Second grade logic and rulers February 23, 2012
Posted by mareserinitatis in education, gifted, math, teaching.Tags: angles, education, geometry, kids, rulers, sir cumference
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Today, I went back to work with the second graders. We’ve been spending a lot of time talking about circles and degrees and Babylonian units and π.
My plan has changed from the original one of trying to teach the kids a bunch of applied stuff. I’ve pretty much given in to teaching them historical discoveries in math simply because there’s a lot of stuff you can do that doesn’t require multiplication and division. It’s been a lot of fun, but I decided to try something different but related: I wanted to teach them out to make a formal mathematical proof. Okay, not terribly formal. What I want them to learn is how to use logic to make a proof. I suspect some of them know already (based on some of the arguments I’ve had with my son who has rock solid 7-year-old logic). However, I’d like them to use their brains for good instead of getting out of (or into) trouble.
The thing about geometrical proofs is that they really aren’t that hard. At least, I never found them to be. I remember sitting in 10th grade geometry and being given T-charts. I would race through them and ace them all. I was horribly surprised to see that my classmates had difficulty with them as well as complaining the teacher was too abstract. I threw the idea of proofs out to Mike, and he said that pretty much the only tool you need is a brain, so it’s probably a good idea. (I’d have to disagree…you need a brain…but you also need a pencil, paper, ruler, and protractor. But otherwise, I think he’s right.)
Today, we started with the concept a line and measuring its angle. I know my former math instructor wouldn’t approve, but I’m teaching them to use degrees (aka Babylonian Units) because that’s what’s on the protractor. Also, I’m not sure how versed they are in fractions, so we’re not going to get into fractional parts of π. (Actually, if anyone has ever seen a protractor with units of π rather than degrees, please let me know as I’d love to buy it.)
Once we had a line, then I told them to draw a point on the line with another line coming out of it, so that it would look like this (without the measurements):
Each of them drew the line coming out an a different angle. They all measured their angles and found that they all summed to 180°. A couple of the kids seemed surprised that they all ended up with the same number. Incidentally, those that didn’t seem surprised were very absorbed with the flexible rulers I had brought to use. (Note to self: second-graders are easily distracted by anything novel.) We then talked about how any two angles, if they formed a straight line, would add up to 180° and how this was known as the supplementary angle theorem.
Once we had that down, we used it to prove the vertical angle theorem. It took them a bit to realize that the line created by adding supplementary angles doesn’t have to be horizontal (like in the picture above).
That’s all we got through today, but I plan on using this to show them that the interior angles of a triangle always add up to 180°. It might take us a couple weeks to get there, especially since next week I’m supposed to read them a couple more of the Sir Cumference books.
Out standing in their fields December 22, 2011
Posted by mareserinitatis in education, engineering, societal commentary, work.Tags: farming, kids, responsibility, work
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I was very surprised to learn that FrauTech apparently reads the Bismarck Tribune.
I didn’t think anyone outside of North Dakota did that. (Although I’m guessing this is not a regular occurrence.)
She linked to an opinion piece in the Tribune about how kids who are under 16 may not be allowed to work on farms unless they belong to their parents. I’ve had very mixed feelings about the whole bill. While I think that in places like California, these sorts of regulations are needed lest migrant children be put to work instead of going to school, the culture up here is different. Kids who work on the farm are expected to go to school, as well. Of course, this is partially because there are still vestiges of family farms up here, and I don’t think such things have existed in California for quite a while.
Contrary to what Frau said, I do have students who come from farms. A lot of them come from rural schools, and going into engineering is not easy for them. I was very dismayed to hear that one of my students had taken AP calc in his school, but his class of four students often spent the time doing things that were not related to calc. The internet has done a lot to make the discrepancies between rural and urban less obvious, but it’s still not completely leveled the playing field.
I tend to agree with the original opinion piece, however. My husband was a farm boy. I was didn’t have much experience on a farm, but my dad was expected to spend summers working on his grandfather’s farm. I’m sure that if things hadn’t gone bust in the 80s, I would’ve been out there once I was old enough, as well. And I see a lot of very bright kids who grew up on farms.
There really is a very different mindset in rural to semi-rural areas. Even though I didn’t work on a farm, I got a job when I was 15 because it’s perfectly reasonable to have a job at that age. Kids seem to be expected to take on responsibility a lot earlier, and I think that leads to a lot of positive life experience…something kids don’t get when all they do is go to school. (Some of this, I think, accounted for the large amount of culture shock when I went off to college and found out that most of my classmates didn’t have jobs in high school…and I’d already had two.) I think it also creates a much greater sense of community awareness. Kids who grow up on farms are out in the community, out working. They know their neighbors better, they are expected to interact with adults, and they are expected to behave as young adults. And in the case of most farming communities, they often pitch in to help each other out when someone needs it. You simply cannot substitute that kind of experience with anything else.
Right now, we’ve already lost a lot of ground. If you want to know what urban parents who are very closely removed from the farm do, they try to figure out ways to get their kids back onto a farm. My family lost their farm, and my husband’s family no longer farms…which means we’d really wanted our kids to go spend time with distant relatives or friends if the opportunity presented itself. These laws would prevent that. It’s even more frustrating in light of the fact that there are very few places that will hire kids under 16 any more. Where are kids supposed to learn responsibility as well as what it’s like to be treated like an adult?
But it’s not just responsibility. Kids do learn a lot of hands-on skills. Not all kids who are handy will be great engineers, but I’ve observed that background gives a lot of kids an intuitive notion of how to approach problems…at least in the ones that want to sit down and think it through.
Maybe not all farm kids will make great engineers, but I know a few that it helped. There are a lot of benefits to growing up that way, and it’s too bad more kids aren’t getting the opportunity. I’m not convinced it’s the only way to get those benefits, but it’s one of the best.
Kids’ misconceptions April 10, 2011
Posted by mareserinitatis in older son, younger son.Tags: kids, misconceptions, older son, younger son
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I’m amused by some of the assumptions kids make about the world.
When my older boy was about five, I asked him the difference between boys and girls. He said that girls were better at math.
The younger one recently told us of one of his misconceptions. His teacher had to leave early from school one day to attend a wedding. The younger boy mentioned that his teacher was attending someone else’s wedding because he was already married. While I know that’s no indicator, I hadn’t remembered seeing a wedding ring (and he’s a very young man who just started teaching two years ago), so I asked how he knew that.
“He’s an adult, so he’s married.”
That explains it. However, I’m not sure where he got that given we have several counter examples.
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Scientist, with kids February 19, 2012
Posted by mareserinitatis in career, education, engineering, family, feminism, grad school, homeschooling, older son, personal, physics, research, science, societal commentary.Tags: feminism, gender equity, kids, parenting, role models, sexism
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FSP has a post asking about the Local Mom Effect. That is, she wonders if being in a department with more women professors who have kids affects the outlook of younger women in the field. I find this post interesting…but also, I hate to say it, irrelevant.
Let’s put it this way: what women?!
When I started school at Caltech, I knew of two women professors out of all of math, physics, and astronomy. I only ever met one of them, knew she had no kids. I knew nothing about the other professor. When I decided to go back to school a few years later, I ended up in a physics dept. where the professors were all men. Later, I ended up in an electrical engineering department where the professors were all men.
I guess that, in my mind, the notion of being one of the few women in the department was no different than being one of the few women with kids in the department. When I went back to school, I had a kid already, so it wasn’t like I really had a choice about whether or not to be a childless woman in physics or engineering.
I will say that when I originally got pregnant as an undergrad at Caltech, I was told by my advisor that women couldn’t do calculus while pregnant and that I should drop out. Of course, he was a guy, so I seriously doubted he understood how women’s brains work while pregnant. (And it turns out that I can do calculus great while pregnant…I just can’t speak a full sentence coherently.) However, I guess I never took it as a message that women with kids don’t belong in science…I inferred that he meant it more personally, and that I myself was not a good fit for science. (Fortunately, major hopping got boring after a while, I ended up back in physics.)
When I went back to school, however, I felt that being the only woman or one of a few was very advantageous for several reasons. First, if I was the only woman or one of a very small number, I was already an oddity. A woman with kids is probably not much more odd than a woman without, and there was really no one to compare myself to (or say that I was doing it wrong). Second, I went back to school in North Dakota, and it really seems like people here more or less expect you to have kids no matter what you’re doing. I know that grates on some people, but for me, it was a blessing: having kids is just another part of life, and most people here learn to do their jobs while having them. (Also, I can’t recall anyone having a fit if I said I couldn’t make it to something because of kid-related issues.) Third, I was older than the average undergraduate or even grad student, so I think people assumed that it was pretty normal for someone my age to have kids. The fact that the younger students didn’t have kids was simply a function of age and never made me feel self-conscious that I did have kids. Finally, when I started my MS, my advisor was fine with the fact that I was homeschooling the older boy and would only be doing my degree part-time. He said this was really no different than other students in the department who were working full-time and pursing their degree part-time, as well.
I have been told, especially when doing my PhD classes, that it was “really cool to see a woman in science with kids”, especially by some fellow grad students. Until I started my PhD, I really hadn’t expected it to be a big deal. It had never occurred to me that I might be a “role model”…but I keep hearing it more than I ever expected to. I also suspect it’s because I often had kids with me or family issues that were more apparent to fellow grad students. Many professors try to maintain a more professional relationship with their students, and it doesn’t surprise me that many grad students don’t see how having kids affects the lives of the professors or that they don’t realize some professors have kids at all.
Realistically, I only got here because I didn’t really know that what I was doing was unusual in any way. If I had been surrounded by women who had kids but never let it on or didn’t have kids, I might have felt self-conscious about being a mom already. With no one to compare to, however, I just assumed that it wasn’t any more abnormal than a woman without kids.