# Questions tagged [undergraduate-education]

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

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### A visualization for the quotient rule

Context: first year didactics of mathematics course for middle school teacher students (in Norway). I have a reasonable visualization for the product rule of derivatives: Consider a rectangle with ...
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### Is there a mathematics core assessment rubric?

Many universities in USA ask their faculty to perform a "core assessment" where they evaluate (typically) freshman students, near the end of semester, on their understanding of the courses ...
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### Math tools for restructured lectures

We are in the process of restructuring our math lectures to a more modern style. For that we want to use some math tools to show students how math is done in a more current state. Our math is more ...
341 views

### How to assess students in real analysis?

Terence Tao says the following in the preface to his book Analysis I: With regard to examinations for a course based on this text, I would recommend either an open-book, open-notes examination with ...
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### Real-World Problems for Teaching Extrema and Derivative Tests in STEM Education

For educational purposes, I am seeking example problems in the realm of natural sciences, engineering, and business that satisfy the following criteria: Consider a one-dimensional real function $f$ (...
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### Dominance of connectives: Why do we teach this?

These were two actual exercises given to students I have been tutoring for a college algebra class: I have been working very hard to convince my students of the importance and utility of learning ...
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### Is it a good idea to give partial points in grading

When grading problems on quizzes and exams, I often break them down into sub-problems, each worth a portion of the total points. I use rubrics to award partial credit for each sub-problem. However, ...
102 views

### Is there national grade distribution data for introductory service courses?

I am looking for US average national or state grade distribution data for courses that are typically considered as math service courses: precalculus, calculus 1,2,3, linear algebra, differential ...
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### How would you prepare students for "Alice and Bob" Putnam problems?

Every year the Putnam Competition features at least one question that describes Alice and Bob playing game, and asks for one player's winning strategy or something similar. Since these questions are ...
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### Resources for designing math degree programs

I'd like to know where I can find resources which are helpful when one has to design or improve grad and undergrad degree programs in pure and applied mathematics. In particular, I'm searching for up-...
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### Regarding finding eigenvalues and minimal polynomial of an operator with limited tools while following Sheldon Axler

I am using the textbook Linear Algebra done right by Sheldon Axler (fourth edition) to teach an undergraduate linear algebra course. Please find here a link to the book here. Now Axler does not ...
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### What books does a Chinese institution use in the undergraduate maths courses?

Can anyone share the books that a Chinese maths undergraduate follows during their course? Also what are some of the problem books and exam papers that the Chinese students use to become better in ...
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### How can we motivate that Newton's method is useful?

If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following: Why do I need learn such a &...
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### Textbook For a Course on Classical Geometry

I have been assigned to teach a first year course in geometry the next academic year. This course has been running for quite a while in the university, but of late, has been thought of as redundant ...
244 views

### Are the standard of questions provided in reputed institutions like MIT, Stanford, Oxford, etc., as good as the problems of IMO?

I did not win the International Mathematics Olympiad, so I was very curious to know the standard of questions asked in the graduate and undergraduate courses of maths and computer science in ...
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### Strategies for Designing Challenging Yet Feasible Quiz Problems for Upper-Level Math Courses

In the past semester, I taught two 7-week courses: discrete math and algorithms designs (which is essentially still math) for undergraduate CS students. I implemented weekly 25-minute quizzes ...
381 views

### Problem of the Week for College Students

Trinity's Problem of the Week and Purdue's Problem of the Week were both weekly problems that were excellent for college math clubs to tangle with at their weekly meetings. However, both of them are ...
1k views

### Special topics for introductory probability

I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
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### Any examples of calculus sequence that deemphasizes calculation tricks?

I'm considering creating a series of classes that explore deeper ideas in calculus without overemphasizing the various computational tricks used in integration and differentiation. My vision is ...
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### "Tools" (literarily) for solving linear or quadratic equations

Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
450 views

### Loaning students calculators during exams

Context: I am an associate professor at a small liberal arts institution in the US. I find in my introductory business math course that students sometimes fail to buy a calculator for the course, ...
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### Bridging the gap between students' intuitive problem-solving abilities and expressing ideas through formal writing

Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to ...
2k views

### Where can I find new types of problems regarding graduate level mathematics?

Though not an undergraduate student , I just wanted to know where can I find hard new types of problems regarding the problems in graduate level mathematics. As per my information , standard books ...
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### How does a math Olympian fare in undergraduate maths courses?

I am a maths enthusiast and have been exposed to maths olympiad problems for some time. I wanted to know how does a math Olympian do in undergraduate courses of mathematics, statistics or computer ...
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### How can we explain intuitively the convergence and divergence of these two series?

It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
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1 vote
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### Summer or Semester Programs which bridge to Graduate Mathematics

A few years back I had a student attend the MASS semester at Penn State. It was a fantastic experience for my student and it certainly helped him find a place in graduate school and I would wager it ...
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### Natural origins or learned habit: Why do students skip concepts before applications?

When teaching elementary mathematics, it takes a lot of time and effort to teach students that our goal is not to learn the examples, but to learn the concepts first, and then apply them to specific ...
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### When is it appropriate to warn about the difficulty of a subject?

I've been a TA across every class in the calculus sequence, under the assignment of professors with different teaching styles and curricula. It's often clear to me ahead of time when a certain subject ...
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### What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, ...
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### Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

Background I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to ...
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### Is there any university or college in any country where failure and dropout rates in Calculus are not so high?

Calculus is a foundational mathematics course that is often seen as a bottleneck for STEM majors. However, it is also a course that is notorious for its high dropout rates. In the United States, for ...
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1 vote
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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 ...
163 views

### 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 ...
351 views

### 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 ...
854 views

### 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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