Math is a #firstworldproblem June 1, 2014Posted by mareserinitatis in education, math, teaching.
Tags: math, teaching
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I was recently having a conversation with a friend about teaching when she launched into a complaint about students not understanding logarithms. The conversation became somewhat off putting because this friend fell into the trap of equating mathematical knowledge with intelligence. A lot of people do it: English majors will imply one is an idiot if one doesn’t appreciate the succinct stoicism supplied by Hemingway, for example. (And I use this example because I’ve been on the receiving end of such criticism: I can’t stand Hemingway, and it was torture having to relive it when the older son was reading and explaining Old Man and the Sea for one of his classes.) Hemingway hating aside, many of us tend to use certain sets of knowledge as a reflection of intelligence, and that’s rather simplistic (and not all that intelligent of us).
The reason this particular discussion irritated me is because there is a level of classism that seems to go hand-in-hand with assumptions about mathematical literacy. While being mathematically literate is a good thing, the reality is that I’ve met very mathematically illiterate folks who were able to navigate through life with no problems. Not knowing logarithms didn’t hinder them professionally or personally. Not knowing logarithms was no indicator of their intelligence. Not knowing logarithms didn’t stop them from appreciating, or at least tolerating, Hemingway.
In my experience, math illiteracy often has a basis in background. Kids whose parents are highly educated and/or wealthy often have a greater chance of both being exposed to advanced math concepts as well as being able to use such concepts more proficiently. In my classes, I’ve noticed a huge problem: kids from larger, urban schools and who aren’t minorities seem to be more likely to stick with engineering than either minority students or those from rural backgrounds. Kids who have engineers in their family are more likely to stick with it, as well. While this isn’t a surprise, and there’s been a lot of explanation as to why this is so, I suspect exposure to and comfort with math concepts is a big factor. Not only are they already feeling at a disadvantage because they are having to start farther behind their peers in the curriculum progression, they are often advised to change majors because their lack of math implies they aren’t cut out for the rigors of a technical profession. I’ve heard about this happening to my students as well as it happening to me. (I was once told that I should never have been accepted to college because I didn’t know Euler’s formula giving the trigonometric form for imaginary numbers.)
Living through those types of experiences has made me go out of my way to ensure that my kids have an excellent background in math before entering college. At the same time, because I’ve made a point to provide that level of education, I’ve become aware of many kids who don’t have those opportunities. There are a lot of bright kids who are forced to stick with grade level instruction despite the fact it’s obvious they’d benefit from acceleration. And then there are the kids for whom rigorous instruction and acceleration aren’t possible because it’s beyond their parents’ means and ability.
Back to my friend, it was hard to convince her that these kids weren’t stupid, and she seemed unwilling to accept that there wasn’t something wrong with the world that kids who don’t understand logarithms can actually go to college. I apparently couldn’t convince her that they’d be okay and maybe they just needed a bit more guidance to assimilate into the world of mathematical literacy. Perhaps we should’ve discussed literature instead.
A Rite (Triangle) of Passage May 13, 2014Posted by mareserinitatis in education, family, gifted, homeschooling, math, older son, teaching, younger son.
Tags: homeschooling, learning, learning styles, math, pythagorean theorem, visual-spatial, younger son
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The younger son recently started his pre-algebra class. Somehow, this has made math a bit better. I think the fact that it has algebra in the title makes him feel very accomplished and that, in turn, has made him more enthusiastic about math.
The other day, he was doing some of his homework, and the lecture was confusing to him. I listened to the lecture and then said, “It makes more sense if you draw a picture.” He responded that, “Pictures always help me learn better. I guess the math program doesn’t realize that some of us are visual learners.” I was both amused and quite stunned. I think I’ve been discussing educational theory a bit too much at the dinner table. I can tell he’s listening to us.
Tonight, he hit a milestone. He called Mike over, and I followed, so he could ask us how to pronounce “pythagorean.” He was sure he’d heard us talking about it before (yeah, we discuss this stuff around the dinner table), and he wanted to be sure that was what it was.
“Oh, wow!” I said. “You’re doing the Pythagorean Theorem. That’s awesome!” Suddenly, there was an impromptu round of cheering and high-fiving. The older son even came over and gave his little brother a big hug, saying, “Woo hoo! The Pythagorean Theorem is awesome.”
As the lecture progressed, it reiterated the terminology, focusing on right triangle legs and hypotenuse. Given I’ve had ZZ Top in my head, I had to immediately sing, “She’s got legs! She has a hypotenuse!” I wasn’t able to come up with much more, though.
Yes, I have to admit that I realized how odd it was, in retrospect. We were having a celebration that younger son had made it to the Pythagorean Theorem, and we were all making a huge deal about it.
But younger son didn’t think so. He thought it was awesome and giggled continuously for the next few minutes. I guess he likes having a math cheer team.
The “dear teacher” letter November 11, 2013Posted by mareserinitatis in education, gifted, math, teaching, younger son.
Tags: gifted, gifted education, math, teaching, younger son
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Last week was parent-teacher conferences at the younger son’s school.
If you don’t know, I dread these things. I had been feeling better after last year, but then I realized I’d been lulled into a false sense of security. In particular, two years ago, younger son’s teacher was having a fit because he wasn’t doing math with all the other kids. The thing we kept getting was, “He’s really not all that great at math.” Last year, we attempted to have the younger son do his math curriculum at school. We kept trying for a month. However, it was very clear that his teacher was unable to help him, so they sent him out into the main office area where there was a lot of traffic…and no one to help him. We said we would take care of it at home and didn’t hear another thing about it again.
At the beginning of this year, there was some noise that he would do the math at home in addition to the math at school. We quickly put a stop to that and said, “You’re punishing him for being smart.” Making him do two sets of math a day is no good.
The thing is, I really don’t understand this. He’s doing excellent by standardized testing standards. What more do they want? I sure hope they aren’t saying, “If Johnny worked just a bit harder, he would be at the 98th percentile instead of the 96th!” Or are they saying that if they worked harder, they could beat Suzie’s score in math? I seriously doubt it…and if they are, then I think they’re a little bit whacked. All I can think is that this is either a control issue or a conformity issue. It has absolutely nothing to do with his math ability.
Which, incidentally, isn’t all that good. “You know, he’s not the top student in the class as far as math testing goes.” That’s what we got. I suspect this is, “He’d be doing better if he was doing math with all the rest of his classmates,” as in I should feel guilty for making him miss out on the stuff his friends are doing.
Unfortunately for her, I really get irritated with things like guilt trips and appeals to social norms. I really don’t care if my kid is doing something different.
The other issue is that it has *everything* to do with his math ability. She’s taking math scores and comparing them to other kids. We already know that his processing speed may not be that great and that he’s not the kind of kid who likes to spend time memorizing things. Math at the elementary level is all about those things: computation and recall. However, his reasoning and visualization skills are really great. Like most elementary teachers, I think she doesn’t understand that math is more than multiplication tables. She recognized that he knows those things, but that maybe he needs time to figure it out rather than having it at the tip of his tongue. What she doesn’t realize is that he’s not the kind of kid who is going to tolerate endless drilling of memorization facts when his real strengths are in logic and reasoning. Would you like math if it was always doing the types of things you hate? This kid is stoked to get into algebra soon…why would I want to kill that and tell him he needs to practice flash cards more?
There are ‘optional’ tests on the MAPs in science and science reasoning. His scores in both those areas were the same for 10th graders and above, according to national norms. Why do they always want to hold kids back to their weakest skills, even when those skills are still obviously above average for their age mates? Even in his ‘weak’ area, he’s still near the top of his class…and they conveniently ignore his strengths and pretend like those have nothing to do with the issue at hand.
I have to write this teacher a letter with some follow-up information. However, there is a part of me that wants to ask why there is such a focus on holding younger son back when they should instead be focusing on allowing ALL of the children to perform at a level appropriate to their abilities.
You see, when she said he wasn’t at the top of the class in math, I didn’t feel guilty. I felt bad for those other kids because they were being held back and not having the opportunity to work on interesting and challenging work the way younger son is. Rather than being ashamed that my son is getting to do things he finds interesting and challenging (so that he’s also learning about having to work hard and deal with frustration), I wondered why the teacher and school aren’t ashamed of what they’re doing to those other students.
You could be a teacher October 16, 2013Posted by mareserinitatis in career, education, feminism, research, science, teaching, work, younger son.
Tags: education, high school, higher education, math, teaching, younger son
The older boy snickered.
“I like to think so,” I responded.
There was a brief silence followed by, “Welllll………you’re good at math, and you’re a teacher…maybe you should teach math at a high school!”
What followed was a long explanation about how I just physically can’t handle the idea of teaching K-12. Teaching 6 hours a day, grading, prep, etc. Actually, it’s mostly the teaching. Teaching more than 4 hours turns me into a puddle that can’t function until I’ve had a good night’s sleep. Teaching high school is not the ideal profession for introverts. There’s also the fact that, frankly, it would get boring to teach high school math after more than a year or two. The math is what interests me more than the challenge of helping students to understand (though that is an interesting problem when the material is also sufficiently intellectually stimulating). I think he gets it, but he still likes the idea of his mom as a math teacher.
This did bring to the surface some thoughts I’ve been mulling over. Does he see me as a teacher because he already knows I teach or does gender roles have something to do with it? I’ve been pondering this a lot because I get the sense that there are some academics who really do view teaching through a gendered lens and therefore think I’d be better off at a community or liberal arts college. In fact, I imagine there’s a blog post where I discussed someone telling me as much, but I’m not going to dig it out now.
One thing that has occurred to me is that, if I want people to look at my research, I may actually actively have to avoid things that will stick ‘teacher’ into their heads when they think of me. That is, it’s probably a good idea to actively avoid involvement in education conferences and societies except at a cursory level. Teaching should be kept at a minimum. I enjoy the service work component and the idea of exploring interesting aspects of STEM education. I also really enjoy interacting with students (but not all day long). I don’t like the idea that it means that my other abilities and accomplishments will be overlooked. Maybe that’s taking things too far, but I don’t really know how to cement the ‘researcher’ thing into people’s brains unless that’s the only thing they see when looking at my CV. Maybe once the ‘teacher’ version of me has been wiped clean, it’ll be okay to begin dabbling in serious educational research pursuits.
That’s obviously not what my son was worried about. He simply wants me to have a job I enjoy…and maybe there’s a bit of an ulterior motive as he hopes I’d be home more during the summers. It’s a nice idea, but the other nine months of the year probably wouldn’t be all that enjoyable for me…especially if doing research was secondary, or worse, nonexistent.
All that being said, I think that if I do ever become a math teacher, I want the above tshirt. (You can get it here, if you’re curious.)
It’s official: younger son is smarter than I am. October 3, 2013Posted by mareserinitatis in gifted, homeschooling, math, younger son.
Tags: EPGY, math, younger son
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Younger son isn’t one you’d pinpoint as being very gifted…at least I wouldn’t. I have had random people tell me that he’s quite bright, but that’s never what has come across to me. He’s very outgoing and socially conscious…VERY big on morals and ethics. Fun. Goofy. Just wants to get his homework done so he can play.
In other words, to me he seems like a perfectly normal little boy.
In math, he’s one of these kids who struggles with computation. Not as badly as some kids (*ahem* older brother *ahem*), but it is his computation that slows him down. He’s enrolled in Stanford’s EPGY program for math, which we do at home (even though the school still grumbles occasionally). I thought he’d get into the program, but I was honestly stunned at his ability to answer logic questions. I remember when he took the test, I was watching, trying to puzzle through some of the questions and he was already onto the next question. It made me realize that there’s obviously some ability there…but because of the computation issues, he struggles to express it.
When helping the younger son do some homework on percentages earlier this week, he made a very interesting comment:
When you divide an even number by an odd number, except five, you get a repeating decimal. When you divide an odd number by an even number, though, you just get a remainder.
Is that right? It sounded like it was plausible, but I’d never come across such a rule. I had to look it up.
According to Wolfram’s MathWorld, if the divisor is a multiple of two or five you get finite decimal expansion. If, however, the denominator contains a prime other than 2 or 5, you’ll get a periodic decimal expansion (i.e. repeating decimal).
So he was very close and might have been able to prove it by induction for very small n…if he knew how to do proof by induction.
It kind of stunned me, though, that he was trying to figure this out and neither Mike nor I had ever given it any thought.
Math illiteracy at the bank September 29, 2013Posted by mareserinitatis in family, math.
Tags: math, Mike, money
The older son received a check, and we went to the bank to cash it. He was supposed to put half in savings and keep the rest for spending money. The check was for $53.50.
When we got to the window, Mike told the teller that half should go into savings and the rest should come back as cash. We were in our car, so said that $26.75 needed to go into savings, but he didn’t pass that info to the teller. After a minute, she asked if we wanted the $.50 back as cash. I could only roll my eyes because I knew what had happened.
The teller had deposited $26 into savings and returned $27.50 as cash. Apparently it was a bit too intimidating to take that $1.50 difference and divide it in half. We just took it and left because it wasn’t worth getting upset about it. However, I told Mike that he needs to stop overestimating people’s math skills…even if the person is a bank teller.
Wordless Wednesday: equations in the window July 10, 2013Posted by mareserinitatis in family, math, photography.
Tags: equations, math, Mike, pictures, refraction
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Math is useless July 5, 2013Posted by mareserinitatis in math, physics, Uncategorized, younger son.
Tags: chemistry, fireworks, math, physics, younger son
A lot of kids later become adults who think that math is a useless field of study. Why would I need to know that?! I’ve come across a lot of math books that are trying really hard to express how one can use math in order to motivate the learner by connecting it to an application as well as make it more interesting. Connect math to the ‘real world’ is not something that comes easily to most people.
Independence Day motivated a lot of discussion with the younger son about fireworks. While driving to our pyrotechnic fix last night, the younger son started asking what he would need to study in order to make fireworks. Mike and I both said, “Chemistry.” We both were assuming you need to know a lot about which chemicals to add to make particular colors. I guess it didn’t help that I’d seen this image earlier in the day:
We were both surprised when the younger boy said, “And I’d need to know math, too!” We agreed. And then he continued:
You can calculate how much of each chemical you need, how high it will go (a bigger explosion should be farther away), how fast it will go, how long it will take to before the explosion happens, how hot it will get…
He elaborated on each point and ended up spending somewhere between five and ten minutes telling us all the ways one could use math in making fireworks. I was completely stunned. There is this huge difficulty in getting a lot of people to understand that you can quantify and predict (through physics) so many things we take for granted. Yet, here is a kid who hasn’t even reached an age in the double digits who seems to understand that all of these things can have some sort of number associated with them and that they behave in ways that can be predicted by mathematical equations. Mike and I both sat there with our mouths hanging open, shocked at what we were hearing.
However, as soon as the fireworks came out of the box, the little kid in all of us came out and just wanted to go blow things up.
I don’t think I’ve ever been that bored February 23, 2013Posted by mareserinitatis in math, younger son.
Tags: math, younger son
Me: “Was this something your teacher had you do?”
Younger son: “No, I was just bored with reading.”
I counted…they both appear to be correct.
Matrix multiplication October 24, 2012Posted by mareserinitatis in math, older son, teaching.
Tags: math, matrix, older son
The older boy was working on matrix multiplication in math. He got very testy with me: “Why do I even need to know this?” I replied that it’s used all the time in calculus-based physics. That disappointed him as he would like to take it some day.
He was super frustrated because the explanation on the computer was very…verbal. Unfortunately, I couldn’t locate my favorite linear algebra book, so I tried to go through and explain it while making some diagrams.
He still had some problems and then kept asking if they were somehow related to Punnet squares. Um…not really.
And then he made this diagram.
I have to admit that it’s not how I would think to multiply matrices…or at least I think there are easier representations. (In my mind, at least.) However, this did work in that it made sense to him, and once he had figured out enough to draw this, he was able to finish the rest of the problems on this concept.
This just goes to show that we don’t all think the same way, I suppose. The way we think about things may not always be the easiest for someone else.