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? Read the rest of this entry »

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. Read the rest of this entry »

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?” Read the rest of this entry »

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