that at some point Louis would enter our apartment. And he did.  As soon as Louis entered, Robert shut the door, stretched his arms as high up as possible, and kept repeating,”Close, close, close”.

Suddenly, the latch from a despicable obstruction changed into Robert’s ally. Robert wanted Louis to stay in our home, and the only thing capable of assuring that was, in Robert’s mind,  the latch.

So Louis stayed for the whole afternoon until his owner, Ann, came to pick him up.

Take It to your Brain

I experienced a lot of chaos while teaching Robert to round up or down natural numbers or those decimals that relate to dollars and cents.
I started to teach rounding to the nearest ten approximately eight years ago. I simply used a segment of a number line, for instance, from 20 to 30.  I asked Robert to find 32 and then decide if it was closer to 30 or 40.   I soon stopped because I I begun to teach  Robert to divide with a reminder.  In a process, I  used a number line in a slightly different way.  I did not want Robert to be confused as to what was expected of him.

To make the matter even more baffling , in a school year 2005/2006, the teacher in a collaborative program was teaching rounding prices to the next dollar.  So for $25.99 and for $ 25.01 the proper answer was $26.  The authors of that part of the curriculum rightly believed that  when the price is  $25.30, you have to handle $26 and not $25 to the cashier.  It made a lot of sense from a practical point of view, but not from mathematical understanding of the values of numbers.

In the school year 2006/2007 Robert’s teacher’s aide introduced rounding up by a set of instructions, identical to those I received in my childhood. I described it in the comment below.

I tried to continue in this manner, but Robert had a lot of problems, I was not sure how to deal with.  So I stopped and waited until the teacher at school would move on to another topic.  Then…. I forgot as I moved to other things.

From time to time, the  need to round the numbers to estimate the result of math operation surfaced.  We returned to the old approach.  It seemed more visual.  To round 47 to the nearest ten, we drew a line segment which had 40 and 50 written at its ends and 45 placed in the middle.  Robert had to place 47 on the proper side of 45.

He had the same difficulties as in the past. I realized that he was looking for EXACT point he should place the number. That was confusing.   I remedied that by drawing one circle above each half of the line segment. Now there was a space to place the number,  Everything became  simpler and more straightforward.

As we worked today on such problems, I realized what I am aiming for while teaching Robert.

In the past I just wanted Robert to be able to turn verbal direction into proper math operations. After reading “find average” , to follow by  adding and dividing.  It was a worthy goal.

That was also my first goal with rounding to the nearest ten or hundred. I wanted Robert to almost automatically follow the steps as I described them above with number 47.

Now, I consider it only a partial achievement, not the goal by itself.

The real goal  for Robert is to draw a line segment with two numbers at the ends and one in the middle… in his head.  Make a mental picture and use it to solve a problem.

I only vaguely understand why I consider this last step so important for Robert that I made it a goal worthy reaching.  Is it because I want Robert to pick up the problem from a piece of paper and take it to his brain or is it because I want a proof that he can do it?