30
votes
Accepted
Should an undergraduate math program contain a course on Lebesgue integration?
I think the existing answers understate how much a standard American math major does not see the Lebesgue integral.
I'm going to poke around at a variety of college websites to see how they cover this ...
- 5,243
28
votes
(How) Do American undergraduate math programs teach complex numbers?
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 ...
- 7,520
18
votes
Accepted
Math activities for fast-finishers
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 -- ...
18
votes
Accepted
Preparing elementary teachers for the praxis exam
This is not an answer, but I think it's too important to leave as a comment.
I strongly urge you to rethink your goals for this course.
Your goals should be to prepare your students to teach ...
- 2,484
17
votes
What is the required mathematical background of a US elementary school math teacher?
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 ...
- 821
17
votes
Accepted
How to be a good math teacher at a liberal art college?
Let me reply as someone who left a university in favor of a Liberal Arts College (LAC).
Although @AlexanderWoo's point is valid, my experience supports the following:
At a LAC, the walls between the ...
- 29.5k
16
votes
Accepted
What is the required mathematical background of a US elementary school math teacher?
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 ...
- 24.4k
15
votes
Should an undergraduate math program contain a course on Lebesgue integration?
Is it standard for a math undergraduate program to have a course on Lebesgue integration?
No (assuming that "have a course" means "require people to take such a course in order to get ...
- 151
14
votes
Accepted
Why are math test scores dropping in America? Lack of student responsibility movement
Some of us would point to political pressures to evidence higher "success" in terms of increased graduation rates, which wind up pressuring institutions to reduce standards and pass students ...
- 24.4k
13
votes
What is the required mathematical background of a US elementary school math teacher?
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 ...
- 7,999
12
votes
Accepted
An alternative to "two column" geometry proofs
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 ...
- 17.3k
12
votes
Accepted
Geometry in the Community College Curriculum
"Geometry," the American high school course, is generally pseudo-axiomatic Euclidean geometry. I don't know whether your claim about the CC curriculum is broadly true, but assuming it is, it'...
- 651
11
votes
(How) Do American undergraduate math programs teach complex numbers?
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 ...
- 24.4k
11
votes
Math activities for fast-finishers
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 ...
- 24.4k
10
votes
What will my academic path look like after testing out of high school math classes?
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 ...
- 20.1k
10
votes
Is there a study that compares 8-week vs 16-week math classes?
In all scenarios, unless the school judges the success of the course by some external metric it is very difficult to objectively compare different methods of instruction. The plain fact is that ...
- 10.7k
9
votes
Is Trigonometry done differently in the US?
As you've tagged this as precalculus, I'll say that there is no standard precalculus curriculum in the United States and very little "official" guidance about what such a curriculum should ...
- 5,609
9
votes
What age student should be able to answer this question?
I'm going to give an answer based on my feelings and memories, but I hope someone will give a more informed answer.
This question is testing
Does the student know how to multiply polynomials with ...
- 5,243
8
votes
When (and why) did geometric means of more than two numbers exit the secondary curriculum?
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 ...
- 159
8
votes
What is the required mathematical background of a US elementary school math teacher?
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:
...
- 18.4k
8
votes
Teaching calculus in AP without the formal definition of the derivative
As a new AP Calculus teacher who just went through the certification process with College Board, I can expand on the answer that Ben Crowell (i.e. user507) gave. Not only is it pretty irresponsible ...
- 5,609
8
votes
Should an undergraduate math program contain a course on Lebesgue integration?
Is it standard for a math undergraduate program to have a course on Lebesgue integration?
Yes, and I find it bizarre that a university would not have one.
Lebesgue integration (or measure theory more ...
- 189
8
votes
Topics covered in Calculus I and II (university level) that aren't covered in the AP Curriculum
It's a very good list already.
I would add that a more fulsome differential equations introduction used to be part of BC (and may still be part of stronger college courses). In particular, the ...
- 81
8
votes
Sources on inequity in precalculus sequence
Here's a hair-raising article I sometimes use as a touchstone:
Kenschaft, Patricia Clark. "Racial equity requires teaching elementary school teachers more mathematics." Notices of the AMS 52....
- 24.4k
7
votes
How can I improve my Retake Policy?
As a college math professor, I have a retake policy. I've been trying to encourage other professors to develop retake policies, and it seems to be becoming more common with resources emerging like The ...
- 3,982
7
votes
Topics covered in Calculus I and II (university level) that aren't covered in the AP Curriculum
I will tell my impressions based on the BC students I've taught.
Important weaknesses/gaps (skills that prepare them for vector calc. & diff. eq.):
Trig. & integrals (OP's ##5,6).
Setting up ...
- 5,345
6
votes
How actually are prime numbers taught in elementary school in United States and how easily do students learn what they're being taught about them?
I would love to get an answer by a teacher who is trying to teach prime numbers to elementary school students about what's happening with their attempt to teach them prime numbers. I would like them ...
- 1,527
6
votes
Courses equivalent to College Algebra in other countries?
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 ...
- 1,685
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