The answer to this problem is the way we teach elementary math and WHO teaches elementary math. 2nd grade teachers who love poetry and are afraid of math do a horrible job of it, and yet they are the ones in charge. Plenty of evidence exists in the poor application of the common core concepts. A perfectly good idea of teaching more approaches to math so that different learning style students will have the opportunity to find a method that works for them has turned into a war of showing your work and a higher percentage of students have no idea what is going on.
Exactly!
If $15/hour is good for the economy and people, then $30/hour or even $45/hour would be even better! It is terrible that a kid who is stocking shelves part time at a 7-11 is not making at least $30/hour for that work. If he did, he could spend it on things thus getting the economy going.
I don’t know why you are tying income disparity with taxes. Are you suggesting that we take tax money and give just give it to other people?
As for tax rates, people get taxed on their income, not their wealth. So a multimillionaire whose main income is tax-free dividends and gives money to charity will have a much lower effective tax rate.
Other people don’t take advantage charitable deductions so they don’t get those deductions (for instance, in 2002, 2003 and 2004 Obama gave less than 1% to charity).
As to Buffet, he gives a lot to charity, doesn’t take a lot of money out of the business and at one point in 2011 had his businesses owe $1B in taxes that they weren’t paying. That is one way to have a lower rate.
That is silly. You can learn a lot about a culture without learning the language and what makes people better citizens is being a better person, not being able to conjugate verbs. Obama, Sanders, Clinton and Biden don’t speak any foreign languages (although they have the occasional phrase for the press conference), and they are pretty “good citizens of the world” (whatever a citizen of the world is).
Exactly!
Nor have they ever had to understand a Shakespearian sonnet or play! Or understand the major elements of a cell and the role of mitochondrion! Schools just “teach” too much unnecessary things. It is time to simplify!! That will not just increase the graduation rate, but also get them to graduate quicker.
Which is the perfect reason why everyone should take a year of high school physics! Maybe even take two years in case you have a two-car family.
Should we lower the standards of what a high school degree is so that more people can pass a lower standard?
No. We should be teaching algebra (and every lower form of math) in a way that will stick and will not make people run away. Just about every other country in the educated world has managed to do it, so it most certainly is possible.
I had a glass of wine, seemed to be good for me. So I followed your logic and drank the whole bottle, now I feel sick.
Anyway employers who don’t care for the high school diploma package of algebra, Shakespeare, a few words of a foreign language, etc. are free to hire people without a high school diploma.
@“Erin’s Dad” Perhaps I was deluded when I used elude rather than allude.
Feel-good-about-our-standards and actual high standards are different things. The rigor should not be reduced, but greater RELEVANCE should be an option.
All most people need are algebra and statistics. Stop with the proofs and derivations, which bore most students to death, and instead show people how math is actually used in the real world. If people really care about proofs and derivations, they can take more advanced math.
We’ll have to agree to disagree. 
IMO, geometry (and its proofs) are one of the few things in HS that teaches/requires critical thinking skills. While I’m a big fan of AP Stats, in reality, its nothing more than using Algebra 1 skills.
Honestly though, I think the way high school geometry teaches proofs is terrible. The way proofs are taught in calculus (or more likely, in real analysis), in prose with more creativity and logic than just memorizing and reciting a few geometric rules, really does more to get people to care about proofs and what they’re actually for.
The logical thinking skills that one practices when doing math proofs are useful in non-math subjects. Consider the understanding of a law written with various “and” and “or” clauses describing the various conditions where the law applies or does not apply.
That’s exactly the point: “just memorizing” the rules will not help in proofs; one has to APPLY them rules in a logical sequence. And that’s where critical thinking comes in. To get from A to E, you first have to go to B, and then to C and then to D.
Why not just teach a logic course like they did eons ago?
I didn’t learn anything from geometry including logic when I took it except how to suffer through it.
Plenty of proofs and complete boredom. I made it through calculus and physics just fine. Go figure (pun intended). And I love logic puzzles if there aren’t cubes involved.
However (in my recent history) I took a philosophy course on-line which was heavily logic based which I found totally fascinating. Not a single triangle in sight.
Personally I’d support integrating discrete math into high school math and real analysis into calculus. Being able to do proofs really changes the way you understand math and what you can do with it.
@blevine " physics for all ? " Yes, absolutely. I wish it were a requirement every single time I have someone tailgating me on the highway. But it’s not, and people die every day for lack of physics understanding.
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We'll have to agree to disagree
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@bluebayou - I totally agree with you. Doing geometry proofs in HS totally expanded my horizon. For me personally, this was probably one of the most important things I learned in HS.
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I wish it were a requirement every single time I have someone tailgating me on the highway.
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On my neighbor’s Prius, he has a red sticker that says: “If this sticker is blue, then you are driving too fast.” . I was laughing so hard when I first saw it.
Easy to tell who the math phobic CC’ers are from this thread!
I’ve always found it very strange that proofs are only covered in Geometry classes. Learning how to do proofs is important to understanding math and logic, and it helps improve critical thinking skills. A lot of people have difficulty interpreting conditionals in introductory philosophy and math courses at my school. If proofs or logic were taught throughout high school it would make learning many concepts easier.
In regards to the point of the book, I think math is as disposable as all other school subjects. Clearly not everyone will directly use abstract math (I’m including basic Algebra with this) in their everyday life, but that applies to every academic field. I haven’t written a thematic statement since high school, but I understand the value of literature classes. If students do not gain a competent math background in high school, they won’t pursue anything math-related in college. That’s pretty troubling considering how important math is to numerous subjects. It’s not a secret that many/most primary school teachers have poor math and science backgrounds. Competent primary teachers need a mastery of basic math concepts as a minimum requirement for teaching, and these are (or should be) developed in more advanced classes like Algebra.
That being said, I don’t like the race to Calculus that’s common in many high schools. Many students would benefit from taking discrete math and statistics classes once they complete Algebra. Set theory is essentially applied logic, so a properly developed set theory curriculum would be very beneficial for high school students.
Obama went to an Indonesian language elementary school for four years and still speaks conversational Indonesian. And the fact that he spent that time immersed in a very different culture does in fact I think make him have a better understanding of the world than one who has never traveled at all overseas before being president.
I loved doing proofs in geometry, both my kids had an integrated math curriculum and proofs got very short shrift. One of the math teachers in their high school really wanted to teach a discrete math course, but could never persuade the powers that be to let her offer it.