Monthly Archives: October 2012

Math, Gently

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After three years of school, my eight-year-old believed he hated math. I didn’t send him to school thinking that, so yes, I consider this a failure on School’s part. I myself am quite comfortable with math; I got all the way up to Calculus, which was required for my BS in Natural Resource Science. I can remember doing my Calc homework as a break. I liked how orderly math was, the problem-solving required, the way the Right and Wrong are clearly defined. My point is that my children aren’t picking up on math anxiety from me.

My oldest, who was homeschooled through first grade using Singapore Math, began second grade in his alternative public school well ahead of grade level and continues to be a top student in math. His early-years math experience (and curriculum) was much different from his brother’s. My younger son had three years of Everyday Math, which, in my opinion, is a terrible curriculum. He never stayed with anything long enough to learn it. The curriculum jumps around, supposedly so lagging students get lots of repetition (but not all at the same time) and advanced students don’t get bored. For three years his only homework was math sheets and reading at home, and even though the math sheet usually took only ten minutes, we had to add in the twenty minutes of fighting about it. And it seemed he wasn’t learning anything. When he finished second grade, he was still shaky on, for example, time and money. All that fighting, and it was all a waste of time.

When I decided to homeschool him, I decided to start with Life of Fred, gently. We began over the summer with the first book, Apples. We began with me reading the chapter aloud and going over the questions with him while he wrote the answers. We did it all together for the first two books, a chapter per day. Some days he fought it, but it got better. By the time we hit fall, we continued with one chapter per day, but I began having him read the chapter on his own, do the questions, and then we’d go over the answers together. Again, he fought this sometimes, but it gradually got better. Now he reads the chapter, does the questions, checks his answers, and moves the paperclip to the next chapter, all on his own. If he doesn’t understand a question or needs help, he tells me. Sometimes he still whines about it. But he does it. He’ll be starting the fifth book soon.

I’ve toyed with the idea of introducing something more rigorous at the half-year point, but I want to tread lightly. I don’t want him hating math. I hope he comes to see it as I do, a useful tool to get to where you need to be. I use math all the time–in recipes, in knitting, in sewing–and I try to talk about it when I do. One day not too long ago we were talking about I don’t even know what when I mentioned an Ancient Greek had used only math to figure out the circumference of the earth, and he came super close to the actual measurement. How? my kids wanted to know.

So I looked up the details. My eight-year-old and I looked at our globe pillow and at the map. He said he pictured the equator as a rope around the earth. Perfect, I said, and we moved to our circle rug. Pretend the edge of the rug is the rope. Pretend we’ve cut the earth in half. He picked two points on the edge of the circle, we tried to find the middle of the rug, we measured the angle, we did the math. Mostly I did the math–it’s not easy math. But he was so excited by it.

This is not like school math! He exclaimed. This is math that really does something!

We borrowed The Librarian Who Measured the Earth from the library and read it aloud. I bought him his own protractor and showed him how to use it. I printed out a page of angles (from this awesome site) for him to practice measuring. Next up is drawing circles with the compass so he knows exactly where the center is, and trying to find the circumference using Eratosthenes’ method, a bit more precisely than we did with the circle rug. I predict we will be outside measuring the angles of shadows before too long.

I can just imagine if I’d decided it was time for him to measure a sheet’s worth of angles just because. Fight, fight, fight. (What’s the point? What do I need this for?) But because he is excited about the way this Ancient Greek used angles to satisfy his own desire to know how big around the earth is, he wants to know how to measure angles. And in this way, I remind myself (deep breath), he will come to learn what he needs to know.

O’Keeffe Leaves

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(Inspired by “Gorgeous Gigantic Flowers” in What’s the Big Idea? by Joyce Raimondo.)

Materials: Watercolor paper (or other paper that can handle paint); paint (we used tempera cakes); pencil; permanent marker (we used Sharpies); leaves for looking at

It’s been a while since I’ve posted a straight-up art activity! My daughter said she wanted to make a painting using one of our Art Explorers books, so I told her to go ahead and pick one out. She chose the activity inspired by Georgia O’Keeffe’s flower paintings, but when I looked at the materials list I realized we didn’t have any fresh flowers on hand.

However, a suggested alternate was leaves–and it being October in New England, we have leaves a-plenty. We headed outside to collect some. When we came back indoors, I took my O’Keeffe book off the shelf and showed my daughter some more flower paintings and the way they took up the entire canvas.

G wanted to follow the suggested process exactly, so after choosing a leaf for inspiration, she drew with her pencil and then traced over those lines with a black Sharpie. Then it was time to add color. We both used the tempera cakes. I quietly noticed a couple of things–her ability to trace over a line, and the fact that she is old enough (and so experienced with art supplies) to remember to rinse her brush between colors.

There is such joy in observing her growing up in this aspect as well–she is so confident in the art room, so comfortable, so sure of her decisions and what she needs for her artwork. Here is her finished piece along with the leaf that inspired it.

She decided she wanted to use all the colors, and she enjoyed mixing them. (The tempera cakes are the primaries plus white, black, and green.) She enjoyed the movement of her line, as well.

I also did this activity–I am grateful for the time and space to draw and paint and this activity was challenging for me. I also tried to follow the suggested directions and make the leaf spill off the page, as O’Keeffe’s flowers do. I discovered that it was easiest to do this if I started from the center, with the veins of the leaf. Here’s my finished page, with the leaf that inspired it.

I’m sure I’ll be trying this again. (We have lots of leaves, did I mention?!) I like, too, the idea of taking something so well known–O’Keeffe’s flowers–and translating it to our own landscape. I think I will be using this activity in the art class I lead at our co-op, too. There are a couple of kids who tend to draw small, and I’ve been looking for ways to encourage them to go bigger; I think this is a good activity for that.

I enjoy following G’s lead. When she is in charge of the day (or at least part of it), we tend to do fun things. I had no idea we’d be using autumn leaves to inspire a painting…now I can’t wait to do it again!

Project Shelf

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Inspired by Kate at An Everyday Story, I cleaned off an existing shelf in the living room in order to display some project creations.

I already talked about G’s map of Egypt and N’s cartouche and cat statuette, in the claywork post. I’m happy to report N’s cat stayed together just fine; we had to glue one paw back on. I haven’t talked about G’s mummy or the pyramid, which she created after the mummy, because that’s where mummies go. No matter the mummy and pyramid aren’t to scale; not the point. She cut out the base and triangles (using guides), let them dry, and then glued them together. It’s all a bit fragile, but it’s a pyramid. N also has plans to make a pyramid, but I needed to get more clay (which I did, over the weekend), and now I’ve commandeered the art table for a day or two to sew a Halloween costume. (We are challenged by needing to share project work space.)

The mummy was created early on in our project work, beginning in early September, and despite all good intentions I haven’t shared about it yet. When I told the kids my job was to make sure they had the materials necessary for their work, G jumped right on that. One morning she told me she had “a mummy in her head” and she would need paper, drinking straws, and paper towels. I provided these, and she asked for other items as the need arose.

Working on her mummy

She drew a sad face on her mummy. “He’s sad because he’s dead.”

(It’s hard to photograph white against white, and I used my phone for some of these.) When her mummy was complete, which took time as she worked out how she wanted the various pieces (including the straws; they’re in there too) to go together, she used the paper towel to represent linen wrappings.

During a later session, she painted and colored the squares that she then attached to both sides of the paper towel wrapping–you can see that in the first picture. This represents the paintings on the coffins.

Is this an artistically accurate modeling of an Egyptian mummy? Not at all. Does it demonstrate that this three-year-old understands what she’s been studying? Absolutely. I am blown away (again!) by the way in which she has translated her learning into her own project representation.

N’s planned pyramid will be too big to fit on the project shelf. We’ll have to come up with some other way to display it. My kids are used to seeing their creations displayed around our house and on our walls. I have many, many of their artworks (and my own) framed and hanging. They didn’t react in any particular way to seeing their project creations on the shelf, although my son did point out to his brother that I’d cleaned a shelf off just for them. I think they all consider the house their own gallery, as I have a high tolerance for random stuff taped to the walls–they do their own displaying, too. I think that’s a good thing.

There is a lot I’m not doing–dedicated display or bulletin boards for project materials in individual work spaces (which we don’t have) would be great. I’m not so good about scheduling in blocks of project time on multiple days per week. But I’m doing what I can, and as is often the case, it turns out that that is enough until I can do more.

{PBH} Identifying Interests

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My daughter was very direct in saying she wanted to learn about mummies (and I do have more to show you on that project), but I’d observed her interest in maps and, in fact, jotted that down as a possible project topic before she informed me she’d be studying mummies. As you saw, her map-making interest found its way into her mummy project (her 3-dimensional map of Egypt in this post). I think–but am not sure–that we may be winding down on Egypt here. Meanwhile, my daughter has been drawing maps.

Map by G, age 3

Her maps are of her pretend park; she has been playing a “park game” with our blue rug as a pond and the play tent as her camp site.

Map by G, age 3

(I can’t help it–I adore the trees.) I think this interest in map-making is quite common at this age; at least, all my children have drawn make-believe maps. Because this interest of hers has been present for a while now, I am doing my own research at the moment, seeking ways to encourage and support it. To start, I borrowed Mapmaking With Children by David Sobel from the local university library. I’ve requested a couple of children’s books relating to maps from our local library, to simply have around and share. I’ve only just begun reading the Sobel book, but it’s fascinating. I’ll keep you posted!

So how and why am I focusing on her interest in maps? After all, she has told me she wants to learn about space, dinosaurs, fish, the sun…really, she has jumped on this “project” idea and wants to take advantage of it! And she has not told me she wants to learn about maps. However, maps is what she does. She draws them, she looks at them, she asks about them. It’s where she is quietly focused–her attention is already there, and that’s why I feel it’s a deeper interest that can support deeper investigation. I am watching what she does, rather than just listening to what she says. When presented with the whole wide world to learn about, she’s listing everything in sight, and no wonder. It’s all so interesting. But I want to brush away the surface and see where she places her focus. That’s the best I can do in explaining how to identify an interest that will support a deeper project.

Running Running Running

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My husband’s been away most of the week. I’ve had the typical dose of solo parenting challenges (and a nasty head cold). He’ll be back later tonight. This afternoon, we went to the beach for a bit of autumn sunshine.

It was really windy though. Really windy. And the sand was blowing right at preschooler height, and it stung! My daughter said she didn’t like the wind so we switched directions and climbed up to the pavilion. I figured we’d look at the view and salvage the trip, but when we got there, we realized an empty off-season pavilion is just begging to be run on.

And so we did, all of us. Into the wind, and with the winds at our back. “Put out your flying arms,” directed my daughter, and I did. A half hour of running back and forth, with the ocean in sight on all sides.

Ahhh.

{PBL} Claywork in the Egypt Project

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I hope I can do this morning’s project time justice in this post. Way back when at the start of this project, my eight-year-old, who internalized a different meaning of “project” from school, decided he’d make a pyramid. I worried he’d jumped to this, that he was approaching this backwards, and we talked about it some, but I also figured I’d let this ride. We picked out some air dry clay and he worked with it a bit to get a feel for it. We talked about how he might want to make a model of a pyramid to make sure the different pieces fit together. (Ok, I talked. A little.) We continued to read about Egypt and the other topics he’d mentioned besides pyramids–King Tut, gods and goddesses–and we visited the MFA, which sparked more interests.

Earlier this week, I hung up the hieroglyphs poster I purchased in the museum gift shop and left out the hieroglyph stencil on the art table. My son was excited to come across this and immediately drew his name in his project notebook and surrounded it with an oval to make a cartouche. This morning he decided to use the air-dry clay to do the same thing.

Using the stencil in clay.

Using the stencil in clay.

Here is his full name, before he cut out the oval:

hieroglyphics in clay

Knowing his interest in the gods and goddesses of Ancient Egypt, I made sure to point out the statuettes when we came across them in the museum. I wondered if he’d want to try to make one out of clay? I hadn’t taken pictures of any of the statuettes, but we do have several books on Egyptian mythology out from the library, and he looked through those for pictures. He decided he wanted to try to make a cat statuette.

Cat statuette in clay, drying.

Cat statuette in clay, drying.

Although he has played around with this clay before–just exploring, to see what it does–this is the first time he’s tried to make something like this, with different parts. He began by trying to carve out from a chunk of it, then switched to making pieces separately and joining them. I showed him how to scratch the surface of the clay at the join and moisten it, but I’m not sure how well this will hold together. I probably would have worked more of it in a piece, but we’ll see how it goes as it dries. I made sure to tell him: we have plenty of clay. If this first attempt doesn’t end up the way you’d hoped, you can try again, using different methods. That’s how you’ll learn how to get the clay to do what you want.

While all this was going on, my daughter was working with Model Magic, which is what she’d picked out when we went shopping for clay-type stuff. She’s been cutting out pyramid pieces for her mummy (which I haven’t even posted about yet!), but they weren’t dry yet–not that I think Model Magic gets really dry, not like the clay, but it was definitely still not-dry. So she began, rather without much notice from me, to work on…something. I figured she was just, you know, playing with the Model Magic. Occasionally she’d ask my help in cutting a chunk off or she’d ask for a certain tool. I was playing with a water-soluble graphite stick in my notebook and puttering around the studio area, not really paying attention. And this is what she ended up with:

G's map of Lower Egypt in Model Magic.

G’s map of Lower Egypt in Model Magic.

She made a map of Lower Egypt out of Model Magic. Now, you probably can’t see it, but it doesn’t matter. What matters is she sees it. She pointed out the Nile River, and a boat on a hill, ready to sail. She made a couple of small mummies and put them near a statue of a dead person who is not a mummy, probably influenced by a statue we sketched at the MFA. She worked on this for at least an hour. I’ve already noted her interest in maps and mapping and had considered it as a possible project area before she informed me she’d be studying mummies. Lately she’s been asking me to point out Egypt on our wall map of the world, and she’s seen the map of Ancient Egypt plenty of times in books. Now I am thinking I need to find a larger map of Ancient Egypt that I can hang up for her.

In some ways, when these convergences happen, when the kids are following their own interests and clearly doing such deep work, I’m tempted to think that project-based homeschooling is almost cheating on my part. It seems so easy! Then I remind myself that I am doing quite a bit of work documenting, paying attention, providing materials, connecting dots, reminding the kids what they wanted to work on (more so with my son, who is still deschooling; my daughter tells me all the time what she wants to learn next and what she needs from me, step on it, Mama!). I write myself lists so I don’t forget what I need to do. And I still feel like I’m not keeping up.

But a morning like this? So, so sweet.