As of Today 11

December 16, 2014

We are still  learning.  Robert and I. But not every day.  Lesson after lesson from Singapore Math, grade 4. We review and relearn but in a new format. We still practice rounding up and estimating.  Today, Robert demonstrated sparks of independence. To estimate (for instance) 384+1217- 848 he drew three line segments: 300__________350_________400;    1200____________1250_____________1300


Next, he placed:

384 on right side of 350 and rounded it to 400;

1217 on the left side of 1250 and rounded to 1200;

848 on the left side of 850 and rounded to 800.

He added and subtracted in his mind.

He seemed  more confident than before and rather pleased with himself.

We followed with unit 54 from Reasoning and Writing Part B. Robert  slightly hesitated while completing  sentences describing routes the character took to reach another point on the grid. For instance, ” X went three miles north and two miles south.” More problems Robert had with exercises related to understanding speed.  After learning that a specific character runs 4 inches per second, Robert almost automatically counts by four to find out where on a picture, the character finds himself at a given time.  And yet, some of the simple questions still baffle him.  The simplest ones are the hardest.  “How many inches in a second does X make?”  It should be easy, because above the picture it has been written, ” X travels four inches in each second”.  But by the time, Robert has to answer the question, he has already forgotten the sentence he read.  He used it to complete the picture, but not to answer the last question.  As of now, he needs my prompt to return to the sentence to find the answer, as if he couldn’t switch attention back from the picture to the sentence.

Discovering these kinds of problems allows me to understand Robert better and to some degree address the issues he has.  It might be that the problems with reading comprehension are the result of similar approach to the text.  When you read, you go down, down, down the page. To find answer to comprehension questions you have to go up, returning to what you have already read.   In case of those exercises, the picture placed between sentence and the question related to that sentence seemed to be an obstacle to retrieving the same information Robert has already used.

We followed with a page from  Talking in Sentences. This time, Robert was  using a sentence structure similar to this one, “Birds have wings so they can fly.” Just the animals were different.

Lately, I am using a lot exercises from Walc 6, Workbook of Activities for Language and Cognition Functional Language by Leslie Bilik-Thompson.

For someone who doesn’t have any training as a speech pathologist, this book is absolutely priceless as it addresses on different levels many troubling aspects of Robert’s language as both communication tool and thinking tool. Some levels are easy, some are difficult. The book allows me to find appropriate zone to start with. For instance level 4, Two-Step Directions With Multiple Object Manipulation was much too hard, Level 2 One-Step Direction with Single Object Manipulation was too easy. Level 3 One Step Directions with Multiple Object Manipulation provided some challenges without overwhelming Robert with complexity.  It was also preparing him for the next level.

Unfortunately, there are tasks which are very hard for Robert on every level.  “Yes and NO” questions are still very hard. The difficulties are caused, in part, by Robert’s reliance on signals coming from my face. Robert can find the right words to finish the sentences , but not to answer “Yes or no” We still struggle.

Robert also has problems with telling sentences with a given word. He was confused by the demand to use “apple” in a sentence. There are too many choices for Robert to be able to zeroes on one.  Too many choices, I have to add, with too little practice and/or exposure to models.

Not surprisingly, Robert has more difficulties with retrieving synonyms than with antonyms. Antonyms come to him almost automatically.

But, Robert has much fewer difficulties asking Level 1 Situational Questions.  The past work we did using two different workbooks (Nashoba WH  and Teaching Children of All Ages to Ask Questions brought some small but encouraging results.





Understanding Speed

December 4, 2014

For the last few days, Robert was reintroduced to the concept of speed via lessons from  Reasoning and Writing, Part B. This is not an easy concept, so I had to admire the cleverness of the authors of the curriculum who developed a series of exercises allowing students to understand the concept of speed. As different pairs of characters race through the rectangles to the finish lines, Robert learns that those who reached the end in shorter time were faster than those who reached the end later.  In the subsequent exercises, rats and beetles ran over congruent rectangles representing units of length and Robert compares the number of feet (rectangles) passed in one unit of time.  That is speed. The concept is formed.

I don’t know of any other curriculum, that would put so much emphasis on concept formation, as does this one.  Most of my experiences were with the subjects where the concept was verbally defined.  The definition served as an introduction.  But for those students whose language lacks proper tools to understand definitions, the other methods of presenting new concepts are needed.  For those students, the definition with its precise vocabulary has to come later, AFTER UNDERSTANDING THE CONCEPT. The new words are there to describe what the student has learned through different approaches.

Today, as we were driving,  Robert and I shared our observations about how fast or slow we went.  Fast, slow.  It was a traffic our, so it was mostly slow. Very slow.

Take It to Your Brain Part 2

In my previous post,, I described how I helped Robert to learn adding numbers up to 20 despite his issues with short memory,.
In a different post, 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.

Recounting Elapsed Time and Other Things

October 11, 2014
Almost a year ago, Robert and I spent a lot of time on finding elapsed time. The easiest way for Robert was to subtract the start time from the end time. He was able, if needed, to change an hour into minutes. He was not able, however, to proceed in similar matter, when the time that passed included 12:00. (And I didn’t know how to teach that.) More general strategy was needed. The strategy that would allow Robert to count elapsed time without pencil and paper.
The first thing to learn was to subtract quickly numbers from 60. 60-27, 60-18, 60-9 and so on.
That would allow Robert to count minutes up to the next hour. For instance, from 10:45 to 11:00
The next step would be to add the remaining minutes. For instance from 11:00 to 11:17.
Thus the elapsed time should be counted as 15 + 17.
That is of course only in a span of one hour. Including longer times would be the next step.
I wrote about our efforts to teach and learn time almost a year ago. Unfortunately, I stopped practicing these skills at home, as learning to count elapsed time was one of the goal on the IEP and it seemed that the teacher used different approach. I found that approach difficult to follow, but didn’t want to confuse Robert with our ways of counting passed time, so I switch to teaching other things.
Yesterday, I noticed that Robert still was not able to count elapsed time even when it was only from 10:55 to 11:05.
So back we went to subtracting numbers from 60 in his head. Although it went smoothly, I didn’t dare to make the next step. YET
In the past, Robert was able to rely on ability to find the difference between 60 and other number to tell the time in the form of expressions” 12 minutes to 7 or 25 minutes to seven. Now, he has difficulties with such statements. It is not surprising. Nobody, and that includes me, asks him to tell time so he has never had an opportunity to use the skill.

October 12, 2014
I made a serious error in teaching Robert subtracting from 60. Yes, Robert performed the operations in his head, but WHILE looking at the written problem. He had, for instance 60-27 in front of him. With the help of that visible expression Robert counted in his head by first subtracting 20 then 7. Only today, I realized that I should help Robert to do similar operations without written representation, just by giving him verbal direction. It is important that he learns to visualize the problem and solve it in two planned steps. And that is what we began doing today.

Still in Fourth Grade

During the last few weeks, Robert was solving problems from 4th grade Singapore Math. He had already known most of the algorithms needed to perform mathematical operations. For instance, he knew how to find a fraction of a number.
With some restrictions.
He quickly could write that 3/8 of 40 is 15, but he would hesitate how to find 3/8 of 344 When he could do the division and multiplication in his head, the answer came immediately. If he couldn’t divide in his head, he was not sure what to do. It seemed as if Robert solved the first problem without realizing what mathematical operations he applied and thus he couldn’t extend the method to larger numbers. The only way I could address that was by slowing him down and having him name each math operation as he was performing it.
But Singapore Math introduced the fraction of the number not by presenting rigid algorithm, but as a few sections of a rectangle divided into congruent parts.
To find 3/8 of 40 or 3/8 of 344, the student drew a rectangle and divided it into eight equal parts .  Then he shaded 3 of those parts. The whole rectangle representing 40 (or 344) was clearly divided by the number from the denominator and multiplied by numerator.


40:8=5      5×3 =15

When Robert followed this method he didn’t have doubts what to do – he divided and he multiplied appropriately even when 40 was replaced by 344.

Moreover, similar drawing could be used to do the opposite, to find a number knowing the value of its fraction. for instance:  Find a number knowing that 3/8 of that number equals 18 (or 345) . I didn’t practice with Robert solving those problems as I was not sure how  to do it without confusing him. The Singapore Math offered easy solutions.




Robert drew a rectangle and divided it into eight sections. He shaded three of them and above just those three sections, he wrote 18. Thus he found out easily that one section was 6 and the whole eight sections had to equal 48.
In the past we often used rectangles to represent sums, differences, products, and quotients when Robert had to solve so-called “word problems”.  But I have never used them as a way to present the ideas behind the algorithm Robert knew already and the one, he did not learn yet.


Besides Singapore Math, Robert is still practicing with calendar doing exercises based on 4th grade Saxon Math.  He is also practicing  other skills with the help from 4th grade Math Sylvan workbook. Although this workbook offers many opportunities to use skills in slightly different contexts, it also has  errors, which its publisher is not willing to correct. This is the problem with hastily published workbooks for children and anxious parents, even publishers don’t take them too seriously. Sad.



From Different Angles

June 12, 2014
This morning, Robert and I studied together.
1. We worked on unit 17 from Reasoning and Writing addressing, among other things, the difference between two “if” clauses: “If you do X AND Y, I do Z” and “If you do A OR B, I do C. Jan, who was going to work later, helped with the lesson by giving Robert a model of what was supposed to be done. A few days ago, Robert and I practiced OR and AND in different contexts. He learned to follow one of the two commands: “Hold a red crayon OR a blue Crayon” and “Hold a yellow crayon AND a green crayon.” Nonetheless, it took Robert a while to grasp the difference between those two conjunctions when presented in different settings.
2.Robert was also naming angles as right, acute, or obtuse. As long as each angle stood alone and was not a part of a polygon, Robert didn’t have any difficulties with completing the task. However, when he had to count how many right, acute, and obtuse angles different polygons had, he was lost. The angles which were determined by vertices and sides of other shapes, were hiding from him. He saw polygons and could easily name them, but he didn’t see angles.
It reminded me of the time, when Robert was learning to name angles using three letters and making sure that the letter next to a vertex was in the middle.
He didn’t have a problem with that. When however the angle was a part of the parallelogram, he had a lot of difficulties. It helped him when I colored the angle and he could focus only on colored rays.
3. Yesterday evening, our water heater stopped working. It was a problem because Robert won’t go to bed without a bath. He wanted us to fix the boiler, but when that didn’t happen, he reluctantly agreed to boil a few pots of water and mix them in the bathtub with the cold water. He was not happy and he was extra suspicious. Nonetheless, the bath he took. That was the day he had a swimming lesson. That called for washing his hair under the shower. So he did! He made a few grunting sounds when the water coming from the shower was not exactly what he expected, but he rinsed his hair anyway. He just dried them a little longer.
4. This afternoon, Robert noticed that his comforter managed to creep out of its duvet cover. Robert tried to put it back, but somehow a part of the comforter got lost in its cover. Robert asked for help in the simplest way, “Mama, mama, mama”, he said dragging the bedding to the kitchen. He did similar thing just a couple days ago. Then, I showed him the “inside out” trick. At that time, as I was turning the cover inside out, Robert protested, “No, no, no!”. Still he let me do that strange thing. Today, he didn’t object. I turned the duvet inside out, asked Robert to reach two opposite corners inside, grab the corners of the comforter and pull them in. He did just that and was pretty pleased with himself. And so was I.

First Check

June 3, 2014
Last Friday, Robert got his first check. He was waving a white envelope when I came to pick him up. He was happy and so was I. Except, I didn’t know what to do with this check. First, I wanted to go straight to the bank and encourage Robert to deposit his first earned money in his checking account. But then, I wanted to take a picture of the check and… frame it. When we got home, I noticed that Robert’s last name was misspelled as one additional letter popped in the middle, so I decided to call the Employment Agency first to get advice on how to proceed.
Meantime, I thought about the check some more and came to the conclusion that the best way to proceed would be to go to the bank and cash the check. This way Robert would learn what earning money really means.
Robert has had a checking account for six years now. He wrote, at least, 30 checks during that time. He paid for his medical appointments and for his ski lessons. But although he wrote dates, proper amounts in digits and letters, and faithfully copied the names of the institutions, I am not sure if he got a clear idea of what all of that meant.
Moreover, in retrospect, I realized that my approach to teaching Robert banking was full of holes and resulted in Robert not understanding the values of the money. On paper, he could do most of the math related to withdrawing or depositing cash and checks. That knowledge, however, didn’t carry over to a real life.
I didn’t notice it, because I “cleverly” gave Robert an ATM card he was using to pay for some of his small purchases. I was proud when he kept sweeping his card in Subway or McDonald’s restaurants or when he paid for his take out from Outback Steakhouse always adding a tip to the bill.

Almost a year ago, as Robert tried to pay $3.50 for frozen lemonade, I noticed that he didn’t know how much money he should take from his wallet. One dollar, in his opinion, should suffice. My response to that was to do more practice at home of rounding to the next dollar. But despite our frequent visits to the grocery store I have never practiced with Robert buying things with cash. He always paid with his debit card.
The last Friday, Robert again wanted to pay one dollar for his lunch. He had twelve dollars in his wallet, but he took out one dollar and expected that it would cover the price.
The previous week, he only had one paper bill and it happened to be a ten-dollar one. So he just took it out and paid for his lunch. This time he had three paper bills in his wallet – two one dollar worth and one for ten dollars. He took one of them and was sure it should suffice.
His job coach thought that Robert’s reluctance to hand an appropriate amount of money was caused by his distrust of her. That was not the case. It was the result of Robert still not grasping the connection between numbers on the bills and their purchasing powers. He doesn’t grasp that connection, because I have never given him a chance to experience it first hand.
It is time to fix that. That is why we will cash the check and make a few trips to different stores and pay with cash.

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.

Journal, Page 3

March 14, 2014
This afternoon, Jan took Robert for a horse riding lesson. They are planning to go to movies after riding. I am trying to pull myself together.
The difficulties in signing for health insurance, already more than 20 hours spent on the phones with people who kept saying different things, exhausted me already in February. After Robert left school on March 3, I realized that I was not able to deal with too many issues at the same time, and stopped calling Massachusetts HealthConnector. I needed to regain my sanity and take care of Robert.
I couldn’t do both things at the same time. Specially since they were not the only things I had to deal with.
Today, I thought I was strong enough for another attempt to sign or at least understand my current status.
So I called. I was told again something completely different from before. This is not a place to write about the maddening details of the series of my contacts with HealthConenctor. It suffices to say, that I was kept for hours on the phone, providing millions of details about myself and my family, and then nothing was done. Nothing!!!!! I was supposed to sign for something I didn’t know anything about – not the price, not the services. The fact that my government is fooling with me makes me both depressed and mad. Today, I thought maybe I would find some sense in Healthconnector. Instead, I heard another idiotic request. I cannot understand anything. I wouldn’t be writing about that here, if that didn’t lead to my performance as Robert’s guardian and teacher.
My energy was depleted. The courage to start new things evaporated.
We didn’t go to the Science Museum to see Louis and Clark movie although that was the last day of the presenting this feature. I did not call the library to inquire about possibility of Robert volunteering informally there. I wanted him to place each morning a few returned books on proper shelves. Good application of alphabetical skills and satisfying occupation for him.
I did not call local food bank to ask for volunteering opportunity there. Robert is pretty good at packing, and placing everything in right places so that might be a good thing to do. I didn’t call about Meals on Wheels to check if He and I could deliver meals at least once a week. I was completely drained.
The only thing to do when the energy and courage are lacking is to fall back on a daily routine. Those are the benefits of lots of practice in teaching. Our an hour and a half of learning together was easy. I went on almost mechanically..
a. We continued with cards for apraxia using them in two ways. 1. Robert was repeating after me using the targeted word in different ways: repeating three times, finishing expression, using in a sentence, rhyming it with another word. 2. Robert was reading the word I didn’t see, and I tried to guess what he said. That was much harder, but it allowed me to find some of the issues he had with producing sounds.
b.Saxon Math lesson 122. Part of the lesson Robert didn’t have problems with – adding decimals, drawing angles of given measures. He had difficulties with following question, “How many hours in May?” Before he even read the question, he had to remember that the day has 24 hours and he had to count on his knuckles how many days in May. He knew that. But to go from that to the proper multiplication of 24*31 was a stretch.
I drew the same sort of picture I usually do when the problem calls for multiplication, and Robert wrote a proper math sentence. Later, I realized that I should have used a real calendar instead and have Robert write 24 on each square of page with May. Oh, well
c. Robert practiced some cursive writing, so I could do some kitchen work, and built from a a construction paper an otter with a clam. (Amazing Crafts)
d. Short text about eclipses from Real Science. I don’t think Robert understood it. But that was only an introduction to familiarize him with words lunar, solar, and eclipse. He would understand better if I made a model. But I was not in a mood for doing anything new. Oh well.
Luckily, Robert found himself something to do and hang or put in the in the proper drawers all the remaining laundry from yesterday.
The highlight of the day, was something I did not expect. Robert ate fried eggplant. Without any breadcrumbs, cheese, or tomato sauce. Completely different texture and taste. That he tried something new and widen his food repertoire really made my day.

On Roman Numerals

During the last few weeks, Robert and I spent a few minutes each day on learning Roman Numerals. At first, I didn’t treat it seriously. I presented it mostly as an interesting fact. Just a curiosity. But as Robert was changing Arabic numbers into Roman and vice versa, I noticed that in the process, Robert could deepen his understanding of values of numbers and their relations. Presenting 3 as III which translates into 1+1+1, 30 as XXX (10+10+10), and 8 as VII (5+1+1) helped Robert to look at the numbers from different perspective.
He built new numbers using a few symbols I, V, X, L, and C by adding them (as in 86 – LXXXVI), subtracting (as in 90 -XC), or doing both.
Those translations from one system to another were supposed to help Robert understand the values of numbers.
Of course, we spent much more time over the last 10 years to understand decimal system – to switch from words to digits, to expanded notations, and back. We compared numbers to each other, ordered them from the least to the greatest and from the greatest to the least. We rounded the numbers believing that ability to, for instance, round 321 to 300 and 371 to 400 was a sign that Robert understood the value of numbers.
A few months ago, I wrote a long and rather convoluted post about different approaches to teaching Robert to round and estimate.
All the methods, however, were based on algorithms. They were supposed to lead to a better understanding of values of numbers, but I wonder if they did.
With Roman Numerals, ciphering 263 as CCLXIII offered a simpler (someone might say. “More primitive.”) way to grasp the connections among the values of symbols representing numbers.
I have to clarify, however, that I did not expect Robert to master Roman Numerals. I did not expect Robert to even memorize the values of L or C. We always ciphered and deciphered together using the symbols as a code. Because after all,it was just a curiosity.