Questions tagged [undergraduate-education]

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

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3 answers
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Is there anything one can do for students who have given up?

In each class, there are often a few students who seem to have given up early on. In my recent discrete math class, when I asked a student a question, he said he was working on his graduation project. ...
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11 votes
6 answers
496 views

What are best practices for building a dedicated space for mathematics majors?

The math department at my institution (a private, four-year college with a total enrollment of about 4000) is in the process of brainstorming about a dedicated study/community space for our math ...
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3 votes
4 answers
348 views

Student forgets to remove dx after integrating

I am tutoring another US college student in a Calculus 1 class. Initially, she was having trouble with basic concepts, but after much prodding most of the conceptual difficulties seem to have been ...
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  • 135
3 votes
2 answers
197 views

How to understand the book and the material to the deepest possible level?

I'm a first year mathematics major and I have a problem with my learning process. In my university, I only have books and questions that the university published, so I have to learn the most of the ...
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3 votes
1 answer
213 views

What kind of general advice for studying math we can offer undergraduate studens who do not major in math?

I have received request from a student, who is not in math major, asking me for advice on How to keep motivated when studying math (calculus, linear algebra, etc.) What does one need to do beyond ...
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8 votes
5 answers
3k views

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? Does Riemann integral suffice for undergraduates? The reason of my question is I read a paper by Bartle titled ...
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3 votes
1 answer
57 views

Resource for International Comparison of Math Education Logistics

Are there resources that compares/lists crunchy facts about the logistics of math education in different regions or countries? I'm talking facts like: Do they use paper homework versus and online ...
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16 votes
18 answers
2k views

Concrete vectors spaces without an obvious basis or many "obvious" bases?

I am teaching a class on linear algebra to sophomore and junior science majors, and am having some trouble illustrating the difference between $\mathbb{R}^n$ and an n-dimensional vector space. The ...
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13 votes
12 answers
6k views

How should I grade true-or-false questions if the student's writing is unclear?

See the attached image: I am having a difficult time grading this paper as I am not sure if the student intentionally wrote the answers in such a way that each answer looks like both "T" (...
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  • 4,015
7 votes
0 answers
154 views

Category theory without categories and without theory

In undergraduate courses, students are often taught that a function is injective if it never maps distinct inputs to the same output, and it is surjective if every member of the codomain is an output. ...
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4 votes
1 answer
218 views

Tips for teaching mathematics with experiments?

I am teaching a first-linear-algebra course for mostly undergraduate Computer Science and Data Science students. Occasionally, I tried to do a bit computer experiments in class and ask students to ...
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1 vote
2 answers
1k views

Is there a College Algebra book that was written by a world-class mathematician? [duplicate]

I have taught College Algebra several times and will teach it again in the next semester. College Algebra, according to the catalogue of my college, is described as follows: This course provides ...
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5 votes
0 answers
151 views

Montessori mathematics for HS/college students

My children attend a Montessori school (as did I when I was a child), and I have visited several other Montessori schools and spoken with their teachers. Numerous times I've had Montessori teachers ...
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10 votes
4 answers
404 views

Should students in a first university linear algebra class be taught to write simple proofs?

I am teaching an introductory linear algebra courses for undergraduate students in math, computer science, or data science at a liberal art university. Most of the students have not decided their ...
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8 votes
1 answer
143 views

Ball rolling down curve simulator

I am preparing a seminar on mathematical discovery for beginner's students, and one of the topics I plan to cover is the brachistocronic/tautochronic curve. For this purpose, I would like to let the ...
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  • 183
3 votes
0 answers
77 views

How to make student work in think-pair-share?

I have been trying the think-pair-share technique in my undergraduate linear algebra class of about 30 students. Some students quite enjoy the experience. But I noticed that some other students simply ...
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9 votes
3 answers
218 views

What's the Deal with Inverse Cotangent?

So, I was minding my own business and I thought I had defined inverse cotangent in the natural fashion. In particular, we define inverse tangent as the inverse of tangent restricted to $(-\pi/2, \pi/2)...
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8 votes
1 answer
142 views

Proofs with Independent Parts

In my Intro to Proofs course I have an activity (more details below) where the goal is to write a collaborative proof of a statement. What makes it work as a whole class activity is that, to prove the ...
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4 votes
1 answer
135 views

What to do with students who are often absent from class?

I have a class of 31 students. There are about 5 to 10 of them absent during each meeting. Right now I am not enforcing attendance because some of them may have legitimate reasons to be absent and it'...
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6 votes
4 answers
736 views

What is the best way to introduce Laplace transforms on an Engineering Mathematics course?

Are there any practical applications of Laplace transform? I would not use Laplace transforms to solve first, second-order ordinary differential equations as it is much easier by other methods even if ...
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2 votes
1 answer
182 views

How and what to teach on a second year Engineering Mathematics?

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. ...
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-4 votes
1 answer
119 views

Is it weird for an undergrad or grad quant/applied maths(/even pure maths) programme to not teach that probabilities of 0 or 1 will never change? [closed]

Edit: i didn't mean it like this programme should do this or that. i mean other people are accusing me like 'your programme should've had this or that' (actually they're saying that i should know this ...
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  • 526
3 votes
0 answers
137 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 ...
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4 votes
5 answers
365 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 ...
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1 vote
0 answers
170 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 ...
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4 votes
2 answers
187 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 ...
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  • 141
10 votes
1 answer
212 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 ...
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3 votes
1 answer
95 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 ...
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5 votes
0 answers
142 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 ...
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6 votes
3 answers
332 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 ...
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2 votes
2 answers
188 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 ...
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3 votes
2 answers
135 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 ...
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  • 189
6 votes
2 answers
319 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 ...
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  • 229
34 votes
10 answers
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 ...
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  • 3,477
3 votes
1 answer
166 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 ...
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  • 133
15 votes
5 answers
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 ...
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13 votes
5 answers
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 ...
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  • 4,362
5 votes
2 answers
234 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 ...
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2 votes
2 answers
704 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 ...
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5 votes
2 answers
202 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 ...
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6 votes
1 answer
276 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 ...
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28 votes
10 answers
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 ...
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  • 419
6 votes
4 answers
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 ...
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  • 2,027
2 votes
1 answer
186 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 ...
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  • 4,544
4 votes
2 answers
488 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 ...
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  • 2,027
2 votes
1 answer
85 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!
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12 votes
0 answers
145 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 ...
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11 votes
2 answers
385 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 ...
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9 votes
2 answers
422 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 ...
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7 votes
3 answers
451 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 ...
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