Questions tagged [undergraduate-education]
For questions about teaching students at the undergraduate (university) level.
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Does answering any math questions you encounter help the quality of what you learn?
I'm an undergraduate math student and I'm trying to maximize the quality of what I could learn.
My strategy a few years ago started by just reading multiple concepts and topics from different fields ...
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Should I apply for teaching assistance given my situation?
I'm a Master of Science Student and I'm really interested in mathematics and thinking about math problems. In my university, one of the courses for the first semester undergraduate students is ...
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Teaching students how to check the validity of their proofs
The question Teaching students to find and correct their own errors and its answers address mainly calculation problems of the types typically found in secondary school and the lower levels of ...
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Reading popular books in undergraduate math classes: Techniques, assignments, methods?
When I was a senior in high school taking calculus, my teacher assigned us the book Zero: Biography of a dangerous Idea by Charles Seife. I found it inspiring to learn about the class in a historical ...
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Is teaching how to solve recurrence relations using generating functions too much for a first year discrete maths course?
I'm teaching discrete mathematics at a local university (some lecturing but mainly tutorials), and as many of you probably know such courses are filled to the brim with content. There's logic, ...
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Examples of different languages with mathematically different names for concepts
Multilingual classroom
Having pupils of many different native languages, and many languages in general, has been getting quite common in Norwegian classrooms, too. In many other countries this has ...
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Truth tables. What does a truth valuation of a formula even mean?
What does a truth table even mean? Does anyone actually spell it out anywhere? (reference please). People feel like the are not taught rigorously like limits are.
Edit: What does it mean for a (non-...
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Which cognitive psychology findings are solid, that I can use to help my students?
I read recently on this site that the growth mindset seems not to be real. I did not know that (I admit that I don't follow research into learning as closely as I would like). Can I turn that ...
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How Can I Encourage Students to Use AI Like ChatGPT Across Math Courses?
I've been using ChatGPT (GPT-4) to help with creating quiz questions, solving math problems, and answering students' queries in my classes. Although it sometimes gets things wrong, with the right ...
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What Basic Math Skills Should Be Expected of Students in a University-Level Linear Algebra Course?
I am currently teaching a university-level linear algebra course and recently encountered an issue that made me question the assumed foundational math skills for students in this course. The issue ...
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What are the essential topics in undergraduate financial mathematics?
When I was an undergraduate 15 years ago I did not take any financial mathematics courses. Recently I was approached by an undergraduate, whose ultimate goal is to go into the financial sector, and he ...
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What is a corequisite course?
My department has eliminated its remedial mathematics courses and implemented a corequisite system.
I did not participate in the original design, so I found myself unable to understand the new system.
...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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In math exams, how rigorous should the questions be?
We have theoretical questions in our exams (often in ABCD format).
For example, I can state the question:
For an indefinite integral, does it hold that $\int f(g(x)) \cdot g'(x) \, dx = \int f(x) ...
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What mathematical topics are important for succeeding in an undergrad PDE course?
I am a student helping to develop a remedial course for other students who have recently failed the undergraduate PDE course at our university. The topics are provided from the syllabus in the ...
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Sources on inequity in precalculus sequence
I'm trying to put together some thoughts on the importance of a strong college precalculus sequence (mainly I'm thinking College Algebra, where much of my experience is) for addressing socioeconomic ...
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Is it better to teach category theory in the background of type theory than set theory?
I have been going over some applied instances of category theory in Programming, and also by a book by conceptual Mathematics by Lawvrere, and I think an issue of applying category theory to real life,...
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How to teach pure mathematics to a well-educated adult who did badly in maths at school
My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is ...
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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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