Poll: With which topics in Mathematics should the average high school senior be comfortable?

[Imp]

1. Add, subtract, multiply, divide
2. Basic trig: sine, cosine, tan, hypotenoeuse
3. Basic algebra to solve for one variable

In other words... grade 7 or lower math.

Fuckers tried to weed me out in college with calculus and linear algebra during first year. Almost never used that shit again through to grad school.

 

[MagnusTheBrewer]

Interestingly enough, those who excell at working with their hands are far more likely to use advanced mathematics if, subconsciously, than those who work at a desk.

 

[Chaotic42]

I'm curious who voted for analysis, topology, and/or modern algebra.

 

[Carson Dyle]

Interestingly enough, those who excell at working with their hands are far more likely to use advanced mathematics if, subconsciously, than those who work at a desk.

Adding fractions or using the trig taught in 9th grade hardly constitutes "advanced mathematics," although it's still more math than probably 99% of the population ever uses.

 

[pete6032]

Our state level High School graduation requirement was that a graduate must have passed pre-calculus. So basically you had to take algebra 1 and 2, geometry, and pre-calc. I'd say about 10-15% of students began algebra a year earlier than the others and thus would finish high school taking a full calculus class. It's hard to answer the poll because many of those topics were touched on in high school math classes, but just briefly.

I think it is unrealistic to expect much more than that out of a standard high school student. That's why there is advanced placement courses for people who are better at math.

 

[MagnusTheBrewer]

Adding fractions or using the trig taught in 9th grade hardly constitutes "advanced mathematics," although it's still more math than probably 99% of the population ever uses.

I was referring to the concepts taught in calculus and topology.

 

[Jumpem]

Algebra and trigonometry are a fine ending point.

When I started my CS degree, I didn't have a concept of either of those. Though, I also didn't go to high school.

 

[Unitary]

I have a PhD in Mathematics and am a Tenured Faculty (10yrs) at a 4-year public University. To me there's really two different answers here. If someone isn't going to college, I'd say a basic understanding of Algebra would be fine. For those going to College, I'd say a strong background in algebra would be fine for non STEM majors. For STEM degrees, strong-algebra+Trig would be nice. With this foundation I can do the rest. On the other hand if they don't have a solid foundation in algebra, they are in for a rough time.

 

[zerocool84]

1. Add, subtract, multiply, divide
2. Basic trig: sine, cosine, tan, hypotenoeuse
3. Basic algebra to solve for one variable

In other words... grade 7 or lower math.

There's no need for anything higher if you're not going to be pursuing anything in that area. It's just a waste of time and effort.

 

[Ken g6]

Interesting thread. It makes me think there should be an "Advanced math By Computer", or ABC, math class, either in high school or college, that covers a bunch of this without going into excessive detail. Let a calculator or computer algebra system do most of the work. If there's one kids can install on their phones and carry with them forever so much the better.

Trigonometry: Learn to identify sin, cos, tan, and their arc versions, and when to use them. No half/double angle identities, no tables.

Calculus: understand that differentials and integrals are transformations of a function. Understand that differentials find slope of a function, and that integrals find area under a function, plus a constant. Understand their meaning in physics. Understand that an integral can't always be computed algebraically. No differentiation rules, and no integration techniques.

 

[Carson Dyle]

I have a PhD in Mathematics and am a Tenured Faculty (10yrs) at a 4-year public University. To me there's really two different answers here. If someone isn't going to college, I'd say a basic understanding of Algebra would be fine. For those going to College, I'd say a strong background in algebra would be fine for non STEM majors. For STEM degrees, strong-algebra+Trig would be nice. With this foundation I can do the rest. On the other hand if they don't have a solid foundation in algebra, they are in for a rough time.

Nice, real-world answer from someone on the front lines. Well done.

I'd be willing to bet that pre-college algebra is one of the most taken courses in any university.

On the flip side, I worked with a fellow some years ago who "earned" a four year degree at a major state university in graphic arts, and claimed that he'd read _one_ book in his entire life. When I see people who don't know the difference between the words "sell" and "sale" I'm no more surprised than when someone says they can't multiply two two-digit numbers.

 

[Jaskalas]

The poll is multi-choice, so choose all of the topics with which you feel familiarity should be standard.

Whatever it takes to work a cash register. So 6th grade basic math from elementary school should suffice.

 

[norseamd]

I'd like to see people take up through integral calculus, linear algebra, combinatorics, and statistics. I don't really remember what we were studying as kids. It was arithmetic for a really long time and then we slowly worked into algebra, I believe. I feel like they could compress middle school math a bit to add in more topics, but I may be misguided.

That would be great, but high school students dont study philosophy, logic, ethics, or epistemology as it is right now, and they already study arithmetic, algebra, geometry, and trigonometry, and the smarter students study basic calculus.

 

[renz20003]

Fractions to decimals

Edit:

And angles, I'm a contractor btw.

 

[Ruptga]

Interesting thread. It makes me think there should be an "Advanced math By Computer", or ABC, math class, either in high school or college, that covers a bunch of this without going into excessive detail. Let a calculator or computer algebra system do most of the work. If there's one kids can install on their phones and carry with them forever so much the better.

Trigonometry: Learn to identify sin, cos, tan, and their arc versions, and when to use them. No half/double angle identities, no tables.

Calculus: understand that differentials and integrals are transformations of a function. Understand that differentials find slope of a function, and that integrals find area under a function, plus a constant. Understand their meaning in physics. Understand that an integral can't always be computed algebraically. No differentiation rules, and no integration techniques.

Wolfram Alpha works on phones and it has a full website as well. If you're familiar enough with the concepts to know the right question to ask, it will compute the answer. It turns typical calculus homework from a 2-3 hour ordeal into a 45 minute one.

 

[lxskllr]

Fractions to decimals

Edit:

And angles, I'm a contractor btw.

We need to go metric. Fractions are bullshit, and impossible to mathematically close. You get dimensions like 17'-11/16"+ Fuck you and your +/-. Also, you have to do math before you get to the math you want to do. Then you get into decimal feet vs imperial. Decimal feet are kind of nice, but not precise enough for typical measuring devices. the smallest increment is ~1/8". Metric makes the math easy, and typical rulers are precise enough for all but the most demanding construction tasks.

 

[renz20003]

We need to go metric. Fractions are bullshit, and impossible to mathematically close. You get dimensions like 17'-11/16"+ Fuck you and your +/-. Also, you have to do math before you get to the math you want to do. Then you get into decimal feet vs imperial. Decimal feet are kind of nice, but not precise enough for typical measuring devices. the smallest increment is ~1/8". Metric makes the math easy, and typical rulers are precise enough for all but the most demanding construction tasks.

.0625 is 1/16 of an inch, close enough for precise calculations for construction

Plus I've been doing this for 14 years I don't want to learn metric at this point

 

[zinfamous]

Trig/probability/wherever compound interest and such falls.

light calculus and limits would be great, but that is pretty much useless to the wider population that will never need to apply any of that. But I think more advanced calculus should be a requirement for 1st-2nd year college students.

 

[lxskllr]

.0625 is 1/16 of an inch, close enough for precise calculations for construction

I don't like close enough. I want the math to be perfect. That leaves room for fucking up later. Math is the easiest to get right, and it won't get any better from there.

Metric is trivially easy. If you were born with, and still have(or can imagine) the typical number of fingers issued, you can do metric.

 

[renz20003]

I don't like close enough. I want the math to be perfect. That leaves room for fucking up later. Math is the easiest to get right, and it won't get any better from there.

Metric is trivially easy. If you were born with, and still have(or can imagine) the typical number of fingers issued, you can do metric.

So your saying that metric construction isn't rounded to the nearest millimeter?

 

[Mai72]

Much of what we expect from our students today has to do with our test scores. They are abysmal. Compared to Taiwan, South Korea, China, Japan, Norway and Vietnam we suck at math. That's putting it lightly.

Many of our children have a difficult time doing basic addition/subtraction let alone algebra. I don't know if I fully agree with Common Core. Does a student really need to know 5 different ways to come up with the answer? The reason Asia is so dominate it's because they thrive on rote learning. Which works well with mathematics. Maybe we should do the same?

 

[Staples]

A lot of people who are not mathematically inclined won't even know how to apply algebra or geometry to real life. For those who think it numbers, they will know how to apply this and higher level math to real life.

Statistics (like your chances of winning the lotto) should be tought in terms that everyone can understand.

 

[lxskllr]

So your saying that metric construction isn't rounded to the nearest millimeter?

It's computed to the nearest millimeter, so you can get exact geometric closure. Whether or not it matters is another question, but exact closure leaves nothing to interpretation.

 

[renz20003]

It's computed to the nearest millimeter, so you can get exact geometric closure. Whether or not it matters is another question, but exact closure leaves nothing to interpretation.

You can do that with inches down to the 1/64 if you so desire. It's as simple as knowing decimals to fractions and vice versa.

The other thing thats severely lacking in construction is how to use angles to make something square.

 

[Humpy]

I don't like close enough. I want the math to be perfect. That leaves room for fucking up later. Math is the easiest to get right, and it won't get any better from there.

Metric is trivially easy. If you were born with, and still have(or can imagine) the typical number of fingers issued, you can do metric.

The names of the markings on the measuring stick don't matter for the math to be perfect.

The people I know who build stuff are able to switch between metric, inches, tenths, and arbitrary measurements throughout the day without a problem. It's all the same thing.