Questions tagged [undergraduate-education]

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

40 questions with no upvoted or accepted answers
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Is metacognition ever bad?

Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page ...
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126 views

tutorial active learning

This is a question I asked on [Academia.se]. It did not get an answer, so I am re-posting it here. In the country where I live, university students studying mathematics usually attend lectures, ...
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370 views

Use of Lockhart's *Measurement* in a course?

I greatly admire Paul Lockhart's Measurement (Harvard Press). Many of you know him through A Mathematician's Lament. One review of Measurement said, “Here Lockhart offers the positive side of the ...
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104 views

Studies into the effects of having fewer classes per term

Have there been any studies done into the effect of having fewer classes per term on a student's comprehension of their mathematics course material? Also are there any examples of schools that have ...
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106 views

Literature on student understanding of assumptions

In a discussion with a physics lecturer he mentioned that one major area where students fail is understanding assumptions - for example, if we are interested in two objects hitting each other and then ...
8
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298 views

The importance of note taking in mathematics

I'm asking this question right now due to the fact that a lower back problem has made it very difficult for me to do much but lie down for large sections of the day when it flares up, and the fact ...
8
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0answers
480 views

Can Compare and Contrast be used in Mathematics Teaching and Research?

I happen to be a fan of the "theme and variations" approach to problem solving. In certain cases, a certain question had drawn enough to attention to generate dozens of solutions. Ways to Prove the ...
8
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0answers
107 views

3-D printing of formulas encoded in LaTex for the visually impaired?

There is software available on the Net for 3-D printing of math expressions encoded in LaTex. What such technology is available off-the-shelf for the visually impaired to learn mathematics? And, ...
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191 views

Effective use of Maple T.A

I am considering using Maple T.A. as a tool for formative assessment (and possibly at some stage, summative assessment) for courses such as calculus and linear algebra. What are your experiences and ...
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250 views

Importance of “Calculus->Analysis Transition Books”?

E.S.E. advisers, I am a college sophomore with a major in mathematics and an aspiring mathematician in the fields of computation theory and cryptography. I am always curious about the importance of "...
6
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169 views

Tablet whiteboard app w e-pencil

(I've generalized the original question as @BrendanW.Sullivan suggests.) I would appreciate recommendations for a whiteboard app for a tablet using an e-pencil. For me: an iPad, using an Apple pencil....
6
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171 views

Mathematical undergraduate education in Syria

I'd like to learn some things about undergraduate mathematical education in Syria EDIT: In particular I'm interested in students 15-16 years old. What are the main differences from the European ...
6
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74 views

Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III

When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
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157 views

Learning math historically

What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...
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234 views

Links between mathematical folklore and educational success

I would like to ask if, in the research field of mathematical education, some work has been done to investigate the relationship between 1) and 2): 1) mathematical education and student motivation ...
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166 views

Undergraduate maths research

I am looking for: an undergraduate research program in mathematics/theoretical physics offered online (e.g. via skype or something) given by a good institution which can be followed while attending ...
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169 views

Catalog of undergraduate's misconceptions / problems while proving

Selden & Selden (2011) listed 41 difficulties their students had in an experimental proving course into 9 categories. Unfortunately I haven't found similar work. Thus, my question is: Is there ...
5
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81 views

the role of context in mathematical discussions of units and measurement in web design

Knowing that pedagogy for each age group is different, I will say right off the bat I am talking about working adults. I am noticing more and more, that despite people's phobias about math, they are ...
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45 views

Looking for papers with teaching-oriented style

I am looking for papers that have the similar style to Hervé Lehning's 1989 The American Mathematical Monthly article "From Experimentation to Proof" (PDF link via lehning.eu). It's like ...
4
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110 views

How must the “ungrading” idea be adapted to work in a math class?

After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...
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155 views

Intuition: 5 regular polyhedra, 6 regular 4-polytopes, and then 3 regular d-polytopes

I have struggled to offer an intuitive explanation (to U.S. college students) why the number of regular polytopes in dimension $d$ is: $d=2$, number: $\infty$. $d=3$, number: $5$, the five Platonic ...
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176 views

How to promote more elegant and beautiful proofs by students?

Following the premise that mathematics is an art as well as a science, I want to encourage students to produce not only correct proofs but also to try to find a particular beautiful/elegant proof. ...
4
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284 views

Seeking Your Recommendation on Problem-Solving Books (preparing for Putnam)

E.S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I apologize for this sudden interruption but I ...
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94 views

The propagation of the wave equation in even versus odd dimension

I am about to teach a second year undergraduate class on applied differential equation (first time) and, while I won't have time to go into the details, I wanted to show my students the difference ...
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71 views

Formal linear combinations: motivating examples

I want to introduce formal linear combinations in an upper-level undergraduate combinatorics class. By this I mean expressions like $7 \operatorname{cat} + 5 \operatorname{dog} - \sqrt{2} \...
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166 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}...
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100 views

How to explain concepts of limit and continuity to non-mathematical students

How to explain fundamental concepts of limits and continuity to a non-mathematical background student? I am a PhD student in Mathematics working in Differential Geometry. As a part of my teaching ...
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159 views

What is the point of using half range Fourier series for standard functions?

If we have a standard function, like $f(x) = x$ or $g(x) = x^2$, defined between $0$ and $\pi$, then why should we be interested in extending this function to give a Fourier series that resembles this ...
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156 views

How important is it to come up with or learn an elementary solution?

Note: by "elementary" I mean "without using more advanced theory and tools". Students are sometimes required or encouraged to solve very difficult problems using limited number of ...
2
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1answer
168 views

Teaching Quantifiers Before Logical Connectives

In this short question, I would like to ask whether it is possibly good to teach quantifier before logical connectives in a logic introduction lecture? I know there is a relationship between them but ...
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108 views

Tactile Learning Activities in Mathematics

Julie Barnes, Jessica M. Libertini. Tactile Learning Activities in Mathematics: A Recipe Book for the Undergraduate Classroom. 2018. MAA Press. AMS Bookstore link. Can anyone comment / review ...
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65 views

Is the annual system still in vogue anywhere in Europe, North America, Australia, or East Asia? And what about the 2-year B.A. / B.Sc. degree?

In Pakistan, we have until now had 2-year B.A./B.Sc. and 2-year M.A./M.Sc. university degrees after our 12th grade F.A./F.Sc. qualifications. Thus the former was a 14-year academic qualification, ...
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0answers
197 views

Introduction of the power set as a collection of *labels* or *names* for subsets

The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
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68 views

Number theory in an introductory course on discrete dynamical systems

Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
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38 views

Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
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97 views

Comprehensive Assessment Test for Undergraduate Math Program

My department uses the Major Field Assessment Test in Math (I think we refer to it as the "MFT") and that is great for its purpose. However, I am currently teaching a capstone course where we spend ...
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91 views

Mathematics after Rube Goldberg (recommendation) - Question for orientation

There are many fields in mathematics, in which one wants to optimize a process, for example finding the shortest way in a graph etc. However I got curious and wondered, if there are also books or ...
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115 views

Have you ever completely covered every topic in a textbook, and if so, which text?

Over the years of being a student or of being a teacher, it's occurred to me that I've never done every topic in a textbook. If it's a workbook that has a few introductory theory pages and then a few ...
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79 views

Prerequisites to study Laplace Transform completely?

Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
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94 views

How to teach year 3 undergraduate courses to high school students?

I see on the webpage of a high school math summer program, SuMac, that they will cover some algebraic topology in a period of several weeks. And they covered every aspect of this subject, including ...