Tag Archives: John Holt

Learning arithmetic

My attitude towards learning and education has been shaped by my own experience as well as by authors like A.S. Neill and John Holt, who represent what might be called the “free school” (“free” as in freedom) approach. Taking a cue from software, this might also be called the “free/open school” approach, an approach that basically gives students much more freedom to choose by themselves what to learn, how to learn, when to learn, and even where to learn. Teachers play a more passive role in the background as advisers. Traditional schools, in contrast, are so regimented that John Holt has called this traditional system a virtual prison for children and youth.

As an example of the free school approach, I’d like to quote the first few paragraphs of Chapter 1 (And ‘Rithmetic) from the book Free At Last (The Sudbury Valley School) by Daniel Greenberg:

Sitting before me were a dozen boys and girls, aged nine to twelve. A week earlier, they had asked me to teach them arithmetic. They wanted to learn to add, subtract, multiply, divide, and all the rest.

“You don’t really want to do this,” I said, when they first approached me.

“We do, we are sure we do,” was their answer.

“You don’t really,” I persisted. “Your neighborhood friends, your parents, your relatives probably want you to, but you yourselves would much rather be playing or doing something else.”

“We know what we want, and we want to learn arithmetic. Teach us, and we’lll prove it. We’ll do all the homework, and work as hard as we can.”

I had to yield to them, skeptically. I knew that arithmetic took six years to teach in regular schools, and I was sure their interest would flag after a few months. But I had no choice. They had pressed hard, and I was cornered.

I was in for a surprise.

My biggest problem was a textbook to use as a guide. I had been involved in developing the “new math,” and I had come to hate it. Back then when we were working on it — young academicians of the Kennedy post-sputnik era — we had few doubts. We were filled with the beauty of abstract logic, set theory, number theory, and all the other exotic games mathematicians had played for millennia. I think that if we had set out to design an agricultural course for working farmers, we would have begun with organic chemistry, genetics, and microbiology. Lucky for the world’s hungry people that we weren’t asked.

I had come to hate the pretensions and abstruseness of the “new math.” Not one in a hundred math teachers knew what it was about, not one in a thousand pupils. People need arithmetic for reckoning, they want to know how to use the tools. That’s what my students wanted now.

I found a book in our library, perfectly suited to the job at hand. It was a math primer written in 1898. small and thick, it was brimming with thousands of exercises, meant to train young minds to perform the basic tasks accurately and switfly.

Class began — on time. That was part of the deal. “You say you are serious?” I had asked, challenging them; “then I expect to see you in the room on time — 11:00AM sharp, every Tuesday and Thursday. If you are five minutes late, no class. If you blow two classes — no more teaching.” “It’s a deal,” they had said, with a glint of pleasure in their eyes.

Basic addition took two classes. They learned to add everything — long thin columns, short fat columns, long fat columns. They did dozens of exercises. Subtraction took another two classes. It might have taken one, but “borrowing” needed some extra explanation.

On to multiplication, and the tables. Everyone had to memorize the tables. Each person was quizzed again and again in class. Then the rules. Then the practice.

They were high, all of them. Sailing along, mastering all the techniques and algorithms, they could feel the material entering their bones. Hundreds and hundreds of exercises, class quizzes, oral tests, pounded the material into their heads.

Still they continued to come, all of them. They helped each other when they had to, to keep the class moving. The twelve year olds and the nine year olds, the lions and the lambs, sat peacefully together in harmonious cooperation — no teasing, no shame.

Division — long division. Fractions. Decimals. Percentages. Square roots.

They came at 11:00 sharp, stayed half an hour, and left with homework. They came back next time with all the homework done. All of them.

In twenty weeks, after twenty contact hours, they had covered it all. Six years’ worth. Every one of them knew the material cold.

That’s the free school approach.

A well-known school that uses this system is Summerhill School in the U.K. The school was set up by A.S. Neill, who wrote about his experiences in his book Summerhill: A Radical Approach to Child Rearing. The books How Children Fail and How Children Learn by John Holt are also illuminating.

Freedom in schools

Being a 55-year old student seems to have given me a unique perspective. I am going through an experience that is usually reserved for the youth, but I do so with the benefit of half a century of hindsight.

I can see clearly now the two parallel strands of school life – the regimented part, and the free part.

Regimented learning. It was educator John Holt who wrote eloquently how regimented schooling, from the primary grades to the university, tended to suppress the joy of learning. The school was a prison, he said. I can easily appreciate that observation, having spent three years myself as a political prisoner. Children who went to school – university students are no exception – are forced to learn one topic at a certain hour and a certain room, whether they wanted to or not, whether they were ready for it or not, whether they were interested in it or not at that particular time. The lecture, and its variations, remains the main teaching vehicle of this regimented method. High technology has not improved things. The computer and the LCD projector has made it even easier for teachers to indulge themselves, with their presentations and bullet points now available for instant display at the push of a button. Under such regimentation, most students gradually lose their innate love for learning. Instead they feel bored, sleepy, uninterested, constrained, and even tense, lest they couldn’t answer a teacher’s probing question.

Freedom lives. Fortunately, the undercurrent of freedom has survived in schools. It is best represented by the library, where one can indulge one’s love of learning, reading whatever gave one joy for that moment. In the library, freedom lives. Students who have not lost completely the innate curiosity and love for learning that makes us human can nurture it here and give it a chance to grow and to flourish. The books in the library have been my best teachers, whenever the textbook didn’t make sense. If a topic was specially hard, I’d pick several books on it from the shelves and browse them. Usually, I’d find a book or two whose authors talked to me as if they read my mind, what I knew and what I didn’t, and what questions I asked myself. When browsing, I would often come across a specially interesting title; I took the book to my desk too. This is real freedom. This is what learning should be. If educators understood this, they would build the learning process around it, not around classroom lectures.

More and more schools are getting connected to the Internet. Unfortunately, some school administrators see the Internet as an extension of the regimented system. They add a subject in the curriculum entitled ‘Internet’, assign that subject a time and a room (the Internet Laboratory, or some such name), like they do with Math, Physics, Biology, etc. How tragic that they can’t see it an extension of the library instead, as a new space where students can exercise their complete freedom to learn according to their own schedule and inclination, on their own time.

If I were a lecturer, I would conduct my classes this way. In the previous meeting, I would have assigned students to read a particular chapter or chapters in the textbook, reminding them to try to understand the chapter content. The class would then start with a question-and-answer session. The students would ask me what wasn’t still clear to them, after taking the effort to understand the material. This part would clear the remaining obstacles to understanding. It would be a discussion, an exchange, not a sterile one-way spoon-feeding of sentences which are better read than heard. Studying from books, one can always go back and reread a difficult phrase, as many times as necessary; it is hard to learn from lectures, because lecturers have no rewind button. By the way, I will even encourage students to write their questions and sign it with an alias, if they want to ask simple questions but don’t want to sound stupid. I’ve often felt the same thing.

When all questions have been clarified, I would give an “unquiz”, basically a problem set that the students have to solve in class, again, either with their true name or an alias. It will not be graded. But it will test them if they could now apply what they just learned to actual problems. I now know that one of the most important phase in learning, which I had underestimated when I was younger, was the actual problem-solving exercises. Pilots accumulate “flying hours”, students should accumulate “problem-solving hours”. It’s as simple as that. If you want to get good grades, solve the exercise problems. The more you solve, the more you learn. It’s a pity most teachers choose to solve problems themselves on the blackboard, to show their students how to do it. What a waste of time. They should be assigning the exercise to their students, and then testing them in class with similar problems. This is how students learn. The “unquiz” would give the teacher a very good window into the strengths and weaknesses of every student in class. Those who need special attention and help should then get it.

The third part of the class will be another question-and-answer session to wrap up the students’ learning experience and questions that arose while doing the problem-solving. This part would cap the students’ positive learning experience. It will be a final chance for the teacher to add icing to the learning cake.

Finally, before leaving the class, I would announce the reading assignment for the next class meeting.