Questions tagged [undergraduate-education]

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

Filter by
Sorted by
Tagged with
4
votes
3answers
206 views

How do people 'master' a subject? What is the difference with 'memorizing' (not purely memorizing, but rather having it drilled inside the brain) it?

I'm in my 3rd year of pure math bachelors, and a thorny issue keeps on reappearing for me. I understand the theory, for a day, maybe two. I've reached the point where our lecturers no longer detail ...
3
votes
4answers
301 views

Applications of abstract algebra outside of mathematics and suitable textbook

The question What are some good mathematical applications to present in an abstract algebra course? asks about mathematical applications of abstract algebra. What are some applications of abstract ...
2
votes
0answers
99 views

Worldwide standard textbooks vs textbooks from one's home country vs lecture notes by various people - pros and cons

So far I've had three types of professors in my undergrad studies when it comes to choosing the main text for the course: Type A: these are the professors who pick some standard textbook(s) in English ...
17
votes
7answers
582 views

Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
9
votes
1answer
192 views

Should I upload slides before or after a class

I used to post my slides before a class. But I noticed that many students simply read it while in class instead of listening . So I am thinking not doing it in the future. But they can still get it ...
0
votes
0answers
140 views

Mental Health in Mathematics

I am not sure if my question is relative to this meta but I still want to put forth my thoughts and concerns and questions because I think its not just me but others too who have similar issues. My ...
3
votes
2answers
169 views

How do you study subjects you're not that interested in

I'm an undergraduate who doesn't find analysis particularly interesting, but I'm taking a calculus on manifolds course next semester, so I'm reviewing measure and integration theory since my grasp on ...
12
votes
1answer
214 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, ...
26
votes
12answers
2k views

Why do students like proof by contradiction?

Every-so-often I come across proofs of the form Assume $X$ is false. Prove $X$ is true (without using that it is false). This contradicts that $X$ is false. Hence $X$ is true. I've seen students ...
3
votes
1answer
92 views

Questions to help better understand the textbook

I am teaching a linear algebra class for math majors and non-majors out of the first 4 chapters of Lay's book. My plan is to have the students read a section prior to each class, have them answer a ...
5
votes
0answers
136 views

What do you think, is teaching on an actual board more efficient than using an online board?

I am a sophomore math undergraduate and so far all of my university courses have been online due to the pandemic. I am really curious what you guys think about the efficiency of teaching mathematics ...
17
votes
1answer
1k views

Is metacognition ever bad?

Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page ...
10
votes
6answers
1k views

Question formats for online tests, to deter cheating

I'm teaching calculus 1 online this term and anticipate being plagued by the perennial problem of cheaters. I have seen suggestions for how to arrange the testing time to accommodate for traditional ...
5
votes
2answers
192 views

Where can I find hard exercises for logic?

I taught propositional logic a few weeks ago using Discrete Mathematics: An Open Introduction, 3rd edition. See chapter 1 and 3.1. The topics includes logical connectives implications converse and ...
3
votes
2answers
227 views

Preparing to be a linear-algebra teacher: Any tips/suggestions?

I'm engineer and I love linear-algebra. I finished a couple of days the Linear-Algebra on OpenCourseMIT to refresh my memory and I have been doing ton of exercises. I would like to teach to engineer ...
22
votes
4answers
990 views

Tutoring a recalcitrant/awkward/exasperating student---special needs?

As part of my duties at a GTA, I spend several hours per week in our department's drop-in tutoring center. The center is open to all students enrolled in 100- and 200-level math courses, with the ...
2
votes
2answers
184 views

ELL textbooks for core university math?

Any references for core textbooks aimed at English language learners at the university level? I have need of them for: Calculus I-II-III, Linear Algebra, and Differential Equations. Most of my ...
34
votes
10answers
8k views

Combative students in proofs classes

When teaching my first discrete math class recently, I found a subset of about 5 out of 35 of my primarily computer science students who I struggled to reach. If these students simply struggled with ...
34
votes
9answers
1k views

How can we help students learn to write about their mathematics?

As a guiding example, imagine an undergraduate Calculus II course where students have to complete a guided "research project" and write a "paper" about their work. This can be a shockingly new ...
6
votes
2answers
314 views

Effective Strategies for Helping Students Recognize Nonsensical Expressions? (HS - Undergrad Level)

I'm not entirely how best to pose this question, so that it fits within the guidelines (so edits / suggestions for modification are warmly welcome). I'm interested in exploring effective strategies ...
3
votes
2answers
129 views

Teaching Solving Linear Equations before teaching evaluating expressions

Traditionally, I have always taught evaluating expressions before teaching linear equations. But, I was recently given a remedial class of students that have to cover the bare minimums (and we have ...
13
votes
5answers
373 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 ...
42
votes
4answers
2k views

Teaching undergraduates who expect a high-school-like learning environment

tl;dr: Some students expect to be told "what's on the test", to memorize and then move on. What can be done to change how they learn while teaching them what to learn? Context: Introductory, ...
3
votes
1answer
164 views

To what degree can the legally blind, with computer induced medical problems, study statistics?

My son graduates from secondary school in 2022. But he shall attend university in Australia or UK — where you must apply for ONE major — not liberal arts in the USA. He wants to pick BSc Math with ...
10
votes
5answers
531 views

How to resolve the new definition of subtraction and division seen in college algebra?

Here's the foundational thing that irritates me the most when teaching college algebra. Up through the secondary level, I think that instructors and students are trained to understand subtraction and ...
15
votes
5answers
4k views

Why the fear of polynomial long division?

Why do people think long division of polynomials is complicated ? I heard this expressed recently and it seems like an odd sentiment. For me, synthetic division is complicated and totally adhoc ...
5
votes
2answers
214 views

How can I encourage students to show up for exercise classes?

I am doing a maths PhD and naturally that involves leading exercise classes for undergraduate students. The idea is that the students just show up and work through the problem set and I'm there to ...
13
votes
5answers
1k views

Where can I find public repositories of past math exams?

I'm looking for public repositories/banks of past undergraduate math exams. No solutions necessary. I just want inspiration for writing my own exams and practice exams. It'd be nice to collect links ...
9
votes
3answers
387 views

Argument for and against giving two different grades at the end of a course

From education theory, there are different concepts how to grade an exam: Either you can say that someone gets only by correct answers or you can say: No matter how good someone is, the best 10% get ...
5
votes
4answers
276 views

Entertaining and fun books about mathematics for (basically) liberal arts students

I’m looking for books of a general interest in maths, like a maths novel, a fun book about maths, a humorous introduction to higher concepts, something outside of tests, something they can read on ...
6
votes
1answer
268 views

Should I ask for a proof-of-work for online exam?

I am going to do an online exam next week. Since this will be done by students at home, there is no way to guarantee that they do not cheat. I am thinking of asking for a proof of work, i.e., photos ...
44
votes
17answers
2k views

How to teach logical implication?

One of the challenges of undergraduate teaching is logical implication. The case by case definition, in particular, is quite disturbing for most students, that have trouble accepting "false implies ...
2
votes
2answers
693 views

Preparing elementary teachers for the praxis exam

I'm teaching a class called "Math for Elementary Teachers." The main goal of the course is to prepare the prospective teachers for an exam that I believe is called "Praxis" (some ...
28
votes
10answers
5k views

Getting students to actually read definitions

I'm teaching a second year "Introduction to Theoretical Computer Science" course, and one of the skills/habits I've tried to instill in the students is to actually read definitions, take ...
30
votes
10answers
10k views

Why do we teach even and odd functions?

I've been either a student or an instructor in Precalculus or Calculus 1 at about 6 institutions now, and teaching the definition of even functions (where $f(-x) = f(x)$) and odd functions (where $f(-...
6
votes
4answers
3k views

How to keep students' attention while teaching a proof?

I taught the proof inclusion-exclusion principle to CS students yesterday. While the proof is not too long, it does involves quite a bit notations. I could feel that most students lost interests a few ...
2
votes
1answer
173 views

Effect of grades versus pass/fail on teacher education students

Context: University studies in Norway, master level, to become a teacher at either primary education (barneskole, classes 1-7) or mostly middle school level (ungdomsskole, classes 8-10 and pupils of ...
4
votes
2answers
479 views

Should I gave a make up lecture if some students found what I taught is a bit unclear?

This semester, I am teaching discrete math for computer science students. Today I taught solving linear recurrence equations. The way I did it was not rigors. Instead I used the method of advanced ...
70
votes
17answers
9k 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. Some challenges: My school provides limited online ...
89
votes
18answers
17k views

Unique candidate that fails

In the comments to David Speyer's answer here, he points out that "the distinction between 'if there is a formula, it is this one' and 'this formula works' is subtle." Does anyone have any simple, ...
2
votes
1answer
80 views

Looking for good examples/explanations of maximum likelihood estimators for discrete random variables

The title basically says it all. I need to prepare material for a whole classroom of elementary statistics students, so if anyone wants to help me out in the name of math education, that'd be great!
12
votes
0answers
139 views

What studies exist, comparing the efficacy of exercise sheets with or without worked solutions?

I've been tutoring mathematics at university level for over 10 years, and one of the more common requests from students is worked solutions for sheets of exercises. Most educators I've worked with ...
21
votes
2answers
1k views

Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?

When I taught courses on algebra giving a first exposition to Galois theory I usually included some discussion of classical results showing the impossibility of constructing certain points with ruler ...
11
votes
11answers
4k views

Ideas for explaining 4D and higher dimensions

I introduced the hypercube (to undergraduate students in the U.S.) in the context of generalizations of the Platonic solids, explained its structure, showed it rotating. I mentioned Alicia Stott, who ...
8
votes
2answers
326 views

Teaching LU Factorization in a sophomore-level Linear Algebra course

I teach this course from David Lay's Linear Algebra and Its Applications, which on the whole is a great textbook and explains things well. It does not explain the steps of LU factorization well, so I ...
8
votes
1answer
381 views

Ideas and/or references for projects for a business calculus course

I have undertaken the teaching a business calculus course for this semester (spring II). The various assesments for the students, include quizzes/hw/midterms/final exams, adjusted with suitable ...
9
votes
2answers
284 views

Differences between Hardy&Wright and Ireland&Rosen for number theory course

My professor advised us to get either Hardy&Wright or Ireland&Rosen for our introductory number theory course. I would like to ask what are the differences between these textbooks in terms of ...
0
votes
2answers
272 views

Real before complex analysis or vice versa?

I used to learn Real Analysis before Complex Analysis in my bachelor study, but now the order is reversed in my university. I would like to ask which order is better to learn the subjects, and which ...
9
votes
2answers
416 views

Should we assess ability to use specific problem solving methods, or general ability to solve problems?

This is my first semester being an instructor of record for a college algebra course. One of the sections we cover is "methods of solving quadratic equations", where we discuss factoring and ...
7
votes
3answers
428 views

Resources for mathematics for sustainability

I am looking for resources (books, websites, etc.) for mathematics relevant to or in the context of sustainability, broadly construed, at upper secondary or early undergraduate level - so not ...

1
2 3 4 5
15