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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.

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How fast does an (unladen Blue) Angel fly? July 26, 2015

Posted by mareserinitatis in Fargo, math, younger son.
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IMG_5600

This weekend, the Blue Angels were in town to perform at the Fargo AirSho.  While we were watching them today, I made some comment about how amazing it is that they can keep such perfect formation despite the high speeds.  The younger son asked how fast they fly, and I responded that they could go up to a few hundred miles per hour.  He came back with:

I bet they’re flying at a trillion nanometers per second.

I honestly had no idea since that required not only a conversion to more reasonable units for such a measurement as well as the fact that we’d have to hop between metric and English units.

I decided to check it out, and it turns out he wasn’t far off.  The Blue Angels use the F/A-18 Hornet, which wikipedia gives a top speed of Mach 1.8 or 1,190 miles per hour.  The equivalent speed in nanometers/second is 531,977,600,000.  In other words, it’s half a trillion nanometers per second, so the younger son was only off by a factor of two when they’re traveling at top speed (which they obviously weren’t).

That’s a wee bit faster than an unladen European Swallow, which has an airspeed velocity of about 11,176,000,000 nm/s (based on Wolfram Alpha’s estimate of 25 mph).  I’m sure you were just dying to know that.

Biased for science December 10, 2014

Posted by mareserinitatis in feminism, geophysics, math, physics, science, societal commentary.
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I’ve taken a couple tests at Project Implicit.  The premise is that we have unconscious biases that may unknowingly affect decisions we make about other people.  I remembered this after coming across an article on race from the Washington Post.  I’d taken a test before that said I had a bias against blacks.  I’m owning up to it, but now that I’m aware of it, I try to recognize it’s there when making decisions.

I revisited the site to see if I could retake the test and if my results had changed, but I was distracted by the shiny things.  In particular, I saw there was a test on the subconscious preference to associate science with male and liberal arts with female.  Given the studies about how labs hire women less often and there is a subtle bias in salary, as well, I thought, “this could be interesting.”

And it was.  I was expecting to show a rather strong relationship between men and science.  Not only is that the most common association, but it seems like working in a male-dominated field would make that a no-brainer.

Iat-gender-science

Your data suggest a moderate association of Female with Science and Male with Liberal Arts…

I’m one of the 3% who took the test who has that association.  If what I read in the Washington Post article applies to this study, most of the people taking this test are younger, more liberal, and more female than the average population, so the test may actually mean that the 10% who associate females with science is actually an overestimate.

Why do I have that association, particularly working in the field I do?  (I feel a bullet list coming on.)

Some potential ideas:

  • Being a female scientist is a very strong part of my identity, so I would naturally equate the two.  While at first guess, I would think this would be a no-brainer, the studies I cited above seem to indicate that’s not the case for most women scientists.
  • I have a lot of female friends that are also scientists.  As an undergrad, I was the only female physics major, but I made friends with a lot of female math, engineering, and physics and math education majors.  In my MS program, I spent a lot of time with other women engineering students, the handful I could find.  Going to a grad program (in earth sciences) means I was in a program with near gender-parity among the students.  Through the beauty of the internet, I’ve also made friends with other women scientists.  I think I’m likely to “see” more women in science than the average person…or even the average scientist.  “Women in science” isn’t a token female here or there but an actual sizable demographic in my world.  I think that this sort of exposure has probably had the most profound effect on my biases.
  • I know a lot of men who are interested in liberal arts.  Probably the most strongly influential one is older son, who is very much into drawing and writing.  I spend a lot of time with him, so that also probably affects my perceptions.

I’m curious how others fare on this test as well as their analysis of their own results.

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

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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.

 

Someone was stupid on the internet November 16, 2014

Posted by mareserinitatis in engineering, feminism, math, science, societal commentary.
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See more on Know Your Meme

Even though I am a woman who is working as an engineer at an academic institution, I have no ability or authority to discuss anything having to do with women in hard sciences.

Totally reasonable, right?

The person who told me this is a man who works in sports medicine.  During the course of the conversation on what causes low rates of women in hard science/engineering fields, I brought up “male privilege.”  I even went so far as to say that it benefits men to ignore this privilege because it keeps it in place.  The response to even mentioning such a thing meant I was a conspiracy theorist.  I obviously am incapable of discussing the issues women face in science because I believe in male privilege.  Despite the fact that I was the one posting links to actual studies to validate my claims (using studies discussed in Nature and Scientific American), I obviously am incapable of understanding the issues.

I was attempting to explain that while I don’t think most of this behavior is explicit (although I have definitely seen that, too), there is a lot implicit bias.  As I said in my interview on the Engineering Commons, there is quite a bit of sexism that is a result of people simply not thinking about the advantages they have or the assumptions they make.  That is the very definition of privilege.  I don’t think most people wield it mean-spiritedly, but that doesn’t mean it doesn’t exist at all.

We were discussing a publication claiming that academic science isn’t sexist, a paper also discussed here.  Let’s be honest: claiming hard sciences aren’t sexist is like saying that relativity (or any other major theory) is wrong.  Not only that, it’s willful ignorance because there are so many studies out there to refute this notion.

The most irritating part of this discussion is that it should never have been about this issue at all.  The discussion was in a forum designed to talk about science communication, and yet he initiated the conversation by claiming that the paper proved there is no sexism in academic science.  There was no discussion about how to bring into account all the other data, how to most effectively communicate or discuss the result, or even about public response to news about this paper.  Instead, this person used the forum as a bully pulpit for his own viewpoint, ignoring contradicting data and viewpoints.  If this is how science communicators approach studies to begin with, it’s no wonder the public has a hard time understanding and interpreting these same studies.  If the communicators don’t understand the science within the larger context, they certainly aren’t going to do a good job explaining it to the world at large.

Never ask a woman her weight…but her kinetic energy is fine August 2, 2014

Posted by mareserinitatis in math, physics, running, science.
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Today, I had one of the most awesome runs I’ve ever had.  In particular, I sustained a much faster pace than I have over a 3 mile distance.

I couldn’t help but wonder, however, about the factor weight plays in one’s speed.  As much as I try not to worry about weight and focus on being healthy, there’s this part of me that thinks it would be cool to lose a bit of weight because then I would go SO MUCH FASTER.  Or at least that’s what I tell myself.  However, I wondered if maybe I was exaggerating a bit, so I decided to check it out.

While it’s a bit of an oversimplification (that doesn’t take into account muscle tone, lung capacity, hydration, electrolyte levels, altitude adjustment, and the 18 bazillion other things that can affect a runner, even as stupid as that kink that’s still in your neck from last Thursday’s swim (okay, that only affects the triathletes here)), a quick check is to use the kinetic energy equation.

First, of course, we have to assume a perfectly spherical runner.  Or a Blerch:

The Blerch

The Blerch

(As an aside, if you don’t know what the Blerch is, you must check out the Oatmeal’s wonderful cartoon on running.  We all have a Blerch deep inside of us.)  Either way, perfectly spherical things are happy for physicists because of all the lovely simplifications we can use in learning about them.  So, if you’re a perfectly spherical runner, remember that physicists will love you.

Anyway, our hypothetical runner will have a mass (m), which is, of course, directly proportional to weight.  (Weight, of course, is also referred to as gravitational attraction, so the more you have of it, the more attractive you are, at least from the perspective of the planetary body you’re closest to.  Also, it may start to be more attracted to you if your velocity starts to approach the speed of light.  Maybe this is why many humans also find runners attractive?  Not sure.)  The unit of mass is the kilogram.  The runner will also have to maintain an average speed velocity (v), and of course your pace is inversely proportional to your velocity.  Your velocity is probably measured in miles per hour by your local race, but since we’re being scientific, we could also use SI units of meters/second.  That being said, if you double your speed in one unit, it will also double in the other.  There’s nothing fancy that happens because you’re using one unit or the other.

The kinetic energy of our runner, assuming an average velocity, can be written as

(1) KE=½ mv2

If we have the kinetic energy and mass, but want to find out the velocity, we first divide both sides of the equation by the mass and then take the square root of both sides.  This leaves us with the following result:

(2) v=√(2 KE/m)

Let’s take an example.  If we have a runner who has a velocity of 5 mph (or 2.2352 m/s) and a weight of 140 lbs. (or 63.5 kg).  If we use SI units to compute this runner’s velocity, it turns out her initial kinetic energy (KEi) is 158.63 J.

On the other hand, we don’t really need to know how much initial kinetic energy the runner has, in terms of numbers.  We can just define it as the quantity KEi. It turns out that physicists are kind of lazy about using numbers, so we’ll try to go without them because, in my opinion, it sort of confuses things. (You’ll see why later.)

How this this help us?  Well, if you want to take a drastic example, let’s assume a runner loses half of her body weight.

First, let’s establish that her initial kinetic energy is defined also by an initial mass mi and velocity vi.  (These would be the same as the 5 mph and 140 lbs. above.)  This means her initial kinetic energy can be written as

(3) KEi=½ mivi2

and her initial velocity would therefore be

(4) vi=√(2 KEi/mi).

If her weight drops by half, we can write this as her initial weight divided by 2:

(5) m=mi/2

If we put (5) into our velocity equation (2) as our new mass and keep the same initial kinetic energy, we get

(6) vnew=√(2 KEi/m)=√(2 KEi/(mi/2))=√2*(2 KEi/(mi))=√2(2 KEi/(mi))

You can see that the last part in six is basically the square root of two times our initial velocity from (3).  That means that by losing half her weight, our runner would run about 1.4 times as fast, or 40% faster.

Now what if she only loses 10% of her weight?  It turns out that (5) would become

(7) m=mi/1.1

so our new velocity would be the initial velocity times the square root of 1.1, which is about 1.05.  Losing 10% of her weight only makes her 5% faster.

After spending time looking at this, I decided that going on a massive diet definitely isn’t going to help me speed up significantly.  (In fact, if I manage to go from my current weight to my ideal, I would maybe get a gain of a bit over 1/2 mph.)  It’s the fact that the mass doesn’t play as strong a role as velocity does because velocity gets squared and mass doesn’t.  If you want to go faster, you are better off practicing running faster.

So please pass the ice cream!  I need it for my fartlek recovery.

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.

 

A filtered education March 3, 2014

Posted by mareserinitatis in education, homeschooling, math, older son, physics, science, societal commentary, teaching, younger son.
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The older son is a lot of fun.  Despite his statements that he has no desire to go into science, he seems to get and make a lot of science jokes.  I know he’s not a scientist, but I feel comfortable that he’s scientifically literate.  As he was homeschooled, I’m feeling pretty proud of myself.

I’m more anxious about the younger son, though.  This weekend, he brought home his science homework, which focused on optics.  The kids were studying filters, and one of the questions asked about what kind of light would you see if you shined a flashlight through a blue filter and then a red one.  I asked him what he saw, and he said nothing.  Unfortunately, he was told that he saw nothing because the flashlights just weren’t bright enough, but that what he should have seen was purple.

I’m pretty sure that if I had ever been bombarded with gamma rays in the past, I would’ve turned into She-Hulk at that very moment and started smashing things.  Fortunately (or unfortunately, if being She-Hulk happens to be a goal of yours), that didn’t happen.

I find it infuriating that, throughout my years of homeschooling older son and teaching younger son math, I have constantly been questioned about my ability to teach them.  The implication has always been that I may have a degree, but they are experts on teaching.  In fact, this particular teacher attempted to take me to task earlier this year about the younger son’s math curriculum…the same teacher who apparently doesn’t understand that light and pigments work completely differently.

After I managed to calm down, I explained that light filters are like sieves, except that they only let one size of particle pass through: nothing bigger can pass through the holes, but nothing smaller can, either.  After this explanation, the younger son was able to correctly explain that the reason he saw no light from his flashlight is that the two filters together had blocked all the light.

I’m going to be watching very carefully to see what kinds of scores he’s getting on his answers and whether the teacher realizes she made a mistake.  This was very disappointing.  There was a new science curriculum introduced this year, one which I was very excited about.  The focus was supposed to be on hands-on, problem-based learning, which is great for science.  Despite that, it seems that younger son’s science education may be lacking.  What good does it do to have a top of the line science education curriculum (or math…or anything else) when our teachers don’t understand what they’re teaching?  And how is it that these same teachers can justify questioning the ability to teach material that some of us understand far better than they do?

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.

 

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