Questions tagged [reference-request]

A reference request is a request to be provided with (links to) documentation, official papers, and specs related to one or more specific algorithms or mathematical procedures, to provide a trusted base for what's being said or written.

Filter by
Sorted by
Tagged with
15
votes
1answer
634 views

The Fundamental Theorem of Calculus and Vegetables

When I was an undergraduate, someone presented to me a proof of the Fundamental Theorem of Calculus using entirely vegetables. I found this incredibly fun at the time, but I can't remember who ...
12
votes
5answers
8k views

Real life examples to motivate the study of linear functions

Some years ago I used mobile phone or internet rates (for example, with basic fees and a given charge per minute or by data volume) to introduce and motivate the study of linear functions. However, ...
10
votes
1answer
177 views

Can we motivate undergraduates by saying they will be able to read famous papers?

I have a differential equations student who said the following (I'm paraphrasing of course): A long time ago, my math teacher told me that when I finished differential equations, I would be able to ...
7
votes
1answer
118 views

Resource about notation for students

Others have already here pointed out that students can struggle with notation in mathematics. I can often think that the lack of proper notation gets in the way of solving a problem correctly. ...
12
votes
0answers
206 views

Exercises to go with Simon's “Representations of finite and compact groups”

I am teaching an independent-reading course from Simon's "Representations of finite and compact groups". I chose this book based on fond memories from a previous reading course in which I had ...
11
votes
3answers
196 views

What to do when a math course needs too many shapes/figures and I'm not good at drawing?

Teaching some courses in mathematics requires drawing too many shapes or figures (e.g. Geometry, some parts of calculus, etc.) but I am not good at drawing shapes. Of course I can use slides, but I ...
8
votes
2answers
541 views

What caused the (relatively) recent popularity of set theory?

When I was growing up during the 1960s, "set builder notation" constituted a large part of what was then the "new math." Question: When and why did "set theory" become popular in math education? ...
7
votes
2answers
203 views

Teaching “and a half” early, possibly before general proper fractions

Fractions are a well-recognised issue in maths learning, with all sorts of complex issues involved. One particular aspect of this is difficulty recognising fractions as numbers which describe the size ...
8
votes
0answers
235 views

Guided Lecture Notes for Calculus

Last semester I taught Linear Algebra using the standard textbook of Lay. Online one can find nice "class handouts" that serve very well as lecture notes for students to follow along with during class....
10
votes
2answers
249 views

Term and reference for the problem of students “overassociating” concepts with each other

I am writing a paper directed at a physics-education journal and I want to briefly refer to the phenomenon of students “overassociating” (in lack of a better term) mathematical concepts with each ...
13
votes
3answers
621 views

Recommendations for inquiry based/aided discovery textbooks

I've recently dipped my toes into the world of number theory; and I've bought a book that to me is quite unconventional: R. P. Burn, A Pathway into Number Theory. I've yet to put the book through its ...
3
votes
2answers
775 views

Examples of cultural limitations on math education

Based on Maggie Koerth-Baker's article, "What do Christian fundamentalists have against set theory?", it seems there are some parts of culture which put some restrictions on math education. ...
12
votes
3answers
935 views

Moving From Rote Learning To Creative Thinking

My mathematics education was essentially rote, you learned the formulas and applied them almost algorithmically to the problems you were presented with; the teacher dictated a method and you followed ...
16
votes
5answers
723 views

Discovery-based and inquiry-based learning

In general, I think (and I am told by students) that I am good as a tutor. However, I would like to become more rigorously familiar with the discovery-based and inquiry-based learning applied to ...
11
votes
2answers
700 views

Are women better math teachers for little children?

Once in a discussion a colleague told me that he thinks: It is better to use women to teach maths to little children including preschoolers and children in elementary school. Also it is better to ...
3
votes
2answers
516 views

''Deep'' maths books

I would like a suggestion on the 'deepest' books in Calculus and analysis (something along the lines of Rudin's) Linear algebra Abstract algebra Geometry (and topology); (even something along the ...
2
votes
1answer
121 views

Advice on studying mathematical biology [closed]

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince I've ...
5
votes
5answers
3k views

Extremely “hard” books (or handouts) for undergrad studies

Can you suggest me some REALLY hard books on calculus and analysis. By hard I don't mean difficult in explanations, but with extremely challenging exercises (all worked out if possible) and useful ...
4
votes
2answers
93 views

Looking for an online mathematics practice resource

Forgive me if this is off topic, but I've been looking for an online resource that I can use to polish up and improve my math skills. I've looked at math.com and purplemath.com but they don't have ...
19
votes
6answers
581 views

Becoming a better instructor: where to start?

I just finished a PhD in math at a top department, but not one that placed much emphasis on graduate student teaching. Grad students here teach only as TAs, and the training is minimal. I got great ...
5
votes
1answer
129 views

Empirical papers on “interactive engagement” in calculus education?

I was discussing this with a colleague, who showed some papers on "interactive engagement" in physics education. Another keyword there was "force concept inventory", and the realted (newer) "calculus ...
13
votes
7answers
698 views

Non-Mathematical Examples of Orders

Different properties of different types of orders including partial, total, scattered and well-orders are a part of any graduate/undergraduate set theory course. I am looking for interesting "non-...
6
votes
2answers
965 views

The seven benchmark numbers?

I was presented with a power point slide by a friend about math education and one of his slides talked about "the seven benchmark numbers". He said that: The seven benchmark numbers to develop a "...
10
votes
1answer
346 views

Alternative remedial courses before calculus

I have seen remedial courses before a first undergraduate calculus course that consist of a mix of algebra, trigonometry and coordinate geometry. However, have there been any experiments with remedial ...
8
votes
0answers
186 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 ...
5
votes
1answer
67 views

Optimal management of mixed-knowledge classes

There is always a risk that the teaching of translation is neglected. Meaning: there is a process to go through to get from a word problem to a collection of variables, equations and constants. Very ...
10
votes
3answers
479 views

References for “high-school mathematics from an advanced point of view”

What are some good references for high-school (or even middle-school) mathematics, written from an advanced point of view, especially texts written for prospective teachers? Some references were ...
14
votes
1answer
603 views

Is there any evidence about the effectiveness of “table proofs” in pre-college mathematics education?

I remember when I took geometry in high school, like most students it's where I was formally introduced to proofs. However, the way we went about them was strange, it really felt like symbol ...
12
votes
4answers
6k views

Mathematics Education Graduate Program List and Rankings

U.S. News and World Report publishes school rankings for many different disciplines, including mathematics. Is there any ranking for mathematics education graduate programs? Weaker question: Is there ...
11
votes
3answers
226 views

How to balance short-term learning outcomes with long-term goals and ethical considerations

Most discussions about teaching often assume that the learning outcome is the important variable (compare evaluations, discussions about clickers, discussions about syllabi, etc.). However, I find ...
13
votes
2answers
630 views

How does a reliance on calculators affect student performance?

Overheard in the Math Office while another Professor was helping a student with Statistics: Always use a calculator when doing decimal arithmetic because you'll eventually make a mistake if you do ...
23
votes
3answers
2k views

Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
24
votes
3answers
1k views

The impact of dyslexia on learning mathematics, and available resources

I have always loved the beauty of mathematics and physics. However I'm severely dyslexic and find it hard to keep numbers in my head, any more than 4 numbers at a time and they melt together and lose ...
16
votes
1answer
398 views

Research supporting “recipe-style” calculus in senior high school?

Anecdotally, I've heard it said that in (Australian) grades 11 and 12 calculus needs to be taught in a procedural way involving merely recipes for doing calculus, rather than teaching for ...
13
votes
8answers
3k views

What are some fun/nonstandard examples of arithmetic/geometric series?

I am teaching those topics (arithmetic/geometric series) just now, and want some not so standard (fun) examples, which can be used essentially at high school/beginning calculus level. I'm ...
12
votes
3answers
682 views

Is there a program like ALEKS for mathematical logic?

ALEKS (http://www.aleks.com/) is a good way of learning procedural math, because it is very systematic and forces you to master the dependencies of a kind of problem before working on that kind of ...
11
votes
1answer
484 views

Ideological Teaching in Logic Courses

Logic and its sub-fields are closely related to philosophy. There is an undeniable mutual interaction between one's philosophical point of view and his/her approach in teaching mathematical logic. In ...
5
votes
4answers
781 views

Mathematics Education in Africa

It seems there are few well-known professional mathematicians in Africa. It is mainly because of the poor quality of elementary/undergraduate mathematics education in African countries. Question 1. ...
16
votes
2answers
1k views

A study comparing effects of calculator usage on later math skills?

Each year my university tries to decide whether or not it will have calculator and CAS based introductory math courses (the calculus sequence, linear algebra, and ODE) or not. Other than some hearsay ...
7
votes
4answers
412 views

Examples of Research Level Math Discoveries Done by Undergraduate Students

A good way for motivating young students in undergraduate level is telling them that you can do great works! Question. What are good examples of research level mathematical discoveries done by ...
19
votes
5answers
435 views

Any support for mathematical “learning types?”

Back when I was an undergrad calculus TA, I participated in a general TA training class. We were taught to be mindful of different "learning types," such as visual learners, audio learners, and ...
2
votes
2answers
61 views

Psychological and Sociological Researches on Teaching [closed]

Teaching is a social activity and very sensitive to any change in social parameters. Even the simplest acts of a teacher could cause some positive/negative reactions of students and conversely. Each ...
14
votes
1answer
3k views

What experimental studies have been done on the Kumon method of teaching and learning mathematics?

My dissertation involved, among other things, the East Asian way of teaching and learning mathematics. (See, for example, Leung (2001).) I was particularly interested in the Kumon method. Although I ...
10
votes
2answers
261 views

Quotations of Great Mathematicians as a Source of Inspiration for Young Students

I like using quotations of great mathematicians as a source of inspiration for young students. I think even a short sentence could have a great influence on forming their research interests and point ...
14
votes
3answers
219 views

Resources for teaching Riemann integration in higher dimensions and on submanifolds, with view toward Stokes' theorem?

Question I am looking for suggestions of good resources (textbooks or lecture notes preferably) for teaching Riemann integration in $\mathbb{R}^d$ with $d\geq 2$ and also for Riemann integration ...
31
votes
26answers
2k views

What are some great books for exploring mathematics? (not kids' books and not textbooks)

People often think of math as facts and procedure - dry stuff. But it is so much more, even at basic levels. What books about mathematics have you been inspired by? There are some real treasures out ...
11
votes
10answers
919 views

What are some great books for inspiring children to explore mathematics?

Starting from a young age, children can explore deep mathematical questions and enjoy thinking about basic math within the context of a story. There are some real treasures out there. Parents often ...
10
votes
6answers
180 views

Books/(auto)biographies/references on how mathematicians study/studied (as students)?

As Geoff Pointer commented: [...] As a composer I've learnt a lot from studying famous composers why wouldn't that also apply to studying maths and mathematicians of note as well? [...] Are there ...
12
votes
5answers
5k views

Best textbooks to introduce measure theory and Lebesgue integration?

What are the best textbooks to introduce measure theory and Lebesgue integration to undergraduate math majors? Many students in such a class will go on to graduate school and be required to take a ...
24
votes
2answers
1k views

Students who know high-level math before going to college

There is a high school in the city I live in which has some high-level math courses in their curriculum. It's a special math class mentored by some university lecturers, and the children basically do ...