Questions tagged [undergraduate-education]

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

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2answers
139 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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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
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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
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2answers
284 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
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2answers
123 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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5answers
356 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
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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
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1answer
151 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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5answers
519 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 ...
14
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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 ...
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2answers
205 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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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
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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 ...
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4answers
273 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
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1answer
263 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
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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 ...
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2answers
685 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
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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 ...
2
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0answers
80 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 ...
30
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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
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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
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1answer
118 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
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2answers
478 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
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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
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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
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1answer
79 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
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0answers
135 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 ...
20
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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 ...
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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 ...
9
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2answers
324 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
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1answer
348 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
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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
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2answers
269 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
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2answers
411 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
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3answers
418 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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13answers
2k views

Examples why university education is important for future high school teachers

At my university, the students in math are mixed up (1/3-1/2 are bachelor/master students, the rest are future high school teachers). A problem arising very often is the discussion dramatically ...
2
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1answer
151 views

How can maths assistants at a college be extra helpful for professors?

I am a maths graduate student. A little background: In the coming semester, I will be assisting a prof whom I admire and whom I also want to thank a lot, and I actually will have a lot of free time. ...
6
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5answers
759 views

Does the way we often introduce the concept of a function make sense?

Here are some ideas and a few questions I've been pondering lately related to the teaching of functions in college algebra and precalculus: Based on my experience, the teaching of functions usually ...
28
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5answers
2k views

How should normal subgroups be introduced?

One standard definition of a normal subgroup is A subgroup $N \subset G$ is normal iff the set of left cosets $\{gN\}$ and right cosets $\{Ng\}$ coincide. There's a class of similar definitions (...
6
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3answers
438 views

How to introduce group theory to a general audience in 15 minutes?

How to introduce Group Theory to a general audience in 15 minutes? I know that it will be quite tough to introduce Groups to a general audience in such a short time. So what will be a good way to ...
5
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2answers
421 views

Undergraduate-level abstract algebra books or courses that don't start with groups or rings

When I was an undergrad studying abstract algebra, we used the second edition of Artin and covered groups first and then rings. Fields, vector spaces, and algebras came later, I think. I remember ...
3
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2answers
291 views

Succinct description of situations where naively obvious is correct, but for far more complicated reasons?

What is the name for a situation where the obvious thing turns out to be true, but the reasoning is more complicated? In abstract algebra we can say the rational numbers - the fractions, $\mathbb{Q}...
7
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3answers
633 views

Is there a study that compares 8-week vs 16-week math classes?

I see a push toward having undergraduate curriculums built around 8-week classes. This is mostly in the online education in the USA. Recently I have seen a number of these in sophomore or junior-level ...
6
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4answers
703 views

Teaching Mathematics to a Machine Learning Class

How and what mathematics must be taught for training engineering students with the mathematics required for Machine Learning? How can one conduct training of mathematics required for application-...
5
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2answers
738 views

Textbooks for an independent study in point-set topology

I am planning to sign up for an undergraduate "course" in point-set topology next semester. It is really an "independent study" in that this course will not have any lectures. It will just have two ...
6
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5answers
1k views

How do math professors select textbooks?

I will describe what I mean by the above with an example. Suppose you are a professor, about to teach a first Calculus course in a university. There are dozens, if not hundreds, of calculus books out ...
4
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2answers
120 views

Textbooks with solutions and catering to different circumstances

Questions: Are we really taking students into account FULLY when writing textbooks for various areas? Also, are we being unintentionally elitist or dismissive when neglecting to take a more humble ...
23
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4answers
4k views

Dyscalculia and studying mathematics (as major)

I am a bit afraid to ask this, but the question has bothered me for some time now. I have a student in my analysis class having a medical certificate of dyscalculia. This entitles her to write tests ...
4
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2answers
202 views

Are there any list of mathematical constructions which can challenge 12-16 year old students?

Mathematical (geometric) constructions are an interesting way to engage students. It also helps in better understanding of different geometrical properties. For example, Sierpinski triangle or square, ...
2
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3answers
195 views

If one wants to conduct a 1/2 day workshop in Mathematics for 12-16 year old students - how one should go about preparing the workshop

The questions that I want ask are the following: What are the most important and effective topics to conduct a workshop? What fraction of workshop should include lectures, activity, problem solving, ...

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