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Questions tagged [undergraduate-education]

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

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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 ...
Theo Bendit's user avatar
11 votes
0 answers
138 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 ...
Tommi's user avatar
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10 votes
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692 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 ...
Joseph O'Rourke's user avatar
10 votes
0 answers
134 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 ...
Mike Pierce's user avatar
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8 votes
0 answers
417 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 ...
Nethesis's user avatar
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8 votes
0 answers
583 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 ...
john mangual's user avatar
8 votes
0 answers
121 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, ...
Tom Copeland's user avatar
8 votes
0 answers
213 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 ...
J W's user avatar
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6 votes
0 answers
73 views

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 ...
JenB's user avatar
  • 161
6 votes
0 answers
218 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....
Joseph O'Rourke's user avatar
6 votes
0 answers
180 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 ...
1123581321's user avatar
6 votes
0 answers
89 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 ...
Sinister Cutlass's user avatar
6 votes
0 answers
191 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 ...
katana_0's user avatar
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6 votes
0 answers
183 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 ...
Stephan Kulla's user avatar
6 votes
0 answers
325 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 "...
MathWanderer's user avatar
6 votes
0 answers
313 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): mathematical education and student motivation the ...
Dal's user avatar
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6 votes
0 answers
175 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 ...
user10024's user avatar
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5 votes
0 answers
166 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'...
underflow's user avatar
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5 votes
0 answers
128 views

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 ...
Paula Cardoso's user avatar
5 votes
0 answers
189 views

Montessori mathematics for HS/college students

My children attend a Montessori school (as did I when I was a child), and I have visited several other Montessori schools and spoken with their teachers. Numerous times I've had Montessori teachers ...
Mike Shulman's user avatar
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5 votes
0 answers
158 views

What do you think, is teaching on an actual board more efficient than using an online board?

I am a sophomore math undergraduate and so far all of my university courses have been online due to the pandemic. I am really curious what you guys think about the efficiency of teaching mathematics ...
MathIsCool's user avatar
5 votes
0 answers
99 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 ...
Cong Chen's user avatar
  • 151
5 votes
0 answers
172 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 ...
Joseph O'Rourke's user avatar
5 votes
0 answers
113 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 ...
john mangual's user avatar
4 votes
0 answers
171 views

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,...
tryst with freedom's user avatar
4 votes
0 answers
103 views

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 ...
Mahdi Majidi-Zolbanin's user avatar
4 votes
0 answers
62 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 ...
Best_fit's user avatar
  • 141
4 votes
0 answers
275 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 ...
Mike Pierce's user avatar
  • 4,845
4 votes
0 answers
452 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 ...
MathWanderer's user avatar
4 votes
0 answers
186 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 ...
matqkks's user avatar
  • 1,243
3 votes
0 answers
89 views

How to make student work in think-pair-share?

I have been trying the think-pair-share technique in my undergraduate linear algebra class of about 30 students. Some students quite enjoy the experience. But I noticed that some other students simply ...
user avatar
3 votes
0 answers
148 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 ...
Giuseppe's user avatar
3 votes
0 answers
75 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} \...
darij grinberg's user avatar
3 votes
0 answers
78 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, ...
Saaqib Mahmood's user avatar
3 votes
0 answers
185 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. ...
Christian's user avatar
  • 544
2 votes
0 answers
103 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 ...
Maesumi's user avatar
  • 1,410
2 votes
0 answers
128 views

"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 ...
Hauke Reddmann's user avatar
2 votes
0 answers
119 views

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 ...
Dian Sheng's user avatar
2 votes
0 answers
157 views

Worldwide standard textbooks vs textbooks from one's home country vs lecture notes by various people - pros and cons

So far I've had three types of professors in my undergrad studies when it comes to choosing the main text for the course: Type A: these are the professors who pick some standard textbook(s) in English ...
MathIsCool's user avatar
2 votes
0 answers
116 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 ...
Joseph O'Rourke's user avatar
2 votes
0 answers
209 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 ...
David Roberts's user avatar
1 vote
0 answers
102 views

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 ...
Humberto José Bortolossi's user avatar
1 vote
0 answers
176 views

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 ...
matqkks's user avatar
  • 1,243
1 vote
0 answers
130 views

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 ...
Ayer AGG'TDd'E-A's user avatar
1 vote
0 answers
124 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 ...
J W's user avatar
  • 4,733
1 vote
0 answers
96 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 ...
paus's user avatar
  • 83
1 vote
0 answers
115 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 ...
Ma Joad's user avatar
  • 1,673
1 vote
0 answers
113 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 ...
James S. Cook's user avatar
1 vote
0 answers
103 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 ...
Imago's user avatar
  • 111
0 votes
0 answers
102 views

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 ...
Sillyasker's user avatar