nt

All calculations correct.

But try to write neater next time . . .

I have no clue what any of that means.

Looks like gibberish to me!

The Navy is a lot more high tech than the Army. He’ll be better off there.

The female of this species tends to have much nicer handwriting than the male does, and the handwriting in that sample is pretty bad.

Given that, whether female or male this student belongs in the Navy, not the Army.

Navy tech:


Army tech:

That is a very risky assumption. Sloppy writing is not gender specific.

You are so right!

It's a boy

The group does a lot of cutting edge materials research, a lot of it non military related (a very lot of it).

I think because the family has a long history in the Army. I'd go Navy for sure.

that I have seen between my high school curriculum and what would have been my daughter's high school curriculum (Precalculus). I went from my Advanced Algebra Trig class in 12th grade to Calculus I in college (my sequence was Algebra I, Geometry, Algebra II, and Advanced Algebra/Trig). I didn't take the last class in the curriculum which might have been something like Precalculus. At some point Algebra II has been dropped.

I actually had my daughter skip Precalculus after 10th grade (Advanced Algebra and Trig) and go straight to Calculus I. She completed her math sequence for mechanical engineering while in high school (Calc I, II, III, and Differential Equations).

Lots of kids at my daughter's high school get through Calculus II before they graduate. I elected to have my daughter start taking college classes after 10th grade. Many kids get screwed by the AP class and have to cover the same material in college (slowing their sequence to graduation). My daughter was able to finish her engineering degree in two years after high school from a Big 12 college.

I was on an engineering track and the most advanced math that it took was solving simultaneous algebra equations. I didn't start calculus until college.

Having said that, I am not sure whether kids today are any better off. What I have learned over a long career in engineering is that being able to connect seemingly disparate pieces of information or data (whatever you want to call them) is more important than being a math whiz. I think kids would be better served by being exposed to logic, where information is presented in fragments, with the full answer somewhere in the fragments or combination of fragments - hard problem solving boils down to horning that capacity more than it does solving an equation. In engineering research a person often develops an equation and must understand the physical meaning of each piece of the equation, the process is a lot more involved than rote solving equations via some established methodology.

For background, I started high school in 1962. I had the amazing good fortune to take UICSM math. Those letters stand for "University of Illinois Committee on School Mathematics" and if you've ever heard of it, let me know. In all these years I'm yet to find anyone who has ever heard of it.

Anyway, it was a completely different program. We spent the first two weeks of algebra learning about positive and negative numbers. Until we really, really understood them. We proved EVERYTHING. And I mean everything. In the geometry portion (which was a semester, which quite frankly is all the time you need to spend on high school plane geometry) we did NOT memorize theorems and then prove stuff. Oh, now. We learned something like four basic postulates and went from there. We derived all the theorems, then worked problems. As a consequence, we had a wonderful understanding of what we learned. And we did some other stuff, that years later, when I asked math teachers at the junior college I was now attending, what that was, they said, "Oh, that's finite math. You don't usually get that until later on in college."

I distinctly remember that we figured out on our own one, maybe two proofs of the Pythagorean Theorem, you know, a2 + b2 = c2. What I recall is that the book then said, there's another classical proof, which you aren't really advanced enough to figure out, so here it is.

Anyway, I then went without taking another math class for thirty years. And thirty years later, when I went back to school and was going to need to take math through college algebra, I was understandably concerned. But I tested straight into algebra 2. And did well in it. Got a B. Then took college algebra and got an A. Hooray for me! At this point I'm 46 years old, and decided to take calculus because I was having so much fun with math. And I got it! It made sense to me. So I kept on asking the math teachers at that junior college why it was I was doing so well at my advanced age, when back in high school I did so poorly. (By the end of the third year of the UICSM curriculum, when we were well into calculus, I was struggling to maintain a D.) To a person the math teachers all said, "Oh, Poindexter. People don't understand that math is developmental, and quite frankly a lot of 16 or 17 year olds are simply not yet ready for calculus. But they will be two or three years later."

I have taken that to heart, and pass my story on to all who will hold still long enough to listen.

So anyway, I wish UICSM had not disappeared. It was wonderful. It taught us to think and really understand the math. And I also wish people would understand that it's okay if your high school student really isn't quite ready for calculus. She will be in a year or two.

Perhaps more to the point, the entire math curriculum should be revised. We've been in this rigid algebra I, geometry, algebra II, precaculus or calculus, trignometry sequence for a minimum of 60 years now. There needs to be an overall integration of the coursework, which should also include statistics. Oh, and let's get rid of year long sequences. That's devastating to a student who does poorly at the beginning of algebra I, who is stuck in the class the entire year with a failing grade, and has to wait until the next fall to start again. Instead, break it up into six week segments (or whatever will work with the school's academic calendar) and if a student fails the first component, can retake it immediately, not wait a year.

would be a great idea, imo.

A big problem with learning math is the intimidation a lot of people feel. Getting more and more confused and intimidated as the year progresses just adds to that feeling. Being able to go back sooner and catch up and "try try again" earlier would get rid of a lot of that feeling of intimidation. Your suggestion would be a great idea, imo.

and that they can't do it. I know I absorbed that lesson, especially as a girl. So I was unbelieving when I did as well as I did in the geometry part of that program.

I do think at least some of the sexist part is less. When my sons were in high school I occasionally said to the girls in their class that I thought I wasn't good in math because I was a girl, and they generally looked at me as if I was speaking Martian. Which made me glad.

And a lot of traditional classes could be broken up into shorter segments, although math is a very obvious choice.

Oh, and what I eventually learned from taking calculus is that calculus is the reward you get for all the earlier algebra classes. Yes! It's a bit hard, but incredibly rewarding. Unfortunately, most people simply think that calculus is impossibly hard. It's the reward part that needs to be emphasized.

I think My Son the Astronomer has told me something like differential equations is the reward you get for calculus, but since I ended my math career with calc, I can't swear to that.

We grew up in the era when it was just assumed that girls didn't do well with math. Many counselors/teachers tried to steer you away from higher math. I was on a college prep track so was urged to take some math, but it wasn't necessary to take calc. Fast forward to my thirties and I begin college as a full time student (married, with two elementary aged children) and in order to get my BSBA it was required that I take a five-credit hour calculus course, probability and statistics, corporate finance, three accounting courses, trig, and now I've forgotten if there were any others. I aced every single one. I graduated at the age of 35 with a 4.0 GPA at the top of my class.

So much for "girls don't do math".

By the way, my son's a math whiz and is a software engineer for NASA at KSC. He took AP Calculus in high school and was able to place out of some of the calc required of freshmen at college. He now tells me that almost half of the new astronaut trainees are female. So there! to the old notion that "girls just don't do well at math".

out of high school.

And the one math teacher I had for two years of that UICSM class was very vocal in his belief that girls were just as good at math as the boys.

Not so well received in many quarters.

My UICSM program was a New Math, but not the kind that has been often denigrated. It taught genuine concepts and thinking skills, and after all these many years some of it still is with me. Heck, I occasionally, just for practice, set up the conversion between Celsius and Fahrenheit.

But more to the point, that program was precisely why, after more than thirty years without a math class, I could test into algebra 2.

The other thing about that program was the rigorous language it used. Something was true "if and only if" something else was true. In the algebra 2 class at the community college we'd learn simply that something was true if something else was true. When I brought up the "if and only if" to the (genuinely wonderful) instructor, she sort of sighed and said that we simply didn't use that kind of language in that class.

My real regret is that I thought that because I was a girl I was not good at math, and so didn't challenge myself, didn't go a lot farther in math. At least my son has done so, and is currently in a PhD program in astrophysics, so I'm not a complete failure.

I love math and do my best to encourage young people to love it also.

as a Freshman and Sophomore in High School (mid-1970's).

In the 8th grade, I got a mild intro to Algebra. I went from a public elementary education, in Chicago, to a
Catholic High School. Huge culture shock, but I digress...

I was getting B's in math in the 8th grade. I didn't do well on the math portion of the HS entrance exam. Based on that poor exam performance, I had to take "Remedial" Algebra, and regular Freshman Algebra.
They were the same damned course! I took the same class twice a day, with 2 different teachers, 5 days a week!

Needless to say, I learned Algebra. Had another year of Algebra, a year of Geometry, and a year of Trig.
I've used Geometry and Trig quite a bit in my work, both as a carpenter and in doing machining.

about how a lot of young people simply aren't ready for higher math.

In fact, the teachers at my community college were collectively in despair at the inclination of the (very good) local public schools to push kids into higher math before they were really ready.

I am myself an excellent example. At the age of 16 I was getting failing grades in calculus. Thirty years later, at the age of 46, I was loving calculus and doing very well in it. While I'm not to suggest that most students delay calculus until they're into their 40s, it may be that delaying it to at least age 18 is sensible.

The problem is that the math geniuses are ready to do calculus at age 12, and unfortunately that tends to become the standard.

In a similar way, the reason we haven't had Shakespeare translated into modern English is that the English teachers, well into the first couple of decades of the 21st century, are the people who first read him when they were 12 or so, loved him, and went on to become English teachers. By the time they're in the classroom, teaching 15 year olds, they no longer need the footnotes and honestly don't get why anyone else needs those footnotes. AAARRGGGHHHH! Meanwhile the bard gets re-translated every few years in German or French or Spanish or Walloon, and people in those countries just love Shakespeare because they always get him in their language, in the current version of their language.

To understand this, look at a translation of The Iliad or The Odyssey from the mid-19th century, and compare it to any of the late 20th or even early 21st century translations. Yeah. The earlier ones are almost unreadable, and the later ones, well you decide.

the math is not remotely the most important tool for me. Reasoning and being able to see relationships between things that appear to have no relationship have proven far more valuable than math, IMO.

The great mathematicians and scientists in history have also either been trained philosophers or were lay philosophers, I believe that is not a coincidental outcome.

I quit high school for college when I was sixteen so that wasn't a problem for me.

Our high school had a calculus class but it wasn't very good.

A few of my high school classmates who later went into engineering, math, or the sciences, attended high school half day and took their math classes at local colleges.

Her last high school math or science class was in 10th grade. After that it was all college classes. She took three of her four college math classes at a community college (Calc I, Calc II, and Differential Equations). She took her Calc III online from a university (finished class right before starting engineering).

She also took her Engineering Physics I and II from a community college and her Chemistry from the local regional university. You would think that would have hurt her in engineering but she graduated Magna in two years from a well regarded Big 12 university in mechanical engineering. Of course she did have me as a tutor (ha, ha).

There are easier ways to do that, but it is verboten to do that until it is understood from first principles!

Basically the first week of Calc II.

I’d expect most students that are getting into elite technical schools to be doing this in high school.

We have a shortage of engineers in this country. Kind of disappointing, but telling that so many don’t recognize calculus. Not trying to condescend toward anyone, I wouldn’t recognize a lot of second semester college material if it wasn’t in my course of study either. Just that we need more math aptitude here.

in real life..

As a practicing engineer with a lot of research and development under my belt, the ability to "see" patterns in information and craft ad-hoc methods of investigating what I see has proven to be more valuable to me than differential equations ever has.

I never did learn how to convert fractions to decimal and decimal to fractions. I haven't a clue as how to do math operations with fractions that have different numbers below the dividing line.

...I “just didn’t get it.”

Turns out a lot of people didn’t get it if they had the same teacher I had. She was a first year teacher, and at the end of the second year, she was fired because people in her classes were doing so poorly.

Did fine in geometry and trig, and enjoyed them. My senior year of high school, the final marking period in math was calculus. The teacher handed us a skinny little black book and said, “Here. This is all self explanatory.” It was not, at least not to me. I got an F.

Many years ago, my husband gave me a book entitled Math Without Tears. I gave up after reading page 6 many times and is not making any sense.