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37

I'm really wondering if this is the end of the world or the beginning of an improvement in the way we teach math. I'll answer this first, and then talk a little bit about the rest of the question. Please excuse my bluntness. I will try to give you the opinion you ask for by weighing what I think may be most important relative to quality of math education. ...


18

I'm sorry not having any empirical literature, but I try to explain the question by commong knowledge. (Feel free to downvote if this is not appropriate :)) Beside political reasons, I think there are two rules of thumb The more mature your students are, the less pedagogical knowledge you need. The more mature your students are, the more expertise on the ...


16

That is because teaching math and knowing math are different skills. Unfortunately, having a PhD in mathematics will not guarantee that a candidate will also be able to manage a class of 35 students, be able to design pedagogically and developmentally adequate lessons that progress in units, how to assess students, deal with the requirements for special ...


16

My strongly held opinion is that some exact solutions are conceptually fundamental. Knowing that $\sin 45^\circ = \frac{1}{\sqrt{2}}$ (rather than approximately 0.7071) may not be important for applications in engineering — although it is certainly necessary in higher mathematics, and I wouldn't be surprised to see it in, say, theoretical physics &...


16

Based on my experience in the US, most school districts teachers teach all subjects including mathematics in the elementary schools. There typically aren't "mathematics teachers" at this level although there are some school districts that have designated mathematics teachers. You should probably not assume anything beyond basic arithmetic- they might ...


14

Supporting the answer by Brian Borchers, and also the comment by aparante001: K-6 elementary teachers in the U.S. will know effectively zero math, or even a negative amount of math in many cases. It's well established that for over a century in the U.S., the very weakest college students, and in particular the ones with the highest level of math anxiety, ...


12

I took AP calculus BC in high school, and since TA's and taught calculus at two universities since (I'm a grad student, but I've lectured as well as TA'd). These experiences have amalgamated together into this answer. I had 170 days of calculus instruction in high school, each one hour long. We used a standard college text of Larson and Edwards (whatever ...


12

Despite what the negative answers, there are elementary teachers who are good at math. I count myself among them. The problem is that there are a broad range of abilities and attitudes among those who will you be talking to. My suggestion is that you look for cool things about math that don't require a knowledge of higher math. One example might be my ...


10

Edit (7/17/14): You can find a very informative flow chart about CCSSM here to show dependencies among standards. At the time of posting, the page covers the standards included for K-8. If by "material" you mean CCSSM lesson plans, then it is important to draw the distinction between standards and curricula. JPBurke makes this distinction in his answer, but ...


10

In the United States, you get a few personal days to use as you choose, some sick days, and some "professional days" to improve your teaching skills. Other than that, you basically get your holidays when the children do. In fact, you lose some of those days for in-services and a few other duties. The school does need to hire substitute teachers for days you ...


10

This is an example of what is usually called a flowchart proof (or sometimes a flow proof for short). A quick Google search for "flowchart proof" or "flow proof" shows many, many contemporary examples of the form, including a whole genre of YouTube videos teaching this style of presentation. This style of proof has been promoted at various points since the ...


9

Excerpt from a 2011 Insider Higher Education article (bold text added by me): In an effort that some are calling the first program of its kind, Georgetown College, a Christian liberal arts college in Georgetown, Ky., is hoping the same high interest in foreign languages in K-12 schools can be translated to the postsecondary level. This fall, the 1,300-...


9

Schools in the US typically have summer breaks of about two months, a winter break of about two weeks, a spring break of one week, and often at least a few days for fall break. The dates for those vacations are usually known well in advance of the beginning of each school year. Therefore, schools generally expect you to plan your vacations for those times ...


8

Some people would consider $1/\sqrt{2}$ as problematic or even wrong (in the sense of incomplete), as it should be further simplified to $\sqrt{2}/2$. The reason why I consider this as related is that it is first of all a matter of convention. It is possible to imagine a situation where the expected solution is the decimal approximation and the exact ...


8

Here are the requirements for Teacher Certification in Massachusetts: The Massachusetts Teaching and Certification Resource Become a Teacher in Massachusetts An image pasted from the latter link: The examination in Massachusetts is called the MTEL. To prepare for it sufficiently (especially in teaching "elementary" as opposed to "early elementary") I can ...


7

I've read a few interesting articles over the past few months in the Notices of the AMS that offer a brief discussion of this. The most notable is a critique and comparison of American and Chinese mathematics curriculum including the beginnings and development of each. It's titled "A Critique of the Structure of U.S. Elementary School Mathematics" by Liping ...


7

While exact solutions involving radicals are estetically pleasing to the mathematical mind, they are next to useless for practical use (Newton was thrilled to have found an easy way of approximating roots with the generalized binomial theorem!). Besides, few angles give such pleasing results. It is a sad fact that what is required most of the time is just a ...


7

Your last para was very reasonable. (I was going to give a mean sarcastic answer, but can't now.) We can crowdsource this: Frank Ayres, First Year College Math (algebra 1 to precalc; Schaum's Outline) 1958 but still in print: Only has geometric mean of 2 objects, but does spend quite a lot of time on geometric progressions. And also discusses getting ...


6

There are some good websites for specific states (e.g., edjoing.org for California and expanding to a few more states next school year. You can just find them through googling) but I never came across to a national secondary education mathematics jobs website (probably the closest website is indeed.com, which is more like a meta-search engine for job ...


6

The question is broad, so my answer will be as well. Students who have been in school for a sufficient length of time have probably learned highly effective strategies for accomplishing their scholastic goals -- whatever those may be. You (it sounds to me) have identified that the learning strategies many of your students have adopted (and likely adopted ...


6

Working in a district that has been "ahead of the curve" in preparing teachers about the CC, I feel confident in what the Core has to offer. On the other hand, the parents are still unsure about it. The negative feedback is the typical stuff you see on FB, etc., coupled with the statement, "My kid already knows how to ______ (in math)." The reality is that ...


5

Instead of a computer simulation, just give them a couple problems that require them to calculate compound interest for different principal amounts and interest rates, then have them plot the results. Use realistic numbers. Or, give them a more extended problem in which they have an annual income, annual expenses, and a compounded-interest loan. Ask them to ...


5

Generalizing from your personal experience with a small, local group of students to trends in "mathematics education in the US" is a tremendous leap. The evidence you have for this "trend" could just as well be evidence that over the last 10 years you have become better at identifying students' weaknesses in arithmetic.


5

I would start by making them produce an amortization table for a compound interest loan "by hand" (in a spreadsheet program like Excel). You can have them do a standard amortization table, and then ask the students to look at what happens when (due to some income-based repayment program or other) they are paying less than the computed payment, or worse, ...


5

Academic, applied, and research math is the world where you come from. [Edit: Much of] Elementary "math" is a whole different world. If you want to know why quotation marks are literally necessary in the prior sentence, check out the writings of Hung Hsi Wu. Then, prepare for something radically worse than that when you ask students to explain their ...


4

The history of this topic in the US is long and complicated. It differs from state to state, and also between rural and urban areas. In rural areas before about 1850, teachers were in short supply; a prospective schoolteacher had to have a very basic education, and also would have to pass an oral exam administered by the local school board. In the second ...


4

This seems to me to be two questions. Is there research backing up the empirically observed trend that teacher-training is necessary for teaching primary and secondary school, but not necessary for teaching at university level and above? Not as far as I know. I do know there is research that strongly suggests that different teaching methods at the ...


4

I took the qualifying exams in my state to teach. All teachers need to pass the general literacy, along with the subject they intend to teach. For me, it was middle and high school math. (The former, about ages 10-13, the latter 13-18) My undergraduate degree was BSEE, electrical engineering, and even though I wasn't working as an engineer, I never lost my ...


4

It seems that it would be beneficial to know both the radical expression and the numerical answer. The radical expression is better for theoretical understanding, the numerical one for computational purposes and application.


4

The introduction of calculators has turned calculus, algebra, and trigonometry into "which buttons do I push" and questions like "Why am I getting 0.8509 for the sine of 45 degrees?" It is, probably unintentinally, de-emphasizing the importance of theoretical mathematics. The sine of 45 degrees is 0.7071 to four significant digits. This is not the same ...


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