So Puzzling, So Easy. Learning Elements of Algebra

May 3, 2017

\frac{1}{3}x^3

There are many aspects of Elements of Basic Algebra B written by Nancy Nichols and published by Firelight Books LLC, I don’t like. As I am using this workbook/textbook with Robert not once I find slightly incorrect statements.  Not once, I think that some concepts could be introduced differently.  Not once I think that I would  present some of the ideas in a simpler, clearer way.

BUT

The truth is, I wouldn’t.  I wouldn’t dare.

I wouldn’t have courage to teach Robert Algebra.  I would consider it too sophisticated, too complex, and too abstract. I would be afraid of failing to teach him and confronting the limits of his abilities.

So although there are many things I don’t like about this curriculum, nonetheless, I am sticking to it because it presents elements of Algebra in the easiest possible way.  In the way that shows how to introduce such concepts as “slope” or “y intercept” and then use them to present graphically linear equations.

No need to plug  in numbers and perform operations on integers which are still relatively confusing to Robert.  It is enough to look at the equation y= ax+b and plot the intercept (0, b) and then go a units up or down depending on the sign and one unit to the right remembering that slope = rise/run.  That has been explained on many pages of the workbook with both positive and negative a and b.

And of course, I feel encouraged to address any possible confusion, Robert might feel,  with additional, home-made, pages of tasks.

 

 

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Daring to Read with Reading Mastery V

April 6, 2017

For three months now, Robert and I have been reading story after story from old Reading Mastery V Rainbow Edition Textbook. This out of print SRA reading curriculum that includes Skillbook and Workbook, two Presentation Books and a few additional books had been waiting on a shelf for a few years before I dared to introduce it to Robert. I doubted Robert’s ability to understand the stories. I also distrusted my ability to guide Robert through reading in a way that would enrich his life.

To put it simply, I was afraid of his and my failures.

I didn’t know if Robert was armed in prerequisite skills that would make it easier to take a plunge into this program.  After all, I didn’t work with Robert on any of the lower level curricula.  We didn’t have Reading Mastery IV or III  or any other. They were too expensive to purchase.  The one in our possession was  bought in a second hand store for a fraction of the original price.

Moreover, I felt intimidated by different approaches to reading comprehension. I read The Power of Retelling and The magic of Story.  They described very sound methods and yet I knew that it would be almost impossible to use them with Robert.  His ability to formulate sentences is so delayed that it renders him almost speechless.  All too often, the deficiency of speech is misconstrued as the lack of ability to think and/or to understand. That happens specially when the reading instructor doesn’t have tools to asses student’s comprehension of a particular text.

Those were the reason I didn’t start Reading Mastery years ago. Meantime, we went twice through some of the texts in Horizon Reading to Learn. We completed a few of the Spectrum Reading workbooks.  Some matched Robert’s developmental and personal needs, some didn’t.

Finally, I pulled the huge binder of the shelf, studied it for a while and presented the first story The Secret Cave to Robert. We analyzed the pictures that introduced the settings and characters. Then,  I read a paragraph.  Robert read the next one. The following paragraph, we read together. We kept switching until the end of the first part. Next, we worked on workbook and skillbook tasks that addressed comprehension in a few of its basic aspects. Mainly “WHO” “WHAT” and “WHERE”  Less of “HOW ” and “WHY”, as those questions would require longer verbal utterances which would immediately  discourage Robert from reading.

As we followed the textbook with The Wizard of OZ and other stories, I stopped using Presentation Book. Although that decision might have reduced Robert’s learning opportunities, it also simplified our reading process.  So, we just read together and then answered the questions as they were presented in student’s materials.  Some of them related to maps representing settings.  Some of them asked which character said something or could have said something.  Some asked if an event happened at the beginning or the end of the stories.   It was easy for Robert to answer because he didn’t have to string words into complex sentences.   It was reassuring to me because I  finally had a tool to check some aspects of Robert’s comprehension and assert that yes, he grasps many elements of the story.  He understands and /or remembers enough to let me go to the next story in the textbook or to the next event in our lives.

Since Robert’s language is delayed so severely that it interferes with expressing his thoughts, the options to answer in one word utterances to demonstrate his level of comprehension was rewarding to both of us. Finding the answer easy to say or write helped build his confidence.  He didn’t have to struggle with multiple syllables which always came out scrambled beyond recognition.  He could clearly say or write a word and be understood.  And I could clearly recognize and appreciate his level of comprehension.

So we kept reading and enjoying it more and more with every new story.

 

It came to my attention that Reading Mastery Rainbow Edition differs in some aspects from Reading Mastery Signature Edition.  For instance at least some of the stories in level V of an old edition are in level IV of a new edition.  

Horse for Prompt Dependency

February 13, 2017

In many of my previous posts I whined about Robert being too prompt dependent. I complained that as soon as I leave Robert alone with the worksheet, he stops working and waits for my return.  I tried to make the tasks simpler.   I went over the worksheets with Robert.  After he  answered every question orally  I let him  write down the answers he had just practiced.  It didn’t help.  I reduced the number of questions.  It didn’t help. Every time, I left Robert alone with the problems he stopped working.  He waited for me not to tell him the answer, but to encourage him with nothing more than,  “Go on”.

 It seemed that my words of encouragement were the switch that could turn on his brain.  He would think when I asked him to think.

I realized that prompt dependency is not just the function of not knowing and waiting for someone to give an answer or to provide more or less subtle cue.  It might be that some of the individuals are so prompt dependent that they delegate to others the right to operate the button that controls their engagement in the given activity.  I realized that as I watched Robert trying to weave his horse, Calvin, between the cones.  Robert has done that many times before.  What was new, however,  was that this time, his instructor Cindy was standing behind the rider and WAS NOT offering constant directions or words of encouragement.  Moreover, Calvin was also reluctant to follow the path because he, too, needed constant reminders to continue.  As soon as Robert lead the horse from left to right and right to left, the horse stopped.  Calvin waited for a gentle nudge from Robert’s heels and the word, “Walk”.  Robert, however, didn’t do anything as he  was also waiting for Cindy to tell him, “Make the horse walk.”  Cindy didn’t say anything.  Since, she was standing behind him, Robert couldn’t even get a clue from her body language. So he waited.  And waited. And waited.  So Calvin waited.  And waited. And waited.  It seemed like a very long time passed before Robert nudged the horse and very softly said, “Walk”.  Calvin weaved from left to right and from right to left and stopped again.  Then Calvin waited for Robert and Robert waited for Cindy.  But Cindy said nothing. Finally, Robert used his feet a couple of times to give Calvin a cue.  Calvin moved again.  From left to tight and right to left.  This pattern of behaviors repeated itself one more time before the horse and the rider reached the end of the line of street cones.

It was an eye-opening experience for me.  There were a few discoveries I made at the same time. They seemed almost too congested to pull them apart for clarity.

  1. Robert needed a prompt almost in the same way Calvin needed a prompt.
  2. At the beginning, Robert didn’t believe that he can control Calvin’s behavior the same way he let Cindy control his own actions.
  3. Robert realized that he can control Calvin himself without being prompted to do so by someone else.
  4. As Robert regained control of Calvin, he also reasserted the control of … himself.  Robert gave command to Calvin AFTER he had given a command to himself.

I am not sure if Calvin was aware of the importance of this lesson for Robert.  Cindy, however, was very aware.  Just a few weeks before, we talked about Robert’s prompt dependency and she understood the nature of Robert’s problem much better than I.  She knew how to design the lesson to convince Robert that he has to decide on his own what to do and that he has the ability to do so.

Of course, Calvin also helped.

Robert’s instructor, Cindy Conquest, sent me an e-mail with more detailed description of her approach.  With her permission, I copied it below. It explains the steps involved in her teaching methodology.

“To give you a little background information if you have interest: I had to build up to get Robert do this gradually. I scaffold all of his lessons in this manner. In previous weeks, we started with the cue “walk around the barrel” and he would have to walk away from me 5 feet to get around the barrel, then turn to face me and come back to me. Sometimes Calvin would stop at the barrel, but as Robert turned around he would see my face and that prompted him to ask his horse to walk back to me.
Then we shifted to “walk to letter H (or any of the letters). I started out at the letters, then moved into Robert’s peripheral vision, then eventually moved behind him.
Finally, we graduated to the cones. Robert had completed the cone task many times with prompting, and Robert had successfully walked away from me many times by then withOUT prompting, so we combined the two. What was different this time was that it took Robert almost twice as long to initiate the task again once his horse stopped walking. However, he did initiate it. Others may consider this a “waste” of time as it appeared that Robert sat for at least a few minutes silently before he initiated the task. But, Robert finally did initiate the task on his own – which made all that waiting well worth the while. “

 

 

 

Forcing Flexibility

February 11, 2017

Writing about Robert is like describing the ride on the rollercoaster.  Before you find  sentences depicting your slow mount to the top, you are already loosing your breath while sliding down  with the speed that in a fraction of a second destroys all of your previously strung phrases turning them back into their gelatin beginning.

Not much has changed since, almost a year ago (February 23, 2016), I wrote the above sentences.  There are calm times when Robert and I are learning.  Robert is reading, answering questions, completing worksheets, speaking, solving problems.  Slowly, with some difficulties we move from one concept to another.  But before I write in this blog describing some of the idiosyncrasies that affect Robert’s appropriation of the specific ideas, something else happens, and I have to use all my resolve to steer Robert and us (his family) out of the path sharply descending into unknown. It might be that Robert wants our guests to leave and demonstrates his wishes in a way that cannot be accepted.  It might be that Robert refuses to go to horse riding lesson with me but for hours keeps demanding that dad, who happens to be sick,  takes him there. It might be that Robert insists that his dad stops working in the garden and returns to the computer.  It would be so easy to give up.  It would be much easier to tell the guests to end the visit.  They would understand.  It is much harder to make Robert accept their presence. It would be easier for dad, even when sick to get up and drive Robert to the horse riding lesson, than to teach Robert to accept that sick parent cannot always do what Robert wants. It would be easier to do garden work when Robert is not at home than to make Robert tolerate dad’s yard work.

It  is  much easier doing everything the same way since for Robert any change provokes his strong and long resistance. And yet we have learned that we have to do everything to make sure that Robert accepts different solutions or outcomes.

Years ago, Robert had to learn that different roads might still lead home.  He wasn’t even three years old when we noticed that he always became agitated when on the way home, we took slight detour.  He noticed immediately that it was a wrong way and acted up – kicking, wiggling in his seat and making noises. It took a lot of road constructions and detours before he understood that different roads might lead to the same place. Ability to adjust to change enlarges one’s world and frees a person from the rigid bars of rituals.  Yes, Robert appears to feel safer when things remain the same. But, the things never remain the same forever.  The change is inevitable. Robert cannot escape it.  That is why we try to help Robert to adjust to the change or, sadly, show the consequences of not accepting it.

Those difficult moments often make me forget about calm hours of learning.  But we still learn.  Following old Reading Mastery V curriculum, we kept reading The Wizard of Oz. We solve problems – two pages a day from Singapore Math 4B . We build birdhouses or assemble 4 cylinder working toy engine.  And we regain our serenity.

Fait Acompli

February 9, 2017

Two weeks ago, Robert wanted to go to his adaptive horse back riding class.  He really wanted to go. However, his dad, who has been taking him there in the last few months, was sick and couldn’t drive.  I wanted to drive Robert, but he refused to go with me.  It was strange since it was  I who used to drive Robert there most of the time in the previous few years.  Robert wanted his dad.  It was their Sunday routine.  Horseback riding, shopping in Costco, and Crispy Chicken sandwich from Mac Donald.  I promised to do the same, but Robert refused.  He kept repeating, “Dad, dad, dad”.  He brought his dad’s pants and sweater, so dad would get up, dress, and drive.  He even tried to pull dad from the bed.  No words would persuade Robert to change his mind.  I had to cancel the lesson.  But Robert still wanted to go.  He didn’t seem to grasp the concept of cancellation.  At least not then and there.  I tried to turn his attention to something else.  We studied a little.  We went to the supermarket. But when we came back, Robert began insisting again,  Insisting!!!.  “Horse, horse”, he kept telling his dad while dad tried his best to sleep.  Over, and over and over.  Since the words didn’t persuade dad to drive Robert to the riding lesson, Robert emphasized his wish by taking a bag of carrots from the refrigerator and bringing it to dad.  “Horse, horse”, he kept repeating and simultaneously pointing to carrots.  Every time dad responded by telling Robert to put carrots back in the fridge.  Robert complied every time only to return to dad without carrots but with the same message, “Horse, horse, horse.”  When that didn’t help, Robert again took carrots to his dad repeating the same mantra “Horse, horse, horse” and then again returning it to the fridge.

It was exhausting.  It was hard for my husband and  for me. But  it was excruciating for Robert. He was clearly in distress.  Ignoring him didn’t help.  Redirecting him didn’t help. So I did the only thing I could do.  When Robert went to his dad again but without carrots, I took all the carrots out of the plastic bag and hid them.  I left, however,  the empty bag in the refrigerator.

Robert opened the refrigerator drawer and found an empty bag,  threw it away, and …. went to watch Netflix on his IPAD.  After four hours of attempts to force his dad to go with him to the horse riding class, Robert calmed down in a second.  Just like that.  He didn’t mention riding class not even once that day.  Maybe for Robert there was no point of going horseback riding since not even one carrot left.

I left an empty bag because of my previous observations of Robert’s reactions.  Many times in the past, when I tried to throw away his socks with holes, Robert would go through all the trash cans to find them and put them back in his dresser.  When I, however, cut  socks from top to bottom leaving a flat pieces of fabric and left them in the open, Robert accepted the fact that they couldn’t be worn anymore and dropped them in the garbage basket.

So I believed that hiding of the whole bag of carrot, would make Robert even more anxious. He doesn’t like when imperishable things vanish without explanation. Thus he would keep looking and persevering even more.  Carrots, after all, could be eaten or used in cooking. Their disappearance could be explained and accepted to everybody’s relief.

Rejecting Entropia

February 6, 2016

As soon as I drop dirty laundry into the hamper, Robert rushes to organize them in his way. He removes the clothes I have just dropped and places them back in the hamper one on top of the other in a the same pattern that he uses for his own garment. He places his clothes in the hamper in the same order he takes them off.  The shirt is on the bottom, followed by the white undershirt.  Next go his socks, jeans, and underwear. Every article of clothing is spread evenly.  In the morning, he does the same thing with his pajamas. He changes pajamas everyday.  Nothing would convince Robert to wear the same pajama two nights in a row.

When he suspects that either his dad or I messed up the clothes, he empties the whole hamper and meticulously places each item inside  making sure that the order is followed. Day clothes, then night ones, day clothes, then night ones.  My clothes are also placed in a proper sequence.  And so are dad’s.  Robert doesn’t rush.  He takes time.  He doesn’t make mistakes.

With similar attentiveness to the details, he places clothes in the washing machine and later in the drier.  When doing so, he separates white garment from the dark, but nonetheless, keeps as much of the original order as possible.  It is no wonder that Robert devotes a lot of his time to the laundry.

I have tried to explain to Robert that organizing dirty laundry is not important since the washing machine and the dryer would mix up all the clothes.    I have told him that we  could just drop the clothes randomly to the appliances and concentrate instead on folding and putting clean laundry in appropriate places.  I have told him that many times, but Robert doesn’t accept randomness. Unrelentingly, he keeps on organizing  each chaotic corner of the universe. One laundry basket at a time.

Decoding, Enforcing, and Correcting Rules

February 5, 2017

Robert tries to find patterns in  our chaotic movements and haphazardly performed everyday chores. If we repeat the same, meaningless behaviors a few times, Robert treats it as a paradigm of how we should behave every time. He insists that we  follow the model he established for us based on his observations.  We usually notice that when, for one reason or another, we abandon our insignificant routines and Robert becomes restless and  tries to compel us to return to our convenient but senseless habits.

We know we cannot allow that, but all too often we are compliant with Robert’s wishes.

  1. Robert wears his socks at home while I usually walk barefoot at home.  So, when I had my socks on, Robert followed me all over the house.  “Socks off, socks off” , he kept repeating.  A few times, I took them off not really caring one way or another.  Only when I noticed how distressed Robert became about my socks, I understood that we had a problem.  So, to Robert’s dismay, I started wearing socks more often.  Knowing, however, how persistent Robert can be, I developed a strategy that would give Robert an indication of how long I would keep them on.  “Socks off, socks off” , insisted Robert.  ” Oh, you want me to take socks off, I will do that when I finish this or that (usually short activity).  “I will take them off when I get on the sofa to watch TV”.  It took a while.  But today, I can proudly say that Robert doesn’t care one way or another if I wear socks at home or not.
  2. Robert doesn’t care if I do some work in the yard or in home.  He cares  a lot, HOWEVER,  if his dad instead of working on the computer decides to do a longer project in the back yard. Dad, s venture into backyard, makes Robert extremely anxious.  He follows his dad every step repeating, “Computer, computer.” He screams with a great pain when dad keeps reinforcing a wobbly vegetable garden gate.  He tries to pull him home.  Well, he is a pain in the neck.  The only tool to  mitigate this behavior was to ask Robert to help.  “Bring me the wrench from the garage”  “Hold this”  “Put this away in the garage.”  etc.  Giving Robert small tasks  didn’t extinguish the behavior completely, but it reduced it.  Still, we could plan it better.  we could tell Robert ahead of time of what dad would do and what would be expected of him.  Of course, Robert’s different reactions to my work in the yard and dad’s work are result of his observations.  Dad works on a computer almost all the time, while I work in the yard and in the home.
  3. I used to drive Robert to his afternoon activities, but for the last few months it has been his dad who has taken him swimming and horseback riding. Everything went smoothly until one Sunday dad get sick and I needed to take Robert to his horse riding class.  No way! Robert insisted that dad goes with him.  Nothing seemed to persuade him otherwise.  We had to cancel horseback riding class that day.  And as of now we are still planning out next move.

 

New Obstacles. New Frontiers. Part 1 Home, Home

February 2nd, 2017

Not so long ago, I had a notion that Robert’s behaviors would only get better.  I thought that as he grows and learns, the problem behaviors we had dealt with in the past would vanish. I believed that acquired knowledge would result in better understanding of his environment and thus result in appropriate adjustment to new situations. I didn’t anticipate new kinds of issues. But they kept emerging.   Some of them were created by Robert’s ideas about the rules controlling his world.  The sources of other remain murky.  Whatever their origins, the main cause of Robert’s problem behaviors remains the same.  It is the lack of ability to communicate the causes of his distresses to others.

Robert used to like going out.  He still does.  He likes going skiing.  He likes going on Saturday’s field trips organized by one of the centers.  He loves SNL parties he can attend in another program. He wants to go to movies.  Yet,in the last year in all of those and other places he expressed very  loudly his desire to go home.

“Home, home”,  he would call in the middle of the movie.  “Home, home”, he demanded not even one hour into 2 hour-long ski lesson.  “Home, home”, he insisted in the middle of the party.  “Home, home, home” he would keep on saying using all kinds of voices, from a low one to a very dramatic high pitch.

It gets more complicated.

In the movie theater, for instance, Robert doesn’t want to leave before the movie is over.  He wants to go home, but not before the ending.  If I get up, and say, ” Let’s go”, he would equally loudly protest, “No, no, no!” .  Because Robert wants  the movie to end just that minute, so he could leave after finishing seeing it.

In the bowling alley, Robert would keep bringing regular shoes to his bowling companions, so they would stop playing, take off their bowling shoes, and leave so Robert could go home.

He can be extremely  persistent.  He can repeat “Home, home” ten times a minute, every minute for an hour or longer.  This is not easy for him, and it is equally difficult for everybody else.

If this behavior happens during his swimming or skiing lesson, it is helpful to tell Robert that he would go home after completing some other activity.  ” Robert’s swimming instructor, tells Robert that he would go home after swimming one or two more times(or three, depending on her assessment of his distress.) She moves her hand back and forth as many times as she wants Robert to swim.  The skiing instructors use similar explanation although they might tell Robert, “First we go on this trail, next on that one, then you will go home.”

The most important thing, however, is NOT to interpret this behavior as a sign that Robert doesn’t want swimming, skiing, field trips, or going to movies and parties. It is possible that when he goes to a new place or the old place he hasn’t visited for a while, he feels confused of how long he should stay there and what to expect.  So we kept going back with Robert.  We tell him what to expect in this place and what is expected of him.

That is why Robert went to two other SNL parties and three other ski lessons. He did better, then he did great.

It is not, that I believe that Robert has already learned not to call “Home, home”  in many new places, or the places he partially forgot and thus become confused and concerned.  He might call, “Home, home” again, but that is not the end of the world, and it shouldn’t be something that would prevent him for coming back.

Back to Writing a Journal, Page 17

January 12, 2017

One month has passed since my last post on this blog. We are still learning. We do a lot of ,so-called, “maintenance” by going over the same old topics that Robert encountered in the past. We review them through new worksheets or through the same ones we did years ago.  Meantime, Robert and I completed all the lessons from Saxon Math 4 and from Horizon Reading to Learn C-D Fast Track. I won’t claim that Robert mastered those curricula, but he grasped a lot and became familiar with the rest.

We started with Saxon Math 5, but after a few lessons and multiple exercises I decided to review fourth grade topics by using Singapore Math 4B.  US Edition which is a little simpler that the original one.  Many topics in Singapore Math are presented in a clear format allowing for better grasp pf concepts.  For instance rounding of decimals was introduced by drawing  appropriate number lines.  For instance to round 4.28 to the whole number Robert had in front of himself a segment with 4 and 5 at the end and 4.5 (or 4.50 ) in the middle.  Number 4.28 was clearly between 4 and 4.5 so the choice was easy to make.

To round the same number to the tenth decimal place, Robert could use a segment with 4.2 and 4.3 at the ends which he improved by adding zeros at the end and thus having 4.20 and 4.30.  He had already placed by the authors 4.25 in the middle and 4.28 on the right side of it, closer to 4.30.

That was exactly as we practiced before when Robert had to  round large whole numbers.  Except, it was Robert’s job to draw a line segment, write numbers at the ends and in the middle of a segment, and place the given number in the correct half.  This process was never easy.  For Robert the exercises which clearly placed all important number cues on the line segments seemed not just easy but also helpful in understanding better the concept behind rounding.

I am not sure, however, if the fact that we started with more difficult, but “hands on” approach  that forced Robert to do all the steps by himself was not beneficial to his learning even if it wasn’t completely understood.

We continue doing speech and language  exercises using worksheets from  Speech Improvement Reproducible Master and the  Fun Deck 4. They are easy because what is easy helps with fluency and reduces the stress Robert feels every time he has to speak.

While I was cleaning drawers I found old worksheets related to time telling and we did many exercises on finding elapsed time. That is a topic that is still difficult.  However, I also found many exercises that seemed to be easy enough for Robert to do on his own.  Some of them required doing math operations, some matching synonyms or antonyms.  Leaving Robert alone for 15-20 minutes to do that work independently was very gratifying.

 

 

Win Some, Lose Some

December 6, 2016

  1. We completed Horizon Reading to Learn program and Saxon Math 4 curriculum. We did that almost two weeks ago.  Of course, this is not exactly true.  Yes, we read all the stories, solved all the problems and answered all the questions.  BUT not even once Robert completed just one of the tests included in those two programs.  Moreover, I didn’t ask him to do so.  Although, he answered many questions correctly, he did that only when I was sitting next to him.  I knew that repeating each unit many times would not necessary lead to mastering the test.  So I had a dilemma.  Should I spent more time teaching many things over and over maybe even applying many other methods hoping to build strong foundations or go forward unit by unit and expose Robert to many concepts that might widen his horizons?  I use different approach.  I repeated first two parts of both curricula a few times, from beginning to end.  I am not sure if that was the right approach, but…
  2. With Daily Geography 3 I proceed differently.  I repeat the same unit three times  hoping that Robert would answer the questions independently without my presence.  It has been hard as I discover so many obstacles.  My very absence causes Robert to stop working all together.  He would sit and wait for my return. From the doorway, I try to encourage Robert to go on his own.  Instead, he answers aloud and observes my reaction.  For reasons I still don’t grasp, my reaction gives him cues about correctness of his answer.  I don’t want to allow that so instead I back off to another room only to notice lately that Robert didn’t write the answer but sad and lonely waits again for my return.  So I do return.  We again look at the map, we underline important words in questions.  Are we looking for name of the state or the river or the ocean?  Are we looking for direction?  We make separate banks of words naming states or lakes to choose from.  We draw arrows leading from one word in the question to another word.  For the question, “What interstate highway passes through Concord, NH?”, the arrows goes from the word ” Concord”  to the words “highway”.  “First we find Concord then we will see a highway”  I explain.  We go over four questions, then I leave again.  I see Robert writing answers on his own. Two are correct, one is partially correct, one is wrong. The problems Robert has with answering those seemingly easy questions allowed me to understand the nature of difficulties Robert has in dealing with words that rely on each other to make sense.
  3. Finally, Robert can do something much easier for him.  He doesn’t have to read anything, just add fractions.  finding common denominator, simplifying, changing improper fraction into mixed fraction are not a problem.  Robert follows an algorithm which directs him to do one operation after another.  Finally, I can leave him to solve all those problems on his own.