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


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:



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.

Monday, March 8, 2010

Reading Update

We’ve been following John Holt’s approach to reading instruction in his book Learning All the Time, which is to say creating a text-rich environment full of stories, printed books, handwriting practice through copying notes to Grandma, but not explicitly teaching reading. Sometimes I wanted to do more, especially when I read the blogs of other homeschooling moms with kids N.’s age who are doing explicit reading instruction. But Tim and I had agreed we weren’t going to push early reading for a variety of reasons, some more idiosyncratic than others (our thinking about this is not slavish devotion to John Holt).

Tim was taught how to read in school at age 7 and my mom taught me to read at age 4; we both have Ph.D.s in English so it would seem that earlier or later reading in and of itself had no impact on our respective literacy and love of reading. Tim and I believe a multifaceted culture of language is the best way to prepare for literacy.* We are also fairly obsessed with the Finnish academic model, which is very successful by a variety of measures, and they don’t teach reading till age 7.* This is not to say that 7 is any kind of magic number. “Readiness is all” is our mantra; when he is ready, I am confident that N. will learn to read.

Without romanticizing illiteracy at all, we have also thought about what might be lost when a person becomes literate. Literacy is a necessary skill and also a wonderful pleasure, but it is simply a very different mode of experiencing the world. N. listens intensely, has an amazing memory, an inventive imagination, and keen powers of visual observation. Will full literacy displace any of these modes of experiencing the world, or can they coexist? William Dalrymple, in a New Yorker article from 2006 called “Homer in India,” describes the ancient oral poetry traditions – bards who recite ancient poems that, when written down, are more than 600 pages long – sustained by the special skills of the illiterate: “Just as the blind can develop a heightened sense of hearing, smell, and touch to compensate for their loss of vision, so it seems that the illiterate have a capacity to remember in a way that the literate simply do not” (p. 54). In some cases, when illiterate bards have been taught to read and write in order to record the poems they perform, their memory of the poems weakens as they become literate. The process of preserving the poems in the form preferred by modernity – writing – ends up eroding the process that had preserved them for centuries – memory. Some older Anglo-American models of education (Shakespearean-era grammar schools,* Charlotte Mason’s pedagogy) emphasized literary memorization as much as if not more than literacy, and I like the idea of trying to preserve N.s capacious memory at least to some degree as he moves into literacy.

In a story-rich environment like N.’s (we read a lot to him every day, and he and Tim tell each other elaborate stories on their daily long walks), there isn’t a lot of incentive for him to learn to read for himself, although he enjoys looking at books on his own very much. N. mentioned a couple months ago that he didn’t want to learn to read, and I pointed out that we would still read to him, that one wouldn’t replace the other, which seemed to reassure him. Jim Trelease’s Read Aloud Handbook (which I’ve mentioned before!) reminds us of the importance of continuing to read aloud after a child learns to read, since there will likely be a huge gap in sophistication between what he can read and what he can comprehend aurally. [If you have access to JSTOR, here is a really interesting account in The Journal of Educational Research (Vol. 95, No. 5 (May - Jun., 2002), pp. 259-272) of a study suggesting that "semantic abilities (i.e. oral definitions and word retreival) not phonological awareness, predicted 2nd grade reading comprehension."]

N. has known the alphabet and the letters’ sounds for a couple years, and he had early whole-word recognition of a few words (bus, off, on, no, cat, etc.) but he could not comprehend “sounding words out.” Sometimes he would ask what something said and I would try to lead him through sounding it out, saying the letters’ sounds and stringing those sounds together to figure out the word. Over the past 6-8 months, no matter how much I modeled this, he just didn’t get it and couldn’t do it independently. I was puzzled by this and it was a struggle for me to remain patient and true to our plan; Tim reminded me that there was no rush for N. to read. I backed off, so that when N. asked what a word said, I would maybe briefly sound it out for him, but I wouldn’t ask him to do it.

Then, suddenly, just in the past two weeks, N. demonstrated that he understands how to sound out words -- even big, complicated words! I have no idea how this happened, but something seems to have clicked in his brain, and he now enjoys sounding words out, and does it all the time. This feels like a huge literacy milestone. N. seems to enjoy our shock at his new skill and to feel pride in having figured it out himself. He can truly feel that this is his accomplishment. Since N. can sound words out, Tim taught him last week about syllables, a little song to remember which letters are the vowels (which he’d been having trouble remembering), and that there is generally one vowel sound per syllable in English. N. absorbed these concepts right away (telling me all about them when I came home from work): readiness is all! He still hasn’t shown particular interest in reading books to himself (and that’s fine with us), although last night as I was reading him a chapter from Robert McCloskey’s Centerburg Tales, N. kept interrupting me to ask about random words or phrases he was noticing on the page; he would get excited when I finally reached those words or phrases in the course of my reading, thus making a connection between his aural and visual experiences of the words.

I see this development as confirmation that the approach we have taken so far to abjuring reading instruction is working for N., that he is on a path to reading that builds on his readiness and makes reading a positive and no-stress process while at the same time not displacing all the other ways of experiencing and interacting with the world that are so crucial to a 5 ½-year-old.

* Many of the studies and policies advocating early reading assume children entering school from non-text-rich (less conversational engagement between children and adults, less reading aloud, etc.) environments. The response to this in U.S. educational policy is to push so-called "academics" earlier and earlier at the expense of play (Google "early reading academic success" and you'll get a raft of examples). But the Finnish model suggests that a more successful response would be to create a multifaceted culture of language in all preschools and kindergartens made up of story-telling, reading, conversation, language-rich play.  See alse: Alliance for Childhood's "Crisis in the Kindergarten: Why Children Need to Play in School."

"[R]eading and writing instruction is not part of kindergarten activities in Finland. Instead, kindergarten focuses on social skills and free play, with rhymes, songs, and listening to stories as popular activities. In many kindergartens, children occasionally use workbooks or teacher-made pages for practicing coloring pictures, drawing lines, and cutting with scissors. The curriculum is typically based on thematic units, which include field trips, listening to books read by the teacher, singing songs, and art work on the theme. Although teachers often read a story to the children, books in the classroom are for teachers to read to children, with no library corners or literacy centers. Nor are alphabet cards posted on the wall, as in American kindergartens, because the emphasis in Finnish kindergartens differs from those in the United States. Finnish kindergarten teachers are trained to work with children from birth to age 6; the training emphasizes child development and care and does not include literacy instruction. Kindergarten children are not expected to learn to read and write, and there is no pressure on their teachers to have them do so." --Journal of Literacy Research, Sept. 2000. See also: 100 Years of Kindergartens in Finland

* I am simply noting the role of memorization in Renaissance English schooling, not advocating at all for its draconian discipline!