Multiple ways to multiply

So … dh commented to me that dd told him that she did not know the 6 times table. Worried, he told me that while it is good that she explores freely and deeply etc , we have to ensure that she doesn’t miss basic things.

I told him, you know the funny thing is, she was telling me something about 6 x 8, which she found difficult because she knew neither the 6 table nor the 8 table. She said, "Well, 6 x 8 is so hard that I just memorized it."

This was somewhat surprising to me because I thought, what other way is there? Don’t we memorize all of them?

But I realized that to her mind, the way she "knew" certain multiplications was different from the way she knew others – for example, if we are doing 6 x 2, we understand that it is 12, we don’t memorize that it is 12. Times two is easy to understand that way. So she has a different approach to multiplication, that varies according to the numbers being multiplied.

Of course dh found all this to be yet another one of my crazy theories.

Later in the evening, he called dd and said, "Stand here, I want to ask you a few questions." Ever ready for a few questions she stood before him. I watched from a distance. His questions are in quotes, her answers are not.

"What is 6 x 8?"

48

"How do you know?"

6 x8 I just memorized because it was so hard.

"What is 6 x 10?"

60

"How do you know?"

When you multiply anything by 10 you just add a zero and move the decimal point one space to the right, if there is a decimal point.

"What is 6 x 7?"

42

"How do you know?"

I know the 7s table.

"What is 6 x 5?"

30

"How do you know?"

To multiply anything by 5 you just cut the number in half and add a zero. Basically you divide by 2 and multiply by 10 because that is the same as multiplying by 5.

"What is 6 x 9?"

54

"How do you know?"

I know the 9s.

"What is 6 x 6?"

36

"How do you know?"

I know all the square numbers.

"What is 6 x 11?"

66

"How do you know?"

I know the 11s!

"What is 6 x 12?"

I don’t know.

(pause)

Well I can just add 66 +6 since 6 x 11 is 66. So it is 72.

The conversation continued with a few more but it was interesting to observe that she had a different answer every time for "How do you know?" Memorization was an exception, not the rule. Even when she said things like "I know the 7s" it was not, by her understanding, a matter of memorizing the answer to a given questions such s 7 x 8, but rather that she had learned to count by 7s – it was part of a skit that she and her friends did some time ago. With 9s she used to use her fingers, but no longer needs to. With 11s it was something else – perhaps visualizing the ones and tens places. Not sure exactly but I realized that she uses multiple processes to multiply.

Zero is Beautiful: Teaching Mathematics as if People Mattered

Can you imagine the time before the discovery of zero? My husband and I got a glimpse of this when we witnessed the discovery of zero, not on the world-historical scale, but by our two-year-old daughter.

It was not an easy road. Counting had come uneventfully, but when numbers became numerals and the number 10 appeared on the page not with its own symbol, but with a 1 and 0, suddenly everything had changed. Till that moment, in her world it was still possible to have a system of enumeration like the one used by Ireneo Funes in Borges’ story, “Funes the Memorius.” Funes gives every number its own unique name. He has “an infinite vocabulary for the natural series of numbers” and no use for the concept of place value.

When our daughter saw that the numeral 10 comprised a 1 and a 0 she flung herself upon a chair and cried. We were taken aback, unprepared for the blow this dealt to her understanding of number and how she would struggle to make sense of it.

This was the struggle of an artist. The world had changed in a fundamental way. Something was lost that would never return. Why would there be a zero in the number ten? Till now the numerical representations were incidental to the concept of number, of quantity, of this thing that could go on forever …. and had now abruptly, jarringly, come back to zero.

Some time later, she confronted a blankness of another kind. In tears, she ran towards me holding a white crayon. It didn’t show up on the paper, she cried. “Therefore I am throwing away the white crayon,” she declared painfully. Her eyes brimming over pleaded for a way out of this harsh sentence. I drew something with the white crayon and painted with water color on top of it The water color surrounded the crayon image to reveal it. Saved! In its own way, the white crayon was a place holder.

We often hear people describe the joy and exultation of mathematics, but rarely the pain and suffering, arising not from inability, but rather from the wholehearted engagement with the ideas in all their beauty and tragedy. Immense was my gratitude when I came across a mathematician who wrote:

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion— not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.

- Paul Lockhart, A Mathematician’s Lament

A few days later, our daughter explained to us that “in the number 10, the zero stands for 9 numbers. In the number 100, the two zeros stand for 99 numbers.”

So if you had to subtract, say 6 from 10, you could subtract it from 9 (instead of from 0) and then add the 1 to get the correct answer. Of course no one would ever do this because when you start doing single-digit subtraction you have your 10 fingers and no zeros are involved. But try it in 2 digits:

If you have to subtract 42 from 100, you could just subtract it from 99 (instead of from 00) and then add the 1. We didn’t do that either because by the time she started doing subtraction on paper, her resistance to zero was long forgotten and she learned to “borrow.” Funny word, but arithmetic can be funny that way. More importantly, it doesn’t matter that we didn’t use her method to subtract. What matters is that she thought about it and explained the solution to her problem.

* * *

How often do we get a chance to appreciate the creative, expressive side of mathematics? Too often, people see it as a mechanical process and if at all they believe in the beauty and thrill of mathematics they perhaps feel it comes only to those who master its mechanics to a highly advanced level. Passionately opposing this approach to teaching mathematics, Paul Lockhart, who teaches in St. Ann’s School in New York, wrote an essay called “A Mathematician’s Lament.” First circulated privately, it was eventually published by the Mathematical Association of America, followed by a sequel, and expanded into a small book.

Lockhart says: “I want [students] to understand that there is a playground in their minds and that that is where mathematics happens.” He insists that mathematics is an art:

… if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category.
Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.

Lockhart wants children to have the opportunity to observe mathematicians at work, practicing mathematics, the way they see musicians sing or artists paint. He also wishes that it would be taught along with its social and historical context, so that we could explore such questions as: why did these mathematicians discover these things at these times in these places? Because the people, not only their formulae, matter.

In spite of mounting pressures to the contrary, teachers like Lockhart are doing what they can to bring humanity and adventure into the classroom. Lockhart urges teachers to play games such as chess, go, hex, to do puzzles, and be willing to get their hands messy and express their ideas through math:

Mathematics is an art, and art should be taught by working artists, or if not, at least by people who appreciate the art form and can recognize it when they see it.

Observing children learn gives us a second chance to appreciate mathematics as an art form. Even one such moment of struggle with the meaning of zero can inspire confidence in our capacity to probe the depths of ideas … if we are allowed that moment.

polyhedron

polyhedron

As artists have urged us to stop telling children what color to use or where to draw, we must also allow for creative expression in the discovery of numbers. We ought to refrain from intruding into the pre-numerate state with our preconceived notions and allow every child to investigate from scratch as if the world had not yet settled on a numbering system, adding system, dimensional system and so on. Would we want to skip the stage when little ones make up their own words and move expeditiously to standardized language? If we delight in the words and usages invented by our little ones, it is because we are so confident in our own language that we are free to tinker with it, to produce as well as consume.

A friend’s toddler started counting, “2, 2, 2, 2 …” At least, it sounded like counting. We may not always get it. But if we believe there is something there to get, we won’t rush to “correct” it. And if we believe in our children’s capacity to puzzle things out we won’t be tempted to give away the ending. Recently, our daughter struggled with the concept of negative exponents. A few days later she extended Cookie Monster’s song “One cookie and one cookie makes two cookies” up to 256 and used it to explain powers of 2. It goes for negative powers as well, “1 cookie and 2 people makes ½ cookie …” (Per person is understood.) When we share such stories we find that every parent has one – or many. Indeed, this kind of thing becomes commonplace when you recognize that math is everywhere.

Shapes and patterns in nature, ideas in our mind, games we play, doodling we do, rhythms we tap all lead us to mathematical discovery. As Lockhart says,

If everyone were exposed to mathematics in its natural state, with all the challenging fun and surprises that that entails, I think we would see a dramatic change both in the attitude of students toward mathematics, and in our conception of what it means to be “good at math.”

Practicing mathematics as an art form is nice work if you can get it. Vi Hart, who calls herself a mathemusician, shares her artwork through Khan Academy and her Youtube channels. Kjartan Poskitt’s series Murderous Maths contains stories full of historical and imaginary characters involved in various mishaps and misadventures, using plenty of math, which the author explains along the way. Popular internet sites like Numberphile air fascinating math puzzles and problems, with guest mathematicians from universities and research institutes around the world. What these artists have in common is that it is hard to watch or read their work without wanting to try it out yourself.

What if you never meet such artist-mathematicians? If I were to paraphrase Picasso, I might say that every child is an artist-mathematician. The problem is how to remain an artist-mathematician once we grow up.


Works Cited:

Jorge Luis Borges, “Funes, The Memorius,” in Ficciones, translated by Emecé Editores. New York: Grove Press, 1962, pp. 107 ff. Accessed online at http://www4.ncsu.edu/~jjsakon/FunestheMemorious.pdf

Vi Hart, on Khan Academy, http://www.khanacademy.org/math/recreational-math/vi-hart

Paul Lockhart, A Mathematician’s Lament, 2002. Published by Mathematical Association of America in 2008. Accessed online at https://www.maa.org/external_archive/devlin/devlin_03_08.html | Selected Excerpts: One Real Teacher

Numberphile, http://www.numberphile.com

Kjartan Poskitt, Murderous Maths published by Scholastic, Inc. Website at http://murderousmaths.co.uk/

One real teacher

Excerpts from the essays of Paul Lockhart
Paul Lockhart teaches mathematics at Saint Ann’s School in Brooklyn, New York.


MC Escher, 1948

MC Escher, 1948

From letter to Keith Devlin, Mathematical Association of America

On teaching mathematics to young children:
“I want them to understand that there is a playground in their minds and that that is where mathematics happens.”


From Lockhart’s Lament, Mathematical Association of America

Mathematics is an Art

… if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category.

Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. Read the rest of this entry »

It’s official! Bathroom schooling comes out of the closet.

You thought I was kidding when I said that we do bathroom schooling.  (Here and here.)  I wasn’t. Well I was but then what would my non-kidding answer be?  Kidding was better than splitting hairs over whether I was homeschooling or unschooling. Read the rest of this entry »

Resources for Continuum Learning

How do we set the foundation for lifelong learning?  In the early months and years of life, these five resources will help you practice continuum learning with your little ones.  Follow-Up to Attachment Parenting and Continuum Learning.  Scroll down for summary table of  Resources and Skills Learned.

Woman Breastfeeding Child

Painting: Abhishek Kumar.

1. Breastfeeding
Breastfeeding helps children learn a vital skill that they need all their lives:  how to eat.

Children’s first introduction to the flavors and feelings of food comes through breastfeeding.  As they gradually increase the variety and quantity of the food they eat, nursing serves as a safety net, allowing them freedom to try foods without any obligation to eat a given quantity by a given time.  Breastfeeding babies have time to acquire taste for a healthy variety of foods, while assured nutrition through mother’s diet.  Nursing also provides antibodies that help little ones as they explore the wider world and come into contact with more germs.  A partially weaned, breastfeeding child will often turn into an exclusively-breastfeeding child (ebf) when ill, and may require little or no other medicine to fight the illness. Read the rest of this entry »

Table of Resources for Continuum Learning

Read the full the post here:

Resources for Continuum Learning

Resource

Requirements

What Baby Learns

How Family Benefits

Breastfeeding

Well nourished mother, togetherness of mother and baby.  Can be met in part by expressed breastmilk during hours mother and baby are separate.

The world is a safe place.

How different foods taste

How food makes me feel

How I feel when hungry or full.

When I fall down, fall ill, or am sad, afraid or unsure, I have a home base where I can restore myself.

Mother believes in her body.

Whole family eats happily without stress.

Sling

Sling.  Caring person.

This is how we go about the day, talk, listen, cook, wash, garden, catch the train, etc.

I can observe and explore from a safe place.

I can communicate my needs without shouting.

I can get down and back up whenever I want.

Each member of my family has a different voice, gait, way of doing things.

Parent / carer is able to carry child hands-free.

Family includes child in their activities.

Variety of settings stimulate parent-child interaction.

Nursing Kurta

Nursing Kurta

My mother takes me to interesting places.

I am safe in the world.

Breastfeeding is normal.

I can meet my needs while my mother does various things.

Mother can go anywhere assured that she can breastfeed anytime.  [Can do with any dress, but some find it easier with kurta designed for discreet nursing.]

Elimination Communication

Potty, bowl or toilet area.

Waterproof sheets to protect bed, furniture, etc in early stages.

Simple cloth for baby’s bottom.

My bottom is normally clean and dry.

When I am wet or dirty, my adult will help me promptly.

I can relieve myself in a clean place.

My body works just right!

Feels good to respond to hygiene needs promptly.

See satisfaction when baby relieves himself or herself.

Supports healthy body image.

Enhances communication.

Family Bed

Mat on the floor or firm bed with space for family

I learn to breathe in my sleep by sleeping near breathing adults.

I am safe while sleeping.

I need not shout to be heard.

I can breastfeed while sleeping.

I can express my hopes and dreams, concerns and fears.

Comfort of child nearby.

Can nurse at night without getting out of bed or fully waking.

Chance to hear thoughts that may not come up in the rush of the day.

2013 in review

The WordPress.com stats helper monkeys prepared a 2013 annual report for this blog.

Here’s an excerpt:

A San Francisco cable car holds 60 people. This blog was viewed about 1,600 times in 2013. If it were a cable car, it would take about 27 trips to carry that many people.

Click here to see the complete report.

On Being Guided

 O n   B e i n g   G u i d e d

 

 

Let us consider the experience of being guided, and ask ourselves: what does this experience consist in when for instance our course is guided?

 

Imagine the following cases:

 

You are in a playing field with your eyes bandaged, and someone leads you by the hand, sometimes left, sometimes right; you have constantly to be ready for the tug of his hand, and must also take care not to stumble when he gives an unexpected tug.

 

Or again: someone leads you by the hand where you are unwilling to go, by force.

 

Or: you are guided by a partner in a dance; you make yourself as receptive as possible, in order to guess his intention and obey the slightest pressure.

 

Or: someone takes you for a walk; you are having a conversation; you go wherever he does.

 

Or: you walk along a field-track, simply following it.

 

Ludwig Wittgenstein: On Being Guided  

from Philosophical Investigations, § 72

The Theoretical Minimum

Book Review written for Home Education Magazine
Leonard Susskind and George Hrabovsky
The Theoretical Minimum
New York: Basic Books, 2013
238 pp.

Thanks to various findings such as the long-awaited Higgs Boson, and the award-winning television sitcom “Big Bang Theory,” key concepts in physics have acquired a coolness factor that launches them into the popular imagination with regular frequency. So it is great time for physicists to lecture and write for a public that is eager to understand more about forces, particles, energy, matter, light, dark, time and space. Read the rest of this entry »

Everyday History – Home Education Magazine

Guided by Home Education Magazine editor Barb Lundgren, I expanded my post on “Studying History” into an article. It appeared in Home Education Magazine as “Everyday History” in the March-April 2013 issue. Please subscribe to the magazine or ask your library to order it.  Here it is along with the photos that appeared in the magazine.


“Everyday History,” Home Education Magazine, March-April 2013, pp 22-25.

“Studying history is …. pretty much useless, isn’t it?” my daughter asked, as if it was fairly obvious. “I mean why read about Columbus discovering America, when it isn’t even true?”

EZCooker_Auto2Alarmed. All senses alert.

Mission: Rescue the field of history. Why?

Think. Think.

Meanwhile, don’t answer. A weak response merely invites rebuttal. Then what? Stay calm. Say nothing. No one need get hurt.

Ah, now I remember what to do. Listen.

Do something. Explain why we need to study history. Justice – that’s right, we can start with justice. Rosa Parks. Freedom struggle. Forest Rights. Let’s just take care not to get too complicated.

The next morning as my daughter ate breakfast, I combed her hair. I had my question ready and eased it ever so casually into the flow of braiding and talking.

“Have you ever come across something that is not fair?”

“Yes,” she said, wailing. She tends to take on the mood of whatever she is talking about. “Like right now, I am finished with my oatmeal but you are only finished with one braid and I don’t have anything to eat during the other braid.”

Okay.

As I took that in, she asked, “why did you ask me that?”

“Oh,” I chirped cheerily, “I just wanted to hear what you thought.”

“That is nice” she said, genuinely appreciating it. Though many of us have come to hear “that’s nice” as an idle dismissal, when she uses the phrase, she means it.

On that happy note, we carried on an easy banter as I finished up the other braid. No further inquiry.

Throughout the day I kept my troubles regarding the beleaguered field of history to myself. I think a couple of times she may have continued thinking aloud about how she did not like history. It was almost as if she liked the sound of it: “I don’t like history.” I thought, but did not say, things like, “you like history, you are only saying that because you have gotten some idea that history is boring …. probably picked this up from some character in one of your booksi.”

Later that night she asked me, “what does Machiavellian mean?” She was reading The Penderwicks on Gardam Street, in which Anna had used the word and said to another character, “When you are older, Batty, I will explain…”

I couldn’t resist. I said, “well I can tell you but it might involve a little bit of … history.” We both giggled.

In small bits, I explained, proceeding further only as the questions directed.

Machiavelli, I said, lived 500 years ago. He wrote a book about power, how to hold on to power.

So does Machiavellian mean powerful?

Well, you can be powerful in different ways – by doing good work or by force. He became famous for writing about how to hold on to power even if you had to lie or cheat or trick people. Or even use force to hold on to your power.

As opposed to what? She did not ask this question, but I think she had an idea. She had seen the inside of a voting booth. She was aware that candidates for public office tried to convince people through public discussion and debate that they would be effective leaders. She was also aware of other approaches to leadership, thanks to some books and conversations that we had had about Rosa Parks and Mohandas Gandhi. We did not talk about these figures at the time. She went back to her novel.

I bring up what we did not say because it was part of the background in which she understood the current exchange, and also part of future conversations that would no doubt come up, probably at the most unexpected moments. Why would I want to pre-empt those moments by drawing these comparisons and contrasts right away? Besides, she asked the question in the context of her novel, and was continuing reading it.

It was not the first time history had sprinted into our conversations, sparked very much by preoccupations of the present.

K & Eshani

Some years ago we had been cleaning our pichkari in preparation for the Holi Festival.
Branded in the plastic cap of the pichkari were the words “Made in Mumbai.”The pichkari, or water-shooter, is used for spraying friend and stranger alike on the day of Holi, a festival of spring and color. One who dares to step out in fine clothes on the day of Holi, will only attract more enthusiastic sprays of colored powder and water. As with many festivals in South Asia, multiple religious traditions have conglomerated over the centuries, and the day is also celebrated with dance, stories, bonfire and other rituals throughout the night.

“Why does this say ‘Mumbai?’” my daughter asked.

Caught! Had I not been using the recently revived “original name” of our city? I explained that Bombay was what the British called the city, based on their own attempt to say and spell the name in English. However it had in earlier times been called Mumba or Mumbai; a few years ago the state government had officially revised the name to Mumbai. Due to indifference or defiance, not everyone had yet converted.Neighbourhood gets wet

Mumbai … Bombay … English … British … India … empire … our conversation went all over the world and back.

Why did the British come to India?

They wanted to buy things, I replied.

What did they want to buy?

Spices. Cloth.

Why?

And so the conversation went its own way. At the time I did not connect their commercial interests with their eventual colonization. Over the months and years ahead, when learning about Gandhi, handspun cloth, home-processed salt, and their role in India’s independence movement, some of the economic, political and cultural dimensions of India’s historic struggle got gradually fleshed out. Along the way we also met handloom weavers and spinners, and even had a chance to try spinning thread on the charkha, or spinning wheel whose image appeared on the early design of India’s national flag.

These were just a few of the questions that came up during our conversation, viewed over a span of three years. Since the British also ruled over that land that Columbus thought was India, and massacred the people whom they called Indians, the power of naming also connected at various points to other questions of society and survival.

Language, culture, power, land, water, salt, spice, east, west … we are still talking about it.

Why do people have to get spices from other countries? We haven’t yet connected this history of British colonization to contemporary concerns with local food, but I can see the seeds of this conversation. It will come up sometime, spurred by some other topic in a way I probably would not anticipate.

Could one study this history over the course of a few weeks, as might happen if one started out with that objective? One could come up with a program that included field trips to visit weavers, an exercise in spinning thread, making salt, or counting food miles. One could investigate and discuss and report on the connections between these issues.

It would probably be more interesting than the history classes I had in school. But I can say from our experience that without the slightest contrivance we have explored, thought through and been fascinated by some serious questions of history. The only planning on my part has been to have the time to hear each question it arose, and the receptivity to allow the broader context of the question emerge in its own time.

Last summer in Maryland, we saw a car with a Delaware license plate. Across the top it said “THE FIRST STATE.”

“Why does that say Delaware – the first state?” my daughter asked me.

By now it was a running joke: “Just to let you know, this might involve a little bit of history.” As it turned out, it involved politics and ontology as well, as she called upon me to explain what makes a state a state and what makes one first.

Were they already called states? she asked. Who named it Delaware? Was it like New York – named by the British, before they decided not to be British?

When? Already? Before …?

Questions about names and dates now needed answers. Rolled into the questions of when a place becomes a place, and whose place it is to decide, they brought out the links between the small and large questions of history, connecting the facts on the surface to the layers of human struggle and aspiration murmuring below.

Once we looked up the dates, how would these help us to evaluate the justice of this name for this place, hammered (by prisoners) into thousands of metal (or, as we learned in the case of Delaware, possibly porcelain) plates to be displayed on automobiles wherever they went? (Forgive my parenthetical digressions.)

We didn’t yet know. Meanwhile, our questions begot more questions. Were they first called states and then they got united? Or later when they decided to call it the United States, did they realize that the first one was Delaware? What did it do first to become the first state? I found myself asking questions too. Is Delaware also a Native American name? Did the Native Americans want to name the state?

How would we know? Whose word could we count on to know the wishes of the people of Delaware nation, before they became part of Delaware state? And what of the Susquehanna and other peoples also living in the area? Who was there first? Did being first confer any rights? Is there really any such thing as first?

This question keeps coming up.

One day we saw Bhakta Prahlad (Telugu, 1967). While observing the crowning of Prahlad, son of Hiranyakashyapu, the king before him, our daughter asked, “how did the first king become king?”

Oh, yeah!

Yet again, we were face to face with one of the central questions of history. Not only how the first king became king, but indeed how any king remains king. (Maybe a question for Machiavelli!)

Such questions concerning people, places, rulers, states, names and things arise so often and inspire such intriguing searches that I cannot help but feel that history is everywhere.

* * *

Now you may ask, can you really pursue history through the questions that come up while walking around and doing other things? What about the people to whom you ask the questions … would the meandering route get you anywhere if those people hadn’t ever learned about the European renaissance, colonialism, post-colonialism, and how the American constitution was ratified? At some point don’t you also have to do the heavy reading for yourself?

And till that fine day comes when your curiosity drives you to read those works, what can you do to prepare? Sure, maybe you spend years randomly asking questions and getting quick fill-ins from Wikipedia and then suddenly start reading Romila Thapar or Amartya Sen or Howard Zinn or Victoria Brown. I can well imagine doing that. I could also imagine missing the boat entirely. Do we leave it up to chance?

Such questions come up from time to time, especially for those whose children are learning outside of school, and possibly without any standardized curriculum. Is there a plan to the learning, or is it driven by whim and fancy? Granted, whim and fancy can take you a long way, usually via the scenic route. But what about structured learning?

I think that structure materializes in various ways, and if we observe we might find, for example, that a child’s mind leaps into active mode while taking a bath or getting ready for bed. Some kids think better when in motion, or when they are interrupting you (as opposed to when you ask them a question and wait for them to answer). Some kids cry when they don’t understand something, but that crying is part of their grappling with the problem. Recognizing and respecting the structure that goes into each child’s learning process will help to keep the channels clear and unobstructed.

Apart from the patterns that emerge, are there practices that we can encourage, that will help to build our capacity to learn various things?

This brings me to another answer on structure. Consider a subject like history. History is not something that others create and we consume. History must be questioned at every turn – who said? how do you know? what if…? But how do we learn how to question history?

College History textbook authors Victoria Bissell Brown and Timothy J. Shannon note that professors’ efforts to teach students to critically examine sources of historical information are often thwarted by the pressure of time and the students’ tendency to “focus on recalling the content of the varied materials they read rather than analyzing them as historical evidenceii.”

Students who are not expected to recall content will be more likely to focus on the questions that come naturally to historians, the questions Brown and Shannon’s textbook aims to teach students to ask, such as who said this, when, how does s/he know, how reliable is s/he, how close is s/he to the event in question.

In fact children do ask such questions about every day happenings. We can draw upon this inquisitive nature and apply it to the study of the past as well. At the very least we can avoid suppressing these questions when they arise. Questioning authority, vital for investigating the past, starts with questions like “why do we have to do this?” that can spark intriguing discussions, not only on the dynamics of authority, but also on society and nature. “Why do we have to keep the door closed?” was one of the earliest, albeit nonverbal, questions I had to face from my one-year old who expected free access to the outdoors. I thought about earlier times and rural places where people spent more time outside, and how our concepts of children’s safety have changed. Thinking about the question historically helped me to recognize that her expectation was valid and motivated me to meet it more often. My information on how our ancestors lived, that helped me address my daughter’s problem in the present, came from my study of history, through reading and visiting museums.

* * *

Khiyali and AravindaWhat I am realizing from observing the excitement and wonder my daughter exhibits when seeking answers from the past to make sense of the present, in contrast to her bland comment on the uselessness of history, is that when she is piqued by the questions that historians investigate, she is learning to work like a historian, to think like a historian. And that is how one should learn history. Before my child reads the history that is written by others, I would like her to try to come up with some of her own questions and to find something out about history.

We have, for example, interviewed people in the neighbourhood. So far we have found out more about the mechanics of setting up and conducting an interview than about any particular historical or social question, but this is important too. When we read interviews of others, it gives us some insight into what it takes to set the stage, and how various factors affect the outcome.

We have also looked around the house and neighbourhood and made a kind of game of asking, “what happened here in the last few hours or days and what is our evidence for saying so?” “How reliable is this evidence?” “What might possibly make us doubt this evidence?” “What alternate explanations are there?”

Once when we did this we came across a round pile of leaves, a few inches high. My daughter said, “this pile of leaves has been here for weeks. I have seen it here many times before.” Seeing the different kinds of leaves, she added, “the leaves have come from near and far trees, because see this kind of leaf did not come from any of these trees.” So we talked about how they might have arrived at this point – by the wind, or did someone sweep them? How long would such a neatly swept pile stay that way? How often do leaves fall? Now did we still think that the same pile of leaves had been there for weeks?

“Why would anyone want to know the history of a pile of leaves?”

“As it happens,” I warmed to my story, “several years ago, a question was answered by asking such questions about a pile of junk in a particular village in the Narmada Valley.” It turned out the location of that debris pile was evidence of the level to which the Narmada river had risen during the floods of 1970. With that piece of data, the people living in that village challenged the government survey records of their village. Accurate land records were crucial in the people’s struggle over land rights and rehabilitation.

This practice of weighing evidence and alternative explanations will equip us to ask similar questions while reading history, so that we can evaluate sources and compare perspectives. At a more elementary level, a game like Chinese whispers, illustrating how a message gets distorted as it passes through various transmitters (people) can also sharpen one’s critical faculties when reading others’ accounts of what happened.


Notes

i Or was it in one of my books? I had recently been reading James Loewen, Lies My Teacher Told Me.

Loewen writes,

“[P]rofessional historical organizations for at least a century have repeatedly exhorted teachers not to teach history as fact memorization. ‘Stir up the minds of the pupils,’ cried the American Historical Association in 1893; ‘avoid stressing dates, names, and specific events, ‘historians urged in 1934. . . . Nevertheless, teachers continue to present factoids for students to memorize.”

I don’t think my daughter read the book, but I am just saying, I need not turn to a juvenile novel to track down the sentiment that history class is boring. Historians themselves have been complaining about it for years.

ii Victoria Bissell Brown and Timothy J. Shannon, Going to the Source: The Bedford Reader in American History. Boston: St. Martin’s Press, 2004.

Everyday History HEM.pdf

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