learning – little thoughts

sqt

small things that keep going even when the big things are broken and scary

Posted on 2020-06-04 by kristinabean

So, our country is going through some tough things right now, and my prayer is that greater equity and justice will come from it, that wrongs will be set right. It’s yet another evidence of the brokenness of our world, coming on the heels of a pandemic and mass unemployment. But for today, here, I’m going to focus instead on the small pieces of beauty and growth and happiness that are like gifts in each new day. And maybe God will give me meaningful words to address those bigger issues another day; right now, everything I try to say sounds so empty.

Our corn is really taking off! This is my first time growing corn, so while I’ve seen it in fields before I’ve never really paid attention to all the stages of its growth. For instance, I’ve never before seen those tall, willowy flowers that bloom before the ears form, or gotten to watch the ears slowly grow plumper within their husks. They also make a good barrier to hide behind when having water gun battles with the kids…

The bed that doesn’t contain any Three Sisters planting (corn, beans, and squash) was intended for tomatoes and peppers and potentially peanuts but has been completely taken over by volunteer sweet potatoes from last year! Last year’s harvest was disappointing, but I think I am better informed now so hopefully this crop does better.
Even if the sweet potatoes themselves don’t fill out well, I’m going to try to make better use of the leaves this year. They have a very mild flavor – akin to spinach – and a slightly firmer texture. I think they’d be good in curry, to be honest, and Limerick invented an amazing green smoothie with them just the other day by combining them with frozen mango, frozen banana, and apple juice.
Limerick also discovered fractals and tessellation in the past couple weeks, and has been trying to build models of them with all the various pattern/construction toys we have around. And then whenever possible he turns them into rocket launchers, with progressively larger fractal rockets 🙂

He also got to help Paul change the oil in the family car, scooting under the engine block to see the oil cap and filter and looking in from the top to check the oil levels (and help identify a cracked part elsewhere on the engine…). He’s starting to show interest in learning practical skills by doing things together with us, which is just awesome for so many reasons (not least of which is the enjoyment of time spent together making something useful).

Rondel, by contrast, has been so absorbed in the world of fantasy and imagination. He’s trying to build every Lego set we have so that he can set up a gigantic battle between them; he’s acting out stories with kings and queens and princesses and princes and good guys and bad guys and extremely dramatic climactic moments; all of his toys have some role to play in the ongoing narrative he creates. He begs me to read more and more of the chapter books we’ve been tearing through, so he can soak up the story, and his own reading ability has been increasing rapidly as well. It is so much fun to listen to all the adventures he comes up with!
So, when we made bendy people earlier this week, it’s not surprising that the first one he requested was a king! (I later made a sword for him as well). Aubade asked for a princess (she is so obsessed with princesses right now), and I also made a grandma for her and an evil queen (not pictured) for Rondel since his king needed an antagonist. I used these instructions from The Enchanted Tree, although the beads I had available for the heads were quite a bit smaller than theirs. While they used embroidery floss for wrapping the dolls’ bodies, I found that yarn worked just as well, as did a strange metallic gold string I have around that is a complete disaster for just about anything else. My sister returned our bag of pipecleaners and my mom is bringing up her hoard of yarn remnants, so I’m expecting a new round of bendy people to join us soon!

Head over to This Ain’t the Lyceum today for the link up!

learning together: infinite series

Posted on 2020-03-302020-03-28 by kristinabean

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!

learning together

learning together: biomes

Posted on 2020-01-292020-01-28 by kristinabean

While the kids were playing together, I set up an activity for the next lull in their imagination. Pulling out two of our giant whiteboards, I quartered them and placed a biome card (from our Waseca materials) into each of the eight sections: Oceans, Wetlands, Tropical Forests, Temperate Forests, Grasslands, Desert, Mountains, Polar Regions. Pulling out the box of toy animals, I began sorting them into the biomes: zebras in Grasslands, tigers in Tropical forests, dolphins in Oceans.

It wasn’t long before Rondel came out and was instantly engaged, asking if he could help sort the animals. So we sorted together, talking about which biomes would make the most sense for animals which are domesticated, for example, or adapted for a range of habitats. When we had at least a few animals in each biome, I brought out the biome question and answer cards.

There were six questions altogether (asking about temperature, moisture, soil, plants, animals, and humans), and each one had an answer for each biome, so Rondel’s task was to match each answer to the correct biome after I read the card. He only needed help on one or two of the cards, and showed a good conceptual understanding of how the environment differs between biomes, how plants and animals have adapted to different biomes, and how humans have interacted with biomes in different ways (both positive and negative).

The pictures show the animal question and answer cards; I thought that matched best with the animals in their biome quadrants! You may notice Rondel added some people to the biomes also, and split the polar animals into Arctic and Antarctic subsets 🙂

I noticed that our animal representation was heavily skewed towards African grasslands and oceans; the Waseca teacher’s guide recommended using animals cutout from magazines, which would increase the diversity, but I didn’t have any that I was willing to cut up. I may just need to buy a big batch of old National Geographics or ZooBooks off of Ebay – old magazines can be really useful craft and learning supplies!

This activity was a good summary of the information we’ve learned about biomes as well as a good overview before diving into more detail on any one area; I think we’ll explore animal adaptations next but I have a lot of ideas.

family life, sqt, wwlw

{sqt} – because limerick loves numbers

Posted on 2019-03-152019-03-15 by kristinabean

If you ask him, Limerick will tell you that his favorite thing in the whole world is numbers. More than milk, more than cookies, more than hugs – numbers are the best. So I thought I would capture seven ways he shows that love for this week’s {SQT}! Join Kelly for the rest of the linkup 🙂

Limerick’s favorite numbers of all are 1, 11, 111, and so on – anything that is all 1’s. So the other day as we were skip-counting back and forth together the way we do, he decided we should count by 11. When he got to 1111 (and he was the one who got to say it!), he was so happy that he stood up on his chair and clapped his hands together while laughing for joy.
This past week he’s been asking me to make number coloring pages for him, where I’ll draw the outlines of numbers on a page and he’ll color them in. Well, for one of those pages, he decided the best way to color them in would be to fill all the little spaces with smaller versions of the number he was coloring – very meta 🙂
Limerick’s coloring page – don’t be too critical of his handwriting! He is only 4 after all 🙂
In addition to coloring numbers, Limerick likes me to make skip-counting number boards for him – this week alone we’ve made one that counted by 499, one that counted by 999, one that counted by 4, and one that counted by 1 but had all the multiples of 3 drawn in a different color. After a board is made we’ll play a game with it once or twice but then it is on to the next one! I sometimes think he just likes watching the numbers appear on the paper as I write them…
Speaking of watching numbers, Limerick’s favorite book, You Can Count On Monsters by Richard Schwartz, gives him plenty of chances to do just that. He will sit for hours poring over every page of the book, noticing how the focal number of each page breaks down into its factors and figuring out how the accompanying monster illustration incorporates those factors (or the number itself, if it is prime). He’s been through it at least three times this week, taking 2-3 hours each time, and it doesn’t seem to be growing old yet.
I pulled out a math workbook for Limerick this week also, thinking he might be interested, and so far he has just been turning the pages looking at all the numbers and math problems and shapes. He isn’t interested in writing anything down, but when I ask him about any of the problems he knows the answer instantly, or knows how to figure it out. There are some fractions later in the book that would be more of a challenge for him, though, so maybe that will catch his attention eventually. It’s a bit of a tightrope balancing between guiding him towards new information and allowing him the joy of freely exploring numbers without pushing or interfering.
I did, however, get to explain different base systems to him this week! I just sat down at the table and started counting in hexadecimal on a piece of paper, and he glanced over and was immediately intrigued. We discussed what place value means in the context of the various base systems, and ended up writing out 1-32 in decimal, hexadecimal, binary, and base 6. I think binary was his favorite because there were so many 1’s and the numbers got long so quickly!
One other fun book we’ve read through a few times (though not as recently) is Bedtime Math by Laura Overdeck. It’s been a great introduction to the application of numbers, and a challenge for Limerick to translate the words into the more familiar arithmetic. He’s actually quite good at tracking along with the question as I read it, deciphering the logical connections, and doing the math in his head – he can for most of the stories do even the most difficult problem on the page already!

All in all, I just have to echo Limerick and say that he really does love numbers the best 🙂 And he has, honestly, since he was 18 months old and would sit on the driveway drawing them in wide circles around himself until he was familiar with each one, and since he was 2 years old and would count the bites remaining on his plate at dinner and practice subtracting them as he ate. I’m looking forward to watching this love continue to grow with him in the years to come!

family life, musings

social learning through play

Posted on 2019-02-182019-02-18 by kristinabean

When I first read Peter Gray’s Free to Learn a couple years ago, I was struck by his descriptions of young children playing together. In the interactions he transcribed, these children were negotiating social hierarchies, defining relationships, experimenting with emotional expression and response, making small talk, and learning to understand the thoughts and feelings of other individuals – all through the context of undirected, independent, imaginative play with each other.

At the time I was both impressed and discouraged: impressed at the ability of the human mind to use pretend play as a means of acquiring important social skills, and discouraged at the thought that I hadn’t yet seen my son engage in pretend play with another child in that way. He could parallel play with his baby brother, and that was about it; other children overwhelmed and even frightened him.

But lately I have watched him playing with Limerick, roaring and yelling and screaming at each other, and when I cautiously peek around the corner they quickly assure me that it’s all part of the game, and their characters are angry, not actually them. Their pretend animals ask each other if they can come in, or share space, or help with something difficult. The boys ask each other, outside of the game, about what they are each comfortable with and what the other one’s preference would be for the kind of game they play, back and forth until they reach a compromise.

I have watched him playing with Aubade, laughing and wrestling and generally being silly, until suddenly she pretends to be sad with a pouty frown and a slump of her shoulders, proclaiming that she is sad, and he instantly changes his mood to match her emotional expression, curling up next to her to give her snuggles until she decides she is happy again.

While his understanding of other people’s emotions may not be as intuitive, and while social norms and niceties may always be more of a second language, he still has the innate desire to connect and belong with others. And so with the people he loves, he works hard to understand them, to compromise with them, to adapt to their wants and feelings. We’ve done a lot of “play coaching” with him and his siblings over the years, to get to this point, but now, every time I see him bend and adjust, every time I hear him ask what his siblings would rather do instead of demanding things go his way, I am so encouraged by how much he has learned, and by how much he can do without any adult around reminding him. Those hours of play have really been effective in helping him pick up and hone his budding social skills – and I have no doubt they will continue to be.

book lists, family life, information, wwlw

what we’re learning wednesday: episode 6

Posted on 2018-08-292018-08-28 by kristinabean

Due to his love of rain and his constant desire to know exactly when things are going to happen, Rondel has begun to ask me questions about the weather constantly. And because I never properly learned about the weather to begin with, there wasn’t much I could tell him.

So we did what we always do when faced with a topic of ignorance and armed with a thirst for knowledge: we went to the library and came home with books!

There are surprisingly few books about clouds, and no books that I could find at our library specifically about Arizona or desert weather, at least not at my kids’ comprehension level. But these three are not bad, and we’ve learned a lot from them.

Look at the Weather, by Britta Teckentrup, is a beautiful, artistic book, filled with gorgeous atmospheric drawings, leading questions and statements about the personal impact of weather, and interesting scientific facts about weather. Each page tends to have only a few sentences, so although the book is very thick it doesn’t take nearly as long to read as one might expect. It will walk you through the build-up to a storm, for instance, painting the gradual accumulation of clouds slowly, until you almost feel the tension of it around it. But it will also give you tidbits of very fascinating information – I never knew how hail was formed until Teckentrup explained it here, for example!

The Man Who Named The Clouds, by Julie Hannah and Joan Holub, is really more of a biography of Luke Howard, the man who invented the precursor to our current scientific classification system for clouds, than a book actually about clouds – but there is a serious amount of scientific information included. I particularly appreciated the diagram towards the end of the book illustrating the current cloud classification system, and we’ve been attempting to classify the clouds we see when we are out and about each day (we saw mostly cirrus clouds today; Rondel is holding out hope for some cumulonimbus clouds since they are the type of rain clouds we typically get with the monsoons!). Overall this book was a bit above the boys’ heads, and not completely aligned with their area of interest, but by skimming and omitting while I was reading it aloud we managed to get a lot out of it anyways. On a second read through I will probably include more, depending on how it seems to be holding their attention.

Clouds, by Anne Rockwell, is probably the book best-suited for answering Rondel’s questions about clouds at his level. But I haven’t read it with him yet! We’ve been distracted with the other books, and he’s caught the virus the rest of us have been passing around so we’ve been a bit preoccupied with that. This book also has instructions at the end for creating a small cloud in a jar, and I’m looking forward to doing that with the boys. From reading the book on my own, this should reinforce the information we gleaned from The Man Who Named The Clouds, and be a short, easy way to soak up more weather-related knowledge. The Let’s-Read-And-Find-Out series, of which this is a part, has been in my experience a good source of basic knowledge on any science topic we happen to have questions about.

While we continue enjoy these books, I’m going to continue searching for books about our local weather; we live in a fairly unique ecosystem, and I’d love to learn more about the weather patterns and seasonal changes specific to the Sonoran Desert. Please let me know if you have a good resource on this!

(And if you were curious about how hail is formed, here is what Britta Teckentrup has to say:

“Hail is caused when the wind sweeps raindrops up into higher, cooler parts of a cloud before they get a chance to fall. They freeze in the cold air. When the ice droplets begin to fall, sometimes the wind catches them and sweeps them to the top of the cloud again. They can cycle up and down inside the cloud several times, adding layers of water and ice as they go.

“Eventually, the ice balls become too heavy for the wind to carry upward, and they fall as hail.”

So the stronger the wind, the bigger the hail can get! Now I understand why we typically only see hail in our craziest, most intense storms – only they have strong enough winds to lead to the formation of hail.)

wwlw

what we’re learning wednesday: episode 4

Posted on 2018-08-152018-08-11 by kristinabean

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.

family life, musings, quotes

wonder

Posted on 2018-05-162018-05-16 by kristinabean

Watching my children play, I am reminded of the wonder and beauty of small and simple things. There is enough joy in a glass of milk to send a three year old dancing around the kitchen; there is enough beauty in a well-done coloring page to keep a distractible, active four year old still and entranced watching it happen; there is enough passion in a stuffed animal to occupy the full attention and imagination of the one year old who walk around snuggling and protecting it. Continue reading “wonder” →

family life

going to the zoo!

Posted on 2018-03-132018-03-14 by kristinabean

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!

This is what I get when I tell the kids to smile at me… I guess Rondel is somewhat close?

Playing together – I think they are subduing the Komodo dragon so it can’t fight them.

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.

musings

freedom in learning

Posted on 2018-01-082018-01-02 by kristinabean

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?

Hardly.

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.