# Hidden in plain sight

I was doing a math moment with the kiddos at Ethel Streit this week. We have a couple who have had negative experiences with math, some who have only experienced math in traditional public school settings, and some who are quite gifted in mathematical thinking but have little facility with math facts or algorithms. To try to set the stage for the idea that we all explore big math ideas together, I made a “simple” drawing on the whiteboard:

I asked the kids how many squares there were.

The answers were immediate: 9. No, wait! 10! As the kids were thinking, I heard L say”9 times 5…?” I have to admit: I had no idea what she was talking about. She tried to explain to me that there were 9 on top and 9 on the right and 9 on the bottom and 9 on the left. She said that wasn’t quite it, and I chose to move on.

Eventually, the kids figured out there were 14 squares (for those of you following along at home, that’s 9 1×1 squares, 4 2×2 squares, and 1 3×3 square).

L piped up again with “times 5?”

I still had no idea what she was talking about. Luckily, my incredible co-teacher, Sara, looked at L and asked if she meant like a cube. Yes! L’s face lit up. She explained that we had only counted the squares we could see, not all the ones we couldn’t see. She was seeing the visible squares as the front-facing side of a 3-D cube…

I didn’t want to lose the other kids, so I decided to stick a pin in that idea. I told L we would talk more about that later, erased the drawing, put up a set of triangles, and moved on with the lesson. L clarified, “We should only count the triangles we see, right?” Right!

A trickier picture with triangles – we found 48. How many can you find?

On the way home, L piped up again. “It’s not times 5! It’s times 6!” She had realized that you had to count the squares on the face you COULD see in addition to those on the faces you couldn’t. I realized that clearly, L wasn’t done with this yet.

When we got home, I printed and cut out a cube net.While I was doing that in the office, I gave her a piece of scratch paper and asked her to represent what she meant mathematically. This is what she created:

I then gave L the cube to represent her work in three dimensions. She asked me to draw the 3×3 grid on each face and then proceeded to complete her calculations.

She began by counting each small square, realizing that her total was 54. I had her check using multiplication to see that 9×6 is 54.

She then said, “But there are 14×6 squares,” remembering that we had found 14 on each side. I gave her a high five and we decided to multiply it out to find the total. We broke 14 into 10 and 4, giving us two problems: 10×6 and 4×6. She immediately knew that 10×6=60. 4×6 was harder for her. She did know that 4×2=8, so we used that fact three times to compose 4×6=24. We then joined the 60 with the 24 to learn that there were 84 squares on the six faces. There are our written notes from the process:

Because L is L, though, we weren’t done yet. She wanted to figure out how to build the cube out of smaller cubes. As she was considering the build, she gasped, “The cubes are all hidden in plain sight!” When I was done laughing, I told her she was right.

We pulled out Cuisenaire Rods to build. I wouldn’t usually use cuisenaire rods for this build, but we had recently taken our base ten blocks into the school and I could tell we needed to do this build right now. I was particularly aware of the fact that we don’t have 27 1-unit rods. I decided to let it ride, though, and see what she did with it.

L began to construct a 3×3 base out of the 1-unit cubes. I went outside to collect cherry tomatoes from the garden (yes, the garden is still crazily producing). L ran up to me and said, “I don’t have enough cubes!” I said, “Oh.” As I was thinking of what to say, she spurted out, “But it’s ok! I can get one that’s 3 long and use it in place of three ones!” She turned around and ran into the house. Ok. I thought. She’s got a plan.

I came back in to find her build complete.

As she began to figure out how many 1×1 cubes were in the whole cube, I kept quiet and watched. She sorted the white cubes from the purple rods. There were 12 white cubes and 5 rods. She counted the white cubes one by one, moving them over as she counted them. When she got to 12, she began touching the first purple rod. She touched it on the end, the middle, and the other end as she counted, “13, 14, 15.” She moved that rod over with the white cubes and repeated the same process until she got to 27 as her sum.

The look of pride on her face was palpable. I loved that this was all self-driven and to solve a question that she had been puzzling over. She’s also been talking about the math on the board and the cube daily since then. Hidden in plain sight, indeed!

# Calming us down

Transitions bring such uncertainty for L. I sometimes forget that she doesn’t have the coping skills of a much older kiddo since she sometimes thinks like a much older kiddo.

This week, she started attending a micro-school that I’m heavily involved with. In fact, as a major part of my service and scholarship work in my teacher education world, I’ll be teaching at the school two days a week. We’ve been very busy this back-to-school season, getting handsome husband ready to go back to his middle grades classroom while he takes on earning an additional teacher certification this year, me preparing my work at the university, me working to set up the micro-school environment, and L preparing to enter a school-type environment. Whew! No wonder we’ve had takeout for dinner a few times recently.

In any case, L has BIG FEELINGS. She always has them, but they really build up in times of transition. These days, she’s really capable when it comes to using her words to express them – 9 times out of 10. The tenth time is around a transition and she uses her body to express her feelings. Huge sobbing screams, stomping, slamming things, slamming her door, etc. The storm is fierce, but as soon as it’s past (usually within an hour), she dries her tears, climbs up for a snuggle, and is ready to move on with her day.

Those storms happened more when she was younger, though, and I often found myself reminding myself that my work during those storms was simply to be there. It wasn’t time to have a conversation (my default mode) or try to fix things. It’s was just to be there. And when the storm passed, I have, for four years now, grabbed this book and read it to her.

When she was 2, we happened upon this book at a local bookstore. I remember my children’s literature professor telling us that as we were building our classroom libraries, if we ever saw anything by Mem Fox, we should grab it. Well, this was by Mem Fox, and I had a coupon!

I didn’t even skim it at the store. I simply grabbed it, paid for it with our other items, and when we happened to grab it as a bedtime story, read it.

The story is simple: Harriet is the girl in the story, and she doesn’t mean to be a pesky child. She just is. She drips jam everywhere, gets paint on the rug, pulls the tablecloth off because she’s sitting upside down at the table, etc. All morning, her mother greets her various “misdeeds” with love, commenting that she doesn’t like to yell and adding a line each time until her refrain is

Harriet, my darling child

Harriet, you’ll drive me wild

Harriet sweetheart, what are we to do?

Harriet Harris, I’m talking to you

And then at naptime, Harriet’s mother breaks. Harriet and the dog make a terrible mess and Harriet’s mom finally yells. Harriet cries. Harriet’s mother regains her composure, apologizes to Harriet for yelling, and the two of them make peace.

Um, hello? Did the universe know I needed this book or what????

We have literally snuggled and read this book hundreds of times. Sometimes just because and lots of times because I needed L to know that all kiddos can be “pesky” sometimes and their mothers still love them. Because I needed to remind myself that yelling once doesn’t make me a bad mom and that L’s behavior is exactly what it should be: a child’s.

In short, if you don’t have this book yet, I can’t recommend it highly enough. We’ve had to pull it back out again this past few weeks.

And when I found a copy of it for the micro-school classroom, you can imagine how much joy it brought me!

Bonus picture of L in her natural environment as a reward to those who made it to the bottom of the post =)

# This is not what I planted!

Two winters ago, we moved to a highly-ranked school district in the hopes that L would be able to attend their schools, grades 1-12, receive a well-rounded education, and thrive.

Those of you who have been following us for awhile, feel free to resume reading when you’re done laughing.

The reasons the school didn’t work for L are complex and have much to do with her wiring and only a bit to do with any individuals. Regardless, our experiences with formalized K-12 school settings led us to homeschooling, and thus to blogging, and thus…

Last summer, we didn’t do a whole lot of gardening because we were still tending to the ‘deferred maintenance’ of the house we bought and moved into. This summer, though, we decided it was time to plant.

My handsome, hardworking husband cut the sod out of an 8′ by 24′ rectangle, enriched the soil with humus and our own compost, and laid a rock border. L and I started seeds indoors and moved them to the patio when the sun decided to spend more time with us. I laid out the blueprint for the garden, checking to see how far away from one another each plant needed to be, and in doing so, we realized that we needed another 8′ of garden. My handsome, hardworking husband cut an additional 8′ length of sod, enriched the soil with humus and our own compost, and moved and added to the rock border. Our garden dimensions this year were 8′ by 32′.

When the appointed day came, L and I used a measuring tape to lay out the garden and painstakingly planted our seedlings, using popsicle sticks with labels to indicate which plants were planted where. We planted corn, summer squash, cucumbers, carrots, radishes, peas, bell peppers, cherry and full-size tomatoes, eggplant, potatoes, and asparagus.

We waited. We watered. We used our most compassionate selves when the deer and/or bunnies ate the tops off of our sunflowers. We watched things grow.

About a month in, we realized that things that looked a lot like tomatoes were growing where we hadn’t planted tomatoes. And things that looked a lot like squash vines were growing everywhere. We pulled the obvious weeds, laughed, and went on with our lives.

We waited. We watered.

Our radishes paid off quickly. We pulled them from the soil with excitement, rinsed off the dirt, and bit into vegetables that proved that when you buy them from the store, radishes have a lot of time for their pepperiness to mellow!

We pulled carrots and ate them. The were oddly formed, but sweet.

We pulled pea pods off of the plants when we were weeding and watering, using their crisp freshness as a reward for working in the hot sun.

We noticed that those mysterious tomato-appearing plants really did look like tomatoes, so we just supported them with wire cages and moved on with our lives.

We noticed that those mysterious extra squash vines were doing just fine and appeared to be producing fruit, so we just kept the path clear for them and moved on with our lives.

Then the summer squash came. And it came, and came, and came. We have harvested upwards of 40 summer squash so far – and they’re still growing. We have become quite adept at using summer squash in a variety of applications. We also all have a good laugh at Kroger now when we see the tables of summer squash for sale. L has decided that we don’t ever need to buy summer squash EVER AGAIN.

We then noticed that those mysterious extra squash vines were, indeed, fruiting, but as those fruits developed, they sure didn’t look like summer squash. We let them go.

We continued to harvest summer squash. And we noticed that there were green tomatoes everywhere. Ridiculous amounts of green tomatoes. Dozens in each square foot. Dozens of square feet. Tomato-o-rama.

One day, it became obvious. One of the mystery squash fruits declared itself: I am an acorn squash, it said. I am green and teardrop-shaped with a pointed bottom. I am not a summer squash. Several others followed suit, and my handsome, hardworking husband and I were perplexed.

We didn’t plant acorn squash.

However, we read about when to harvest acorn squash, pulled them when it was time, and are thrilled to have them sitting on our shelves in the basement. What a treat it will be when, in winter, we can eat bonus squash from our garden.

Another day, it became obvious. Another one of the mystery squash fruits declared itself: I am a pumpkin, it said. My rotund green self is turning bright orange. I am not a summer squash, and I am not an acorn squash. Several others followed suit, and my handsome, hardworking husband and I were perplexed.

We didn’t plant pumpkins.

However, we read about when to harvest pumpkins, pulled them when it was time, and made delicious pumpkin butter from them. We have a few in the basement also, and we will be thrilled to eat them this fall.

And then, it became obvious. Another one of the mystery squash fruits declared itself: I am a butternut squash, it said. My oblong green self with the bulbous bottom is turning tan. I am not a summer squash, and I am not an acorn squash, and I am not a pumpkin. Several others followed suit, and my handsome, hardworking husband and I were at our wits end.

We didn’t plant butternut squash! We didn’t plant pumpkins! We didn’t plant acorn squash!

What on earth is going on here?

I was explaining all of this to a friend over brunch one morning, when the metaphorical lightning bolt hit me – THE COMPOST!

We had been throwing all of our plant waste into it the previous summer and fall, and we’d certainly eaten butternut squash, pumpkins, and acorn squash. And come to think of it, we’d eaten a ton of tomatoes as well!

Our compost had seeded our garden the way it wanted, regardless of our plans. Some of the things we planted didn’t thrive. They dried out, or animals ate them, or they were crowded out by our bonus plants. We didn’t get to eat what we’d planned, but what we did get to eat was unexpected and delicious. Our plants didn’t even grow the way they were supposed to – check out this squash that thinks its a tomato!

And for those of you who have read long enough to make it to this part – and I appreciate you sticking with me – here’s why this post was important for me to make.

In my last blog post, I was totally freaking out. That same dear friend who I was talking to when the compost revelation occurred was talking to me about my total freak out. She listened lovingly when I said I was onboard with an unschooling approach for everything but math. She gently helped me see that I might not be onboard with the same approach for math, but that L might need that approach regardless of my comfort with it. She helped me to see that I can build persistence and challenge in other ways, like through swim, gymnastics, and authentic projects which L chooses to do and which also build executive functioning.

When I was harvesting in the garden today, it occurred to me that our garden is like schooling L. I might have plans. I might measure things and have expectations. As she has taught me repeatedly, and as I’m sure she will continue to teach me, those plans and measurements and expectations bear little resemblance to the learning that she needs. She will seed the garden with what she needs and the things that are meant to grow will grow. I can water and weed the garden, and I can figure out what supports the bonus plants need to thrive. It’s not my garden, though. It’s nature’s garden. Wild things cannot be controlled. They’re not meant to be controlled. They’re meant to be protected and supported and awed by.

I will continue to work on remembering that it is my job to protect and support and be awed by L’s learning, not to try to control it.

# I can’t keep up with my kid!

Why am I writing at 1:00 in the morning, you may ask? Midway through the first week of teaching classes at the university? Just a little freaking out, of course.

I’ve been really worried lately about how L will respond to what’s coming her way – her involvement with a micro-school designed for a handful of kiddos to work at their own pace. That part sounds great – the part I’m worried about is that I’ll be leading instruction there two days a week and she and I still haven’t figured out how to work together on a daily basis.

L doesn’t respond the way I anticipate a child will respond. Doesn’t matter what I incentivize her work with. Doesn’t matter what I attempt to use as consequences.

She will do what she will do when she wants to do it.

For the most part, I try to breathe deeply and trust that. It’s easy for me to do with reading, since she reads voraciously. Recently, I attempted to remind myself how to do running records by practicing on her. I downloaded some grade-leveled passages and sat down with her, asking her to read them out loud so I could practice taking running records. I anticipated that the second grade passage would be too easy and the third or fourth grade would be just about right.

Grade level Words per minute Accuracy Comprehension questions
2 102 98.6% 2/2 questions
3 69 (proper nouns were a struggle) 96% 2/2 questions
4 92 97% 2/2 questions
5 73 96% 2/2 questions
6 74 96% 1/2 questions

She turned 6 years old last month. So, yeah. I don’t worry about her reading. She is constantly lugging a book around (DK Eyewitness Books: Ocean and others in the series are a huge hit these days).

Her writing is a concern, for sure. She struggles with letter formation and isn’t drawn to production of text. I am playing around with cursive for her (which has been better than printing) as well as typing, but we don’t have a magic bullet yet.

I don’t worry about science. At all. She is constantly reading and watching videos and documentaries and conducting experiments. She’s probably most advanced in science, which is ironic given that I am not drawn to natural sciences. She came by that one all on her own!

Social studies? Well, I would have argued that she’s not interested in social studies, but I think I’ve been too narrow in what I defined as social studies. She knows where many countries are and what their flags are from looking at a map on her wall. Same for the states and the state flags. She was deeply interested in the American enslavement movement and Civil Rights era for awhile and read deeply on those topics. She has onboarded much of the events covered by the musical Hamilton and has enjoyed reading the lyrics and asking questions about them. She has also followed along with NPR coverage of the presidential election season and has explored the ideologies behind the Democratic and Republican parties, even going so far as to define herself as an “environmental one-issue voter.” So maybe that’s pretty good coverage of social studies at age 6?

## But math!

Anyway, this brings us all to math. Math is the source of today’s hijinks and is why I am still up (it’s almost 2 now, for those of you following along).

L has been “fighting” about math, pretty much always. Her fight is saying she doesn’t know how to do something or she’s bored. There was a great period early on when she used Todo Math (which she blew through but enjoyed), Slice Fractions (same) and Dreambox (which was new for awhile but she became bored with it). Even Beast Academy, the “go to” for elementary g&t kiddos, was interesting to her to read (she lugged books 3A-D as her bedtime reading for awhile), but she was never interested in the practice books.

And yet, we’re going to be working together in this micro-school, so I need her to be able to sustain work in math. I grabbed a couple of story problems from a third grade problem set and gave them to her as today’s work.

Let me be clear: I was at work and she was in my office with me. My attention was clearly divided and I couldn’t reinforce to her that she should continue working. However, she essentially didn’t do anything for long enough that I gave up. I decided that the battle wasn’t worth it today, that I needed to get a bit of my work done, and that we would try again tomorrow.

However, after school, she was fighting my husband as well, and he decided that she was going to work through these 6 problems because, well, sometimes you need to listen to your parents.

So she sat down and figured out the answers to all six problems. Most of them in her head.

Sample 1: There are 2,532 students at a school. 1,312 of them are girls. How many of the students are boys?

She picked up her pencil and wrote down 1,220. Didn’t write the problem out. Didn’t use manipulatives. Nothing.

Sample 2: Mom has 11 apples. She needs 5 apples to make 1 pie. She wants to make 5 pies. How many more apples does she need?

She circled the words “5 pies” and wrote out “25-11=14”.

I posted about this on my favorite facebook group and another mom suggested that maybe she is bored. Her kiddo presented with “it’s too hard” when it was really boredom.

Bored? No! She couldn’t possibly be bored! She is just now 6 and has had almost no formal math instruction. It’s all been picked up through apps and occasional problem-based lessons. And I pulled those from a third-grade book.  When she got bored with Dreambox last year, she was 84% finished with second grade.

Seriously?!?!

## The freakout

How am I supposed to stay ahead of this kid? I feel like every time I have an idea of where she is, I turn around and she’s past it. I have felt that way for three years now.

I think I’ve made significant progress in changing how I think about education as it relates to L. Instead of thinking of myself as a teacher who sets out the path, I think of myself as an intense kid watcher. I watch her for emerging interests and skills and then scour the world for the most appropriate resources, which I place in her path in the most time-efficient manner I can manage. She is thus constantly picking up high-quality, high-interest materials and, since I know her pretty well, they’re typically in alignment with her interests. I don’t lead her down a path. I don’t even walk next to her on the path. I walk behind her on the path and slip goodies onto the path, hoping not to be seen.

But I’m at a loss here.

I don’t even know how to assess her appropriately to figure out where she is mathematically. I don’t know what curriculum to turn to. I don’t know how far off my estimate of her progress is.

I was re-reading an article about the opportunities the internet allows for gifted kiddos. The article refers to the Art of Problem Solving, a name I’d certainly heard bandied about (and the middle- and high-school wing of the Beast Academy company).

Tonight, I checked the diagnostic test to see if she’s ready for their first class – prealgebra (for students who have completed elementary math – grades 5/6). To be clear, I know she wouldn’t pass all of it right now, because we haven’t talked about division. She could nail about half of it (basic arithmetic with negative numbers, addition and subtraction of fractions with same denominators, basic fraction comparison, and some of the word problems).

Dear me. She can nail about half of the assessment for the prealgebra class “specifically designed for high-performing math students”. And she’s 6. And we don’t really do math in a sustained way.

But I’m pretty sure that if I introduced division and decimals, she could be ready in a month or two.

And then I look back at the online prealgebra class schedule and it occurs to me: she can’t take this class anyway, because it goes past her bedtime! How ridiculous is that? A class that she could be ready for in a month or two that she can’t do in a month or two because she still goes to bed at 8 BECAUSE SHE’S 6 YEARS OLD!

And it hits me again. She is atypical. She is asychronous. I am so lucky to get to be her mom. It is so terrifying to be her mom. And I’ve simply got to get some sleep.

# February, you are a cruel, cruel month

It turns out February and Mr Burns have a lot in common. We’ve had a few great moments as homeschoolers and as a family, this month, but it’s mostly been a month where whatever our plans were, February decided to upend them.

We had house guests. Lovely, but disruptive to routine. Each of us, first Little, then husband, and now me, have been sick. Throw in a few holidays and the whole month is shot.

And extra day this month? Ha! Turns out Leap Year means that we’re going to leap over our routine this month. And I can kick and scream and worry about it (and believe me, I did), but not a damn thing is going to change.

I’ve had a fever for the past 72 hours.

Well played, February. Well played.

But March? Oh, I’m coming for you, March.

# Getting out of the way

Why is it so hard for me to learn some basic ideas?

Seriously. I’m pretty bright, generally speaking. Ask around. People will tell you I have many faults (and I’ll agree with most of them!). However, a lack of intellectual firepower and/or curiosity is not generally one of them.

And yet, I still can’t seem to remember one simple thing: L likes to do it herself!

Very early on, my handsome husband was attempting to transport L from one place to another. She replied in indignation, “No mommy carry you! No daddy carry you! L do. A-self!”

She likes to be independent.

I have previously written about how difficult it is to divorce myself from the processes and norms of school. As a former teacher and teacher educator, it is particularly hard for me to let go of the idea of gradual release of responsibility.

The basic idea behind gradual release of responsibility is that the teacher is the mentor in the classroom. As the resident expert in a given content area, it is the responsibility of the teacher to support the learner in their apprenticeship in that area. As a part of the apprenticeship, the mentor begins with heavy support and eventually, the balance shifts to the apprentice having the majority of the responsibility.

Another way to think about this model is that first, the teacher models the content. Then, the apprentice tries the content while the mentor giving hands-on with assistance. Finally, the apprentice is able to demonstrate mastery over the content.

This is such a great model. I believe in it strongly, particularly in my experience teaching middle grades in a workshop format. The only big problem? L hates it.

We get a monthly delivery of Tinkercrate. It’s a great hands-on, exploratory, all-in-one service. After looking closely at the different levels and formats the service offers, L decided she wanted the Tinker version, which is building and experimenting with projects. It’s advertised for children ages 9-16+. L’s hands aren’t particularly strong, so I suspected she would need support with some of the physical work.

Our delivery last month was the automaton.

L grabbed the crate out of the mail as soon as it arrived. We sat down and looked at the project, reading the first few pages of the guide. I told her there was a video on youtube, but she wasn’t interested in looking at the video. Instead, we pulled out the materials and got started.

By “and got started,” I mean that I asked her thoughtful questions and offered help as I thought she might need it. She replied with feigned helplessness.

She didn’t know how to pick something up. Or how to peel the backing off a sticker. She looked at me – no, through me – when I asked her questions. I felt my frustration growing, but knew that she needed me to help her, as I am the mentor and she is the apprentice.

I persisted with my helping. I am very persistent.

She persisted with being floppy and without ideas. She is very persistent.

An hour passed.

As far as she got with an hour of my help

I finally got so frustrated that I walked away. I told her, “L. I know that you know how to ask for help if you want it. I will be in the other room, reading my book and drinking coffee.” I then went in the other room, feeling quite smug. Ha! I showed her! She needs my help and soon she’ll come and ask me for it. Then, I will help her and things can proceed.

I was about 15 pages into my book when I happened to glance back into the kitchen.

She had completed about three-quarters of the project now that I had simply left her alone. I decided to walk over and refill my coffee, snapping the picture below.

As far as she got after 15 minutes of me leaving her alone

My own ego gets in the way of homeschooling (heck – of parenting!) on a pretty regular basis. I’m going to continue applying my intellect to the idea that I need to trust my child. If something is too hard, she’ll let me know. If she wants help (not needs it, but wants it), she’ll let me know. My expectations and routines are just that – my expectations and routines. It is my work to provide her with an environment that supports her inquiry and curiosity. Beyond that, it is my work to get out of the way.

If you need me, I’ll be in the other room, drinking coffee and reading my book.

# Faulty socialization and homeschooling

That’s usually the first question I hear in response to the information that we’re homeschooling, as I know it is for lots of other homeschooling parents.

There are lots of great posts about there on the subject of socialization, including passionate posts about what’s wrong with the school-based socialization in the first place, those sharing results of research on socialization of homeschoolers (both pro- and con-), reasons its hard to avoid socializing homeschooled kids, tips on how to find opportunities for socialization, and those embracing a lack of socialization as an advantage.

I’m not going to weigh in on any of these aspects of homeschooling. Frankly, the territory is well-covered.

Those who know us know that L is often out and among others – those younger than her, her age, and older than her. Those in multi-age groups. Those in formal lesson-based settings. Those in open-ended, creative settings. Weekly brunches. Daisy Girl Scouts. You get the idea. And anyone who is still concerned about our form homeschooling and socialization is likely not going to be convinced by anything I say here, anyway.

I want to explore a different perspective the problem of homeschooling and socialization.

The problem isn’t with L’s socialization. It’s with mine. It’s the extent to which my socialization gets in the way of homeschooling.

I attended traditional schools from primary school through earning a doctoral degree. I taught in middle schools. I teach teachers how to teach in schools. I am firmly socialized into the context of schools.

I am socialized into the idea that learning happens on a schedule, whether daily, weekly, thematically, or otherwise. The way I experienced school and enforced school on others, there were defined times for defined subjects. The time and schedule were the constant, with the learning as the variable. As a student in a class of 30, my individual needs and preferences weren’t the primary drivers of instructional planning (nor is it realistic for my child’s to be – particularly given how specific and different from the norms of school they are!).

I am socialized into the idea that a child’s grade matches their chronological age. I struggle with not knowing how to answer (or help L answer) when people ask what grade she’s in. Typically, we fumble around for a minute and then mumble something about her being 5 and homeschooled. People feel awkward enough at that point to let us off the hook, I think.

I am socialized into the idea that we must all achieve a set amount of learning in each subject in each year. I have no doubt that L will eventually even out in terms of her interests, and she learns quickly and easily enough that I don’t fear that she’ll reach college and be functionally illiterate in any subject. However, she’s simply not interested in social studies right now. My urge is to enforce pursuit of everything instead of trusting that my child has wide-ranging curiosity and that curiosity will lead her to in-depth understanding.

I am socialized into the idea that learning must produce something. Something that I can judge or grade or assess or whatever you want to call it. Today in co-op, there were a ton of great activities out for children to explore. Making an articulated hand from drinking straws. The book Stick Man complete with a huge pile of sticks and material and hot glue guns to make your own. 3-d construction with paper tubes. Painting sticks. Valentine’s mad-libs. Instead of trying any of them, L engaged in three hour-long open-ended play sessions. She spent significant time playing with Playmobil animals and creating an imagined reality. This time was partially alone and partially with other children. She created an open-ended set of creations with Duplos, an activity we have at home but she rarely gravitates toward. This was time mostly spent with other children. She pulled other children in a wagon and was pulled in turn by them. I heard lots of narration about the ocean and she sang songs constantly.

I laughed about it with some other moms, but I genuinely had to check my feelings that she should have been creating some products that we could then have as evidence of her learning. I know she learned a ton! I know that free play is essential for learning and there’s a strong link between free play, the development of social and emotional skills, and achievement. But I’ve been socialized to expect a product.

I am so lucky. As Karen Maezen Miller reminds us in my favorite parenting book (Mother Zen: Walking the Crooked Path of Motherhood),

“Your child is a tireless teacher, constantly probing your self-imposed limits boundaries, your self-centeredness, your sheer stubbornness. It is a thankless job, and who would want it? But each day your child comes to work again, taking up the monumental task.”

Thank you, L, for reminding me every day that my own socialization is simply that: the model I’ve internalized for what education ought to look like. There’s nothing inherently right or true or good about it. It’s not more natural or more effective or better than all the alternatives. It’s simply what I know. What I’ve learned and now believe to be true.

I am socialized to believe that as the adult, I teach, and as the child, L learns. I am so lucky to get to re-learn this relationship.

# MC Escher and tessellations: Where math meets art

In our ongoing quest to keep L engaged with math without necessarily pushing her through more and more abstract concepts. I still harbor fantasies of her going back to school at some point, and I worry that the growing disconnect between her age and her abilities is only going to make finding a fit harder. However, I want her to continue to push past the zone where things are easy and have to persist on some difficult tasks, too. She already struggles with shutting down if things don’t come instantly to her (or if she doesn’t do them “correctly”) so one of my goals for her educationally is to grapple with that which is just out of reach.

We recently completed a lesson in Beast Academy related to using polyominos to fill defined spaces. We’ve also been using pattern blocks in relation to our study of fractions, so it occurred to me that we could use pattern blocks to begin to explore tessellations.

A tessellation is a repeating pattern that has no overlap or gaps between the pieces. You can tessellate lots of shapes, but if you want to see how cool tessellations can be, you’ve got to check out the artwork of M.C. Escher.

I found a really cool link that shows how to make your own tessellating shape, but I knew that opening with that level of open-endedness was likely to freak L out. Instead, we started with our pattern blocks.

I took a cookie sheet and used washi tape to define a small (about 4″) square on the cookie sheet. We defined this as our field. We then sorted the pattern blocks by shape. L chose a shape to begin with and we began seeing how we could cover the entire field with that single shape with no overlap and no gap.

Tessellating squares is easy!

We then moved onto hexagons, which were also simple to tessellate.

We had a nice connection to the honeycomb in nature when we did this one

We then moved onto a shape which I’m not sure they had “when I was a kid” – or if they did, I certainly didn’t know anything about it… rhombuses! L loves the shape and the word – and I love the way she says the word (a mildly trilled “r” and like rum-busses). She first arranged the small rhombuses in a non-standard pattern, which we decided also looked like nature.

Like the wing of a bald eagle!

When we moved onto the larger rhombuses, I asked her to arrange them differently than the previous set of rhombuses. One of my strategies with her is always to ask her to reflect on what she’s just done and find a slightly different take on the task. Here’s what she came up with for the larger rhombuses.

A different arrangement of rhombuses

I decided at this point that she clearly understood the basics of the task. I asked her to remove most of the blue rhombuses from the field and instead, use a few rhombuses to make a different shape. Instead of tessellating rhombuses, we would tessellate this new shape she created.

L put together three blue rhombuses to create a hexagon. She was concerned that they didn’t fit together perfectly, but I told her that we could pretend there were tiny white rhombuses filling in the gaps because the gaps themselves were regular. She then began tessellating the sets of three rhombuses and came up with quite a cool pattern.

As we were admiring the work, L decided that we could now add some of those whole yellow hexagons to the field. I asked her to think about how to add them in a pattern, like she might find on a floor or a wall. She came up with stripes.

Yellow and blue striped hexagon tessellation

And then, of course, she decided to input the red half-hexagons in sets of two to complete the stripes.

Full on hexagon stripes

Very cool!!

Building off the idea of altering patterns, we then picked up the final shape we hadn’t yet used: the humble equilateral triangle. She designed a tessellation in which the vertex of one triangle rested at the midway point of a side in each line.

Each line is the same with the triangles in the same places

She then pushed over lines two and four to line up the lengths of opposing triangles with one another to form a slightly different pattern – and in it, she found hexagons! We had a conversation about how we could re-create the three-lined hexagon tessellation above with additional green lines or how we could use three triangles in the place of any one of the red half-hexagons to complicate it further.

Look, mom! Hexagons!

I was feeling pretty good about the open-ended result we’d experienced so far on this day, and I stepped away to take part in a quick phone conversation. When I returned, she’d created this tessellation. The green triangles are the wingspan and the single triangle above them serves as the head of one bird and the tail of the next bird.

The birds in mid-flight

She also used this time to find tessellations on the floors and walls of our bathrooms. Since she was still really into it, I pulled out a recent supply I’d ordered from Nasco, anticipating both her enjoyment of this concept and her love of animals.

Animal. Tessellation. Templates.

I kid you not.

I mean, what in the what? Right?!

Anyway. They were a hit!

Look at how fun these are!!

Let me be clear: I am jealous that we didn’t have these.

She tessellated fish

The fish was the end of it for the day for her – I mean, she had been at it for a solid few hours. However, a few days later, we revisited the templates again. This time, I urged L to think about coloring in a pattern to enhance her tessellation. She picked up the dog and came up with this.

Red and black tessellated dogs.

We’ll get to the self-made templates in the coming weeks. Overall, I feel relatively certain that she engaged her pattern-making brain, build some fine-motor skills, and also had a pretty darn good time, too.

#HomeschoolWin

# How do we spend our days?

Almost everyone who I consult about homeschooling argues that there’s a significant period of time right after you leave formalized schooling in which the job of everyone in the family is to relax and find their rhythm. Almost everyone says that this can take months and that there’s really no point in doing “lessons” in this time frame. Instead, time is best spent at the library, museum, and zoo; curled up reading books together; and baking yummy treats. This time is known as deschooling and is the transition between formalized schooling and whatever form your homeschooling takes.

Um, sign me up. It turns out that I’d like my career to be deschooling!

At least, it felt that way for the first few weeks. We pulled L from first grade at the end of October. I knew that through the holidays, we would be doing minimal formalized schooling. I also know me, though.

I do very well in life when I am achieving something. When I have a goal, a metric or two by which to measure my progress toward that goal, and then I achieve that goal. Without a framework like that, I get a bit adrift.

I really like to have a goal

Most of our homeschooling routine is about L and her needs and preferences. The reality, though, is that when I try to totally let go an approximate an unschooler, I get a little… itchy.

I’m trying to not pass that trait onto L. I recognize how it limits me. I work hard on messaging and behavior that reinforces the inherent worth of everyone regardless of their actions or achievement.

But I get a little itchy.

So, even though we were technically deschooling through the holidays, we did some lessons, too. Not a lot. And not the first few weeks. But when I felt myself getting short-tempered and knew that had more to do with my comfort with the environment than anything L did or didn’t do, we did a few lessons. And now that we’re post-holidays, we’re into our homeschooling “routine”. Which isn’t really a routine at all, of course!

We have a schedule: a self-directed, democratic homeschool co-op one day a week, an in-home nature-based play school two days a week (so I can have my meetings and office hours), and then four days a week at home. We host a weekly brunch on Sunday mornings at our place, which is an additional opportunity for that all-important socialization that so many are concerned about. L has Girl Scouts twice a month and is usually in one weekly class (right now it’s basketball – which is HILARIOUS). Add all that together with the one aspect of her dabble into formal schooling this year that she loved: Fun Fridays. The idea of celebrating on Friday afternoons seems really appropriate for us all.

So, how do we arrange our time?

First of all, we don’t homeschool any earlier than 11 AM, sometimes later. L is not a morning person. I have no idea where she could have gotten that from! She does best when she has time to wake up slowly, eat breakfast, watch a Wild Kratts, and do some free play.

After a snack (or sometimes after lunch), she’s ready. I’ve usually asked her what she thinks she might want to work on today and if she wants to work on a few ideas or really work on one idea.

I typically have an idea of 3-5 lessons that explore big ideas we could spring into on any given day. I have the materials and have outlined it in my head. We typically start with an independent activity or two, because L really likes to be able to do it herself.

In the past few weeks, we’ve had homeschool days that included:

• find 10 verbs in any book that you choose and write them down
• work a number puzzle and find the rule to predict which numbers can go in the corner
• complete two experiments from chemistry kit
• play chess online
• do a half hour of math apps
• tessellate to our hearts’ content
• read for an hour and a half on the couch
• finger knit
• watch Nature episodes on Netflix, stopping to write down animal facts
• write a book about kingdoms in biology

I think we’ve found a framework that works for us, at least for now. One of the things that it helps me to keep in mind is that she has learned the vast majority of what she knows and is able to do organically. Really, my intervention simply gets in the way much of the time (there’s a blog post brewing on that, too!).

Time on task is not the goal for us. Plowing through isn’t the goal, either. Helping her choose. Helping her see the value in being engaged in learning. Helping her stretch herself into areas she’s not as confident or strong in to build stamina and perseverance. These are our goals.

So, while it is most natural for me to recreate an elementary school classroom in my own home and schedule accordingly, I know that structure doesn’t work for her. While it might be most natural for her to throw away all structure entirely, I know that doesn’t work for me. And this is the compromise that we’ve reached that seems to work. At least for now.

# A note on our curriculum choices

As a teacher by training, I like curricula. I like pacing charts and a spiraling curriculum. I like scaffolding big ideas. I like anchor charts. However, I already know that when I’ve tried to use curricular resources, we do a big lesson and then skip the next 10% because L’s already figured out and applied the pattern. Have I mentioned that she excels at patterns? It doesn’t help that she’s got massive gaps between what she can write and what she can express, or that she focuses on subjects of interest to the exclusion of everything else. These traits make it hard to find an “all in one” curriculum. Instead, we would be best described as eclectic (a word my husband hates), relaxed, thematic, and passion-based homeschoolers. Here’s what we’re using now (age 5).

Language Arts

I could care less if she can spell words right now. She’s 5. Spelling will come. It may be an area of strength for her (as it was for me) or an area of frustration. Just as she learned to read when she was ready and using her own method, so too will spelling come. I could care less if her handwriting is legible right now. A huge part of that is that she’s 5. I want her to focus on the idea that she has important things to say and recording them allows them to be shared with others who aren’t with you right now. So we jot things down all the time and I scribe for her when she requests it. Our house is littered with notes.

Th closest we come to spelling practice is pointing out word parts like prefixes, suffixes, and word roots as we decode complex texts. We also read Grammar Island  on the couch as if it’s a read-aloud. We have a moveable alphabet and stamps. We don’t use them often. We play Wordsearch and Pathwords Jr.

L reads. Beautifully. Narrowly. And far above grade level. She hates most fiction. She doesn’t like reading for strangers. And she absorbs everything she reads, so working on non-fiction graphic organizers is a waste of time right now. We just read. A lot. Vociferously, in fact. And I often curl up and read my own books while she reads hers. (The link at the beginning of this paragraph is her reading a page from Almost Gone: The World’s Rarest Animals – Lexile AD1020L, DRA 34).

We also do a ton of stuff that strengthens her hands. Sewing. Play doh. Drawing. Snap circuits. Lego. Her handwriting will come along as her hands grow. So I call all of that hand-strengthening stuff “language arts” too!

Science

We don’t go more than a few hours ever without doing science. She reads science books. Plays science apps. Watches documentaries and other science shows. Is known by name at both our zoo and natural history museum. Her pretend play with animal figures is based in actual appropriate behaviors for the species represented.

Oh, and we make stuff. Snap circuits. Building with “garbage”. Tinkercrate. Chemistry kit. Marble run. I think we’re good on science.

Math

I have really struggled with math for L. One issue we consistently have is that she gets bored (habituates) quickly. This manifests itself in a number of ways.

First, she is not interested in repetition, especially if the repetition is intended to do things like teach math facts. Exploring addition? A-ok. Practicing number pairs which compose 10? Only in context, my friend.

And how does she manifest said habituation? Well, through stubborn shutting down, of course! I will not be moved, her behavior says. One thing we work on is helping her learn to tolerate (and it is literally that – tolerate) that which she doesn’t find engaging. However, I feel pretty strongly that my 5 year olds world shouldn’t be primarily or even a lot about learning to tolerate disengagement!

Where that lands us, then, is in a land where what we find that appeals to her get used manically for some period of time and then discarded, never to be touched again.

Good times. Expensive times.

Some of you may recall how L was obsessed with dinosaurs for almost 2 years. She now won’t look at them. Literally. She keeps her eyes down at that part of the museum. Because she’s done with them.

In the past, she worked through all of Todo Math which contains PreK-2nd grade concepts aligned with several domains of the Common Core (which, to be clear, I’m not opposed to as a set of standards). She has outgrown that app. She tried the Redbird mathematics curriculum and didn’t respond well to the format. That was very quickly a struggle. She responds really well to the Dreambox Learning app (aligned pretty broadly to Common Core), but she powers through it in pretty big chunks. A few months ago, she walked through a review of kindergarten, all of first grade, and most of second grade in about 6 weeks. She then got stuck on a particular concept the app had her working through (perhaps it was at the edge of what she could do?) and started fighting about it.

We use a variety of approaches right now, mostly low-cost ones! As I mentioned in an earlier post, we have some mad love for manipulatives right now. We also continue to use Beast Academy on a very casual basis. I also surf pinterest and grab ideas that look interesting. Anytime we come across a math app that looks interesting and seems reasonably priced, we grab it. Right now, we’re playing with Slice Fractions, Quick Math, Jr., and Attributes.

We also play lots of logic games. We love Rush Hour, Blokus, Kanoodle, Pattern Play, Set, and chess.

Social Studies

L was interested in enslavement earlier this year, so we spent an intense 6 weeks learning a bit about US history and specifically those who didn’t escape on the Underground Railroad (she told me that since so few people ever escaped, it was better to really focus on those who didn’t escape). Luckily we live very close to the National Underground Railroad Freedom Center, so we were able to visit several times and obtain lots of information.

Very quickly, that interest passed.

This will shock you, but we listen to NPR. I’ll give you a second to recover from your shock. In any case, we were listening in the car and I attempted to talk with L about one of the stories. She cut me off and said, “Mom. I only care about the people I already love and nature. Not anyone else.” Ok. We’ll come back to social studies another time.

So overall…

Follow her passions. Watch closely. Be prepared with lots of high-quality, open-ended, inquiry tools. Drink a lot of coffee. These are the things that make our homeschool work.

At least, it works sometimes.