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Meet the old math, same as the new math January 22, 2016

Posted by mareserinitatis in education, homeschooling, math, younger son.
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The younger son is beginning adventures in algebra, and I had a hard decision to make.  He’d been using computer-based programs to learn math, but Mike and I decided we didn’t want to go that route any longer.  I had spent a lot of time looking into curriculum with the older son, so I already had a textbook available (Jacob’s Elementary Algebra), and it’s one that has received excellent reviews.

It’s also 37 years old.  Apparently there’s a newer edition, but that’s not the one I bought.

I had one concern with using this book.  A lot of the standards surrounding math curriculum have changed and become standardized.  There are a lot of texts available that have been evaluated and measure up to those standards.  I was worried that by going with an older book, I was going to shortchange the younger son in his education.  (I think that’s something almost every homeschool parent worries about.)  The problem with a lot of the modern curricula, though, is that  I really don’t like it.  While I think the sciences generally benefit from taking a problem-solving approach, I’m not so sure that’s the best way to do it with math.  Sure, I think there are ways to teach it more effectively, especially in terms of using active learning strategies and hands-on learning.  Reasoning is important, but so is process, and kids need to come out of the classroom very fluent in process and computation.  I’m one of those old-fashioned types that thinks you’re better off giving your kids a multiplication table than a calculator.

I had issues with one curriculum that was being used locally, for instance, because it taught division as repeated subtraction without teaching long division.  It also taught matrix math and repeated sums without teaching the standard multiplication schemes.  For those who are familiar with all the controversy over curricula and math standards, I’m sure this is old hat.

I was pleasantly surprised, then, to find that this 37 year old book assumes that the student knows long division and standard multiplication.  However, in the first chapter (which is review), it introduced both matrix multiplication and repeated division as alternative methods.  Repeated division was done side by side with long division as a way to show how long division works.  However, it was not suggested as a good way to do division but to augment student understanding of long division.  Matrix multiplication was proffered as a bonus problem, but I made sure younger son understood how to do it.  I found with the older son that he was less likely to stumble on multiplication problems if he used the matrix method but would have a hard time keeping things straight with the standard method.  It’s a good tool to have in your toolbox, and I have even pulled it out when I had to do a fairly large problem by hand despite only having learned it about 10 years ago.

This left me feeling like this book was going to work just fine.  In fact, I’m rather disappointed that I didn’t get to use this book in high school.  (It was already out of print, sadly.)  Apparently, though, Amazon reviewers, internet philosophers, and other homeschooling parents really do know what they’re talking about.  Feynman may even have approved.

Stop telling boys to go into STEM December 18, 2014

Posted by mareserinitatis in education, engineering, feminism, science, teaching.
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Stereotyping is always a bad thing, and most people don’t realize that men suffer just as badly from stereotypes as women.

Let’s look at science: there has been a ton of work going into how to attract girls and women into scientific endeavors, particularly those that are very math-intensive.  Much of the discussion centers on countering two issues: the first is the societal expectations that women go into ‘caring’ professions like teaching and nursing and the second is the stereotype that men are better at math.  There is nothing wrong with these efforts, but there’s a flip side to this stereotype that has a negative impact on men: there are a lot of men who go into STEM fields (probably engineering moreso than science) that probably don’t belong there.

Lest you think I’m just being negative toward men, this is actually something a man told me.  I had an English professor who was one of the best college teachers I’d had, I think in part because he was very knowledgeable in science.  In fact, he’d received a degree in engineering from Stanford but then shuffled around for several years before finally getting a master’s degree in English.  During one conversation, I asked him why he got a degree in engineering when he really loved literature.

There’s a strong expectation that if you’re a smart boy who’s good at math, you’re going to go into engineering.  That’s what everyone expected, so that’s what I did.

During the course of my teaching career, I’ve seen a lot of this.  I like to have students write me an introductory essay so that I can learn more about them and what they were hoping to learn from the class.  Many of them reiterated almost exactly what my professor said: “I went into engineering because I was told it was a good career for someone with good math skills.”

I’m not saying it’s not a good career for someone with math skills of either gender.  However, making a career choice should not be an either/or proposition based on problem-solving ability (lots of careers use that), and people are multi-faceted.  People can be good at math as well as art, literature, music, biology, communication, caring for others, etc.  Just because you’re good at something doesn’t mean that’s what your calling is nor necessarily where you should focus your energy.

While the majority of my best students were men, strictly as a result of the skewed sex ratio in my classes, the women were almost always in the top 20% of the class.  None of them were there simply because they were good at math: they almost always really wanted to be an engineer.  However, the least engaged students were always men: a lot of them were there because they hadn’t found their passion and felt they had to do something.  Engineering was it.

The flip side of the ‘men are good at math’ stereotype is that many of them go into it even when they would be much better off doing something else.  They’re discouraged from pursuing more ‘feminine’ careers and made to feel like failures if they don’t enjoy it.

So do the boys a favor: if they’re not sure where they want to go, don’t make engineering the default answer even if they are good at math.

 

Friday fun: The Rubik’s Cube November 21, 2014

Posted by mareserinitatis in math, younger son.
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As a freshman in college, I remember going to a toy and puzzles shop in Old Town Pasadena.  I became engrossed in a 3D puzzle display.  You know the horseshoes connected with chains that have a metal ring?  That’s the kind of puzzles in the display.  I spent an hour and a half looking for one I couldn’t solve because I decided that if I couldn’t solve it, I would actually buy it.  An hour and a half later, I’d gone through almost 30 and the store owner was giving me the stink eye, so I left.  My date was also rather annoyed, too, though apparently impressed with my puzzle skills.

The one puzzle I have never solved, however, is the Rubik’s cube.  The younger son just received one about a week ago, so I decided to go ahead and buy him a book to solve it.  I had one as a youngster, but was never able to solve it except through the brick removal-and-replacement method, which, while extremely efficient, kind of defeats the purpose.  I’ve decided, however, that it’s about time I learn how to do it, so this will probably be something we can do together over Thanksgiving.  I did some searching for a video tutorial, as well, and came across several as well as a lot of fun videos.

This was one of my favorites, and it makes me wonder what are some other unusual ways that people solve Rubik’s cubes.  While I think I could feasibly do it one-handed (at some point), juggling with the other hand is probably out.  I’ll have to see what the younger son thinks his chances are.

 

Math is a #firstworldproblem June 1, 2014

Posted by mareserinitatis in education, 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, 2014

Posted by mareserinitatis in education, family, gifted, homeschooling, math, older son, teaching, younger son.
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pythagorean_catThe 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, 2013

Posted by mareserinitatis in education, gifted, 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, 2013

Posted by mareserinitatis in career, education, feminism, research, science, teaching, work, younger son.
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math_teachers_tshirtAs we were settling in for the ride home after swimming, the younger son asked, “Mom, you’re good at math, right?”

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, 2013

Posted by mareserinitatis in gifted, homeschooling, 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, 2013

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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, 2013

Posted by mareserinitatis in family, math, photography.
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