Hot answers tagged

38

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. ...


28

The following is anecdotal, but based on experience as a student and instructor in American high schools in three states, as well as my undergraduate and graduate experiences. High School: In the high school curriculum, complex numbers first appear in algebra courses. The usual curriculum first introduces complex numbers as a way of interpreting the ...


19

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 ...


18

Stuff for fast finishers/gifted kids should be out of the stream --stuff that isn't what you're covering next week or next year. Look at puzzles -- especially geometrical ones. Graph theory -- Bridges of Konigsburg, three houses, three wells. Chess board problems. There are lots of good puzzlebooks out there. Logic puzzles too. Mechanical puzzles too. ...


17

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

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

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

Undergraduate students should be aware of their academic advising offices. Essentially every school employs full-time academic advisers to answer questions precisely like this one. If you go to a larger school, the math department (or at least the college of education) at your school will have a professional adviser just for that content area. You need to ...


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 ...


11

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 ...


11

At my institution we do not discuss complex numbers at all in calculus, but we assume that students are somehow familiar with them in differential equations and linear algebra (to analyze real-linear mappings with complex eigenvalues). A study of single variable holomorphic functions is an upper level course, and most math majors will graduate without ever ...


11

One option is to assign tasks with a low floor, but high ceiling. That means that almost everyone has the background to start tinkering, and accomplish something, but there is enough complexity and variation that one could keep discovering new things for a very long time. This naturally differentiates instruction. Engaging tasks of this form are hard to ...


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 ...


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

So you dual enroll at the community college while you're in high school, and you finish up in two more years. While you're at it, consider some computer science courses. Also, physics is a lovely course. (I was put into chemistry and hated it. I would expect almost anyone who loves math to at least like physics.) Do you have a high school counselor you trust ...


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

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 ...


9

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 ...


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

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 ...


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 ...


8

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 ...


8

I teach physics and occasionally a little math at a community college in California. My students come from all over the place, so I think their exposure to math is somewhat of a representative sample of what kids in the US learn in high school and the first couple of years of college. In our three-semester physics survey course for STEM majors, I review ...


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

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

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 ...


6

In the UK, what you describe lies somewhere in between GCSE and A-Level Maths. Both of these exams are intended for secondary school students. It is unusual for these topics to be taught at the university level, and if they are taught, it is often not by the Maths department. For example, the Economics department might have such a course for their first ...


Only top voted, non community-wiki answers of a minimum length are eligible