Questions tagged [undergraduate-education]
For questions about teaching students at the undergraduate (university) level.
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Studies on the effects of using online platforms in teaching mathematics on students' beliefs about mathematics
Are you aware of any research examining the impact of utilizing online platforms in teaching mathematics, on students' beliefs about mathematics? To give you an example of the kind of beliefs that I ...
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Joint Teaching of a First Year Engineering Maths Class
My department is considering using more than one lecturer (sequentially, not in parallel) to give lectures in our large first-year classes (e.g. 500 students doing engineering mathematics).
In other ...
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Good analogies for teaching error correcting codes
I'm trying to find a good real-world analogy (or even good visualization) for teaching about error correcting codes and erasure encodings. The most natural way to talk about it really is in terms of ...
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Why do we teach linear algebra in precalculus classes?
When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't ...
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Why don’t we teach a topological view of continuity instead of epsilon-delta?
I would like a critique of this approach to teaching continuity to calculus 1 students.
Show them that for an increasing function on (a,b) we have that (a,b) is contained in the set of solutions to $...
user22312
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Discrete Probability Modeling with Desmos or Spreadsheets
In my Finite Math course* almost every section includes a part where students have to create a file (from scratch) in Desmos or in Google Sheets. For example, they use Desmos to plot piecewise linear ...
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simpson paradox in classroom: reports?
he Simpson's Paradox is a statistical phenomenon in which a trend or relationship observed within a dataset disappears or reverses when the dataset is divided into smaller groups. It occurs when a ...
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Comparison of texbook for "how to write proofs"
I posted this question in the math stackexchange https://math.stackexchange.com/questions/4681694/comparison-of-textbooks-on-how-to-write-proofs and one person suggested that I cross-post it here. I'...
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What is a theoretical contribution in mathematics-education research?
I am an early-career mathematics-education researcher. Recently, I received a request for major revisions for a manuscript I had submitted on opportunities to learn provided by undergraduate ...
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Seeking Advice on Allowing Students to Skip a Quiz in Linear Algebra Course
I am currently teaching a linear algebra course at a university and have chosen to assess my students using five quizzes throughout the semester, instead of assigning homework. I have encountered a ...
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Interpreting the derivative as instantaneous rate of change in real phenomena
When interpreting the meaning of the derivative in real phenomena, it may seem that the interpretation is in conflict with the definition of the derivative itself. The confusion is caused by the units ...
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Best category theory textbook for undergraduate students
Title is pretty self explanatory. All recommendations welcome. Comments and answers which reject the premise of the question will be met with eye rolling.
If I don't see a good enough answer I'll have ...
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Parentheses around negative numbers
We teach students that a notation like
$$17 - -59$$ is not acceptable or at least not good. Instead we want them to write $$17-(-59)$$
The main reason seems to be that it's more readable if you ...
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How to give exercises when students can use ChatGPT
I tried some math exercises we will give to students and ChatGPT does really well answering these. It excels at proofs and often gives details that were not our the example solution, and makes some ...
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Homework in a Flipped Classroom
I'm in the middle of teaching first-semester Calculus where, for the first time, I'm trying to implement a flipped classroom. (Background: Small university in U.S.; Calc 1 for STEM majors, 50 minute ...
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What to cover on a first ordinary differential equations module?
I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books, have Laplace Transforms which is fine but I would not use LT to solve ...
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Is there a fair way to increase the grade of students who did not do well in exams?
How can I fairly compensate a student who showed passion and dedication for my undergraduate course but performed poorly on the final exam, without unfairly advantaging them over other students?
...
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Is it possible to learn some basic mathematics using an app?
I am interested in developing an app for students that are starting a grade career involving mathematics. It is a real problem that they start with almost no knowgladge of basic mathematics and there ...
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How do/should administrators estimate the cost of producing an online introductory mathematics class?
With the advent of the Internet administrators used to allocate release time or summer salary for making online course content. The pandemic made a Sal Khan out of most of us and making online content ...
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How to formalize high-school (Euclidean) geometry?
I have unsuccessfully attempted several times over the years to formalize high-school (Euclidean) geometry, or even a working subset of it. Think very simple, diagramless geometry.
The usual two-...
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Are there examples of central symmetry, without axial symmetry, in nature?
Examples of axial symmetry abound, but I could not find an example of pure central symmetry (that is, without axial symmetry)! Do you know of any? A butterfly shows axial symmetry, what shows point/...
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‘Lies to children’ in mathematics and statistics education
In teaching, we sometimes necessarily oversimplify concepts. Terry Pratchett famously referred to this as Lies to children:
A lie-to-children is a statement that is false, but which nevertheless ...
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Common mistakes in probability
$\DeclareMathOperator\Var{Var}\DeclareMathOperator\Bern{Bern}\DeclareMathOperator\Pois{Pois}$Question: What not-trivial mistakes do students often make when solving problems in probability theory, ...
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Relearning math after long COVID using AoPS or developmental math textbooks?
This is a little bit of a niche topic.
I've dealt with a pretty bad dose of long COVID that has caused some serious gaps in my mathematics (basically causing terrible arithmetic skills and a really ...
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Math curricula\programs or any experience using "The Road to Reality" as the\a primary textbook
Primarily a reference request, collaborator search-tips requests, and question-improvement request (including improveent by deletion and re-posting to more appropriate stack, meta, wiki, etc). Rank ...
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How to teach the concept of probability distribution?
I observed that my students do not understand what a probability distribution is.
We do not treat probability axiomatically on the course, so the required level of understanding is knowing all the ...
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Potential topics for a university level mathematical thinking module
Social science training typically involves statistics as equivalent to "quantitative methods", particularly statistical modelling but also some material about data quality and exploratory ...
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Encouraging students to see value in things that can't be measured
It's very tempting for a student who is overly excited about mathematics to discount intellectual work in other fields, particularly the humanities, where the nature of knowledge and knowledge ...
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What do you do in order to drag out lectures?
I posted earlier about how I was surprised that a typical Calculus 1 course that meets 3-4 hours each week for 15 weeks only barely manages to reach the fundamental theorem by the end of the course. ...
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What is a good pacing for a Calculus 1 undergraduate course?
I am going to teach a Calculus 1 course next semester, and I have 15 weeks for the course material. The class meets MWF for 50 minutes each. I have taught this class before using the same syllabus, ...
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Examples of random variables that are measurable with respect to a strict subset of $\mathcal{P}(\Omega)$
When teaching random variables for the first time, most of us say that it is a function $$X : \Omega \to \mathbb{R}$$ without any further restriction. Of course, a more general definition is to say ...
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Should we require students to take notes in class?
When I teach undergraduate level math course, I make slides with a lot of white space.
In my classes, I write on my slides with an iPad and project the screen to a big TV.
After a class, I provide ...
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Why is a Calculus III student more likely to solve this problem?
Consider this elementary problem:
Define an operation $*$ between integers as follows: $a*b=ab-a+b$. Solve the equation $4*x=36$.
If we give this problem to Pre-Calculus and Calculus III students (...
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What are some research-level opportunities in mathematics that do not focus on proofs?
The research level of mathematics (what is done by professors and upper-level graduate students) tends to be heavily portrayed as focused on writing proofs to the exclusion of most anything else math-...
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Is there any way of explaining the Cayley/Beltrami–Klein metric to undergrads?
How to explain the Cayley-Klein or sometimes called Beltrami–Klein metric concept to find the distance between two points in a hyperbolic space to an audience with no higher education than maybe a ...
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How can I help/tutor a friend who is taking the same course as me?
I am a STEM major and have a good friend who is a non-STEM major. We are both taking a CS minor, me because it is relevant to my field of study and he because he wants a backup plan in case his ...
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Fitch Style Deduction in Non-Logic Classes
Has anyone experimented with using Fitch-style proofs as a teaching aid in courses outside of logic specifically and if so, how was the technique received by students?
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Policies and practices for supporting students in crisis
I have noticed a common pattern followed by many students in crisis:
They experience a crisis or setback (injury, illness, tragedy, etc)
This causes them to miss a lot of class.
They may stay away ...
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How to differentiate the two notions of convergence order?
In the context of iterative methods for equations and linear systems, one usually says that "linear convergence / order 1" is when the error $err$ goes to zero with the number of iterations $...
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What are the essential mathematics skills that uni based STEM math educators want high school to teach students?
The question in the title mostly covers the question I want to ask. After seeing a number of questions here on ME and having taught/TA'd a number of introductory math classes, I wonder what people ...
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References to learn modern functions applied to integration and numerical series problems and how to teach them to Calculus students
I think most of us have met integration problems concerning the trigonometric, polynomial, exponential, hyperbolic and power functions in the calculus courses. But many of the problems in this website ...
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Is the Wronskian still assumed for graduate education?
About thirty years ago, in a practice GRE (Graduate Record Exam) math
test in the US,
a question assumed the student knew the definition of the Wronskian. I had never heard of this determinant
before.
...
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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.
...
user11702
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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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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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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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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 ...
user11702
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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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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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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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