Questions tagged [undergraduate-education]

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

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12
votes
4answers
970 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 ...
3
votes
1answer
94 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 ...
-3
votes
0answers
33 views

`How to partially differentiate implicit function [closed]

I need to figure out how to find the following: partial of Y with respect to f and, partial of Y with respect to g. The implicit function is Y = x - z(f,g,h). Right now I think the answer is ...
2
votes
2answers
667 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 ...
2
votes
0answers
76 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 ...
6
votes
1answer
257 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 ...
27
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 ...
5
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
86 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
473 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 ...
2
votes
1answer
73 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
126 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 ...
9
votes
2answers
322 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 ...
9
votes
2answers
405 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
413 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 ...
2
votes
1answer
149 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. ...
0
votes
2answers
264 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 ...
6
votes
5answers
732 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 ...
5
votes
2answers
412 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 ...
5
votes
4answers
700 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-...
6
votes
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
votes
2answers
119 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 ...
7
votes
3answers
480 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 ...
4
votes
2answers
200 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
votes
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, ...
2
votes
1answer
204 views

How to teach if calculations and algebraic manipulations are off limits

This question may be just too broad in scope, but some form of it has been on my mind during this year of remote learning as I imagine a future cycle of educational upheaval. Much of what we teach in ...
4
votes
0answers
86 views

Objectives for group work in undergraduate pure maths

Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...
2
votes
4answers
377 views

Is it necessary to teach the definition of a limit for engineering majors? [closed]

I have always wondered whether it is necessary or not. For me, it seems that it is enough to teach them the intuitive idea, that is, limit is just an approximation of a certain process. what do you ...
3
votes
2answers
203 views

How to make an introductory course on Statistics interesting

I am going to teach this probability and statistics course in a couple of weeks. The probability part can be made very interesting, in my opinion, easily. But I am a little worried that I might make ...
2
votes
1answer
160 views

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
-1
votes
2answers
168 views

What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]

What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
5
votes
1answer
120 views

Students reliant on answers provided, but not their own reasoning?

Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998). Students ...
6
votes
1answer
428 views

"Flipped classroom exercises" resources

I was reading this book: "Dynamics of Particles and Rigid Bodies: A Self-Learning Approach" by Mohammed F. Daqaq In the preface, the author explains of his "flipped classroom ...
7
votes
1answer
914 views

How to be a good math teacher at a liberal art college?

I am thinking of taking up a position at a liberal art college. I have taught mathematics at large public universities but I have no idea what is it like to work at a liberal art colleges. So what are ...
15
votes
2answers
207 views

Tension between the most intuitive definition vs. the most common definition of a concept

Many definitions in mathematics are "fully crystalized". Sometimes the form of these definitions might be somewhat baffling to the uninitiated. For example, the definition of a relation ...
2
votes
3answers
238 views

History of discrete math curriculum

I will be teaching discrete mathematics. I’m wondering if anyone can tell me a couple topics that were classically in this class (in any undergraduate version) that were probably discarded over time, ...
5
votes
3answers
260 views

I need strategies for tutoring a bright, motivated student currently taking college algebra who just doesn't seem to retain the things I teach

I have a college student who I've been tutoring over the past two semesters. He's a hard worker and quite bright. Unfortunately, I do not feel like I am having much success in helping him learn ...
7
votes
3answers
275 views

Rings in parallel with groups in abstract algebra

In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - ...
2
votes
1answer
153 views

Improving exposition of a proof about polynomials over infinite fields

This question concerns teaching a proof of the theorem that if a polynomial $f \in k[x]$ over an infinite field $k$ is the zero function (i.e. $f(a) = 0$ for all $a \in k$) then it is also the zero ...
19
votes
11answers
5k views

Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?

The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the ...
4
votes
2answers
184 views

Pros/Cons of using a single story in multiple examples to demonstrate different points

Judea Pearl, in his book "Probabilistic reasoning in intelligent systems" uses a handful of stories over and over again, each time to demonstrate a different point. (His "Alarm" ...
8
votes
3answers
257 views

Seeking references for why it is good that students understand why mathematical rules work

I am currently advising a student at his final project (it is a graduation course for people who will become math teachers). We've chosen to pick some basic mathematical rules which are (or at least ...
13
votes
3answers
2k views

Finding the Balance in a Math Question (Teaching)

As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such ...
0
votes
4answers
333 views

Defining mathematics to primary/elementary school teachers

I'm looking for a simple way to define mathematics to primary/elementary school teachers and explain some of the confusion children have. I'm hoping some Algebraist could help me properly state the ...
6
votes
1answer
281 views

Complex analysis books/resources where solutions are difficult to find

I am teaching complex analysis for undergraduates using the textbook Complex Variables and Applications, Brown and Churchill. I am looking for resources that I can use to find good problems for ...
5
votes
2answers
282 views

Curving grades without creating competition among students [closed]

I've recently taken a new position within a math department at a large university. The department has an official policy that in most lower-level undergraduate classes (let's say anything in the ...
2
votes
0answers
75 views

creating an easygoing mathematical course that covers basic concepts that are not in main focus of standard courses [closed]

I want to know which topics should be covered if one wants to create an easygoing mathematical course that covers basic concepts that are not in main focus of standard courses i.e. what those concepts ...
35
votes
6answers
4k views

How can I give feedback that is not demotivating?

Background: To cope with online education, I taught linear algebra using a variant of the flipped classroom. I recorded videos and put them up on YouTube and students presented the content in these ...
7
votes
7answers
1k views

Advice on teaching abstract algebra and logic to high-school students

NOTE: This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
10
votes
2answers
341 views

Weekly quizzes as an alternative for midterms? What is this called?

I have seen (by some of my former instructors) the following strategy applied as an alternative to traditional "midterms and final" assessment in a math course: Students take a quiz weekly. ...

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