I asked Limerick the other day what was, in his opinion, one of the neatest things he knew about math and numbers.
In response he told me he thought the neatest thing was that if you start with the powers of 2 (say, 128 for example) and kept dividing by 2 (32, 16, 8, 4, 2, 1, 1/2, 1/4, and so on, he said), you would go on forever and never actually reach 0.
Basically my five year old uncovered on his own the concept of an infinite series approaching a limit and (very naturally!) decided it was just about the coolest thing numbers do. I love how his brain processes numbers and analyzes the world in their light!
As usual I’m joining the seven quick takes link up at This Ain’t The Lyceum today – head over and read some of the other blogs!
I missed out on the book theme last week, but I did have a very exciting book moment this week: my mom (who is a professor at the local community college) came home with a big cardboard box full of books that another professor was giving away, and told me to take anything that looked interesting. They seemed brand new and were non-fiction spanning the spectrum from memoir to science to investigative journalism. In other words, they were a treasure trove and I selected quite a few of them… I’ve started hinting to my husband that we need to put shelves up high on the walls because we have no more floor space for another bookshelf!
The only one of these books that I’ve had a chance to finish so far is Teeth: The Story of Beauty, Inequality, and the Struggle for Oral Health in America, by Mary Otto.The book is primarily about public health policy, and explains quite a bit about both the history of dentistry and the current state of dental health access and expense. But it covers this potentially dry topic in a manner that is both rationally and emotionally powerful, drawing the reader in through stories of individuals affected by societal pressure for “perfect” teeth or by societal neglect of oral health. Before reading this, I had never realized the extent of either the available cosmetic dentistry services or the overall risks of poor dental health (I guess I live in a comfortable middle-class bubble here…), and I was surprised and saddened by much of what I learned. This book does not engage in a lot of philosophizing; it accumulates stories and statistics and allows the reader to come to their own conclusions.
Another thing I have discovered this week is that drawing my own conclusions about medical issues is probably not a great idea, as they are likely to be wrong. Most of us have been sick this week, and Aubade had a cough and seemed miserable, so I called in to the doctor to ask for a refill on her Albuterol. The doctor asked us to come in (that is, the triage nurse called us at 3:25 and said that they wouldn’t refill the medicine without an appointment and that she had an opening at 4:00; we live 20 minutes away and the kids were in various states of undress and hadn’t had an afternoon snack yet), so we drove down there (and miraculously made it with three minutes to spare!) only to discover that Aubade wasn’t actually wheezing and thus didn’t need the Albuterol, but did have pinkeye and a double ear infections. Oh, and also that Limerick was extremely wheezy and did need the Albuterol, and had a higher fever than Aubade despite not feeling warm to my touch at all. So now they’re both drugged up, I’m nursing a sore eye, sore ears, and a headache, and Rondel is getting cabin fever from being cooped up all day with sick family.
To occupy our time while quarantined in the house, we’ve been playing a lot of homemade board games, both on the number boards and with a rainbow-colored board game path we designed together (Rondel came up with a set of rules that are consistent, creative, and fair – I was really impressed). There are giant foam dice everywhere (we only have two, but they are always getting thrown around and lost and re-found), and the little animal toys we’ve been using as game pieces keep disappearing and reappearing and getting dumped out in the hallways, and the Duplos have literally made their way into every single room of the house such that walking around is an obstacle course (mostly afflicting poor Aubade who keeps tripping on them). Cleaning not only seems futile but requires a lot more energy than I have available being sick myself…
We’ve also started coloring, drawing, and writing more again, since we’re stuck sitting around! Rondel even told me he wanted to learn how to write his letters, and persisted at it diligently until we left for swim lesson. He still switches hands when he writes, and he seems to see the parts of the letters instead of how those parts fit together to make a whole (his first “A” looked like a UFO before I verbalized for him a different way of perceiving and drawing it), but he did surprisingly well! Limerick is able to copy the letters well but doesn’t really pay any attention to direction and more often than not draws them sideways or upside down or reversed, without realizing it.
Another thing that went surprisingly well was hiding tofu inside the popsicles I make for the kids, to increase the protein content (since they like to eat them as meals). It ended up just contributing a slight nutty flavor, which went really well with the peach-vanilla blend I was using. I loved it as a smoothie and the kids ate up all the popsicles!
Also from the popsicles I’ve learned that frozen pineapple whips up in a food processor like egg whites or cream. If you process it with a little bit of milk it gives you something almost identical to whipped cream, just a bit more airy, that literally melts in your mouth. It is so good – I just want to eat it all plain every time I make it as a popsicle base. And I imagine if you used a non-dairy milk it could be a pretty decent whipped cream substitute!
I hope you all stay healthy and have a great week 🙂
Rondel and Limerick are very different academic beings. Rondel’s first love is stories – he tells them, he listens to them, he invents them, he demands them, he constantly (since before he could talk) brings us books so he can hear their stories too. He soaks up facts about animals, and then populates his worlds with monsters generated from conglomerations of the different animals he loves. Limerick, on the other hand, has always been intrigued by symbols and patterns. He knew all (and could write most) of the letters and numbers by 18 months, spent a good 6 months nearly inseparable from a Duplo pattern board he created, and currently puts a lot of energy each day into creating symmetrical designs and exploring the world of numbers.
When we introduced Cuisenaire rods (a really great math manipulative, by the way – I grew up using these with the Miquon math curriculum and have always felt that they gave me a strong conceptual foundation in mathematics) for the first time this week in preparation for more kindergarten-type activities, this difference in their inclinations was immediately evident.
Limerick went through each color rod, noticing how long each one was as compared to the small white unit blocks. When he reached the longest rod, he began to line up the smaller rods next to it, to see how he could split it up. Ten is ten groups of one, he realized, and five groups of two, but when you try to split it into groups of three you end up with one empty space.
We made squares (one group of one, two groups of two, three groups of three, etc.) and talked about the difference between the perimeter of a shape (how long all the edges are, put together) and its area (how many white unit squares could fit inside it).
Meanwhile, Rondel was using different sizes and color of blocks to retell the story of the Three Little Pigs with house-building fleas and a predatory lion (I think he chose fleas because they are too small to see, and he didn’t have any prey animal toys on hand to use with the lion figurine). He went through all the steps of the story with sound effects and drama, creating and destroying as necessary, completely immersed in his imagined world.
When the boys play together, I see these inherent differences leading to growth in each of them. Rondel’s love of imagination draws Limerick along with him into wildly creative and unrealistic pretend games, while Limerick’s fascination with numbers and patterns motivates Rondel to learn the vocabulary and concepts of math also. It makes me glad all over again that they have each other to grow up with.
So what are we learning, this Wednesday? We are learning about how numbers work together, how they split apart and recombine in consistent ways. We are learning about the trial and error it takes to finally build a house that can keep out a powerful lion. And we are learning about each other, and how we can help each other learn in grow in different ways.
Sometimes it seems like there is a lot of pressure to do things for rather external and arbitrary reasons. Preparation for adulthood is a big one, for example – learn these math facts now so that you’ll be educated and prepared for your job as an adult; exercise and eat healthy now so that you’ll have better health when you’re older; practice a musical instrument as a child because you’ll regret not having done so when you’re older; and so on. Of course, if you attempted to prepare for adulthood in every possible way (even limiting yourself to a single culture), you would lose your childhood and probably wouldn’t be able to cover everything anyway…
Happiness is another oft-cited reason, and an even more arbitrary one, as the things which lead to a fulfilled and happy life for one individual can be radically different than the elements that are necessary for another. There might be pressure to get married and start a family when a person honestly does not want children or is not ready for the commitment of marriage. There might be a push to get off social media as a sort of “spiritual refreshment” when a person struggles to connect with their friends and communities through other means, so that the lack of social media pushes them into isolation.
And worst of all are the cultural “shoulds” – the things that people thing you ought to do, just because they are considered normal, or aspirational, or “good.” You “should” read these books, or listen to that music, or study American history in junior high, or clean your house with only vinegar and baking soda, or live in the city to fight suburban sprawl, or live in the country and try to be self-sustaining, or ride your bike as much as possible, or eat only these types of food, or dress in these types of clothes – just because that is what everyone else, in a large amorphous and vague blob, things you should do.
I’m trying to keep my kids sheltered from these “shoulds” for as long as I can.
I want them to be free from that pressure long enough to gain confidence in who they are and in how they process the world.
I want them to have the time and space to form their own goals, to explore their own interests, to decide what path makes the most sense for themselves, and to develop their own motivation.
I don’t want them to be so exhausted from trying to live up to everyone else’s expectations that they have no margin left to imagine a future of their own choosing.
I don’t want them to feel self-conscious about the judgment of others when they take a step backwards, or make a mistake, or pause to observe and analyze their course – the “shoulds” of perfection and speed are powerful and deadly.
And whatever their goal might be – if it is finding a perch to sit on to study the world in its beauty and complexity, or taking a flying leap for the rush and satisfaction of a challenge overcome, or some path that never even occurred to me before they charted their course – I hope that they continue to live free and wild and bold and uniquely themselves, whether they accomplish that goal or not.
(Images are of Limerick playing on a spiderweb-type piece of playground equipment. In each image he is a bit more confident in his body language. In the second-to-last image he sits on the corner looking away from the camera, choosing his next step; in the last image he is leaping from one step to the next, completely airborne.)
After eight years of working in a genomics research center, I’ll be transitioning to being a stay-at-home parent a week from now. Technically I’ll be working eight hours a week, in a sort of consultant role, which will keep me connected to the science – but it will still be a big change. It’s what I’ve been wanting ever since Rondel was born almost four years ago – but as it approaches, I find myself becoming more and more anxious.
I like my job, and I am good at my job. My supervisor respects me and my opinions; the researchers who rely on the services our facility provides respect me and my scientific knowledge and experience. I know what types of problems are most likely to arise, and I have tools and strategies for troubleshooting them. And I know that if I put in time, effort, and energy, I will have a successful outcome.
To be totally honest, I really like having the respect of other professionals whose opinion I value and who do innovative and important research. It gives me self-confidence: I may be a complete wreck if I have to call my doctor to schedule an appointment, but when I sit down with a researcher to discuss their experiment and figure out the best plan for them to take moving forward, I am completely at ease. It also gives me a sense of identity and self-definition: when acquaintances ask what I do, I can tell them about the science and feel that I’m doing something of worth, something that uses my talents and gifts, something beyond just staying at home and cleaning and cooking like any other person could do.
At the heart of my nervousness about the transition, then, I think, is a fear of losing that respect and identity – of becoming part of the crowd, no one in particular, no one with any valuable skills or gifts to offer my community. When I spend time with other moms, I feel so inadequate in the areas they are gifted in: my home is rarely clean, laundry and meals happen on an as-needed basis rather than with planning, small talk eludes me, playdates terrify me, schedules and extra activities overwhelm me, my children are dirty and wild. My mind is usually lost in a book, or an idea, or a project, instead of focusing on the people around me. I say nothing and feel isolated, or I say too much and still never manage to connect with anyone else. I simply don’t have the skills that these other women have, and without them, I’m not sure where I can fit in or belong in the mom world (especially the homeschool mom world… those women are so organized that I give up just at the thought of trying to be like them).
In the workforce, in academia, where everyone is a bit weird and everyone is valued simply for the expertise they offer, I knew where I fit in and I knew how I could flourish.
In this new world, I’m afraid I won’t ever be able to flourish – and that in my lack of flourishing, I will stunt my children’s future as well.
I’m not going to let my fears make a decision for me, when I believe on principle that a self-directed education is ideal for children, and when I observe pragmatically the stress that a classroom environment would add to our family life. I’m going to choose to let my love for my family be the motivating factor here instead!
The boys – especially Rondel – have been deeply interested in dinosaurs for quite a long time now, and are beginning to branch out into animals of all types. It really began with the Planet Earth documentaries that I would put on for them during Aubade’s nap times, and has continued with a short series called Africa’s Deadliest that is just as overly dramatic as the name suggests but which contains some great footage of wild animals as well as a lot of scientific facts. When we found and caught a lizard (well, rescued it from a bowl it had fallen into, to be more accurate) not too long ago, he was entranced: he understood intuitively how to hold it gently and carefully, and let it climb all over him with no fear, and ended up playing with it for 45 minutes before releasing it so it could return to its natural habitat.
So I was not surprised when he asked to go to the zoo this week, nor when he actually showed in interest in seeing the animals instead of just the dinosaur exhibit and the splash pad! And it was a good day to go!
We did of course have to visit the dinosaurs:
Obviously we couldn’t observe any live, wild, natural animal life here – but we had some discussions about the different types of nests made by different dinosaurs (we compared the twig nest of the Citipati – a feathered broody dinosaur – to that of the Diabloceratops, which was too large to brood its eggs and most likely made a mud nest like a crocodile), as well as about how the different types of dinosaurs might react if they saw us!
From the dinosaur trail the bighorn sheep exhibit is also visible, and Aubade got very excited when I pointed them out and told the kids what they were. She leaned forward in the stroller as far as she could, waving and yelling, “Hi!” – and then she turned to me, smiled, and matter-of-factly said, “Baa!” It was neat seeing her make the connection between the distant animal on the mountainside and the fuzzy white blob in her Moo, Baa, La La La board book by Sandra Boynton.
When we left the dinosaur trail, it seemed like a lot of the animals were active and awake – we got to see baboon, mandrills, oryx, cheetah (unfortunately they were difficult to see, but we did manage to spot them), otters, flamingos, zebras, and more! The flamingos were standing right by the fence, so we stood on one leg like they did, and noticed how they could turn their heads all the way around backwards to use their back like a pillow, and wondered why their large beaks only ever opened a very small amount.
Per Rondel’s request, after a cool-down break at the splash pad we visited the Tropical Birds trail, which includes a small aviary. Apparently, it is mating season at the zoo – so all the birds were awake and showing off their finery! The male peacock had his full tail fan extended, and kept shaking it at the peahen, making a surprisingly loud rattling noise when he did so. In the aviary, the male argus pheasant was strutting around on the path, making a call that the zoo keeper told us he only made during this season, instead of hiding in the back corners as he tends to do the rest of the year.
Rondel was absolutely captivated. He approached the bird slowly and quietly, and held his hands tightly back so he wouldn’t accidentally touch it (he would jump out of the way if the bird turned around so that he wouldn’t end up touching his long tail feather!), and just squatted down gazing at him for a long time, as other groups of people came and went.
Limerick was a little less certain, but he eventually went over as well. I was super proud of both of them – they are often very impulsive and active kids, and they had no trouble at all adjusting their behavior to what was needed by the animals. We talked a bit here about how a lot of viruses can jump between birds and people, so if we touched the birds we could get them sick or they could get us sick… my molecular biology background always ends up showing itself somehow 🙂
We finished up with the tiger and the Komodo dragon. I had never actually seen the Komodo dragon exhibit at our zoo, but Rondel instantly remembered them from the new Planet Earth series and was incredibly excited about them. They weren’t moving much – just soaking in the sun – but they are impressive creatures. We noticed how it was basking in the sun to soak up the energy it needs as a cold-blooded animal, and counted its claws (five on each foot, just like us, in case you wondered).
And of course we played on the Komodo dragon statue for a while!
The most wonderful thing about homeschooling is the ability we have to follow our interests – obviously in going to the zoo for a whole morning instead of adhering to a lesson plan or a class schedule, but also in deciding when to linger at an exhibit and when to move on, when to talk about the details of how an animal lives and when to stick to the basic overview, when to focus on the live animal exhibits and when to simply just have fun. The experience we had today was so real and so rich that I wouldn’t trade it for any classroom I’ve ever known.
What is the goal of education? Or, for that matter, what is the goal of parenthood? Is our aim to shape the children in our care into a certain type of person, to give them specific skills, to qualify them for certain careers, to prepare them for expected circumstances? Do we envision their future selves as the complete products toward which we are currently laboring, and the ends which justify all the unpleasant activities we must force upon them in their childhoods?
Or do we see our role as parents and educators to be one of providing opportunities to explore and grow, while allowing our children to choose the direction, rate, and nature of that growth? Are they like plants which we tend with loving care – providing soil, water, and space to flourish – but over which, ultimately, we have no true control? I remember one year planting peas, all in a row in a single garden bed; I watered them and fertilized them synchronously, and yet some sprouted days before their neighbors, and some grew to twice the height of others, lanky stems reaching up to the sky much farther in between each set of leaves and tiny tendrils. Nothing I did caused or could have eliminated the differences between those plants (though I certainly could have affected their development negatively by forgetting to water them, in which case the height difference may not have been so noticeable…).
Perhaps it is the same way with children. Some will shoot out intellectually, reaching with insatiable desire towards the skies of knowledge and academic learning, constant thirst for the sunlight of information driving them onward. We could stunt that growth by neglect or empower it by attention, but we cannot create (and can only with great difficulty destroy) the passion that motivates it. Others may grow in more embodied ways, developing craftsmanship and skill in professions such as music, art, or manual trades, and pursuing the creation of tangible beauty rather than the acquisition of knowledge. While we can offer the opportunity to learn those skills to all children, not all will desire to hone them to mastery, and it is most likely counterproductive to attempt to force it.
The knowledge and skills that align with a child’s natural talents and inclinations will be the easiest for them to develop, as well as the ones most likely to bring them joy and success throughout their lives – regardless of how “one-sided” it may make them appear now.
We may fear that, if children are allowed to choose the direction of their learning, they may choose incorrectly.
Does a tree choose the wrong place to grow a branch?
Does the blackberry bush extend its vines the wrong way?
To paraphrase C. S. Lewis (I believe from Mere Christianity), the tree and the bush are following the rules of their nature and are not wrong or incorrect in doing so, although they may be quite inconvenient indeed for us!
And while it is quite fine to trim back a plant for the sake of our comfort and convenience, it is not at all fine to trim back the growth of another person for the sake of our own convenience. Providing a trellis to support their growth is one thing; stunting or restricting that growth simply because it doesn’t fit our idea of what their growth should look like is quite another.
Children are human too, after all. And humans, we believe, in fundamental democratic terms, are entitled to life, liberty, and the pursuit of happiness (always being aware of how our actions infringe upon the rights of others, of course).
Coercive education – forcing a child to learn something in which he has no interest, for no purpose at all except the nebulous expectations of adult society, at the expense of time and energy that could have been devoted to the unique and explorative learning that his heart desires – seems to me to be quite far from those exalted human rights.
We can attempt to control, and set ourselves and our children up for disappointment, failure, and bitterness – or we can let our children provide the directing and motivating force while we provide the rich and nourishing environment in which they can flourish in beauty and individuality. We can give them the gifts of freedom, acceptance, and support, and marvel at the different ways they blossom before our wondering eyes.