Category Archives: math

Transitions

I’m not ready for summer to end. Nope, not at all. Winter here was cold and snowy and dragged on and on well into spring. My oldest didn’t get out of school until the last week of June. He starts up again tomorrow, and our youngest will be joining him, trying out kindergarten. I have all sorts of mixed feelings about this. My heart is in homeschooling and all the serendipitous connections and freedom it allows. Watching my kids learn is amazing. I am sad about the academic-looking daily schedule we received that has no block labeled “playtime,” the 20 minutes allotted for lunch, the increased demands placed upon younger and younger children. But my extroverted girl wants to try it, so I’m swallowing my tongue, practically, at times and giving it a go.

On the plus side, I’m hoping our middle child thrives with the focused parent time with no sibling distractions. He’ll still be home, and he’s most excited about our new microscope.

new microscope at amyhoodarts.com

After looking at a few choices for science curriculum, he decided upon R.E.A.L. Science Odyssey Biology, and I’m super excited. I’m also impressed with the scope of what it covers, and how. (I have a degree in Wildlife Biology and took college courses in ecology, genetics, biology, and botany.) He’ll be using this microscope quite a bit.

at Beavertail State Park at amyhoodarts.com

He already knows a lot about ecology and habitats because of the things we like to do.

He also requested a curriculum to improve his spelling. He told me he’d enjoy writing better if he didn’t have to ask me to spell so many words for him. He had spelling lists in kindergarten and first and second grade while schooled, and predictably, he wasn’t at all interested in rote memorization of spelling words at that age. I don’t feel it’s developmentally appropriate, and felt that spelling would either come around as he gained mastery of reading, or he’d be motivated to improve it himself. And lo and behold, he is. After looking at several options, I chose Sequential Spelling.

We’ll be continuing to use Story of the World (we’re up to Volume 3) and A History of US for history, and Singapore Math for math. He reads voraciously, and writing happens organically. We’ll also be setting aside time for projects.

way up high at amyhoodarts.com

He loves to climb.

This spring and summer, we’ve been learning more about what makes our middle child tick and where he could use some extra support. Slowly, we’re building ourselves a village to help with this. It was suggested that I attend this seminar on executive functioning, and I have to say, I’m looking forward to it. Not the long drive or the long day, but getting useful information that I can implement at home, definitely. I’m glad we have the resources to send me to it.

So that’s where I’m at–sad that summer is ending, that it was so short, but trying to get in gear for a new season. I’m not happy about the shortening days, the crispness to the morning air, the signs of impending coldness and darkness. It feels like we only just emerged from winter! But I’m optimistic about what N and I can accomplish without distractions, and hopeful that my daughter enjoys kindergarten (because she is so excited about it) and that my oldest is finally challenged now that he’s in 7th grade. Transitions.

Schooling Update

9yo using Cuisenaire rods to help with Singapore Math.

Friday was conference day at my oldest child’s school, when we sit down together with his teacher to check in and set goals. The pre-conference paperwork asked us, as his parents, to list our goals for him for the upcoming year; we wrote that we wanted him to set his own goals, as our goal is for him to be a self-directed learner. Honestly, I can’t think of any other answer to that question. It seems absurd to state what I think my son’s goals for himself should be.

At the same time, it’s been about a month since we began our non-summer homeschooling schedule. While learning happens all year round, we do add in more required work in the fall. Because I have one child in school, it makes the most sense to stick to the same sort of schedule, although that has its frustrations–I don’t enjoy being beholden to an outwardly imposed schedule. However, it’s a good point at which to check in with how we’re doing.

I began using Singapore Math with my 9yo this year, and I’m happy to say it’s going well. He knows more than he thinks he does; the main thing is overcoming his own self-doubt. A year ago, he’d have fought me on using a workbook and textbook; this year, he sometimes complains and needs reminders to focus, but he gets the work done. I’ve noticed that he does best with word problems (even though he says he doesn’t like them). He also took really well to Life of Fred last year, which is story based. I noted this and pointed it out to him—he seems to comprehend the numbers better when they are presented in a verbal way.

Another great help for explaining some of the concepts are Cuisenaire rods. We’ve had these for quite a long time and they have been useful many, many times. Most recently, I used them to demonstrate the concept of borrowing in subtraction. He needed a visual in order to understand that I wasn’t telling him to get rid of any numbers; we were just regrouping. After seeing it with the rods, it clicked in about a minute. Now he understands what’s going on when he borrows to subtract, rather than just doing it because he’s been told to but without any comprehension.

My 4yo, of course, wanted her own math to do. She was making up her own rather baffling worksheets, so I picked up a workbook for her. She’s happy, and I get a little bit of time to teach the day’s concept to my 9yo without her chatting our ears off.

The other area that has me really excited is language arts. We’re transitioning into using Brave Writer; we read August’s book, The Lemonade War, in September, using the copywork assignments and discussing grammar and a bit about writing style. We haven’t begun October’s book yet because we moved right into the sequel, The Lemonade Crime. This is my main logistical problem with using Arrow; we read aloud as a regular part of our homeschool, and trying to make one chapter book stretch out all month is limiting; there are other books we want to read too. I haven’t quite figured out how to handle that. We’ve also done some free-writing exercises and list-making; gentle ways to get my 9yo writing more often.

But then! I saw the book Guy-Write on the library shelf and asked him if he’d like to read it. He said yes, read it in about a day, and then…began writing a book. Something in that book hit him just the right way, and his writing is alive and exciting. He reads each chapter to me when he’s done. He told me the spelling is all wrong, but I told him when he was done writing, we could type it into the computer and worry about the spelling then. He declared I could be his editor. I’m a bit dumbfounded; he has “hated” writing for a few years now. I am cautiously optimistic, hoping this new-found love of writing will stick around.

My daughter is also writing—asking how to spell words and either writing as we tell her the letters or copying the words she’s dictated to me from another piece of paper. She’s been reciting letters off of signs, asking me what they spell. Just recently she began doing that in reverse, saying words and trying to sound out the letters they contain. Her brain is working constantly, it seems, on the puzzle of reading. It’s really cool to watch.

One area I’m not totally up on is project time. I’ve failed thus far to carve out predictable blocks of time for project work. I keep waiting for our weeks to settle down into a routine, but I think our routine is that there isn’t one. As much as I try to contain the errands, things like doctor’s appointments go where they fit, and we seem to have lots of those. So I’ve begun just claiming the time where I see it. I need to do a better job of reminding the kids what they wanted to accomplish, though. So project time is still a work in progress this year.

Of course we’re continuing our studies of history and science, supported with library books and so on, but math and language arts have taken such a huge leap lately, so that’s where I chose to focus on this recap. It seems like overstating the obvious, but a huge advantage of homeschooling is the ability to work with my child right where he is, to take advantage of leaps of understanding, and to take the time to work on trouble areas…as well as having the time to be patient and wait for the progression of things without feeling pushed and rushed to meet an artificially imposed standard. I’m thankful we can do this right now.

Homeschooling Plans

This photo has nothing to do with this post. It’s just nice to look at.

As we ended our first year of homeschooling my middle child, much was up in the air (my least favorite place to locate things). So I put off planning too much and took a wait-and-see stance for a while. But we’re now definitely homeschooling this year, too, and a few things have fallen into place.

We’ll be continuing with Story of the World as our spine for history, and when our world history gets up to the Age of Exploration, I expect we will start with the first book in A History of US, by Joy Hakim. We’ll also continue with her science text, The Story of Science, supplemented with hands-on science as we go along, primarily based on interest.

Last year for math I used Life of Fred; I talk more in depth about my gentle approach to math here. This year I feel he’s ready to move into something more rigorous, and I’m going back to Singapore Math, which I used for my eldest. It gave him a great foundation in math. We’ll take it as slowly as necessary, and of course real-life math is a part of our days. I’ve noticed my middle child likes to explain his thinking process in his own way. I’ve learned to be quiet and let him have the time he needs to explain what he’s figured out on his own about whatever math concept he’s been thinking about. He doesn’t want to hear me say it; he wants to get there on his own. His train of thought is not necessarily the school/textbook train of thought, but if he gets to the same station in the end, I don’t really care.

My 9yo also came out of school really not enjoying writing at all. I gave him space on that last year and didn’t push it, hoping he’d come around. He had fits and starts but no regular interest. This is something I don’t want him to abandon entirely, so this year we’ll be using the Brave Writer curriculum. He is in the Partnership Writing age group, and I assured him I’d be doing the same writing exercises as he. Actually, I was surprised by his response when I told him we’d be using a writing program this year. A year ago, I’m sure he would have protested immediately. This year, he said okay, as long as it wasn’t like the writing he had to do in school. We each bought three new notebooks: one for copy work (from the Arrow portion of the program), one for lists (because lists are fun), and one for Friday freewriting.

We’ll continue to start our mornings reading aloud together, whether it’s the book for that month’s Arrow or other books. And we will get more focused about project work, which kind of fell by the wayside this spring and summer. I’m enrolled in Lori’s Project-Based Homeschooling Master Class, which begins this week. I expect it will get me more focused and on track to get even better about mentoring my kids’ interests. I’ve already gotten a head start by beginning to tackle our studio space to get rid of some accumulated stuff and improve ease of use. I have my eye on the office/play room too, which has never been used well. (It tends towards entropy.) My hope is that by signing up for the first session of the class, I can take advantage of the natural beginning-of-school-year momentum and keep that ball rolling all the year through.

A big change from last year is that I’m taking a break from our homeschooling co-op, at least for the fall session. This was a hard decision, but several families with older kids left, leaving no offerings for my 9yo’s age and interests except a class I was teaching. I looked at the two classes I was to teach and the effort and time required (which is considerable, because I don’t use a prepackaged curriculum but instead plan as I go based on the students I have), versus what my son would be gaining, and decided it wasn’t the best use of my energy right now. I’ll miss the other moms, but given some challenges at home this winter and spring, I am wary of overextending this fall. My energies need to go to my own kids and family first, my own self-care (running, exercise class, and hopefully art classes), and my work (both shop and classes).

And those are our homeschooling plans, which look quite comprehensive when I write them all out. My biggest challenge, I think, will continue to be that my 9yo and 4yo bicker. They love to play together, but they experience quite a bit of friction, too. My second biggest challenge is that my oldest is in school, so I have to juggle a homeschool rhythm AND a school schedule, and those often work at cross-purposes. Also, I realize I haven’t mentioned plans for my 4yo at all. She’ll do what her older brother does, because she won’t have it any other way. She is practically teaching herself…she is writing more and more, copying down words and reading them back to me, making up her own math games….homeschooling a preschooler is easy as pie, in my opinion. She is also a pro at project work; she just needs her mama to get back to being a good mentor.

We all have our work this school year! I think it’ll be a good one, though. The second year of anything is always a little easier than the first.

{PBL} Give a Goat Project

g's goat cards

Several years ago, blogger Teabird sent us her review copy of the book Give a Goat. I read it to the boys right away, and it now sits on one of our storybook shelves. Periodically my daughter chooses it as part of her bedtime stories. Not too long ago, after hearing it again, she decided she, too, would like to give a goat through Heifer International. We talked about different ways she, at age four, could earn some money, and she began earning quarters every time she helped set the table, fold laundry, or clean the bathroom sink. (Normally I don’t pay for routine helping-out-type chores, but she’s four. Her earning options are limited.) However, a goat costs $120. We brainstormed some more.

Eventually she decided she would like to make note cards with a drawing of a goat on them, so we Googled for images of goats and she picked some for me to print out. Then, she drew some pictures of goats, using her reference images. Finally, she picked out two of her drawings (a mama and a baby, she told me), and together, we turned them into stamps.

Her goats are smiling because they are happy. Of course! Next, she picked out colors of card stock and ink, and we set to work printing.

Here’s a closer look at the mama goat:

And the baby goat:

When the cards were dry, she counted out six envelopes to go with her bundles of six cards, I wrote out a tag to her specifications, she signed the tag, and we bundled the cards and envelopes with pretty ribbon.

g's goat cards (2)

She settled on $5 for a package of six cards, and we began by emailing family members. Her next step is to brainstorm other places that might agree to sell them as well. Meanwhile, her dad gave her all his dimes, nickels, and quarters for her Give a Goat bank, and she and her 8yo brother sorted the coins; then he counted, added them up, and let her know she had just over $10 towards her goal.

So much going on with this project. So much!

Math, Gently

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.

The Times Tables

Sometimes, you just need some flashcards.

My oldest, who returns to school this week, began learning multiplication two years ago in the third grade. But they don’t require them to memorize them anymore, apparently. This summer, I decided he was memorizing those multiplication tables before starting fifth grade. Mind you, his grades in math are fine. But as he moved into division this past year, I could see it was harder than it had to be. Do you remember chanting the times tables as a class? It was boring as anything, but knowing those facts make everything that comes after easier. My son, however, was really resistant to memorizing them. Eventually, early this summer, he was able to verbalize why: “I want to figure out the answer on my own.”

A-ha! He thought that memorization was somehow akin to cheating. I picked a neutral time–we were alone in the car together, on the way to the supermarket–to try to explain my reasoning to him. I told him that if he didn’t understand the process of multiplication, if he didn’t realize that 8×3 was the same as 8+8+8, then I wouldn’t want him memorizing the facts. Facts without understanding is no good. But he does understand the process, and now it was time to know these facts so well that his brain isn’t wasting time with 8+8+8, it just spits out 24. Just like he doesn’t have to start from A just to know what letter comes after T–he memorized the alphabet in order a long time ago without even thinking about it. That’s not cheating, he agreed.

He thought this over for a bit, and then he said, “I think writing them out would be a good way to memorize them. Often when I write myself a note so I don’t forget something, I end up not needing the note because writing it down made me remember it.” I told him I thought that was an excellent start, and chose not to remind him that I’d suggested this months ago and he refused. He needed to understand why he was doing this, and I was glad he came up with this strategy on his own.

Once he understood, the rest was relatively easy, because he was on board. I’d read somewhere to group the like tables, so we started with the 2s (easy), and followed that with the 4s and 8s. He wrote out the table, and I quizzed him with flash cards. I got out our Cuisenaire rods and we grouped them different ways to see how 2s, 4s, and 8s are related. Then we moved on to 3s, then 6s, then 9s, and finally 12s. I reminded him to use what he knew–if 7×2 is 14, then 7×12 has to end in a 4. If he wasn’t coming up with 12×8, I’d ask him 10×8 and then 2×8 before repeating 12×8. We left the 7s for last, because they’re not really related to anything else, but we’d covered everything in them by then, at least. (5s, 10s, and 11s didn’t need much work at all.)

They’ll need to be reinforced, of course, to make sure they stick. Sometimes I just ask him multiplication questions out of the blue, which has led to my youngest randomly stringing numbers together into math problems for us to answer. I wouldn’t have said I’m a fan of rote memorization, but it turned out I felt strongly that he should know these, really know them. Again, if he didn’t understand what multiplication is, I wouldn’t want him memorizing facts with no understanding. But I can also remember having to memorize oral presentations when I was just a little older than he is, and it certainly trained my mind in a certain way. Maybe next summer we’ll memorize some poetry…

A Plan, of Sorts

[Insert your own metaphor here] The other day at the beach, it was so clear we had a great view of Block Island offshore. But this is rare.

As I described in the last post, I’m not one to plan the learning step by step. But I’m not unschooling, either. That’s where I thought I’d fall, when I started homeschooling way long ago. The reality, though, was that my oldest wanted and needed a bit more structure. He liked workbooks. (Me? They give me hives.) He liked seeing tangible progress of work completed. He was five. I adjusted. I even bought a complete curriculum for his first grade year, but I ended up changing and adding so much that I was going to take a completely different approach the next year, except then he began school.

This time around, with my younger son, I’ve gathered some books and I’m keeping it loose, with a very short list of items that need to be completed daily. Because three years of school has him convinced he hates math, I started him with Life of Fred over the summer. The addition in the early books is below his current ability, but those books have reinforced some items that just didn’t stick at school, such as telling time and the order of the days of the week and months of the year. My only math requirement to begin the year is a chapter of Fred a day. I know without a doubt that math will be included in all the other subjects we do, in his daily life, and in his project work. This child needs to see the practical use of something; he’s not going to learn anything just because somebody tells him to. (And I don’t think he will ever be asking for workbooks.)

My state doesn’t even require we teach history, just geography and civics. Perhaps this is why he apparently learned no history through second grade. (My older son had a completely different–and better, in my opinion–second grade experience at the same school with a different teacher, but that was before they revamped the second grade. He did learn history, though. We’d already covered many of the same topics in our first grade homeschool, but still.) Nevertheless, I asked him if he’d like to start at the beginning, in the ancient world. He’s very enthusiastic about learning more about the ancient Egyptians. I bought the first volume of Story of the World to help us tie everything together in historical context, something I was having a hard time doing myself with books that focused just on Egypt. I’m not using the activity books, though, since having somebody else decide what to do takes all the fun out of it! We’ll be supplementing and going more in depth with library books, the local art museum (which has a wonderful collection of ancient art), and whatever related projects my son decides he wants to pursue. We’ll move on when he’s ready.

He also asked to do chemistry experiments. We’ll be using Adventures with Atoms and Molecules, Amazing Kitchen Chemistry Projects You Can Build Yourself, and library resources (including a science dictionary for any terms that need to be looked up).

And finally, we’ll be incorporating project time.

I’m keeping the extras light. I think he needs to unwind from school and rediscover how much he likes learning things when he has a choice of what to learn. His knee-jerk response to anything schoolish is “I hate it” and “it’s boring.” After years of struggling to get him up and on a bus, I don’t plan on spending most of our homeschooling time trying to get him in a car on time. We have one co-op day, and I’m really excited to be part of a great group. We are planning on enrolling him in karate; we think this might be a very good fit for our intense, oppositional child. (Team sports? He can’t stand them.) And that’s about it, at least to start the year.

We will begin where we are and see what develops, maintaining flexibility at all times. That’s the main gist of any plan I’m making.