Dreaming of Solomon's Knots

Looking through a crochet stitch dictionary, I saw Solomon's Knot. I think it's beautiful but didn't think much else about it until days later when I saw a woman wearing a poncho in Solomon's Knot. She couldn't confirm that that was the stitch as a friend made it for her, but I'm pretty sure it was the stitch.

I just found a youtube video on how to make it and thought I'd post it here for when I get around to making something in this gorgeous stitch.

Unschooling Math - sort of, so far

Unschooling math isn't something I'm completely comfortable with, yet I find it preferable to the alternative of using a math program or curriculum. Perhaps no parent is ever completely comfortable with how their child is learning math -- every program has deficiencies and we always wonder if there is something better suited to our children out there. I'm not offering any insights or advocating my way of seeing things. I'm just documenting why I'm taking the approach I take so that in the future when I ask myself what the hell I was thinking, I can come back and see this post and say "ohhhhh...."

I don't think I'm having any new epiphanies on the matter, so maybe this is a progress report. Also, since I started this blog, Blogger has added tags, so maybe I can tag this and find it more easily than my older posts on the subject. Someday I will get around to tagging those, but for now, this will be a recap and an update of how math is going in our homeschool.

I'm a collector/hoarder of books and educational paraphernalia. I suppose that what I'm thinking is that if we have everything we could possibly need, my kids will find it and use to as it helps them best. I'm also a big believer in natural learning - that so many needed skills can be learned just through the normal course of life and that this knowledge learned through application will stick better.

Back when I first started to homeschool, I read alot about homeschooling and education. Some things that stick out in my mind were reading Mary Pride mention that her father taught her all of elementary math in one summer. Well, that sort of takes care of my concern about elementary school and it reinforces my feeling from school that most of the math seemed to just repeat itself year in/year out. I always liked math, found it to be a game and I enjoyed it. I was never in the highest math group but always did well where I was. What sticks out most in my mind was how much I loved algebra and geometry. Most interesting, though, was that I truly found high school geometry to be a reiteration of what we had been learning up until then. I suppose there was the added element of proofs, but I recall that they were very simple and fun for me. Beginning with trigonometry, I found math tedious and uninteresting. Maybe I'm just not the math sort. Luckily, I have a husband who did not find it so and went further in math than I did, so I can balance my math thoughts with his, though his thinking is very similar to mine.

After Mary Pride seemed to confirm my suspicion that there is not all that much to elementary math (or perhaps math before algebra), we found Gareth Lewis. I admit I have not read One-to-One in years, but what my husband took from it was the importance of keeping math mental for as long as possible.

Since my older daughter is such a reader, we have lots of math books in our house. A few are text books from used book sales, but I don't think anyone looks at those. I have found the E.D. Hirsch books helpful. FUN books has a great selection of math books and I've heard good things about the Jacobs series. We've also acquired the first Life of Fred book, though we may not be ready for it, but it's on my radar. Just looking through his website, I found what probably best sums up my approach to education - "Let them have a happy childhood." What he writes for how to learn the times tables is true of our house -- my husband quizzes my daughter in the morning with the math fact of the day. It's a "fact family" - what is 5 x 3? 15. What is 15/3, what is 15/5 sort of thing. We have the multiplication charts on the back of the door of our downstairs bathroom. I have tried to interest my daughter in the multiplication grid without much interest. I should try again. Just playing around with the multiplication chart and a 100 chart (easy to find on an internet search) helps to learn the times tables. John Holt recommended in one of his books to learn the tables by using a multiplication chart with blank spaces and letting the child fill it out.

I suppose what is most important to me is that my children learn to add, subtract, multiply and divide, so that is what we are focussed on right now and it seems to be happening fairly seamlessly. I buy the placemats with the tables on them, they may be ignored. I hang the hundred chart and the multiplication tables. We talk to our kids, peppering then with questions throughout the day (it's easy to incorporate multiplication into many daily tasks, especially trips to the grocery store).

Up next....

Mathematicians lament.

American Girl books.

Freedom in education blog

Homeschooling 4th grade math

I'm an unschooler. It's not something I aspire to be, it's just who I am. Sometimes I think about homeschooling in some other way and I always decide against it - I really believe my children know how to learn best and they'll show me how best to help them. So, for most of the year, things are fine and dandy and we learn so seamlessly that I'm always hard pressed to demonstrate or describe what's going on in our homeschool. I guess it's like brushing my teeth, I do it every day, but I'd have to stop and think to describe exactly how I do it and I always seem to bore myself in the explanation. An odd analogy, perhaps, but perhaps I'm an odd person.

Our state requires that we give proof of progress annually. I don't mind this regulation as it seems reasonable and fairly unintrusive. To give proof, we use the California Achievement Test (CAT). We've also been using the Spectrum Test prep books, though they are far more intensive than necessary to prepare for the test. However, they give me the chance to see what my kids know (to a limited degree) and whether they understand how to take the test. I have found them very useful in the past, though I must say that their utility seems to be decreasing as my kids get older. Starting around 3rd grade, Spectrum does not seem well correlated to the CAT. If I remember correctly, Spectrum introduced long division and did not review subtraction with regrouping. The CAT at the same level did not have any long division and did have subtraction with regrouping. So now I'm careful to do more math review than the Spectrum offers and to use it as a way to introduce new math concepts without too much worry that it will be on the test.

My oldest is in 4th grade now and, as has been my habit, I ordered the Spectrum Test prep earlier this month. My youngest is in 1st grade. I pulled out the books and started the review. My oldest is learning long division. I don't use a math curriculum, an issue I am constantly reconsidering and so far have always decided against - I blame Mary Pride who wrote in her Big Book of Home Learning that her dad taught her six years of math in the summer after first grade. So, when it's time to prepare for testing, I need to cobble together material other than my own tutoring that can help my daughter. She is a strong reader and loves books, so I usually go the literature route. We have the whole E.D. Hirsch series, What Your X Grader Needs to Know. Like the Spectrum grade levels, it seems I have to consult two grades in Hirsch to get what we need. Two digit multiplication and division can be found in the third grade and fourth grade books. I have assorted other math books (text and otherwise) that I look at, but I think the Hirsch books do a nice job of displaying and explaining what is going on in the problems (how they are done). As you can tell, I am not into drill and kill, I want my child to understand what she is doing and why - not just spit back the procedure. I'm not advocating that this is the proper approach, just explaining that it's mine.

While at the library today, I also checked out some books on division that I also thought seemed to illustrate the procedure clearly. I got Division Made Easy is from the Making Math Easy series (one I was unfamiliar with). Hey, cool, there are reproducible worksheets for the book on-line. I also got Dazzling Division by Lynette Long, which looks much more games oriented but might be a way to extend the concept and make it more concrete. We shall see. As much as I love the idea of using games to learn math, I tend chafe at using a contrived "math game" and prefer to play real games. I don't know that it reaches long division, but most card and dice games at least offer a lot of practice in addition (thinking of my younger daughter here). Maybe it's time for me to try some math games.

I also picked up a couple of video tapes from the Math for Children series. I got Multiplication and Division and was very pleased with how entertaining and educational they are. My kids seemed to like them and perhaps they will even watch them a few more times. Can't hurt, right?

Crocheting Through the Darkness

My church is having its annual December craft fair and I've decided to make flower pins. This has been a great reason for me to go through the many flower patterns I've been collecting for years but have made only once or twice, because, really, what are you going to do with flowers? I've made a flower here and there and it seems that I've given most of them away. The few I have at home, I just don't seem to know what to do with. Guess I'm one of those pragmatic people who sort of need a reason for doing something (I'm a Taurus); creativity alone is not reason enough for me.

As I work through the various patterns and post my projects to Ravelry (I'm MissMookus over there), I have been thinking about what I like and don't like about various patterns. I think I'll do another post with links to those patterns, but this post is about what I've come up with as a result of my deep ruminations on the subject of yarn flowers.

First of all, I should thank Ska Mama, because it's her 5 Petal Flower on which my creation is most closely based. She generously shared her pattern on her blog and I've been having fun trying to make it, failing, trying again, succeeding, trying again, and getting it wrong in new and exciting ways.

So here is my own version of a 5 Petal Flower, which I need to rename because it sounds too derivative. How about....

"I Dream of the Number 5, in yarn"

Yarn: Lambs Pride Worsted, Victorian Pink

Hook: H (5.0 mm)

My flower was 3.25" in diameter

Chain 2

Round 1: 5 sc in 1st ch; sl front loop only (flo) to join. Mark the blo of this stitch, you'll need it later and it may be hard to find. Guess how I know.

Round 2: ch 1, sc in same st (flo); *(sc, ch1 or 2, sc) in flo, repeat from * around. Join in marked blo of Round 1 stitch. Sorry, don't know the stitch count on it, but it will resemble a pentagon.

Round 3: (same as ska mama's) *ch 2, sl st blo of next sc (again, you may want to mark this, things get confusing); repeat from * around ending with sl st in first ch-2 space

Round 4: *ch 3, 3 dc, sl to next ch-2 sp; repeat from * around. Join with sl st into base of first petal of round

Round 5: ch1, sl to back of 3rd st in petal; *ch 3, sl to back of 3rd st in petal; repeat from * around. Join with slip st to base of first petal

Round 6: *ch 3, 8 dc, sl to next petal around. Slip to base of first petal. Finish off. OR (sl, hdc, 6 dc, hdc) around.

Add a pin to the back or add to a barrette or headband and enjoy!

UMW Feminist Survey Feedback

Hello,

The survey did not have a place to leave feedback, which is why I'm sending you this e-mail. I appreciated the opportunity to participate in your survey. I found it very interesting. I'm a married, homeschooling mother of two young girls and I have a JD. I left my work as an attorney for the federal government with the birth of my first and have not returned. In a completely unanticipated turn of events, I have become a homeschooling mother. I have always considered myself a feminist -- I was very active in feminist issues while in law school, volunteering with a battered women's shelter and serving on the staff of the William & Mary Journal of Women and the Law. The unpublished note I wrote was about battered women's syndrome and a proposed answer to that in the form of an abuser's profile.

While I consider myself a feminist, I realize that others may not consider me to be a feminist. In talking to one friend, she labelled me as post-feminist, I believe. My take on feminism is that it seeks equality for women in all aspects of life so that the individual woman may have the same choices are men. I strongly believe that feminism does not dictate what choices a woman should make and I have written on this subject, as least within the tiny confines of my blog.

Now, for the feedback on your survey. I skipped many of the questions that asked about what I thought a "typical" feminist might think. I don't believe in a typical feminist, in some ways, I suppose this approaches essentialism. My view is that feminism is about women as individuals, not as a group that should be told what to do. I am not interested in trading oppressive systems of male-dominance for oppressive systems of female-dominance. The survey seemed to suggest a rather narrow-minded way of thinking of feminism and that feminism is an authoritative dogma as to the thoughts and behaviors of it's adherents. The idea of feminism as consisting of a group of controlled individuals indoctrinated into group-think is disturbing and your survey's questions about what a typical feminist might think contribute to that. I realize it's part of research only but wonder if perhaps your survey if influential to the thinking of young feminists in college who are taking this survey.

Frankly, I don't see what breast-feeding, home birth, or c-sections have to do with feminism. Having the choice for any of those things is a feminist issue, but the choosing of them should not be.

The tone of the questions in the survey suggested to me that feminism is about living life in a certain way and I certainly hope young feminist college students are not internalizing that message and stand ready to accuse other women of anti-feminist activities if they don't make certain decisions deemed to be feminist choices. I'm not sure the survey questions on having and raising children aren't poised to stoke the Mommy Wars. What I want to know is where are the Daddy Wars?

I also found the questions about the roles of men very interesting and tended to answer neutrally on them. Just as a woman is an individual who should not have her life path dictated for her by dogma, so should a man be treated as an individual. I believe men are vastly different in their approaches to gender roles, house-keeping and child-rearing. Ultimately, if a woman is so timid as to be unable to approach her husband about the division of household labor and other marital issues then I fear that feminism (or something) failed her long before she got married.

Sincerely,

Exercise Tapes and Raising Girls - I just don't need a 'sexy' workout

As I get bored of (and adapt to) the exercise tapes I own, I find myself exploring the offerings at the local library. I've written about my samplings before and I often find something I like.

One thing that I've noticed is how many have themes I don't necessarily want to expose my daughters to. Because I homeschool my kids, they are home when I am doing my exercise tape. Sometimes they are elsewhere around the house, engaged in scholastic, academic, challenging work, or downstairs in the basement lab exploring cures for the most dangerous pathogens known to man, but other times they want some downtime and hang out in the family room while I do my exercises. I've always been pretty aware that body image can be a problem for young girls and I want to do everything I can to show my girls that I exercise because it makes me feel good and healthy and it also helps me from injuring myself if I keep in shape (and I do my best to shuttle them out of the room when their father starts comparing his waistband to that of his brothers. Seriously, he is such a problem).

I have to say, I love my Reebox Versa Training Hi-Lo Aerobics video from 1995. Not only does it include a man in the workout trio, but the outfits and people look normal and all the messages are new-agey and not body oriented at all. I like the workout, too, but I get tired of it after awhile.

More recently, I have bought the 10 Minute Solution Fat Blasting Dance Mix. I like the tape and the workout girls look normal. I'm not too jazzed about the title segments - Simple Slimmer, Calorie Meltdown, Fat Burning Party. Nor am I too thrilled about the comments about looking sexy and working your way towards a slimmer you. It's not too bad, but I did have to field a question asking me if most women want to lose weight. I think my answer was that some probably do, but I like to feel strong and healthy. Think it will work?

Today's workout sample was Self - Dance Your Way Slim. I only did half the tape (another aspect of exercising around the kids is I need/want to keep it to 30 or 40 minutes and this is a 52 minute workout. I like the 10 minute solution series because it's easy to stop a complete workout). I like this tape, 3 very normal looking women in normal clothes. It really reminded me of the exercise classes I used to take (gulp) 9 years ago. It was fun enough, easy enough, and gave me a nice little workout (might be too simple for some). What I also liked was there was no commentary in the first half about body appearance or being sexy. Well, not until around the 30 minute mark when she started saying something about sexy.

I guess I'll keep up my exercise tape sampling, I just wish I could find more aerobic workout tapes that omit references to body appearance and sexiness. Why must everything in our culture always be 'sexy'? It's so annoying. And how am I going to field those questions from my girls?

Yeah, yeah, I know the most important role models are the parents but why must our culture make things more difficult? I think an ABBA song addressed that topic (money, money, money).

Schizophrenic Christian

I don’t understand the crucifixion. Most of the time, I don’t think about it, but Lent and Holy Week and Good Friday, especially, are just so in your face about it that I feel I must have some sort of response.

Over the years, I’ve had different responses. During my evangelical years, it was so great that Christ died for our sins and gives us hope for salvation. That’s easy enough, you tow the party line and everyone is happy.

Later, it was, well, I’m not sure that really makes sense to me, but how about I chalk it up to ‘mystery of faith.’ That satisfied for a few years.

And then the darkness fell and I really struggled with the idea of the crucifixion being the ultimate passive-aggressive act. “You are bad and I have to suffer this horrible death for you. But it’s okay because, though you don’t deserve it and can never earn salvation, I’m doing this for you because I love you.” Looked at in that light, it’s really twisted. So I had to dispense with that view – not sure how I did it, but I know I wrote a blog post on it.

Then there is the metaphorical/psychological view. Christ shows us the importance of dying to our ego/our self, so that we can reach transcendence. Nice, sort of an East meets West view. That could work but for a long time I was hung up on why such a nasty story was written if it didn’t actually/literally happen. Maybe reading Joseph Campbell on the Power of Myth would help with that, but then why do I choose this particular myth? Maybe because it’s the one I’m most familiar with and it takes a lifetime of meditation on it. That is my closest understanding right now but I don’t seem to have the time or energy or interest to read Campbell or Marcus Borg. Lamb, actually, was pretty satisfying with Jesus cast as a bodhisattva to his people and the crucifixion being his reaction to the practice of sacrifice. Yes, I think truth can be found anywhere and much of my religious understanding springs from fiction (I love Susan Howatch’s Starbridge series).

I’ve said that pondering the crucifixion makes me sad and angry and confused. Sad, because it’s so much suffering – the violence is almost pornographic. Angry because, well, maybe that’s the natural response to violence and sorrow. Angry also because I don’t know why I’m so bad that some poor man/God hundreds of years ago had to endure what he did. Confused because why must there be substitutionary atonement or why there must such a useless atonement as killing? Confused because maybe I’m not a Christian and then what? Where would I go? My religion is only partly about my beliefs, a large part is my heritage and my family and, at bottom, I feel that Truth runs through everything – all religions, all ethics, everything. Which is probably something else that makes me not Christian.

But I’m active in church and that embarrasses me because I’m not sure I believe what I’m supposed to and I feel like a faker. I also am embarrassed because I know to some, church involvement is interpreted as an assertion that I think I’m holy or want to be holy or have any clue what holiness might entail. So I make jokes.

Why do I go to church? Is it because I was raised in the church or have a longing for a religious community or I thirst for God? Well, I might have all of those, but that’s not why I go. I go because I had a Baptist boyfriend in college who mentioned once that when you move to a new town, you join a church, it’s the best way to get connected and involved in the community. Strange, huh?

I don’t feel the need to church shop or religion shop because I do have faith that anywhere I go I will find myself lacking, sad, angry and confused. And maybe that is the point of faith, to lead you there so you can let go and relax a little. I really don’t know.

Ultimately, much of my belief rests on what an on-line friend, a Quaker, said to me. He said that he thinks God tells us all something and that maybe what God wants is for us to talk to our neighbors and find out what God told them. I really like that and maybe that explains why I’m posting this note.

Well, I feel better now, thanks.