Thursday, December 30, 2010

Geography: Collecting Quarters

Tim and N. have been collecting the special "states and territories" quarters for more than a year and they have them all except Puerto Rico and the Northern Mariana Islands.  My sister recently bought N. a folder in which to display them and it turned the quarters into an amazing geography learning tool that N. has really loved.  He likes quizzing us on the dates when the various states entered the Union, and testing himself on his recognition of the states by shape and location.  My sister also got us the folder for the "National Parks" quarters so we've begun collecting them.  5 new designs will be minted each year until 2020, when N. will be 16 (which is completely unfathomable).  We'll see if he's still interested in collecting quarters then!  In the meantime, I recommend quarter collecting as a fun way to learn the U.S. map.

Tuesday, December 28, 2010

Learning and Games: Christmas Edition

Tim picked out two games to give N. for Christmas and they were a huge hit: Parcheesi and Squadron Scramble.  None of us knew how to play either game, so we've been having lots of fun learning the games together.  Parcheesi is an ancient game of strategy, chance, and counting.  Squadron Scramble is a card game invented in 1942; it is basically rummy, but the cards are bomber and fighter sets from both the Allied and Axis fleets.  N. loves World War II planes, so he loves this game (and, like Parcheesi, but unlike, say, Candyland or Chutes and Ladders, it is equally stimulating for adult and child players).  The game prompted N. to bring out his long-neglected sets of little American WWII planes and to draw the planes pictured on the cards.  And he's been doing lots of independent reading of the plane names and info on each card.  As I've written before regarding Monopoly, it is easy as an adult to forget just how intellectually productive board and card games can be for kids in the early stages of literacy and numeracy.  Equally important is the fun the three of us have playing together.  Hooray for new-old games!

Wednesday, December 22, 2010

James Herriot at Low Tide

Our homeschool had been in high-tide mode for much of the fall semester, with lots of written number work, handwriting practice, and more formal learning (along, of course, with lots of play).  Then right at Thanksgiving N. got quite sick, and all he wanted to do was lie on the couch and listen to one of us read aloud to him.  Like, all day.  In the first few days of his illness, he only wanted comfort-reading: favorite chapters from favorite books re-read -- no new books.  I spent most of the Thanksgiving weekend on the couch with him, reading The Railway Children, the Betsy-Tacy books, and Homer Price.  Then as he started feeling just a little bit better, he and Tim resumed their reading of James Herriot's books, which they've been working their way through all fall.  They've read All Creatures Great And Small, All Things Bright and Beautiful, All Things Wise and Wonderful, and they are now on The Lord God Made Them All.  N. just loves these stories, and he loves the serial nature of them; like the fairy tales Tim read to him nearly every weekday last year, these books offer seemingly endless episodes. 

As N. continues to feel under the weather, and with the disruption of the holidays, most of Tim and N.'s "school" time lately has been primarily long stretches of James Herriot reading and piano practice.  I've been so grateful that we can change pace to suit N.'s needs as he's been sick.  N.'s immersion in James Herriot's Yorkshire in the 1940s has been just as valuable as his more formal learning.  Of course there's vocabulary; N. used "subcutaneous" in a sentence the other day, and we all learned that the term "husky voice" comes from the raspy cough that animals get when afflicted with "husk."  There's history and geography; for example Herriot enlists during WWII and in the 1960s he travels to Lithuania where he encounters Soviet life.  Most important, there are countless nuggets of life wisdom as Herriot interacts with the complicated people whose animals he treats.  Herriot's gift as a story teller is to render that complex humanity in such rich color that it is fascinating both to a six-year-old and to his dad.  We've all really enjoyed our James Herriot "curriculum" and are grateful for his books, as well as for the opportunity homeschooling gives us to immerse ourselves deeply in them.

Thursday, December 9, 2010

First Principles: Categorizing & Classifying

Brick masonry patterns
N. likes categories.  Most of his major interests thus far in his life (construction vehicles, trains, cathedrals, butterflies, etc.) lend themselves to sorting and differentiating by categories, and one of the ways he masters a subject he is interested in is by learning all the iterations and types associated with it.  For example, recently, he and Tim have been studying styles of brick masonry (as a subset of N.'s passion for buildings) and everywhere we go they identify the brickwork of buildings as "running bond," "common bond," "Flemish bond," etc. and the positions of the bricks as "stretchers, headers, soldiers, or sailors."  N. loves learning specialized terminology! 

Tim drew on this mental tendency in order to introduce scientific classification.  In November, after reading about the classifications and the organisms in each category, N. copied out lists of the 5 Kingdoms of Organisms and the Classes of Animals and invented little accompanying illustrations, as you can see here.

We did not go into the full (fascinating!) history of scientific classification and the various schemes that have been introduced over the centuries and only lightly touched on the disagreement among scientists about the current "kingdoms" (are there 5 or 6? what should they be called?) and the classes of animals.  The idea of classifying organisms was the main concept to learn at this point, to think about why and how we can group living things for comparative purposes.

While building on N.'s interests in their learning together, Tim has tried to emphasize what John Barth (in a very different context) calls "first principles:"

"But my talent for doing correctly the small things that constitute the glorious whole was defective -- I never mastered first principles -- and so the finished product, while perhaps impressive to the untutored, was always mediocre to the knowledged.  To how many of my youthful achievements does this not apply!  I dazzled old ladies at piano recitals, but never really mastered the scales; won the tennis championships of my high school -- a school indifferent to tennis -- but never really mastered the strokes; graduated first in my class, but never really learned to think."  [The Floating Opera by John Barth]

We try throughout our life as a family to emphasize that process trumps product, that it is infinitely more important to learn to think than to graduate first in your class.  At the same time, the product of one's thinking is of course going to be much better if you've mastered the process.  

Tuesday, November 23, 2010

On Anonymity

I blog pseudonymously (no really, Fanny Harville is not my actual name!) primarily so that my professional work remains prominent when you Google my real name.  I have been feeling guilty that by using my son's real name I may not be affording him this same luxury (that is, the luxury to control his online presence at some future point in his life), even though I have never used his last name on this blog.  So over the next few weeks I am going back over posts to remove his name and replace it with an initial N.  This won't affect comments where his name appears, but I hope it will at least minimize its appearance.  I'd be so grateful if those of you readers who know his name would use the initial to refer to him as well in your comments going forward.

Even though I justified blogging about my child in my Blog Mission Statement a year ago and I try to be as mindful of N.'s privacy as I can in my posts, I still occasionally feel somewhat vexed about the act of blogging.  For me the blog is a productive interactive space for thinking through homeschooling issues.  But how would I feel as a child to be the subject of such a blog?  (N. doesn't know about this blog, or about blogs in general).  I've tried to remember what it felt like when I was a kid and I overheard adults talking about me, but that is not really comparable.  I hope by reducing the presence of N.'s name on the blog, he will feel less like a public object when he does read this.

Piano Composition

One of the many things I love about N.'s piano teacher is that she has him working on his own compositions right from the start.  She understands that he learns so much from making his own music and he doesn't need to wait till some later point of mastery to begin.  Here's a song he wrote this week.  First he came up with the tune and wrote it out.  Then he added lyrics and title!  I love it!

Friday, November 5, 2010

Piano Lessons

N. began piano lessons in September.  As I mentioned here, this was one of our goals for this academic year, and by "our" I mean, Tim's and mine.  N. was resistant, as he is about all suggestions for formal instruction by people other than Tim or me, whether it's swim lessons, language class, art class, summer camp, or school itself, all of which we have in the past suggested and he has rejected.  We've always honored that resistance, even though sometimes I think it is based at least in part simply on discomfort with the unknown or unfamiliar.  Some people think you should push kids to do things that they say they don't want to do because once they get past that initial discomfort, they discover they really enjoy the activity.  I think there is plenty of time to learn this lesson later in life.  I'm not going to force my son to go to summer camp if he says he doesn't want to, even if I suspect he might actually enjoy it; it's not an important enough activity to warrant disregarding his wishes.

But music lessons did seem important enough to us that we decided to override N.'s resistance.  As an amateur musician myself, I know that learning to read music at a young age is very valuable.  N. really loves music and he plays the piano a lot, making up songs, working at them so he could play them again and again consistently.  He clearly had a strong interest in the piano and as much as I love that he made his own music, I know that piano instruction, if done well, would give him the tools for a much deeper satisfaction in his playing, a greater range of expression and understanding of what he was creating.  When we mentioned lessons, he said, "But I already know how to play the piano!"  This goes to the heart of my very mixed feelings about autodidacticism.  As much as I value passion- and interest-led learning, I believe that a person simply can't teach himself everything.  I explained to N. my belief that he would ultimately be able to do a lot more on the piano if he took lessons and learned more about music.

I found a piano teacher through friends' recommendations and when I explained my concern that lessons  build on and not counteract N.'s love of music, she seemed to understand, and promised a focus on fun.  I silently reserved the option to cancel if N. wasn't enjoying the experience after a couple lessons.  After all, we had tried one piano lesson before, when N. was 4, with a teacher who turned out to be a totalitarian; before that lesson was over we knew the teacher was not the right one for us!

The morning of his first lesson this fall, N. again said he didn't want to take lessons, but when I came home from work in the evening, he reported that he loved the lesson!  He liked the teacher, Lori, and he told me all about what they did in the lesson.  She eased into practicing, asking him only to practice 10 minutes a day that first week.  I was relieved and pleased and excited for N.

Then later that first week, one night at bedtime, N. started crying and said that Lori was making him forget all his own songs.  I felt so sad!  I think what he meant was that what he was learning was making him think about the piano in a different way, and he could feel the conflict between that and his earlier mode of interacting with the piano.  Or, that now when he plays the piano, he has to practice for his lesson rather than playing his own stuff.  This broke my heart because it was exactly what I had worried about, that lessons would deprive him of his direct Wordsworthian encounter with creativity, even though I ultimately believe this Romantic vision of creativity is limited and limiting.  So, I suggested to N. that he set aside some time every day to play his songs so he can be sure to keep them fresh in his memory.  And I assured him that Lori wasn't trying to make him forget his songs, that she wanted him to keep playing them.  This seemed to comfort him, and he liked the solution of setting distinct times for practicing the lesson and for playing any way he wants.

Now about six weeks have passed and N. has never again said anything negative about the lessons.  He continues to enjoy them and has been learning at an amazing pace.  I've been really impressed with the books the teacher is using; their method seems really to click with N.  He learned songs right away, rather than only focusing on fundamentals, so there is an immediate sense of accomplishment and pleasure.  In October, he had a whole lesson book with funny little Halloween songs to learn.  When we've had guests over, whether his friends or ours, he has voluntarily played some of his lesson songs for them (we do not ask him to do this, wanting to avoid pushing him to perform) and taken great pride in doing so.  And he still plays the special songs he made up.

There have been occasional moments when Tim and N. have wrangled over practicing, but for the most part they've successfully incorporated it into their daily routine.  As a homeschooler, N. can practice early in the day when he is freshest; Tim has noticed that his practicing goes much less well the few times they've had to do it late in the afternoon.  Since so much of N.'s learning is very unstructured, the structure of practicing provides an interesting contrast to the rest of his sprawling, cumulative, additive learning, and I think this contrast itself is a good experience for him.  Finally, beyond the musical knowledge he is gaining, N.'s familiarity with fractions, counting, and reading are all being reinforced through learning to read musical notation.

So far, then, all three of us feel good about N.'s piano lessons.  Since so much of our approach to homeschool is based on non-coercion, I felt somewhat conflicted about beginning the lessons in the face of his expressed resistance.  And he did express some sorrow as he transitioned from one mode of engaging with the piano to another; it was painful to have caused that sorrow.  Yet I believe the pleasure he is taking in his rapidly increasing musical fluency vindicates our action.

Wednesday, September 29, 2010

Drawing Update


As I have written before, N. loves to draw and spends lots of time every day drawing.  He especially loves to draw buildings, and over the past 6-8 months he's drawn many many buildings that exist in the  imaginary world about which he tells long elaborate stories.
Two houses for sale in N's imaginary world
N's own caption explains this imaginary building.
As you can see, Tim has been using N.'s drawings to encourage him to practice handwriting and numbers.  Recently they learned about dates during their random encyclopedia reading, so N. drew a date tree and wrote an amazing fact he learned about date trees.  There are...
1,700 dates on one cluster of fruit!

N. has also been doing some drawings of real places recently, either from a photo or from his knowledge of the place.  Here's a drawing based on a photograph of a gorgeous old building in Duluth, MN, The Lyceum, which was demolished in the 1960s.

Our living room (l.) and new kitchen addition
N.'s passion for drawing and for buildings plays a huge role in our commitment to unschooling.  I love that he can spend as much of his day as he wants on this.  Not only is it a fundamentally crucial activity for him -- there is some way in which he simply needs to draw -- but it gives us so many learning opportunities as we study principles of building, the history of architectural styles (which leads to many other areas of history), learning about different cities where his favorite buildings occur, etc.  His art is central to his experience of school, instead of an extra-curricular interest.

Tuesday, September 21, 2010

Unschooling Tests

When I was in first grade, I was required to take timed math tests that had a negative impact on my sense of my aptitude for math.  This experience has made me very resistant to the No-Child-Left-Behind testing culture of today's schools and was a crucial influence on my interest in homeschooling.  I wanted to homeschool our son to give him an education focused on real learning, not tests.  My ideal vision was that we would never have tests (beside the yearly standardized test required by the homeschool law in our state).  I thought that we don't need tests since we know what N. is learning because we spend so much time with him.  I am concerned that tests orient children toward external motivation for learning, learning in order to do well on a test, rather than encouraging intrinsic motivation.

Tim disagreed slightly with me on this issue in part because he had no negative associations with tests from his childhood.  He's been doing little math tests with N. and calling them tests.  (See picture at left for an example of one of their "tests").  At first, I was upset when I discovered this.  But then serendipitously some articles in the New York Times helped reframe tests for me so that I could think about them as learning tools rather than only in terms of my own negative previous experiences.  As one recent article points out, "cognitive scientists see testing itself — or practice tests and quizzes — as a powerful tool of learning, rather than merely assessment."  Taking tests or quizzes helps reinforce knowledge; according to this article, studying for one session and taking a test in a second session leads to better long-term retention than studying for two sessions.  

There's no question that the timed tests I took were not productive in reinforcing knowledge, but I think we can structure little low/no-stakes quizzes to be a productive part of N.'s learning.  These can take the form shown in the picture above, or of the Charlotte Mason-style recitation that takes place daily when Tim and N. tell me at supper about what they studied during the day.  Tim and I have agreed that written "tests" not be graded or marked with stars in order to keep the emphasis on intrinsic motivation and to keep tests oriented toward learning, not assessment.

It's easy in homeschooling to try to correct all the perceived wrongs that we parents experienced in our own childhood schooling.  Our discussion of tests highlighted for me the importance of maintaining our focus on N.'s educational needs and of refraining from projecting my own past on him.  Furthermore, I am happy to take advantage of experiments in psychology and cognitive science that illuminate how our brains learn and work.  Much of unschooling dogma seems to be based primarily on anecdotal accounts, and I think it is important to bring that dogma in conversation with rigorous science.  Sometimes that science may inspire adaptations of unschool dogma, while in other instances scientific findings will support our educational methods. 

Thus, while some kinds of tests can be effective learning tools, I still believe that the multiple-choice testing model in much of education is counterproductive to and a poor measure of learning.  In a recent Times op-ed, psychology instructor Susan Engel describes what assessments should try to gauge: "the qualities of well-educated children: the ability to understand what they read; an interest in using books to gain knowledge; the capacity to know when a problem calls for mathematics and quantification; the agility to move from concrete examples to abstract principles and back again; the ability to think about a situation in several different ways; and a dynamic working knowledge of the society in which they live."  This eloquently captures our primary homeschool goals.  Little quizzes can play a role in N.'s homeschool learning while we remain focused on these broader goals.

Friday, September 3, 2010

Butterfly Identification

We are seeing more butterflies on our out-of-control cosmos this year than ever before, and Tim and N. have spent much of this week watching and identifying them.  They've spotted Eastern Yellow Swallowtails, Gulf Fritillaries, Monarchs, Viceroys, and different kinds of Skippers.  N. has learned about the markings and shapes of the different kinds, and loves shouting out the name as soon as he identifies one.  They are using the excellent Butterflies Through Binoculars as their guide.  This activity appeals to N. because he loves categorizing things, and the immediacy of the butterflies in our yard makes identifying them far more compelling than simply reading about them would be.

Thursday, September 2, 2010

Learning and Games: Monopoly

Last week, before I left for work in the morning, N. caught sight of a box on a high shelf that has long tantalized him because it has a picture of a train on it, and he asked if he could look at it.  I told him it was a game called Monopoly but it was for older kids.  He still wanted it, so I took it down and of course he immediately wanted to know how to play.  I started teaching him the basic rules, and he was completely absorbed.  It was all I could do to get him to pause so we could eat breakfast; I promised Daddy would take my place in the game after we ate and I left for work.

I called home to check in with Tim and N. later in the day, and heard that they'd played Monopoly for 3 hours, until they finished the game we'd begun.  N. won!

It had been many years since I last played Monopoly, and looking at it through the eyes of my six-year-old, I was impressed by how much the game develops the main learning tasks N. is focused on right now: he had to work hard to read the property cards as well as the chance and community chest cards.  He had to do lots of math as he managed his money.  In the game he finally seemed to understand the concept of making change with bills, something that had been confusing to him in real-life situations.  He learned about auctioning and mortgaging and rent.  And playing with Tim, he learned about thinking strategically and logically because Tim is all about optimal play.  As N. told me, he made a particular choice in the game because "that's one of Daddy's principles."  A true card player, Tim plays games to win, partly because he likes winning, but mainly because he likes the intellectual challenge of figuring out the optimal move or play at any given moment and in the long term.  It drives him a bit nuts that I don't generally play games this way but am much more haphazard (and am no card player).  I suspect he and N. have many hours of games ahead of them!

Wednesday, September 1, 2010

Unschool in Kids' Books: What to Do About Alice


What To Do About Alice?: How Alice Roosevelt Broke the Rules, Charmed the World, and Drove Her Father Teddy Crazy! by Barbara Kerley tells the story of Roosevelt's unconventional oldest daughter.  She was a wild, physically exuberant girl.  Before her family moves into the White House, she shudders as she watches the prim girls of a New York boarding school walk down the street while she has dreams of climbing trees and owning a monkey.  When her antics in D.C. (including joining an all-boys club and requiring the boys to dress as girls in order to sneak into the White House to their club meetings) get to be too much for her father, he threatens to send her to that fancy girls' boarding school back in New York.  After weeks of crying every day at the thought of going to school, she presents an alternate  plan for her education to her father: she'll teach herself by using his extensive library.  And that's what she does.  Her antics continue into her adulthood, providing ample tabloid fodder, but she also becomes a very effective representative for her father, both at home and abroad.  She also becomes one of his most trusted advisors.  She eventually makes a savvy political marriage and remains a crucial institution (nicknamed "the other Washington Monument") in D.C. throughout her long life.  We loved this story for its representation of independent learning enhancing the life of an irrepressible child.

New York Times review here.

Friday, August 27, 2010

On Routines, or Back to (Un)school

Over the course of last academic year, N.'s kindergarten year, his and Tim's days evolved organically into a quite predictable routine that they enjoyed calling "doing school."  After N. and I ate breakfast together and looked at the newspaper, I left for work (around 8:45) and N. would usually go to the sunroom to draw or the living room to play while Tim ate his breakfast.  Then they'd both go to the sunroom to "do school," which meant Tim reading aloud, N. practicing numbers or writing, looking up a random encyclopedia entry and following ideas and connections that arise from that, etc.  This usually lasted for a couple hours; at noon they would take a long walk around the neighborhood, usually around 2 miles.  They take turns telling each other made-up stories on these walks.  Tim's are called "Original Huka-Buka Stories," about a princess of that name, and N.'s stories all take place in an elaborate make-believe country where he and Huka-Buka and other friends live and own a train yard.  After their walk, Tim and N. ate a late, long lunch while listening to CDs, talking, reading.  The rest of the day was devoted to playing independently or with our neighbors inside or out, sometimes more drawing or reading aloud, household tasks to do together, (gardening, laundry, cooking, or baking).  We continued this routine until the beginning of July, when I finished my teaching.  Then our homeschool went on summer vacation until this past Sunday.

I use the word "unschool" to describe our homeschool method because we don't use a boxed curriculum, don't make detailed learning plans in advance, we follow learning cues as they arise out of real life experience, we emphasize noncoercive learning and learning through play.  There might be other words that better describe our approach, such as "interest-led learning."  And as I've mentioned before I like Melissa Wiley's "tidal homeschooling" metaphor to articulate our movement between more and less structure over the course of the year.  The routine I've described above might not seem very "unschooly" to some (the combination of "Unschool" and "Academy" in my blog's title indicates that we aren't conventional unschoolers), but I maintain my use of the word unschool to describe what we do because our routine evolved organically and is not imposed by us on N.  I was affirmed in my belief that what we are doing works for N. when I saw his excitement to resume the homeschool routine, to "start First Grade."  He asked to begin on Sunday, the day after his 6th birthday party and all week he has been really energized by his learning.  He thrives on the regularity of his school routine and on the intensity of focus and attention he gets from Tim during these times.  

That's not to say he wasn't learning during our vacation.  We're concluding a kitchen remodeling project, and N. loved watching and talking with the various tradesmen who've been working at our house.  He and I read many chapter books, especially during our road trip to Minnesota.  During our month-long visit to Duluth (see here here, here, and here for descriptions of last year's Duluth vacation), we spent lots of time hiking, socializing, looking at old buildings and learning more about Minnesota history, communing with Lake Superior, learning about rocks, watching the amazing cloud formations over the lake, kayaking and canoeing for the first time, picking wild raspberries and blueberries, learning about Great Lakes mining and shipping, and more.  It was a rich summer.

We found inspiration during the summer for further study during the academic year.  Tim and N. spent a lot of time on a cloud book last spring, and the gorgeous sky vistas in Duluth made them both want to continue learning to identify clouds and to understand what they signify.  Tim bought a history of Iron Ore mining when we visited a mine overlook in northern Minnesota and he and N. have already spent a lot of time with that book this week; its early chapters lead to them learning about the Louisiana Purchase, Jefferson's presidency, and a bit about the relationships between the French, British, Americans, and Indians.  We don't make daily lesson plans, but we have some broad goals for the year: to continue regular practice of reading, writing, and numbers; beginning with the cloud book, to build on science knowledge; continue building on geography and history knowledge; piano lessons (pending).  I suggested we sign him up for a homeschool Spanish class but N. rejected the idea of taking a class with others and anyway he wanted to learn French because he's already learned a few words from "Eloise in Paris."  So at his request I agreed to start teaching him French myself with short lessons a couple afternoons a week.

We're all feeling refreshed from the summer and excited at the beginning of our second official year of homeschooling!

Tuesday, June 15, 2010

A Kindergarten Year in Chapter Books

.As I wrote last summer, N. got interested in read-aloud chapter books in earnest last spring.  Here's what what we've read to N. between roughly March 2009 and June 2010, excluding daily fairy tales, nonfiction, and of course many picture books.  Several of these books were read multiple times.  A few, as you can see, were abandoned unfinished because N. didn't like them or lost interest.  Reading chapter books to N. has primarily been my province, for some reason (Tim reads many other things to N.!) so I've noted if the book was read aloud by Tim.  The books are listed roughly in the order in which we read them.  I am keeping records both at LibraryThing (click the "chapter book" tag for complete book info) and at Listography.  I readily admit I am bragging here; I think this is an awesome list.  And I think it's accurate to say that N. loved every book on this list that we completed. It's been a very fun read-aloud year!  What should we read next?  Recommendations?
  • The Five Little Peppers by Margaret Sidney
  • The Railway Children by E. Nesbit
  • Pippi Longstocking by Astrid Lindgred
  • Betsy-Tacy by Maud Hart Lovelace
  • Besty, Tacy, and Tib by Maud Hart Lovelace
  • Betsy and Tacy Go Over the Big Hill by Maud Hart Lovelace
  • Betsy and Tacy Go Downtown by Maud Hart Lovelace
  • Strawberry Girl by Lois Lenski
  • Complete Tales and Poems of Winnie The Pooh by A.A. Milne
  • Mrs. Piggle-Wiggle by Betty MacDonald
  • Homer Price by Robert McCloskey
  • James Herriot's Treasury for Children
  • The Wind in the Willows by Kenneth Grahame
  • A Bear Called Paddington by Michael Bond
  • More About Paddington by Michael Bond
  • Just So Stories by Rudyard Kipling (did not finish)
  • Tales from Centerburg by Robert McCloskey
  • Rabbit Hill by Robert Lawson (did not finish)
  • The Boxcar Children No. 1 by Gertrude Chandler Warner
  • Stuart Little by E. B. White
  • A Little Princess by Frances Hodgson Burnett (read by T.)
  • Winona's Pony Cart by Maud Hart Lovelace
  • Caddie Woodlawn by Carol Ryrie Brink (did not finish)
  • The Family Under the Bridge by Natalie Savage Carlson
  • Little House in the Big Woods by Laura Ingalls Wilder
  • Encyclopedia Brown, Boy Detective by Donald Sobol
  • Charlie and the Chocolate Factory by Roald Dahl
  • The Cricket in Times Square by George Selden
  • Frindle by Andrew Clements
  • Half Magic by Edward Eager
  • Knight's Castle by Edward Eager
  • Felicity: An American Girl, 1774 by Valerie Tripp (almost finished)
  • Mrs. Piggle-Wiggle's Magic by Betty MacDonald
  • Pygmalion by George Bernard Shaw (read by T.)
  • The Odyssey by Homer, translated by Robert Fagles (read by T.)
  • The Hundred Dresses by Eleanor Estes
  • Magic by the Lake by Edward Eager
  • Higgins and the Great Big Scare by Rebecca Caudill
  • The Magical Ms. Plum by Bonny Becker (did not finish)
  • James and the Giant Peach by Roald Dahl
  • Little House on the Prairie by Laura Ingalls Wilder
  • The King in the Window by Adam Gopnik (did not finish)
  • Mr. Popper's Penguins by Richard Atwater
  • Ginger Pye by Eleanor Estes
  • Gone-Away Lake by Elizabeth Enright
  • Charlie and the Great Glass Elevator by Roald Dahl
  • The Phantom Tollbooth by Norton Juster
  • The Children of Green Knowe by L. M. Boston

Monday, June 14, 2010

Delivered to Our Door

Newspapers and magazines (home delivery, not online) are a major homeschool resource for us.  We subscribe to our local daily paper, and even though it has declined shockingly in the past few years and beyond local coverage is barely a worthwhile news source for adults, it is a perfect newspaper for a 5-year-old boy.  N. and I read the paper together every weekday morning over breakfast.  There are almost always front-page stories with lots of big photos about local road work and other construction projects as well as stories that help us learn about the history of our city and upbeat local stories about kids and cultural events.  The national and international news is very basic, and thus just at N.'s level.  Through reading these stories we've had lots of good introductory civics lessons on elections, protests, forms of government.

Even though our newspaper is politically right-leaning, it is still relentlessly cheerful in tone, and nothing like TV news (which we don't watch).  Depressing stories are buried deep in its very slim pages, making it easy for me to censor what N. is exposed to (for example, I shield him from photos of bombings in Afghanistan or elsewhere).  Although I don't want him to think the world is perfect, I am very wary of exposing him to images that are too disturbing for a five-year-old to process, that will make him too worried and sad about the future he is growing into.  The other downside of the newspaper is the huge ads.  Tim and I have always found Rousseau's exhortation in Emile (1762) so compelling, if hopelessly romantic: "form an enclosure around your child's soul at an early date."  I would love that enclosure to be ad-free; I wish N. never saw an airbrushed face, a lingerie model, or a brand logo, but that is obviously impossible.  I fold the paper down to get large ads out of our sight-line when I can, and when I can't I explain what I don't like in the images.  We also get the Sunday New York Times (though not everyone in our household agrees that this is a worthwhile expense), which right now is much less useful as a homeschool resource for N. precisely because it is an adult newspaper with adult content and even more inappropriate ads.  N. and I do, however, enjoy the Travel section! 

We get other magazines, but our National Geographic subscription comes in N.'s name and plays an important role in our "curriculum."  He looks forward to getting it every month and Tim and/or I read through it carefully with him, learning what we can from it as well as using it as a point of departure for many other inquiries.  Science and nature, history, geography, and anthropology are just some of the academic subjects that the magazine regularly spans.  We like the adult magazine rather than National Geographic Kids because the photography is so compelling, the articles have much more depth, and the approach doesn't pander to kids' supposed interests or supposed short attention span.  Again the magazine has ads, and they are ads that are particularly hard for a kid to distinguish from editorial content, which is more pernicious (luscious photography of a luxury car in an exotic locale, for example).  But we still think it's a good resource.

So, reading the newspaper daily and National Geographic monthly has become part of our learning routine, although we didn't exactly set out explicitly to make this happen.  I read the paper every morning over breakfast, so I started sharing that with N. from an early age whenever there was a story I thought he'd like, and the habit has grown as his interests have expanded.  We subscribed to National Geographic when N. was born, hoping he would like it, and it too has become habitual.  The daily newspaper is so important to N. that if I am running late for work and skimp on reading the paper to him (or God forbid, try to skip it all together), he gets extremely upset.  He loves routines and regularity, so it is easy to make anything he enjoys a regular part of our daily life.  Too bad journalism is a dying industry.  N. will probably grow up to be the last American reading a print newspaper.

Thursday, June 10, 2010

Reading Update: Dick and Jane


I had never actually seen a Dick and Jane reader, but Tim bought one of the reissued "treasury" compilations a few years ago and stored it away for future use.  Since N. was sounding out words with great pleasure and read Dr. Suess's "Hop on Pop" completely by himself, we thought we'd pull out Dick and Jane, just for fun.  The books are every bit as ridiculous as I'd always heard: dull, repetitive, saccharine, white, and blond.  Once you see them you can easily understand why they became controversial both from a pedagogical standpoint (the vocabulary is limited to train children through repetition to recognize whole words rather than to sound them out) and a political standpoint (they do not depict the multicultural America, even with the addition of a black family to Dick and Jane's neighborhood in the 1960s).  It's easy to imagine that, as Rudolph Flesch argued in Why Johnny Can't Read (1955), these books would turn a child off of reading rather than inspire him.

As it happens, however, N. loves Dick and Jane.  He loves the pictures, he thinks the repetition is hilarious, and he enjoys the stories.  With his taste for all things vintage and retro, he admires the dad's car, the kids' toys and clothes.  He's proud of being able to read the stories; each one is very short and quickly produces a gratifying sense of accomplishment in the reader.  We don't do any formal reading lessons with Dick and Jane (or any other text) but N. routinely asks to read a few of the stories aloud to me at bedtime.  Since part of the books' fall from favor was due to a return to phonics-based reading instruction rather than Dick and Jane's whole-word/look-see method, I was interested to see that N. uses both methods when reading these stories: he sounds out new words, while the repetition reinforces words he can read without sounding out.

I certainly wouldn't want Dick and Jane to be any child's only exposure to the world of reading, but I've been pleasantly surprised by N.'s enjoyment of this much-maligned classic.  Next I want to get my hands on the McGuffey Readers that Dick and Jane replaced!

Wednesday, June 9, 2010

Plus ca change: Joseph Andrews

In Henry Fielding's novel The History of the Adventures of Joseph Andrews (1742), the eponymous hero and his mentor Parson Adams engage in a dispute about the merits and disadvantages of "public schools" (such as Eton, Harrow, or Westminster, what 21st-century Americans would call elite private boarding schools) and "private education" (which in eighteenth-century England meant the education of a small group of children in a domestic setting by a local clergyman or perhaps a parent).  Their discussion turns on the issue of what is known to today's homeschoolers as socialization.  Is the socialization, or initiation into the social codes and behaviors of a large community, provided by school beneficial or detrimental?  

Parson Adams is partial to a private education, since he offers that service to boys in his parish.  He takes a protective stance and believes the socialization learned in large boarding schools has a negative effect on boys' moral development.  "Public Schools are the Nurseries of all Vice and Immorality.  All the wicked Fellows whom I remember at University were bred at them. . . . Joseph, you may thank the Lord you were not bred at a public School, you would never have preserved your Virtue as you have."

Joseph, although privately educated himself, demurs, citing the views of his employer, Sir Thomas Booby.  Joseph and his employer make the familiar argument that children need to learn to navigate the school community as preparation for navigating society at large after completing school.  "It was his Opinion, and I have often heard him deliver it, that a Boy taken from a public School, and carried into the World, will learn more in one Year there, than one of a private education will learn in five.  He used to say, the School itself initiated him a great way, (I remember that was his very Expression) for great Schools are little Societies, where a Boy of any Observation may see in Epitome what he will afterwards find in the World at large."

"Hinc illae lachrymae [hence those tears], for that very Reason," replied Adams, "I prefer a private School, where Boys may be kept in Innocence and Ignorance: for... Who would not rather preserve the Purity of his Child, than wish him to attain the whole Circle of Arts and Sciences; which, by the bye, he may learn in the Classes of a private School?... A Lad may have as much Learning in a private as in a public Education."

Joseph points out "And... he may get as much Vice, witness several Country Gentlemen, who were educated within five Miles of their own Houses, and are as wicked as if they had known the World from their Infancy."

The discussion ends at an impasse; Fielding does not advocate one side of the question or the other, but highlights with typical Augustan balance both pros and cons of each mode of education.  Children are not automatically protected from vice by a domestic education, neither are they automatically learning less by not going to a large school.  We shouldn't complacently assume that the mode of education we happen to favor is actually superior.  Instead we have to be engaged actively as teachers, parents, and students to make our education yield the results we desire and to counteract its disadvantages.

Tuesday, June 1, 2010

On Barbies and Sewing Lessons

N. and I have been sewing Barbie clothes for some time now.  It's a collaborative process: he chooses the fabric and has a strong vision for what he wants the clothes to look like.  We measure fabric, cut pieces out freehand and together talk through the process of machine sewing: threading the needle, placing the bobbin, the different presser feet,  etc.  Sometimes N. pushes the treadle while I guide the fabric through or vice-versa.

















Here he is experimenting with the various fancy embroidery stitches on my machine, working the whole thing by himself. 







Recently, inspired by some adorable clothes my mom made for the Barbies and gave N. for Easter, we actually used a basic pattern.  Here he is tracing the pattern markings on the fabric.  So we had a little lesson in garment construction and the art of turning a flat piece of fabric into something three-dimensional.  What is the effect of darts?  Why do we sew with right sides together?  The end result is every Barbie's dream: a floor-length strapless Bob the Builder gown! 

It's fair to say that this year N. interacted with fewer kids his own age than he would have if he had gone to kindergarten.  He plays almost daily with the neighbor girls and he has other friends he gets together with, but as the neighbors start school next year, one of my major goals is to get us more plugged in to the local homeschool networks for regular play-date purposes.  Meanwhile, however, I think that because N. hasn't been to school and doesn't watch TV or movies, he doesn't restrict his play by socially imposed gender codes.  He loves playing with trucks and Barbies, often together.  I am really proud of this, even though as a feminist I am ambivalent about Barbies.  I played with Barbies as a kid but in a strongly feminist household where we talked a lot about the consequences of cultural images of women.  I don't think that in and of themselves Barbies are damaging to girls' self image, but Barbies can work in concert with images that can have negative effects on girls.  So, what about their effect on boys?  I am pretty sure I have never read anything studying this!  The main thing we worry about is that the Barbies become some kind of female ideal in N.'s eyes.  But from the moment he saw two Barbies in a box of my old toys in the basement, he wanted to play with them, and we couldn't justify denying him this pleasure.  Instead, while still validating N.'s play with dolls, Tim has talked to N. about why he personally doesn't like the impossible physical proportions of Barbies, and we try to counteract the image of the generic blonde by not calling them Barbies (and by seeking out brunette dolls); instead N. gave each an individual name.  His current tribe (whose provenance is the basement and rummage sales) includes Iris, Linda, Myrtle, Violet, Tulip, Millicent, and Nora.

Overall, the Barbies have provided N. with myriad opportunities for pretend play and an introduction to sewing, a very useful life skill that I hope to help him develop.  I'm so glad that no one has told him he shouldn't sew or play with dolls.

Thursday, May 20, 2010

Fun and Games

Here are two games N. has been playing a lot lately: word jumbles and marbles.

He made up the word jumbles after seeing them in the newspaper; we each take turns writing a jumbled word for the other to rearrange.  This is a great example of what John Holt describes in Learning all the Time, namely that an important part of learning to read is learning what arrangements and combinations of letters don't make words in English.

N. recently bought an old-fashioned wooden marble shooter and we play a darts-style game with it and keep score on the sidewalk. We write down any points a player gets, and verbally keep a running tally, compare scores, quiz each other about how many points each player needs to take the lead, etc.

I think N. enjoys these games so much because they are building on skills that he is (unconsciously) working on very intensely right now: reading and math.  I believe strongly that child-led activities and games like these are the most productive kind of learning, much more so than empty adult-initiated busy work or drills.  And being able to solve problems flexibly in situations where the answer matters to you is more important than being able to answer a question on a test.



Saturday, May 8, 2010

Unschool in Kids' Books: Stuart Little

I've been making a mental list of the depictions of conventional school in some of our favorite children's books.  Whether for the necessities of plot (a sedate school day might not provide many story opportunities) or because compelling characters are spunky and unconventional, children's literature often critiques traditional schools.  What happens when the hero is a mouse in a human world?

When E. B. White's Stuart Little volunteers as a substitute teacher for a day, he quickly dispenses with traditional subjects of instruction in favor of stimulating conversation. 
'What's the first subject you usually take up in the morning?'
'Arithmetic,' shouted the children.
'Bother arithmetic!' snapped Stuart.  'Let's skip it.... What next do you study?'
'Spelling,' cried the children.
'Well, said Stuart, 'a misspelled word is an abomination in the sight of everyone.  I consider it a very fine thing to spell words correctly and I strongly urge every one of you to buy a Webster's Collegiate Dictionary and consult it whenever you are in the slightest doubt.  So much for spelling.  What's next?'....
'Writing,' cried the scholars.
'Goodness,' said Stuart in disgust, 'don't you children know how to write yet?'
'Certainly we do!' yelled one and all.
'So much for that, then,' said Stuart.... 'Instead of taking up any special subject this morning, why wouldn't it be a good idea if we just talked about something.'
Stuart's cavalier dismissal of the subjects is funny, but also worth pondering.  I believe "arithmetic" in the early years is best learned in the context of real problems, and that arithmetic is only one part of the necessary mathematical thinking we want to help children develop.  Dedicated use of the dictionary is indeed a very good way to learn how to spell (dictionary use in general seems to be a dying practice; it thoroughly amazes me how few of my college students ever look up unfamiliar words in the course of their reading).  I love Stuart's assumption that the only purpose of Writing as a separate subject of instruction would be for students who don't know how to write the letters of the alphabet.  Although it is important to practice handwriting, divorcing writing from content and occasion makes the "subject" of Writing meaningless (not unlike "teaching" content-less Reading as described in a New York Times op-ed last year). 

Instead of leading lessons, Stuart proposes a conversation (which happens to be Tim and N.'s primary mode of instruction).  Stuart is a rather autocratic pedagogue; instead of working with his students' suggestions, he rejects outright their somewhat narrow suggested topics ("'Could we talk about the way it feels to hold a snake in your hand and then it winds itself around your wrist?' asked Arthur Greenlaw.  'We could, but I'd rather not,' replied Stuart") and instead suggests "Let's talk about the King of the World."  This idiosyncratic conversation-starter ends up leading the students through major problems of government and ethics (is there a King of the World? what is the difference between a rule and a law? should we have sympathy for the despised among us, such as rats? is a law such as "Absolutely no being mean" enforceable?).  They talk, question, and role-play.  They establish "what is important:" "A shaft of sunlight at the end of a dark afternoon, a note in music, and the way the back of a baby's neck smells if its mother keeps it tidy."  Also: "ice cream with chocolate sauce on it."

Stuart's teaching concludes with musing on the pleasures of summer, when you aren't in school, but might be playing by the lake, rambling, swimming, flirting.  "Summertime is important," Stuart says, and he leaves his students with this parting bit of wisdom: "Never forget your summertimes, my dears."  The children "all wish they could have a substitute every day, instead of Miss Gunderson."

Tuesday, May 4, 2010

Handwriting Practice

Tim looks for meaningful occasions to encourage N. to practice writing letters, and this often means writing notes to mail to family and friends.  Valentine's Day, birthdays, Mother's Day, thank-you notes for gifts all warrant an N. card (hint to family and friends: send N. more mail so he can write back to you!).  Tim and N. start by talking about what N. wants the note or card to look like and what he wants it to say.  N. will dictate the message to Tim, who will write it down for N. to copy.  Sometimes N. practices on a piece of paper before writing on the card.  Here's a recent sympathy card he sent to my mom and dad, whose cat had died.  It's pretty much the sweetest thing in the universe.

As you can see, N. still prefers to write in all capital letters.  As he is doing more independent reading, I've noticed that there are still a few lower-case letters that he mixes up (b, d, p) so it makes sense that when he is writing he uses the letters he is most comfortable with and for which he apparently also has an aesthetic preference.

These notes make handwriting practice a meaningful task; they also feed into his developing literacy, and they provide important lessons in socialization.  N. is very proud of them and so are we!

Monday, May 3, 2010

Gardening 2010

We love growing vegetables every summer, and this spring Tim and N. revamped our main garden because Tim was concerned about possibly contaminated soil in our old urban yard (where we regularly find "clinkers" emptied long ago from someone's coal furnace).  He and N. built this raised bed together, had a big load of dirt delivered, which they then had to transport from the alley in wheelbarrow loads (N. working alongside Tim with his own shovel and little wheelbarrow), and planted seeds and plants.  Here they are planting marigold seeds outside the perimeter of the bed for pest reduction.  We also have a second smaller bed elsewhere in the yard.

We have some favorite plants that we grow every year: eating pumpkins, butternut squash, kale, arugula, mixed salad greens, a huge variety of tomatoes, zucchini, black-eyed peas, pole beans, basil, dill, cucumbers, peppers, nasturtiums.  We're on the second year of nurturing several asparagus plants, but they take several years before they produce edible spears.  This year we are also trying broccoli, leeks, and Japanese eggplants.  There is probably more that I am forgetting right now.  Tim has written everything out on a garden map this year, because later in the summer the vigorous growth tends to overwhelm us, and we lose plantings among the squash and tomato vines. 

In the spring, before the mosquitoes come out in full force, work on yard and garden projects is a regular part of Tim and N.'s day.  N. loves these kinds of projects, whether it's placing paving stones, moving dirt, planting seeds, or watering plants.  He and Tim talk the whole time about all kinds of things.  N. is often working right beside Tim, but when he wants to take a break to play, he does.  Either way, he's getting sun, air, and exercise, building up his knowledge about plants and food growth, participating in a long-term project that requires planning, regular attention, and teamwork.  It's our own Edible Schoolyard!

Sunday, April 25, 2010

Greens 2010

As I described last year, we grow lots of kale and a bit of collard greens over the winter.  This is the second year we've harvested, blanched, and frozen the whole crop before planting the spring garden.  Last year, N. wanted to help me with the greens, and his self-assigned task was swirling the blanched greens in an ice bath.  This year he wanted to take on a bigger role in the process.  In addition to cooling the greens, he filled the freezer bags with chopped greens and weighed them repeatedly on the kitchen scale till each bag weighed precisely 8 ounces, then carefully squeezed excess air out of the bags and sealed them closed.  After I labeled all the packages, he insisted on putting them in the freezer without assistance.  Throughout the whole process, it felt more like I was assisting him than the other way around!

It seems funny to chart N.'s growth and development through his participation in the annual freezing of greens, but I was struck by how very much older he seemed this year as he took charge of parts of the process.  Although it would have been easier, faster, and less messy to do the whole task myself, taking advantage of N..'s desire to participate gave him opportunities to practice thinking about fractions and multiplication as we talked about the various components of 16 ounces, to be engaged in the production and preservation of his own food, to follow precisely a multi-step process, to take a responsible role without being asked or required to.  As I ceded more steps of the process to N., I was also able to be more conversationally engaged with him, which helped me maintain my patience as the whole process inevitably slowed down in a 5-year-old's hands.  Being truly present in our conversation made the process more intellectually rich for both of us.  So, the moral of the story is that greens are delicious, easy to grow, and good for you in lots of ways!

Tuesday, April 13, 2010

Tell me, O Muse

Tim tutors the 11-year-old homeschooled son of our friends/homeschool mentors. They meet more or less weekly to discuss literature and papers the boy writes on the readings (or on his passion for art history as it intersects with the readings, which are chosen precisely for these intersections).  Although N. doesn't participate directly in the tutorials (he plays while Tim and his student talk), every week as Tim prepares for his tutoring session, N. asks him to read the works to him.  Last year, they read major portions of the Hebrew Testament together.  This year, N. has heard some of the Metamorphoses, which seemed to fit in with his predilection for fairy tales (almost daily, Tim reads to him from Calvino's collection of Italian Folk Tales, Grimm's, or African Folk Tales).  Inspired by Ovid's story of Galatea, Tim and his student read Shaw's Pygmalion, which N. absolutely loved because the Broadway soundtrack of My Fair Lady has been in heavy rotation on our kitchen CD player for at least a year.  Not only did N. comprehend the play as Tim read it aloud, but he was so absorbed in it that he made Tim read it to him all in one sitting.  For the past month or so, they've been reading The Odyssey.  Fagels' translation makes for a riveting read-aloud, as do the poem's origins in oral performance, and N. has been really enjoying it.  I don't expect that N. fully "gets" everything he is hearing in these readings, though he and Tim pause frequently for questions and discussion.  Though it never would have occurred to us to read The Odyssey to a 5-year-old, we aren't checking this work off some list of classics, as if we have now "done Homer."  Instead, we hope this is merely the first exposure that he'll have to this great work, that since he's enjoying it, he'll have a positive memory of it that will inspire him to return to the poem, weaving his cloth over and over.

Tuesday, March 30, 2010

New Mexico

We recently traveled to Albuquerque, New Mexico for three days so I could attend the annual meeting of the American Society for Eighteenth-Century Studies (ASECS).  One of the basic things I love about our homeschool life is that Tim and N. are not prevented by work or school obligations from traveling with me so they can take advantage of the learning stimulus that travel inevitably provides; we are grateful for these opportunities (I wrote about our ASECS trip to Richmond, VA last year).   

None of us had ever been to New Mexico before.  Anticipating our trip, Tim and N. studied bits and pieces about New Mexico: adobe architecture, the state capital, the Rail Runner train that runs from Albuquerque to Santa Fe, petroglyphs, etc.  In Albuquerque, they hiked among the petroglyphs, spent a full day at the zoo and aquarium, and explored the city by car and on foot.  We ate lots of delicious food (an education in itself!); N. is moderately adventurous about restaurant food, especially since he can almost always find meat, which we eat very rarely at home, on the menu.  We took a day trip on the Rail Runner to Santa Fe where N.'s passion for old buildings was slaked by our visit to three churches: the Basilica of St. Francis (cf.  Cather's Death Comes for the Archbishop), the Loretto Chapel (complete with so-called "Miraculous Staircase"), and the San Miguel Mission Church (built in 1610!).  N. really liked the Zia Sun that adorns the New Mexican flag (as you can see in his picture above; his version of the flag also includes the Rail Runner train).  He was also totally entranced by the New Mexican music played by local artists on the public radio station KANW and he would have been happy to listen to it in the rental car for hours.  In the days since we returned home, N. and Tim have followed up on some of the topics the trip generated that they wanted to learn more about: the Zia people, sting rays, aviation, the Sandia Mountains.

When we travel as a homeschool family we experience what Melissa Wiley calls "tidal homeschooling" because travel shakes up our normal rhythms and routines.  Travel provides new stimuli and new objects of inquiry and at the same time coming home makes the simple routines, the low-tide times, that much more dear.  I enjoyed seeing N.'s anticipation of the trip build just as much as my heart was warmed by his happiness to be home again when it was all over.

Monday, March 29, 2010

Metaphor

Out for an evening stroll, we walked past the house of a neighboring family; we consider the parents friends of ours, but their son and ours don't get along well and never have.  They've always rubbed each other the wrong way.

"I wish I was as old as O." (the son, who is 6 1/2), N. said.  I was surprised, because usually N. laments the idea of growing older.  I wondered where this sentiment came from, and where it was leading.  I said, "You'd like to be as old as O."  Norris responded, "It's a castle with the drawbridge up, and I can't get in.  O. and R. (O.'s even older best friend) are inside but I can't join in."

I was so moved by the aptness and poignancy of this metaphor.  I wanted to tell the college students in my introductory literature classes who don't see the value of literature, who resist reading: this, this is why we read! Stories help us make sense of our lives and express that to others.  Stories give us images, a metaphor like a castle that helps a boy think through the complexity of his adversarial relationship to someone who doesn't intend to be mean, but whose age gives him defensive strength, whose play has a sophistication that remains impenetrable to the young outsider's forays.

Friday, March 12, 2010

Math in School

One of the reasons I am so much enjoying N.'s developing numeracy is my own traumatic experience of math in first grade.  It would not be an overstatement to say that my experience of math instruction in school scarred me for life; because of this I am especially drawn to Holt's account and thrilled with N.'s experience of math so far.

When I was six years old and in first grade, we had to take timed tests of addition and subtraction problems.  We were supposed to complete a sheet of problems in a certain amount of time without error.  If we did that successfully, we moved up to a test to be completed in a shorter time, and then another and another, each test to be completed in a shorter time than the last.  The point was to drill math facts so that you could eventually do them automatically without thinking.  I couldn't progress beyond the tests with the longest time allowed.  I understood how to add and subtract and I could do it correctly, but not quickly. My parents were concerned, so they had me practice the timed tests at home.  I still vividly recall my father's desk in the dining room where I sat to take the tests, the florescent glow of avocado green desk lamp, the menacing red numbers of the digital desk clock. 

Timed math tests constituted my first experience failing at something in school.  And I definitely felt like a failure.  It was humiliating to see my friends moving up through the test levels while I had to take the longest timed test again and again.  I hated practicing the tests at home.  I felt anxious about my parents' concern because I knew that doing well in school was important, and I wanted to do well.  Describing it here, I find it hard to believe these little tests ended up looming so large in my life, but in some ways I never really got over my inability to succeed on those tests.  I developed a phobia about timed tests more generally to the extent that my mom had to ask my teachers throughout elementary school not to announce the time remaining on the yearly California Achievement Tests; I was afraid I would freeze up and not complete the test if I heard how much time I had left.

The consequence of my first grade timed math tests was that I thought I wasn't good at math, and I thought this all the way through high school, even though what I wasn't good at at the earliest stage simply was doing math quickly.  I also had a very difficult time memorizing the multiplication tables, even though I had a very good memory for words.  I think now that in addition to the anxiety I had already developed about math thanks to the first grade timed tests, I struggled with the multiplication tables because I hadn't really internalized the relationships of numbers to each other.  The times tables were content-less to me, a series of meaningless numbers.  My favorite experience of math came outside of school, in a book my mom bought me called The I Hate Mathematics Book which presents mathematical concepts in real-world contexts (I still remember the pages on permutations and combinations of ice cream flavors).

Despite have an analytical and logical turn of mind, and good spatial relations abilities, I came to define my identity as a student as someone who couldn't do math.  I took the bare minimum required math to graduate from high school (Algebra II) and am embarrassed to say that I have never taken pre-calculus, trigonometry, or calculus.  I didn't like taking courses that were really difficult for me and that I didn't enjoy working hard in (I was willing to work hard in classes that I was interested in); I didn't like failing.

My own dismal experience of math in school shapes my approach to N.'s education in several ways.  First, what happens in the early years does matter, and can have a profound impact on a student's later learning.  Second, we try to cultivate a holistic and deep understanding of the many facets of mathematical thinking in N. rather than focus on the surface "math facts."  Third, speed doesn't matter, understanding does.  Fourth, it's okay to fail.  Or, better yet, we hope we create a learning environment where there is no failing, only learning, where everything N. does is recognized and valued by us and by him as an important part of his learning and development.  I hope he feels that it can be fun to struggle at something that is hard and that his sense of self-worth or his self-definition do not derive from whether something is hard or easy for him.  In fact, isn't it better to try to cultivate in children (in adults too!) an open definition of self?  What if I hadn't let my struggles with math in first grade become such a strong part of who I thought I was?

Unschooling Math in the Early Years

John Holt's Learning All the Time offers a compelling account of the ways that some conventional instructional approaches to math can hinder children's understanding of the relationships between numbers; he describes alternative ways to foster children's sense of the connections and relationships between numbers rather than focusing on "math facts." For example, you can explore all the different ways to make six rather than concentrating only on 3+3. Math is all around us, and children don't necessarily need to master addition before subtraction or even multiplication.

So far, N.'s exploration of numbers has naturally followed Holt's account and it's been fascinating to watch. His interest in numbers has arisen out of his play and his passions. For example, when he was 4, he learned that steam train engines are described by the number of bogey, driving, and trailing wheels they have. So a 2-6-4 has two bogey wheels, six driving wheels, and four trailing wheels going from the front of the engine to the back. But when you look at a 2-6-4 from the side in illustrations (in the zillions of train books we own!) you see one bogey wheel, three driving wheels, and two trailing wheels. So to identify the train properly, you have to double what you see in the picture.  I don't recall us explaining this to N. (because frankly I had no idea what this chain of numbers was that was always listed with the make and model of a train), but he looked at a lot of books and apparently from pondering the disparity between the identifying label and the picture, he figured out how to multiply by two.  And when he figured this out, he took immense pleasure in doing this operation.  Whenever he looks at a picture of a train he says what its wheel configuration is.  So now he has a concept of multiplication that we can refer to when we talk about other ways that numbers can be put together or split apart.

Whenever questions about numbers come up in conversation (and they do all the time), we try to build on them and extend them.  So, if N. asks us what five and seven make, we'll say 12, and we might follow up by asking him what seven and five make.  Usually he likes to think about it and respond; if he doesn't we'll answer our own question.  If he's wrong, we'll just say pleasantly what the answer is.  We're not quizzing him, but engaging in thinking with him about numbers.    

Other ways that I've observed N.'s math skills developing include his extensive play with blocks and legos.  Not only is this kind of manipulative play crucial for understanding quantity and number stability, but it also gives him lots of opportunity to add and subtract, to create symmetry and asymmetry, to consider the relationships of shapes to each other (proto-geometry).

I remember his excitement when he first realized that two particular triangles could make a square after he'd run out of square blocks, and his difficulty getting two other triangles put together in the proper way such that they'd form a rectangle.  Turning those blocks this way and that, again and again, patiently trying out positions till they fit develops the spatial relations skills that are crucial to mathematical thinking.  Because this happens in the context of play, there is no failure, and there is complete motivation because N. wants to make something that he can see in his head take shape in front of him.  My crucial role here was to be stay in the background even though I was ostensibly playing with him, to let him figure it out even though my first impulse might have been to show him how to do it!

We also do a lot of cooking and baking together, which of course provides a great opportunity to play with fractions.  I've enjoyed watching his slow grasp of "half," "quarter," and "third" (which has been especially tough).  It's been really interesting for me to see how hard these concepts can be and so it seems important to provide lots of opportunities to talk about them, explore them, and get them wrong.

The two dominant modes of N.'s math development so far have thus been through conversation and manipulation.  But N. has also said to Tim "Let's do some math, Dad," or "Let's do numbers," so they've done some practice with written numbers.  Here are some examples:

Writing 1-100:














Even and odd numbers:








 


Adding:











Writing numbers in different fonts!


N. is by no means a math prodigy, and what he's done on his own and our numbers work with him is not anything out of the ordinary.  I've tried to describe here both that he has an innate interest in numbers and in other mathematical concepts and that we've tried to build on that in positive, no-stress, non-coercive ways.