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30 votes
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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 ...
David E Speyer's user avatar
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 ...
Xander Henderson's user avatar
  • 8,225
19 votes
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Is it a good idea to give partial points in grading

Is it a good idea to give partial points in grading? In my opinion, yes because it makes the grading more fair. Do you give partial points when you grade? Yes. I set a criterion and adapt it according ...
Pedro's user avatar
  • 1,800
18 votes
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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 -- ...
Sherwood Botsford's user avatar
18 votes
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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 ...
Alexander Woo's user avatar
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 ...
Brian Borchers's user avatar
17 votes
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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 ...
Joseph O'Rourke's user avatar
16 votes
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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 ...
Daniel R. Collins's user avatar
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 ...
user19682's user avatar
  • 151
14 votes
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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 ...
Daniel R. Collins's user avatar
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 ...
Amy B's user avatar
  • 8,017
13 votes

Is it a good idea to give partial points in grading

I always allow the possibility for partial credit. Unless the problems are quite simple, there will be a good amount of room between a perfect solution and a solution that deserves no credit. If you ...
user1149748's user avatar
12 votes
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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 ...
mweiss's user avatar
  • 17.4k
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 ...
Steven Gubkin's user avatar
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 ...
Steven Gubkin's user avatar
11 votes
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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'...
Kevin Carlson's user avatar
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 ...
Sue VanHattum's user avatar
  • 20.8k
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 ...
James S. Cook's user avatar
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 ...
Matthew Daly's user avatar
  • 5,619
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 ...
David E Speyer's user avatar
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 ...
guest's user avatar
  • 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: ...
Benjamin Dickman's user avatar
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 ...
Matthew Daly's user avatar
  • 5,619
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 ...
otah007's user avatar
  • 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 ...
guest's user avatar
  • 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....
Daniel R. Collins's user avatar
8 votes

Is it a good idea to give partial points in grading

In my experience, binary credit on sub-problems is the way to go. Once you open the door to interpretation on partial credit, you get your time burned by pointless debates (pun intended) with ...
Justin Skycak's user avatar
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 ...
TomKern's user avatar
  • 4,425

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