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Second grade logic and rulers February 23, 2012

Posted by mareserinitatis in education, gifted, math, teaching.
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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.

My many hats February 9, 2012

Posted by mareserinitatis in computers, engineering, gifted, homeschooling, math, teaching, work, younger son.
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A couple weeks ago, my blog was promoted by a couple of sites and the hits started flowing in.  I commented to someone (most likely Gears) how it’s nice to be recognized for my blogging about engineering but frustrating for the lack of recognition for my actual engineering work.  Guess I should’ve waited a couple weeks.

Normal work has also been crazy. I’ve been given full control of the Minion and have thrown him in on a new project where he’s learning everything from scratch.  It’s similar to projects that I’ve done, but even more complicated and using a different program.  So our next couple weeks are going to be real fun as we’re going to be trying to make our way through using this new program and occasionally resorting to the old program for reality checks.

The other serious challenge I’ve been dealing with this week is long division.  It’s pretty scary stuff, especially when you have a seven-year-old who is fighting some rather strong perfectionistic tendencies.  He’s been getting to the long division portions in his computer math, and he starts to shut down.  I’ve been getting more and more frustrated with it, so I decided to put an end to it tonight.  I went back and printed out some of the older homeworks so that we could take a couple steps back.  I think the problem is that he really thinks he can do everything in his head.  I have to admit that his ability to do mental math far outweighs mine: I simply have to write everything down.  However, he’s starting to hit the limit of this particular ability, and so he freaks out whenever he has to do a problem where he can’t do it all in his head.

I told him that tonight’s homework was going to be doing some work sheets.  With the problems written out on paper, he didn’t seem to have this idea that he had to do everything in his head.  The first couple were challenges, but then he started getting the hang of things and was able to execute the last few problems very quickly.  By the time we had finished, he was doing 3-digit numbers divided by 2-digit numbers with no problem.  We’re going to do some more difficult problems tomorrow and then try heading back to the computer.

We tried a similar approach when he started to get stuck on multiplication a couple months ago.  I guess there are some things that really have to be written out to be understood.  I just hope he starts to make regular use of his notebook from here on out.

Evals! Oh happy day! February 6, 2012

Posted by mareserinitatis in education, engineering, teaching.
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I had to make a run down to campus and, while there, I picked up my evals from last semester.  Apparently there were no comments on the evals because I just received a sheet for each class summarizing my ‘grades’.

I had been dreading this day for quite a while.  I had a couple of cranky students at the end of last semester.  I was also worried.  When teaching geology labs, it seemed like I got some very pissed off students who left simply nasty evals.  (I discussed this on my old blog a couple times.)  Compared to some of the other TAs, my evals usually came out worse.  A lot of this had to do with the perception that I was a harder grader.  In reality, I graded more easily on labs and more harshly on exams, so my averages were about the same as everyone else.  But that’s not what the students think.

Anyway, so I sat down with my numbers and discovered that some classes had better or worse perception than others.  For instance, my first Thursday class gave me the lowest scores (3.6 out of 5 for a couple questions) while the class right after that gave me the highest scores (4.5 of 5).  My Tuesday classes were somewhere in between.  The smallest class was the happiest, but the largest class wasn’t the unhappiest.  I’m not sure what happened with that one Thursday class, though, as it was a lot lower than the others.  Maybe I need to make sure to regale future students with my huge stack of nerdy science jokes.

They said the average for the department was around 4.2…but I realized that they were talking about the University Studies department, not engineering.  (The class is listed under University Studies, but some departments choose to have their own teachers for the class, as was the case for the sections I taught.)  I’m actually relieved that my scores were on par with the rest of the University Studies department given I heard many complaints about how much more work my students had to do relative to other sections (which weren’t being run by engineering).  Despite the fact I “worked them to death,” they were still okay with it.

That’s good because it’s not going to get any easier for them.

It’s looking,therefore, like last semester went as well as could be expected, especially given it was my first time teaching it and the whole thing was an experiment.  I wish there was some way to see if the kids really did get anything out of it to help with their long-term academic goals, though.

Are grad classes a waste of time? February 5, 2012

Posted by mareserinitatis in education, engineering, geophysics, grad school, physics, research, solar physics, teaching.
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I have seen both Gears and Massimo post comments about how grad classes are a waste of time.  Last week, Gears said this in his EngineerBlogs post (which I’d like to address several points, but this will have to suffice for tonight) and Massimo has suggested ‘workshop’ classes. I have to say that I disagree with both of them, but I think it’s because of my weird background.

For review, I did an undergrad in physics with a math minor, my masters in electrical engineering, and my PhD will officially be in geophysics (as was all my coursework) though my project is actually on solar physics.

Honestly, I’m not sure I could have done that without the coursework.  On the other hand, I think my attitude would be different if I’d stayed in one field. In my work in electrical engineering, I use almost every class I took, especially the grad courses.  I use antennas and microwave engineering a lot…so much so, that my circuits classes are probably the most rusty.  (I know, that’s completely backwards for an EE, but that’s how it goes sometimes.)  I find myself often wishing I’d had the opportunity to take some advanced signal processing, as well.  And one of the most useful courses was numerical techniques in electromagnetics.  Not only does it help me with the work I’m doing in EE, it’s also helping with many of the things I’ve run into looking at geo- and solar physics research.

The flip side to this is that if I’d continued on to get a PhD in EE, any further coursework would not have been terribly relevant.  I think there’s an optimum point, and that may have come earlier if my undergrad was in EE.

My classes in geophysics were not as useful, and I think there were probably 2.5 classes that had anything at all to do with my research and what I’m doing now.  Realistically, for the stuff I was interested in, I probably should have looked at a PhD in physics or astrophysics…but that may not have been much better if I was taking a bunch of classes on stuff that had no bearing on my research, either (which is likely).  However, the 2.5 classes that were useful have been REALLY useful.

I’ve got a breadth in classes that most students never get.  This is one thing that I think is a bit of a sticking point for some students.  Most places have a ‘breadth requirement’ – i.e. so many classes outside of their department.  I think this is a good thing as it helps people to see what other types of things could be relevant to their research.  I really think this is something that should be required because of all the ideas that come from seeing how different disciplines approach their fundamental problems, and even having some exposure to what those problems are is a benefit to students.

The real problem, in my opinion, is that so many places require a LOT of credits.  It’s fairly common in most good EE programs to require somewhere between 50 and 60 credits of JUST coursework.  I don’t like the idea of no classes, but I really think you could trim them back and just make students take classes that are relevant to their research as well as a couple classes for breadth.  I was very disappointed with my PhD program because once you hit advanced candidacy status, you’re not allowed to take any more classes unless your advisor is willing to foot the bill.  Not likely because most advisors want their students working on their research and getting done (not that I blame them).  The down side is that there are a couple classes that I could have really used but was unable to take because they didn’t fulfill the requirements for my degree.  Most of my classes had to be in the department as I’d already fulfilled my breath requirement, so taking a class here or there outside the department was viewed as a waste of time because they didn’t allow me to tick off some of those boxes in the red tape.  And of course, it becomes obvious that you would really benefit from a course once you’ve hit advanced status and can’t take any more.

It would be nice if there was a system where your advisor could sit down with you and figure out where you’re interested in going research-wise and plot a course through the classwork that makes sense and is flexible.  Wouldn’t it be nice if you discovered you need to learn about a particular topic and could then go take the course on it? It makes more sense to me than filling in boxes to get to a certain number of credits or hedging bets that something will be useful later on.

Let’s face it: research degrees are already very specialized and take a long time, so it would make more sense to cut the classes down to those that are relevant.  This would ideally save time without sacrificing the background required for a research project. Finally, a really good option, which more universities ought to allow, is independent study classes.  During my MS, I took one class as an independent study working on emag stuff.  It was awesome as I got the material I really needed in a more structured way and was able to do a project which (I’m still hoping) would be a foundation for some decent research down the line.  Therefore, I don’t feel grad classes are a waste of time, as long as they make sense, and I wish universities would be more flexible in some of their requirements.

Am I missing something here? January 27, 2012

Posted by mareserinitatis in education, engineering, science, teaching.
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Like everyone else, I came across the article on why college students leave engineering.

I was reading it with my jaw hanging open.  Specifically this:

The typical engineering major today spends 18.5 hours per week studying. The typical social sciences major, by contrast, spends about 14.6 hours.

My first thought was: Where the heck can you go to school and study for 18.5 hrs/wk and still manage to pass enough classes to get an engineering degree?!

My second thought was that it explained something that has been puzzling me.  Last semester, my students complained about the amount of homework I assigned for my 1-credit class.  There was about 1  homework assignment per week, and I figured this meant they’d be spending an average of 1-2 hours outside of class on assignments.

When I started school, the rule of thumb was that 3 hours per week outside of class PER CREDIT was required for an A, two for a B, one for a C.  This meant that if you planned to go to school full time (which was 12 credits per semester) and get an A average, you needed to be spending about 36 hours per week just on homework in addition to your 12 hours of seat time in a classroom.

I also learned that, for some classes, this was a significant underestimate (usually math, engineering and physics classes) while for other classes, it was an overestimate.  I remember one senior-level sociology class that I took where I spent, on average, three hours per week on homework and still came out with one of the highest grades in the class.  This is why I always felt it was a good idea to have a nice balance between technical and non-technical classes: it would even out the homework load a bit.

My understanding of a typical homework load is obviously a couple decades behind.  (Although I am not sure I plan to change my tune any time soon.)  However, I did feel good about one point in the article:

STEM fields (science, technology, engineering, mathematics) have also had less grade inflation than the humanities and social sciences have in the last several decades.

Apparently you can study less in engineering than you used to have to obtain a degree, which I have to admit bothers me a bit.  However, it’s still harder than humanities and you’re more likely to actually have to earn those grades.  Despite the fact that we’re probably pushing STEM fields more than we really need to, I do hope employers take that into consideration.  STEM students have to be more committed to make it through their fields, which are also more technically challenging.  I’d think that should be worth something.

Why are the women so good? January 21, 2012

Posted by mareserinitatis in education, engineering, feminism, teaching.
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I’d been thinking about writing this post last semester.  However, it slipped my mind until some trollish comments showed up on EngineerBlogs today.  I think that Chris, Gears and Katie gave the troll a good smackdown, but one comment bothers me:

few women are capable of handling these kind of demanding environment.

I’ve heard this before (pretty much since I started as an undergrad).  However, after teaching my class last semester, I have to wonder what the hell these people are talking about.

I had 90 students last semester, 5 of whom were women.  All five of those women were easily in the top 25% of the class and were more likely in the top 10% of the class.  They were the students who repeatedly handed in assignments on time and seldom (if ever) had to redo any of them.  I will say that none of them chose to do the programming – but that is likely because they had turned in all the optional assignments required for an A before the matlab assignments were given.

If anything, what I saw was puzzling to me.  The women seemed the most prepared to meet the demands of a college class, were able to communicate well both in written and verbal form (and one of them was a non-native English speaker), and contributed well and frequently to the class.  It was almost strange how they were on top of things when the majority of their male classmates were struggling.

I’ve heard it argued that the women most likely to be in engineering are generally those who are in the top of their classes.  Women who may be good at math but not outright brilliant will be swayed to go into other careers.  From what I could see, this was true.

If you listen to trolls on the internet, you get the impression that women are incompetent engineers, however.  The women in my class were some of the most competent and motivated students, but I admit that they were more passive than the male students, which I still think leads the male students (and probably later on, male professors) to believe that the female students don’t know anything.  But it’s interesting to hear this comments after witnessing the exact opposite of what everybody “knows to be true”.  I can only think that people who make these comments are really overestimating their own abilities or wrongly judging what it takes to be a good engineer.  Maybe both.

Outnumbered January 5, 2012

Posted by mareserinitatis in gifted, math, teaching, younger son.
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Today I’m going to be working with the elementary students again.  This will be interesting as I completely switched gears from what we were doing before.  The stuff we were doing before was fun, but as we move through the book, it looks like they need a lot of multiplication and division…which most second graders don’t have.

Today, we’re going to learn about other number systems.  In particular, I’m going to have them pick a number using Indo-Arabic numerals and ‘translate’ into other numbering systems – Egyptian, Roman, Babylonian, Mayan, and Chinese.  This will give us an opportunity to talk about different bases, positional numbers (i.e. the concept of place value), and how many systems don’t have a zero.  (Although, there’s debate in some cases.)

After doing the prep, I’m SO glad that we don’t use the Babylonian system.  Base 60?!  No wonder my math professor got annoyed when we used degrees.

Thanks to the MacTutor History of Mathematics Archive for the picture!

Lessons learned: teachers need organizational skills, too December 19, 2011

Posted by mareserinitatis in education, teaching.
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I have now developed a greater understanding of a strange professorial quirk that I observed over the years. I had at least one professor each term who would get visibly annoyed if you tried to give them an assignment at any time other than the first thirty seconds of a class period.

My understanding is due to that fact that I have recently become eligible to join the Super Secret Society of Teachers Who Have Lost a Student’s Assignment.  (I’m suffering from a cold, so I was unable to come up with a snappy acronym.  Please feel free to make an effort on my behalf.)

*headdesk*

When I was teaching geology labs, I was usually teaching four sections each week in a different building. I found that the best way to keep track of student work was to have four plastic filing envelopes. Each envelope was a different color, and I always knew which one to grab before each class.  At the beginning of class, I’d hand stuff back.  At the end of class, it would all get filed away in my envelope.  This was straight-forward, and I never lost any homeworks this way.  The labs were done in class and handed in at the end.  If they had to hand something else in, it went into my mailbox, which was in the same building as my office (but different than the labs).

This semester, I had 90 students in four classes, in three buildings.  My mailbox was in a different building than two of my classes, and all of them were in different places than my regular office.  I usually had two of my envelopes with me (two classes were on Tuesday and two were on Thursday).  Students also had the option of submitting homeworks online, as much as I hate grading those.

What I hadn’t anticipated was running into students who would randomly hand me homeworks between classes, leave them at the department with the admin staff, or all sorts of other unexpected things.  And, as it happens, I ended up misplacing some homework.  In fact, I went through and filed everything on my desk, and still never found it.  I believe it has ended up in the same place that unmatched socks end up…except that paper always ends up falling back out and will likely be found in the spring of 2013 or some similarly odd time.

If I end up teaching this class again, I think I’m going to make it a policy that homeworks be handed in online.  Sadly, this means that I can’t use the stair distribution when grading:

(Thanks to Concurring Opinions for the image.)

I hate grading in front of a computer screen, but I have to admit that it significantly reduces the organizational demands required to keep track of all the assignments.  Lurking in the back of my mind, however, is the idea of having to teach a very large class where homeworks simply must be dealt with the old fashioned way.  (And no, I’m not talking about burning them.)

Lexile ranges December 19, 2011

Posted by mareserinitatis in education, gifted, homeschooling, older son, science fiction, societal commentary, teaching, younger son.
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The younger boy’s school sent home a bunch of information on lexile range.  I’d never heard of this before, but it’s a way to rate books so that kids are reading at an appropriate level.  On the surface, it seems like a good idea: it’s very hard, as a parent, to provide reading material for your kids that’s appropriate.  Aside from the basic issues of whether they’ll understand the language and sentence structures of a book, there are the themes and situations: are they too complex or adult-oriented for a child to read?

A lot of this, of course, depends not only on cognitive ability but emotional maturity, as well.  I remember how my older boy started reading Harry Potter very early.  Sometime in third grade, he read the fifth book.  I began to wonder about him reading the fourth and fifth books at such a young age because of the adult themes.  We were fortunate, however.  Reading books about such emotional and adult themes started giving him words to explain a lot of his thoughts and feelings with minimal emotional fallout.

After receiving these results, I dutifully trucked my troops down to the library (no complaints from said troops) where they had a program to help us find books in the appropriate range.  However, I forgot the letter with the lexile range and so had to guess where he was at.  The younger boy had already been reading Magic Tree House books, so I figured some of the Dragon Slayer Academy books might be up his alley.  We got those and some Bionicle books and headed home.  He really seemed to like the Dragon Slayer Academy books and has been reading bits at a time.  Language-wise, they seemed perfect, although their length is a bit intimidating for him.

It turned out, I had remembered the incorrect values.  The books we picked were near the top of his range.  And yet, I was confused.  If these were supposed to be too difficult, why was he having no difficulty reading them?

Mike, unbeknownst to me, had also started looking at lexile information on specific books.  He was curious where he would’ve been placed when he was in various stages of school.  After we returned from the library, he started telling me about this and that he didn’t buy the results.  He’d been comparing some of his favorite sci-fi books, and he was puzzled at the results.  I threw out some books I read as a kid and made some comparisons.  Books that I thought were very difficult showed up as supposedly easier to read than ones I’d zipped through.

We looked up the criteria for determining lexile range:

A Lexile measure does not address the content or quality of the book. Lexile measures are based on two well-established predictors of how difficult a text is to comprehend: word frequency and sentence length. Many other factors affect the relationship between a reader and a book, including its content, the age and interests of the reader, and the design of the actual book. The Lexile measure is a good starting point in your book-selection process, but you should always consider these other factors when making a decision about which book to choose.

Both Mike and I read this and shook our heads.  We both had different takes on it.  I found that one thing that made a book challenging for me was dealing with vocabulary.  It’s not clear to me whether or not this is reflected in the “word frequency” measure.  (Do they mean word frequency in the book or relative to the English language?)  Mike felt he struggled most with books that had very adult themes, something not reflected in the range.

Our take on this is that this is only a very rough guideline, and probably not a good one to use.  We both felt that interest in a book or topic was probably going to be a far better predictor of readability than using the lexile range.  I suppose that’s what they’re saying about considering other factors.

My concern in this is that some schools go a bit overboard with these things.  When the older boy was in fifth grade, he was going to public school part time.  I got a couple calls from the school librarian because he wanted to check out books that were designated for 7th-9th graders.  I felt this was silly because he’d been reading at above that level already, and probably had come across themes in his reading that were more adult than what was in those books.  I told her it alright for him to check the books out, but she seemed to be very opposed to it.  I finally gave up and told older son that he should just probably check most of his books out from the public library.

I’m hoping I don’t see something similar happen with the younger son, i.e., that he not be allowed to check books out from the library if they’re outside of his lexile range.  On the other hand, I’m glad that they seem to be promoting reading at the upper end of the scale so that kids will stretch their mental muscles a bit as well as that they make the point that within any grade level, you’ll have a wide variety of reading levels.  In other words, it seems like they’re trying to get rid of the fantasy that kids all read at the same level and thus require the same reading level.  Therefore, while I may disagree with assessments of individual books, I think they’re definitely taking a huge step in the right direction.

The end is nigh December 10, 2011

Posted by mareserinitatis in engineering, teaching.
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I’m through the ‘grading semifinals’: that is, I have no more grading until after the “all assignments are due” date on Monday.  Unfortunately, I have a bad feeling about how this is going to go with some students.  I have several students who handed in last minute assignments.  It also appears they didn’t read the criteria for the assignment carefully and will not be getting credit for some of those assignments unless they redo them before Monday and submit them again.  Some of these assignments are the required assignments.

I had structured the class so that there were six required assignments and 9 optional assignments.  To pass the class, you had to do all required assignments.  These included things like a personal essay, filling out a curriculum sheet so that the students knew how to plan what classes to take, a presentation on a subfield of engineering, how to keep a lab notebook, and how to write a lab report.  The optional assignments involved a lot of metacognitive items like homework and test wrappers, a couple things on learning styles, a library quiz, and the dreaded Matlab assignments.

A couple weeks ago, I gave everyone a little piece of paper that showed what assignments were outstanding and what their current grade was.  Realistically, this has always been available on blackboard.  However, it was very disconcerting to see how many people were failing to turn in certain required assignments and thus were failing the course.  This also led to an onslaught of homework that needed to be graded.  What’s disappointing, however, is that a good chunk of these assignments were poorly done and didn’t fill the criteria outlined in the assignment.  I had more than one student who handed in a lab report that was three paragraphs in essay form.  No sections, no data, no cover page, etc.

I’ve never had to fail too many students in the past.  In fact, the only one I can really recall was someone who did dangerous things during lab and then showed up to a makeup lab drunk.  I guess facing the prospect of failing a large number of students (>5) is rather disconcerting.  It makes me even more glad to get this over with, although I’m going to be very disappointed every time I have to put down an F.

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