Science, July and August 2020

Over the summer she practiced reading nonfiction for 5-year-olds. I practiced writing it. I browsed wikipedia and fed her little bits of it like she was a baby bird. A reading might tire her out but she could read it and understand it. If two weeks later I showed it to her again she could read it faster and understand it faster.

She was building a skill and a habit, but I don't know if the facts stuck with her. Today she can read well but I doubt she remembers anything about Aragon or Castile. I have kept on including details like that anyway.

Whether or not it was sticking, in the second week of June I found a way to double her enthusiasm for a reading lesson: I could put her name in the last paragraph. She would spot it when she was sizing up the page before we started. "Why does it say 'Maria' here?" and I would tell her to read it and find out. Once it was about dinosaurs and the last paragraph told a story about our outing at a museum. It was a true account that she remembered, but written in the third person.

I only pandered like that some of the time. Here is a less personal passage that I wrote for her after two sessions about dinosaurs-and-Maria:

Paleozoic Mesozoic six sixty million change changed living growing ocean forest swamp reptile frog

Life began in the ocean

All of the dinosaurs died out sixty million years ago. That was a time before people.

There was also a time before dinosaurs! The time of the dinosaurs is called "Mesozoic time." The time before dinosaurs is called "Paleozoic time."

During Paleozoic time, there were no dinosaurs. At the start of Paleozoic time, there were no living things on land at all! All of the plants and animals lived in the ocean.

Plants and animals changed a lot during the Paleozoic. At the start of it, everything lived in the ocean and nothing lived on the land. At the end of it, the land had lots of forests and swamps with tall ferns growing in them, and lots of bugs and frogs and reptiles living in them.

But dinosaurs came after.

I changed the subject to light, with the idea that I was going tell her about Newton working with prisms during the plague. I dropped it before getting to Newton, we spent September-October-November-December doing something else.

Earth planet universe sky why light right night eight whole bounce bounces minute minutes

Light from the sun

Some light comes out of light bulbs. But most of the light that we see comes out of the sun. The light starts out at the sun and then it comes to our planet. Do you remember what our planet is called? Yes, Earth.

Light moves very very very fast. It is the fastest thing in the whole universe! But the sun is very very very far away. After the light comes out of the sun, it does not get to Earth right away. It takes eight minutes to get here.

We need light to see. At night the sun is not in the sky and we don't see most of its light. That is why it is harder to see at night. But a little bit of the sunlight bounces off of the moon onto Earth. We call that light moonlight.

The next day

of off bounces bouncing different color strawberry together warm white blue brown green red goes eight

Light and sight

Last time we read that it takes eight minutes for light to get from the sun to Earth. At night, some of the sunlight bounces off of the moon and onto Earth. That way we get a little bit of light at night.

Light is always bouncing around. That is how we see things! We can see the moon when light bounces off of the moon and into our eyes. We can see a strawberry when light bounces off of the strawberry and into our eyes.

Light comes in different colors. The strawberry looks red to us because only red light bounces off of it. All of the rest of the light goes into the strawberry and warms it up a little bit.

When you mix green and blue and red paint together, you get brown paint. But when you mix green and blue and red light together, you do not get brown light. You get white light!

Two days later

Earth bounce bounces sometimes magnify magnifying off glass eye eyes through strange focus focusing water

Light and glass

Light comes from the sun to Earth. We see an apple when the light bounces off of the apple and into our eyes. Only green light bounces off of green apples. Only red light bounces off of red apples.

If you use a magnifying glass, some of the light goes through the magnifying glass before it goes into your eyes. The magnifying glass bends the light that goes through it. It bends it in a strange way, that we sometimes call focusing. That strange bending of the light can make small things look bigger!

Light also bends when it goes through water. Sometimes when you look at something through water it will look different. It might look like it is in a different place than it really is.

I will show you a magnifying glass after you finish reading this.

A couple of weeks later

-scope telescope through magnify magnifying probably spread eye

Telescopes at Night

When light goes through a magnifying glass, the light spreads out. When that spread-out light goes into your eye, the thing that it bounced off of looks bigger. Four hundred and twelve years ago, someone invented the telescope using two magnifying glasses.

We don't know the name of the person who invented the telescope, but they were probably Dutch. That Dutch inventor put one magnifying glass at the end of a long tube, and the other magnifying glass at the other end of the tube. When you looked through that tube, things that were far away seemed closer.

We don't know the name of the person who invented the telescope, but the first person to use a telescope to look at the night sky was named Galileo. When Galileo looked through a telescope, he saw things that no one had ever seen before. He saw the rings around Saturn!

She had seen those rings before. I didn't think she would know about Jupiter's moons.

The next day:

build building straight might eight heavy light Galileo Saturn Earth Italy Italian Pisa

Galileo in Pisa

Galileo spoke Italian. He lived in a city in Italy called Pisa. In Pisa there is a very famous building. It is a tall building that does not go straight up. It leans to one side. It looks like it might fall over! But it has not fallen over for eight hundred years.

That building is called the leaning tower of Pisa. There is a famous story about Galileo and the leaning tower of Pisa. Galileo was a real person but this might not be a true story. But it is a nice story.

Galileo wondered whether heavy things fall faster than light things. To find out, he went to the top of the leaning tower of Pisa, and he dropped a small stone and a big stone out of the window. People thought that the big stone would fall faster. But Galileo saw that the two stones fell at the same speed! He dropped them at the same time and they hit the ground at the same time.

A week later

-scope telescope microscope Galileo interesting -tion nutrition respiration digestion use used

Telescopes and microscopes

A piece of glass that can bend or spread out light, like a magnifying glass can, is sometimes called a "lens." When light went through Galileo's telescope it went through two lenses. Then it went into his eye. That way things that were really far away looked like they were closer. When he used the telescope to look at the sky he saw the rings of Saturn, and the moons of Jupiter.

Saturn is very, very big. It is a planet and it is bigger than the Earth! But you can also use lenses to see things that are very, very small. That kind of "scope" is called a "microscope." With a microscope, you can see cells!

Even though cells are so, so small, they are not simple. They have an inside and an outside, and there are lots of interesting things inside of them. They are alive! They need nutrition to live. They do respiration and digestion.

We are made of cells. What are cells made of?

 

Adding one

Even last year, Maria knew how to count on her fingers to find the sum of small numbers. When we were staying home together in March and I asked her if she'd like to practice math, I learned that she was using this method not just to find out what is 3+5 but even to find out what is 2+1. "Do you think you could find out 2+1, and 3+1, and 4+1, without using your fingers?" The question made her tense, and I backed out of it right away.

The reading lessons had started to go really well. People can be fragile about math and I thought we had time to wait for a more perfect moment to start. But for a few months I was nonplussed about how I was going to teach someone to compute 4+1. Was I supposed to give her a seminar about +1?

"Give your child a superior mind" came in July, and I saw that the answer was yes. Here is Zig and Therese Engelmann's detailed outline of a lecture series for 4-year-olds (but Maria was 5) on how to add one:

Showing the Relation between Counting and Adding:

1. Draw 2 small circles on the board 

                    ◦    ◦

2. Count them, pointing as you count: "1...2..."

3. Let the child count them. "Your turn."

4. Define adding so that it ties in with what the child knows about counting. "If I add 1 more, I'll have...:" Draw another circle, and count them.

                    ◦    ◦    ◦ 

"Three circles." Repeat. "I have 3 circles. If I add one more, I'll have..."

                    ◦    ◦    ◦    ◦

"...1...2...3...4. I'll have 4 circles. If I add 1 more, I'll have..."

                    ◦    ◦    ◦    ◦    ◦

And so on. Add circles until you reach 20. Repeat the procedure several times.

As soon as the child catches on to the idea that when you say, "Add 1,:" you're going to the next number in the counting series, start speeding up the operation. "I have 7 circles and if I have one more, I'll have...yes, 8. I have 8 circles. If I add 1 more I'll have...Good."

5. Present the rule for adding 1: Draw 5 circles on the board. "Here's the rule for adding 1. You first see how many you start out with. How many are here? Sure, 5. And you say, "I have 5. If I add 1 more I'll have...if you don't know ask yourself, what comes after 5? What's the next number? Sure, 6. So if I have 5 and add 1 more, I'll have 6."

Reading addition problems: 

1. Present 3 + 2 = 5.

2. Identify the + as plus, the = as the equal sign.

3. Then read, "We read just the way we do in the book. We start over here [left] and say, 3 ... plus ... 2 ... equals ... 5—3 plus 2 equals 5. Your turn. ..."

4. Point out that you can add any two numbers together. Demonstrate with various examples. Let the child give the numbers and you write them down. "Pick any numbers you want."

5. After he can read addition problems and properly identify the terms (which may take at least an entire session), show him how to interpret addition problems. Begin by pointing out that in addition you start out with on number and end up with another. Put the problem 3 + 2 = 5 on the board. "The problem tells us that we start out with 3 and end up with 5." Give the child practice on several other problems. Then present the problem

         

                    4 + 5 =

"What about this one? We start out with 4 and we end up with—you don't know. That's what we have to figure out. I know that when you start out with 4 and add 5 you end up with 9, so I can write . . ."

                    4 + 5 = 9

"I solved the problem. Read it . . ."

Repeat with examples until the child catches on to the idea of starting out and ending up. This is an extremely important notion. Make sure he learns it.

Translate symbols into the operation of adding.

                    3 + 1 =

"Look at what the problem tells you. It tells you to start out with 3. Then the plus sign tells you to add. It says, Get more numbers. How many more? [Point to the 1.] Look. It says get 1 more. Start out with 3 and get 1 more. And when you do that, you'll end up with 4.

                    3 + 1 = 4

"Read it."

Keep the presentation straight and simple: start out with the number on the left (at least in the present problems); the plus sign tells you to get more, the number after the plus sign tells you how much more; and the number after the equal sign tells you what you end up with.

6. Diagram the problem.

                    ◦    ◦    ◦    +    ◦ =

                    ◦    ◦    ◦          ◦ 

The top row shows you what you start out with and what you add. The bottom row shows what you end up with. The bottom row is equal to the top row because you can draw a line from every circle in the top row to a corresponding circle in the bottom row.

                    ◦    ◦    ◦    +    ◦   =

                    |    |     |          |   

                    ◦    ◦    ◦          ◦

To find out how many you end up with, simply count the symbols in the bottom row. You can see where each one came from. You can see the relations between the three terms.

Stress the idea that the term you start out with and the term you add are reflected in the answer. Point to the bottom row, "See, here's the 3. And here's the 1. 3 plus 1 is 4." 

Rule: For every circle in the top row there must be a circle in the bottom row.

7. After the child understands how to read an addition problem and how to interpret it (which will probably take three sessions and 40-50 examples), introduce the rule for adding 1 to other numbers.

                    3 + 1 = 

 "What do we start out with? . . . Yes, 3. And what do we do (pointing to the + sign)? . . . Yes, get more. And how many do we add? . . . Yes, 1. . . . And what do we end up with? . . . We don't know. But I know a way to figure it out. Is there a 1 in this problem? . . . See if you can find it. . . . Yes. So I draw a circle around the 1.

                    3 + 1⃝ =  

 "We're adding 1 to which number? . . . To 3. [Pointing to the 3.] When you add 1 to a number, you end up with the next number. We're adding 1 to 3 so we're going to end up with the number that comes after 3. What comes after 3? . . . Sure, 4. So we're going to end up with 4. Let's write it down."

                    3 + 1⃝ =  4

Summarize the problem as an addition fact. "3 plus 1 is 4. Say it."

8. Follow with a series of problems. Include some in which the 1 is first (1 + 3 =) and last (7 + 1 =). Have the child read the problem. "7 plus 1 is . . . we don't know." Then ask, "Are we adding 1?" Have him locate it. Circle it. "What's the rule when you add 1?" Help him state the rule. "When you add 1 to a number, you always end up with the next number." Have him find the number to which 1 is being added. He should have no trouble, because it's the only uncircled number in the problem."What comes after 7? Good. So we'll end up with 8." Write the answer.

                    7 + 1⃝ =  8

Diagram the problem with circles.

9. Don't introduce 1 + 1 or 1 + 0 until after the child has worked on +1 problems for a week or so. Solve them the same way you would any other +1 problem. In 1+1=, circle only a single 1 and ask what comes after the other 1. In 1+0 =, explain how to handle the zero )which the child already knows vaguely from counting backward). "We call this zero. And zero means that you have nothing. When I say I have zero shoes, it means I don't have any shoes." Give other examples. Then tell the child that 1 comes after 0. Tie this in with what he knows about counting backwards.

10. Demonstrate that the rule about the next number applies only when you're adding 1. The child will probably get the idea after the first few sessions that addition is simpler than it actually is. Find the 1; look at the other number; then say the number that comes next. Pretty easy. To keep him honest, present a series like this.

                    1 + 4 =
                    5 + 4 =

                    5 + 1 =

                    6 + 11 = 

                    1 + 9 =   

"Now remember, we can't use the rule for adding 1 unless we find a 1 in the problem. Do we find a 1 ion the first problem? Good. Then we can use the rule. Let's do it. Do we find a rule in the second problem? No. So we can't use the rule. The problem 5 + 4 is 9 is one you just sort of have to remember. Say it . . ." 

11. Present continuity exercises. For the next month, spend about five minutes at the beginning of each session on the +1 problems. Here are several series of problems you can present. They show the relation between +1 and counting. 

                    0 + 1 =                     9 + 1 =

                    1 + 1 =                     8 + 1 =

                    2 + 1 =                     7 + 1 =

                    3 + 1 =                     6 + 1 =

                    4 + 1 =                     5 + 1 = 

                    5 + 1 =                     4 + 1 =

                    6 + 1 =                     3 + 1 =

                    7 + 1 =                     2 + 1 =

                    8 + 1 =                     1 + 1 =

                    9 + 1 =                     0 + 1 =

Stress the addition facts "2 plus 1 is . . . well, what comes after 2? . . . 3. So, 2 plus 1 is 3. Say it . . . 3 plus 1 is . . . What comes after 3? . . . 4. So 3 plus 1 is 4. Say it . . ." These are quite similar to the What comes next? games the child played during the previous year.

Word Problems Involving Adding 1: Introduce word problems after the child has been exposed to +1 problems for at least two weeks. The idea to get across is that the rule for adding works with dogs, sheep, cows,  or anything else the child can name. The idea is not that these prove the rule. You wouldn't try to convince the child that a red ball proves the concept red. It is merely an example of red, just as adding pies is an example of adding.

Present problems like these: "I have 8 dollars. Then I get 1 more. How many do I have?" "A farmer buys 4 sheep. Then he buys 1 more. How many does he have?"

1. Tell the child specifically how to translate the words into mathematical symbols. The parallel between the every-day language we use and the language of mathematics is not obvious—not even logical. Conventions: The first number you mention is the one you start out with. If the first number mentioned is 7, you start out with 7. The words more, adds, gets, buys tells you that you're adding. You indicate these on the chalkboard with a plus sign. Then you add as many as the farmer gets or adds or buys. If he steals 1, you write 7 + 1. Next, you put an equal sign, and ask the question the problem poses.

                    7 + 1 = 

How many does he end up with? We don't know. That's what we're going to figure out. 

2. Diagram the problem on the board, using circles for each number in the problem. If the farmer has 8 bulls and buys 1 more, diagram the problem this way: 

                    ◦    ◦    ◦    ◦    ◦    ◦    ◦    ◦    +     ◦   =
                    |    |     |    |     |    |    |     |           |

                    ◦    ◦    ◦    ◦    ◦    ◦    ◦    ◦           ◦   

Explain that each circle stands for a bull. "For every bull we have in the top row we must have 1 in the bottom, so we draw them in the bottom row and count them—that's how many bulls the farmer has."

Introduce one or two word problems during each session for at least two weeks. Don't be afraid of repeating problems framed in the same situation (such as bull-buying). The only way the child will learn the key words is to hear them over and over. 

That is about 6 pages, ending at p. 202, of a 300 page paperback. The instructions are much more dense than "Teach your child to read," but I was able to follow them without confusing myself or confusing her. It took two or three weeks to get through it, half an hour a day at the dining table with a tiny whiteboard. 

The rest of page 202 is another outline, even more compressed, to teach the number pairs: 1 + 1 through 5 + 5 at first, and 6 + 6 through 10 + 10 after another two weeks. On page 203 a new section starts with the heading "Algebra Problems."

ReadWorks

She was reading. Could I just get her a library card, and let her educate herself? 

In June she was still unsure about words that end in y, and about double effs and double esses and double ells. In November, so far, I'm still not raising a bookworm. I once in a while catch her reading the side of a cereal box, or one of her old board books. But I'm glad we kept on doing reading lessons.

If it was complicated, she couldn't read it. Not in June. But if most of the words were familiar, and the sentences were short, and there was lots of repetition, she would bring all her concentration to it. At least for one page of big print. She might read it from start to finish, or she might stop after every sentence and react. Talking to her is not the same: she zones out or interrupts or tries to change the subject. Our conversations are fun but they are not didactic. Reading lesson was a new channel of communication between us.

What should I send down this channel? Most of the world's written knowledge is news to a five-year-old. When I was counting the days until I ran out of the "100 easy lessons", I found this idea on a website called ReadWorks:

Article-A-Day is a 10-15 minute routine designed to be done every day to build background knowledge, vocabulary, and reading stamina. Article-A-Day complements a broad range of curricula and is recommended for kindergarteners to eighth-graders. ... The Article-A-Day sets are grouped topically or to systematically build vocabulary. Find sets that gradually become more challenging as the school year progresses and are coordinated by topics across grade levels.

They don't cost money but you have to make an account to see their articles. I was disappointed when I did. What they have that is pitched at kindergarteners is meant to be read aloud by a teacher. The kids fill out a worksheet after. "If the students cannot write yet, they can draw their responses." For a new reader it wasn't great for practice, and I wasn't excited about the content.

But I liked the idea of a little bit of nonfiction every day. After one false start it wasn't hard to write 100 words about a subject that was new to her, in words she could handle. I made it easier to write that much the next day, and every day, by having a big part of each passage recapitulate yesterday's passage.

I wanted to write about history but she knew very little about calendar dates, or even about numbers. The day after "Cats and dogs," I didn't make her read anything but this:

five, zero, ten, one, two, hundred, thousand

Each of those in large handwriting, an arrow drawn underneath, and a box to the side for her to print numerals. It was a worksheet. She already knew in speech the words "hundred" and "thousand," but only now in November is she maybe starting to know their magnitude. "Five" and "zero" were established favorites for her. The irregular spellings of one and two drew out a nice conversation. "A thousand years ago I think they actually said it t'whoah but we don't say it like that anymore."

Here's the lesson from the day after that: 

Spain, Genoa, India, Bahamas, America, ght, caught, light, bought, hundred, tried, year, years, month, people, explore, explorer, exploring, think, thought, heard 

A new way to get to India

Five hundred years ago, the king and queen of Spain paid an explorer to find a new way to get to India. That explorer was from Genoa and his name was Columbus. The king and queen thought that he was good at exploring.

The old way to get to India was by land, but Columbus looked for a new way to get there. He tried to get there in a ship. Two other ships went with him.

After one month, their ship found land. There were many people living on that land. He thought that he had found India and that those people were Indians. But that land was not India. It was the Bahamas.

The Bahamas are close to America. Until then, the king and queen of Spain had never heard of America. No one in Spain or Genoa had heard of America.

and the day after that:

Columbus, Ferdinand, Isabella, Spain, India, Aragon, Castile, first, paid, country, marry, married, merge, merged, treat, treated, people, prince, princess, remember

The first king and queen of Spain

Remember the king and queen who paid Columbus to find a new way to get to India? Their names were Ferdinand and Isabella. They were the first king and queen of Spain. Before they got married, there was no country called Spain.

Ferdinand was the prince of a country called Aragon. Isabella was the princess of a country called Castile. They were born almost six hundred years ago. They got married and then later they merged Aragon and Castile into one country. That country was called Spain.

Ferdinand and Isabella were a prince and a princess once, but they were not heroes in a story. They treated some of the people in Spain badly. Sometimes you get that from kings and queens!

If I had read them aloud to her she wouldn't have listened. She engaged with them when I made her read them aloud to me. If part of the reading went over her head, I sometimes would expand on that part the next day—it didn't have to be important to me, it just kept away writer's block.

For one session a couple of weeks later, I had too little time or maybe I did have writer's block. I didn't have something new ready for her so I had her read "The first king and queen of Spain" again. It took her almost 40 minutes the first time and only 10 minutes the second time.

Lesson 103

Once it gets going the showcase of each lesson in "Teach your child to read" is little story and a little cartoon. You cover up the cartoon and reveal it to the kid after she finishes reading the story. "What do you think you will see in the picture?" and the kid makes a good guess. It's fun.

Before reading the story, tutor and child go through enumerated "tasks." A little bit of something new and a lot of review from previous lessons.

What kind of tasks? There is a giant h to one side of the script, with an arrow underneath it. "Here's a new sound. We always have to say this sound fast. My turn to say it fast." Then you run your finger along the arrow as you say a pure aspirate "h," careful not to say "huh" or "hah".

Or, there is the word said off to one side, the same size as the h. A little ball is printed under the s, a, and i, and a little tick mark under the d. "Sound it out," and the child says "sssaaaiiid." Her "aaa" and "iii" are separate sounds, she doesn't say "sed." "Very good. That's how we sound out the word. Now listen to me say the word: sed."

The distinction between saying a word and sounding out a word, and many other careful distinctions and explications like it, kept her over 100 lessons from ever getting confused.

The long task in each lesson was to practice reading a list of words, some of them new to her, that would appear in the story. For "lots of cars" it was

farm, are, cars, lots, of, has, old, his, sheep

She had to go through the list twice. The first time through to sound out and then say the word—after she read "haaasss" I had to reply "Good. What word?" and she would either remember "haz" or I would tell her.  The second time through to say the words the fast way. It takes a while. When she flagged, or complained, it was usually during this part. The story at the end was dessert, it took concentration but she was happy reading it.

For lesson 101 I gave her a short kids' book, by Crosby Bonsall. The epilogue had recommended it along with a list of words to "preteach": bigger, dead, does, fault, it's, mine, she's, smart, yours. I told her the lessons from now on would be different, and showed her the sheet with the practice words on it: my big handwriting and a hand drawn arrow under each word. When she was through with them I revealed the new book. I might have succeeded to make it seem like a prize. She was proud to be able to read it to herself, and later that day to her grandparents.

The next day I wrote something, about snakes. I made it way too hard, like an encyclopedia article and not like a prize. For the lesson after I thought I should scale it way back:

igh, night, right, light, fight, sigh, day, strange, stranger, saliva, hurt, people

Cats and Dogs

Some people like cats and some people like dogs. Some people might not like cats or dogs.

Some people might like dogs at night and cats in the daytime. Some people like both cats and dogs, all of the time.

Cats and dogs might bite you if you are a stranger. Their saliva does not have any venom but their bite can still hurt!

That was all it took for her to learn to read "people" and words with "igh."

Zig

She would have learned to read anyway. Her 100 lessons took 100 days. There are 180 days in a school-year, if you don't count the weekends. Maybe she would have made the same progress if we had spent the time another way.

My own experience of learning, in childhood and now, is of sometimes feeling ahead of where I was 100 days ago but never feeling ahead of where I was yesterday. Taking a class or reading a book is confusing. It is hard to follow along but I can hope that I will have gotten something useful out of it in retrospect. 

"Teach your child to read" showed me a different model. The glass filled up with water. It felt like I was holding the pitcher. I wasn't scientific about it, I was just impressed. Who made this curriculum?

Siegfried Engelmann died in 2019. He has a website that was updated at least as recently as 2012. "Teach your child to read" was published in 1983. He might have been on the Merv Griffin show in 1966, promoting one of two books he wrote that year. Before that, he was in advertising. He was born in 1931.

It looks like a lot of that long career, maybe everything after 1966, he spent developing a curriculum called "Direct Instruction" and pitching it to public schools and to politicians. That's a battlefield. Zig has critics.

Lots of his writing online is addressed to those critics, and I don't understand it. "Teach your child to read" is crystal clear and it seemed to work, but it was not easy to find out what else you can do this way with a five-year-old. There are other "Direct Instruction" products but they are expensive, not available by interlibrary loan, and probably can't be used like "Teach your child to read." They are for classrooms.

But there are two videos on his website, one from 1963 of his twin four-year-old boys, one from 1966 with seven children who had not yet started first grade, who might have been in a preschool he ran with Carl Bereiter. They are showing off what math they can do. The twins in 1963 are a little ahead of the class in 1966, who were way ahead of Maria in 2020. 

The twins methodically work out the sum of 355 and 297, solve for R given D = 9R and D = 36, add fractions like 2/7+33/7 and 2/2+20/4, find one of the sides of a rectangle given its area and another side, and more. They take turns with the problems and only make one mistake, in between reels.

The kids in 1966 had memorized a little more of the times tables than the twins had. The twins will study the problem for a moment, say something like "count by nines how many times to get to 36?" and then consult a big sheet of paper behind them with a handwritten multiplication table on it to find out. They think out loud about each problem, and it sounds like they really know what is going on as they work.

In June my daughter was a full year older than these boys and didn't know that 8+1=9. If Zig Engelmann had written a book called "Teach your child math in 100 lessons," I would like to find it. Here is a hint from elsewhere on his website:

Jerry Silbert had been urging me to put Give Your Child a Superior Mind online. I didn’t want to do that because a large part of the book provides instructional sequences for reading and math. We have better ways to teach these subjects now than we did back in 1966, so I resisted Jerry’s suggestion. Finally, he urged me to put the first part of the book online. After quite a few urgings, I decided that I should at least read the first part, which I hadn’t done since 1966. I read it, and I was very impressed. I didn’t think that what I wrote back then would hold up so well.

I don't mind the boasting, he might have earned it. That title bothers me but maybe it wouldn't have in 1966. The book is long out of print. The part that Zig put online doesn't have any math in it, and I still haven't found out what "better ways to teach these subjects" he is talking about. I ordered a used copy for 60 bucks. It came in July, it looks just like a crummy paperback self-help book. Maria is almost through it.

Lesson 100, lesson 101, and lesson 250

In each lesson of "Teach your child to read" the tutor reads a script, printed in small pink letters. The child reads phonemes, words, sentences, and eventually stories, printed in large black letters. The print shrinks gradually from lesson 1 to lesson 100, never to the adult size. It switches suddenly from the Distar font at lesson 74. 

At lesson 53, the stories start to have titles. Here it is without the Distar:

lots of cars

a man on a farm has lots of cars. he has old cars. he has little cars.

are his cars for goats? no. 

are his cars for sheep? no. 

are his cars for cows? no.

his cars are for cops. he has lots of cop cars.

Upper case is introduced close to the end. Here's the story in lesson 100:

Hunting for Tigers—Part 2.

An old man was shooting at a tiger.

The tiger sat down and started to sing. The old man shot. This shot hit a rock. A bug was in back of that rock. "Stop making this rock jump," the bug shouted.

But the old man did not stop shooting. The man shot a hole in the sand. An ant said, "Thank you, that is a good ant hole."

The tiger kept singing and the man kept shooting. Then the man stopped. He said, "I am out of shots. So I must stop hunting."

The tiger came over and licked the old man on the nose. The old man said, "You can not do that. Tigers do not lick. They bite."

The tiger said, "Not this tiger. I am a tame tiger." Then the tiger said "I love to lick noses and I love to sing."

The old man said, "I must get out of here, but I can not see. So I can not find my house." 

The tiger said, "I will take you home if you give me a good coat."

So now the tiger has a tiger coat and a coat from the old man. And the old man has no coats.

This Is the Last Ending.

I was anticipating this last lesson throughout the second half of the book. I loved and Maria accepted spending 30 minutes a day like this. It's likely it was good for her. The school was (and remains) closed. So what should we do for lessons 101-200?

The story in lesson 100 fills a page of the book, so maybe she could read a page out of a children's book every day. The epilogue to "Teach your child to read" suggests something like this:

It might seem that if your child has mastered the first steps in decoding, the child should easily be able to read other material that is ostensibly designed for beginning reading, such as the easy-to-read books that are advertised in stores and on TV. The problem is that your child probably reads at the second-grade level (if the child has completed the program successfully). Most of these books are written for the third-, fourth-, and fifth-grade level. Most of them contain an outrageous vocabulary. The best of them are good listening books, but not very good reading books for the neophyte reader.

However, of the incredibly large group of children's books that is available, there are a handful that can be presented with some preteaching to a child who reads at the second-grade level. Below is a list of twenty books that you can introduce. 

That was written in 1983, I don't know if the landscape of children's books or the meaning of "3rd grade level" has changed since then. But I ordered some off of their list a few weeks before we finished the book. I was ready to go with "Mine's the Best" by Crosby Bonsall for lesson 101. But it was clear when I got it that it would be good for only one session: it is 30 pages long but with only 3 or 4 words on each page. "Nate the Great" was good for three sessions. Keeping it up every day took more thinking. 

This blog is for keeping track of that thinking. I started writing them myself. Here's a lesson from last week, I haven't been counting but let's call it lesson 250:

Bricks, wood, and stone

In Sumer there was always plenty of mud. The people living in Ancient Mesopotamia learned how to make bricks out of the mud. But those bricks did not last for very long. Archaeologists think that they might have started to crumble after just fifty years. So fifty centuries later, they can't find many Sumerian buildings.

Do you think that Gilgamesh and Enkidu would have liked to live in a building made out of cedar wood, instead of mud brick? But even cedar wood cannot last for fifty centuries. Bricks and wood won't last for fifty centuries. Will any buildings last for fifty centuries?

Stone buildings can last for a hundred centuries! Long before Sumer, long before Uruk was built in Lower Mesopotamia, there were people making big stone buildings. Somebody made a big stone temple in Upper Mesopotamia. Do you remember what we call that temple now?

Who built Gobekli Tepe? We don't know much about them. They didn't have writing.

The Ancient Egyptians did have writing. They had hieroglyphic writing. And they buried their pharaohs in big stone buildings called pyramids. When the pharaoh died, they wrapped him in linen, and they put his mummy into a golden coffin, and they put that coffin into a big pyramid.

And do you know what? We know the name of the man who built the first pyramid. His name was Imhotep.

That's supposed to be nonfiction. Corrections welcome.

Discipline

My kid gets along with me. She is not a brat or a terror. Usually, I have more fun with her than I have by myself. Sometimes, I appreciate a break.

She accepts my authority about when to come inside, when to turn off the computer, when to turn out the lights. But she also employs charisma and whining to get out of following the rules. I usually have trouble getting and keeping her attention.

Lesson 1 of 100 was very easy for both of us. The book provides a script for the tutor to read. That is a characteristic of Engelmann products—except for his early ones, more on that later. Listen to me say 'sss' as I run my finger under the letter. Now you do it. Listen to me say 'sssaaammm' as I run my finger under the letters. Now you do it. Now I'll say it fast, 'sam.' Now you say it fast.

It doesn't require any preparation and it's over in twenty minutes.

Lessons 5, 6, and 7 (or so) were harder. She got bored and wanted to stop. I got through it without threats or bribes. Past a certain length of time, lying down on the floor is more boring than reading lesson. I'm more patient than a five-year-old, I was able to win the battle of wills a few times in a row.

Then we had a streak of many easy-going lessons. She got a little bit better every day, and I sometimes picked up a small insight about reading, or learning, or teaching. For the tutor, some lessons are more fun than others. But if those small insights went over my head some days, overall I picked up something big about the role of repetition in learning.

Einstein was impressed by compound interest, a "powerful force in the universe." But even accretion is a powerful force. At lesson 40 the kid is not a bad reader, not of children's books.

(Well, a footnote about that. At the beginning the kid is being trained to read in a weird font, called Distar. There are visual cues that tell if a letter is silent, or if a vowel is long or short. There are some children's books printed in the same font; sadly "My Pet Goat" is a very famous example. The readings are printed normally from lesson 75 or so, and the kid adjusts quickly.)

Besides building a skill, we had built a habit of doing a lesson every day. At lesson 40, I thought I would miss it after we got through the book.