Questions tagged [undergraduate-education]

For questions about teaching students at the undergraduate (university) level.

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14
votes
7answers
1k views

What is the best way to intuitively explain the relationship between the derivative and the integral?

This is my first post so bear with me, but something I've been thinking about lately is: Why didn't I ever question the relationship between the derivative and the integral when I was taking calculus? ...
-1
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0answers
77 views

Should teaching how to write a formal proof be a part of a standard mathematics education? [closed]

There is good reason for teaching how to write a formal proof as part of a standard mathematics education. Mathematicians think that the logic of the proofs they write is completely obvious, but our ...
3
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3answers
842 views

How much does it cost to develop an online course?

Due to the coronavirus outbreak, and other local problems, we are seeing the need of developing most of our teaching online. Just "do a class like always" (but with no blackboard) via some network ...
6
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1answer
139 views

How to conduct online testing for Calculus?

Due to COVID-19, I have been planning to transition to online teaching (which, of course, includes online testing as well). The LMS that we use is Blackboard which is integrated with Proctorio. ...
1
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2answers
93 views

Topics for undergraduate seminar for mathematics educators

There are some general questions about potential topics for undergraduate seminars: topics for an undergraduate Math seminar Undergraduate Math Seminar topic I am looking for topics for a 15-hour ...
6
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0answers
115 views

Tablet whiteboard app w e-pencil

(I've generalized the original question as @BrendanW.Sullivan suggests.) I would appreciate recommendations for a whiteboard app for a tablet using an e-pencil. For me: an iPad, using an Apple pencil....
59
votes
16answers
6k views

How shall we teach math online?

Many universities, including mine, are now requiring we teach our courses online because corona. How shall we do this? Let’s brainstorm here. The challenges: My school provides limited online ...
5
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4answers
165 views

About the effectiveness of self-studying maths (compared with other subjects)

An important feature of mathematics is that it is relatively easy (compare to many other subjects) to know whether or not one's understanding is correct. There are plenty of ways to check: one can ...
15
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4answers
265 views

Should we stop teaching “interchange $x$ and $y$” when finding the inverse function?

In one textbook I use for College Algebra, the author teaches that one should interchange $x$ and $y$ when looking for inverse functions. For example, the inverse function of $$y=2x+2$$ is $$y=0.5x-1.$...
6
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1answer
89 views

Data on textbook adoptions in universities (math/science)

Does anybody know if there is a website/database/... on textbooks adoption in the US or some other country? (math/science textbooks) It would be interesting to see which textbooks are (and have been) ...
7
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3answers
170 views

Evaluating textbooks in math and physics

I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this ...
6
votes
0answers
104 views

Let P be a polygon

I've encountered the following misunderstanding. I pose a question (to undergraduates in the U.S.), for example: Let $P$ be a polygon of $n$ vertices. Is it true that every triangulation of $P$ ...
2
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1answer
109 views

Teaching Quantifiers Before Logical Connectives

In this short question, I would like to ask whether it is possibly good to teach quantifier before logical connectives in a logic introduction lecture? I know there is a relationship between them but ...
0
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1answer
100 views

Making epsilon-delta proofs not just precalculus

In trying to find lecture-length videos of epsilon-delta proofs, I've found that almost all of them just start with the definition and then work through the algebra to get the answer. In effect, it ...
18
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1answer
223 views

Taxonomy of bad proofs

I am interested in finding examples of poorly written proofs that exemplify the types of mistakes made by undergraduate students in their first year or two of writing proofs. I am interested both in ...
9
votes
2answers
330 views

Fear of 3-dimensions

Contrasting 2D and 3D in my field (Discrete & Computational Geometry1) is essential. For example, every 2D polygon can be triangulated (with vertex-to-vertex diagonals), but not every 3D ...
30
votes
6answers
2k views

Allowing nonstandard mathematical language and/or notation

How important is enforcing standard mathematical language and/or notation? Today, I was questioned by a writing instructor as to how vital it is to correct students when they explain something using ...
5
votes
4answers
224 views

What math courses should I take in order to become a secondary math educator?

Seeing as this is the math educator site, perhaps someone can help me out: I am looking to become a math teacher, but I am having a hard time figuring out which math courses I need to be taking. ...
7
votes
7answers
2k views

Teaching Calculus I to engineers

I am in a research project where one of our jobs is improving the first year university experience for our students. One of the topics we are looking into is changing the way we teach our introductory ...
1
vote
1answer
142 views

Math undergrad courses [closed]

Awhile back I was very weak with my trigonometry so I came to this site asking for help, and it turned out the few answers I got made a huge difference. I excelled at the trigonometry section in my ...
10
votes
4answers
197 views

How to read chained equalities out loud?

I find that my community-college students are usually very hazy on the status and meaning of chained equality statements (or other relational statements). This seems like a really critical element of ...
0
votes
0answers
93 views

How to teach year 3 undergraduate courses to high school students?

I see on the webpage of a high school math summer program, SuMac, that they will cover some algebraic topology in a period of several weeks. And they covered every aspect of this subject, including ...
7
votes
3answers
457 views

Doing research projects when one's knowledge is limited: is it preferable?

In some universities, high schools, and summer programs, students are required to do their own research project in maths and write their own essays/research papers. At the same time, however, many ...
5
votes
2answers
254 views

Redesigning college math courses and curriculum to be self-paced

I imagine there must exist a fair amount of literature and discussion about the idea of somehow redesigning college math courses, and the entire college math curriculum, to be self-paced. Question: ...
3
votes
1answer
148 views

Why teaching undergraduate-level mathematics is so complicated? [closed]

Many of my professors are experts in their field, but they are just not able to teach. I mean: most of the times they are confusing, don't follow a logic sequence in their speech or keep a superior ...
3
votes
2answers
312 views

How to teach linear programming and reductions?

Do you know any textbook with problems+solutions to support teaching of linear programming and reductions, and in particular, cover standard and slack forms, formulation of problems as linear programs,...
17
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7answers
5k views

Learn university maths or train for high school competitions: which is better?

I sometimes see people arguing against concentrating too many resources in high school maths competition (such as IMO) training. Their reasons they give are usually the following: Competitions are a ...
5
votes
1answer
122 views

Developing abductive (problem-solving) skills

I am looking for long-term (over the course of many semesters) strategies, including specific types of in-class activities, for developing the abilities of students to come up with intermediate steps ...
4
votes
2answers
219 views

How much math would a non-STEM major have studied in 1950?

I've spoken to several people who attended US universities in the decades before I was born, and I was somewhat surprised to find that it seemed to be common (based on the anecdotes I received) for ...
35
votes
11answers
4k views

Beautiful planar geometry theorems not encountered in high school

I would like to impress college students (undergraduates in the U.S.) that there is more to planar geometry beyond what they learned in high school. I would like to show them beautiful theorems they ...
3
votes
5answers
337 views

Are degrees of polynomials illogically defined in elementary algebra, intermediate algebra and college algebra courses?

In most of books on elementary algebra, intermediate algebra and college algebra, the degree of the non-zero polynomial $$f(x)=a_nx^n+\cdots a_1x+a_0$$ with $a_n\neq 0$ is defined to be $n$. But I ...
-2
votes
1answer
58 views

Where can I find the partial order relation of prerequisites of undergraduate courses in the United States?

Let $A$ be the set of all undergraduate mathematical courses in the US and define a binary relation $\leq$ on $A$ such that for elements $a,b\in A$ (that is, $a$, $b$ are undergraduate mathematical ...
2
votes
2answers
149 views

Which textbooks on College Algebra, Trigonometry, Pre-calculus, Calculus, Linear Algebra, ODE are written by world-class mathematicians?

For example, Trigonometry was written by Wolf-Prize winner Israel Gelfand, one of the top mathematicians in the 20th century. I am wondering if other world-class mathematicians have written textbooks ...
14
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8answers
1k views

How do you attract more math majors at a liberal arts college math department?

It seems to me that we all might benefit from an answer to this question, since math departments must defend their performance within their institutions. I imagine there will be standard answers like:...
8
votes
3answers
2k views

Take-Home Examination on Ordinary Differential Equations?

I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my ...
3
votes
0answers
85 views

The propagation of the wave equation in even versus odd dimension

I am about to teach a second year undergraduate class on applied differential equation (first time) and, while I won't have time to go into the details, I wanted to show my students the difference ...
19
votes
8answers
2k views

How can I learn to write better questions to test for conceptual understanding?

I'm worried that I'm bad at realizing when a question I've written requires little or no conceptual understanding to answer. Like, when I'm writing a question for a homework assignment or exam, I'll ...
6
votes
2answers
149 views

Why is there an emphasis on analysis courses in undergrad progams?

In undergraduate maths study, there are three main areas: analysis, algebra, and geometry. (There are of course other small topics as well, but they don't have to be learnt by every student.) I have ...
-1
votes
1answer
136 views

How helpful are university subject rankings when choosing a place to study math?

There are many university ranking consultancies trying to compare one leading maths department with another and to conclude which one is better. Although this doesn't seem to be a very reasonable ...
8
votes
0answers
93 views

tutorial active learning

This is a question I asked on [Academia.se]. It did not get an answer, so I am re-posting it here. In the country where I live, university students studying mathematics usually attend lectures, ...
9
votes
8answers
2k views

How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios?

I am a teaching assistant for an intro programming course. One assignment asked for the averages of a certain ratio, but most students, rather than returning $$\frac{\text{sum of all ratios}}{\text{...
1
vote
1answer
147 views

How to improve mathematical skills(University level)?

I am doing Ph.D in Mathematics, I feel I lack few of the skills, if I can improve those skills I think I can do better as a Math scholar. I need some suggestion on these following(below I am talking ...
1
vote
1answer
108 views

Calculus book for basic calculus and repetition from videregående (Norwegian high school)

Does there exist a textbook in Norwegian (bokmål and nynorsk should both be fine) that covers the more advanced mathematics (needed for calculus) from videregående (secondary school, includes both ...
3
votes
1answer
95 views

Applied ODEs for Numerical Methods

I am looking for a list of ODEs to use as examples in the teaching of a numerical methods course for engineers. I am looking for first and second order examples - the more applied (to engineering) ...
4
votes
2answers
1k views

Asking students to define “unique”

Context: This is for introductory linear algebra course, near the beginning. As a sort of "exit survey" after one of my lectures, I would like to ask my students to try and define what "unique" is ...
14
votes
7answers
456 views

How should students say in words the notation for a limit?

$$\lim_{x\rightarrow a} f(x)=L$$ Which way should students best get in the habit of? The limit of $f(x)$, as $x$ approaches $a$, equals $L$ The limit of $f(x)$ equals $L$, as $x$ approaches $a$ The ...
4
votes
1answer
222 views

The most transparent exposition of Bayes' Theorem

I am seeking the most transparent exposition of Bayes' Theorem (for undergraduates). I would prefer to avoid mentioning "prior" and "posterior," and instead focus on frequencies. The Wikipedia entry ...
11
votes
4answers
436 views

Why is absolute value difficult?

My understanding is that students find absolute value to be challenging to learn or understand. Off the top of my head, I can come up with two possible reasons for this. Absolute value is a piecewise ...
18
votes
5answers
8k views

What is the most difficult concept to grasp in Calculus 1?

I would say it is not the Fundamental Theorem of Calculus, but rather some notion connecting limits and continuity, perhaps the $(\epsilon,\delta)$-definitions of limits and continuity. But I would be ...
13
votes
6answers
3k views

Is it a bad idea to offer variants of a final exam based on the type of allowed calculators?

Background/rant: I am in charge of teaching our single quarter course on vector calculus (don't ask me why the department head thinks the area can be covered in half a semester). The two biggest ...

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