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.

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21
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3answers
1k views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
4
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1answer
148 views

What is a good reference for (this way of) generating a logarithmic scale?

I am interested in answers to the title question without parentheses, but I found this method below rather interesting, and I am hoping to find it published somewhere, along with a teacher's guide ...
12
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2answers
466 views

Resources on how to mark a maths exam

I am looking for some resources which tells someone how to mark a (1st year undergraduate level) maths exam paper. Ideally it would cover the basic stuff, like making an error at the top doesn't ...
8
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0answers
78 views

Literature on skill transfer

Motivated by this other question I'm interested in getting to know the literature on mathematics skills transfer within itself. All I know is what I've read in David Perkins's book "Knowledge as ...
12
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2answers
295 views

Research on how mathematics skills transfer to other areas

Briefly: I am looking for research on the extent to which learning mathematics (let's say "college algebra" if we want to be specific) impacts problem solving skills, abstract reasoning, etc. Less ...
12
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2answers
336 views

Mathematics and the hermeneutic circle

Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations. This leads me to ...
14
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3answers
412 views

Calculation versus writing in mathematics

Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas ...
8
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0answers
274 views

What else we miss?

Context: Some time ago there was a post on a brief study conducted by Alexis Wiggins (she was shadowing two students for two days), you can find it here, which got quite an attention. One interesting ...
4
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2answers
265 views

Promoting intuition (for undergraduate students): visual thinking, geometic approaches, etc. in the classroom

Note: This question is ment to extend the scope of some related questions of mine. I would appreciate very much any suggestion to improve the way the question is posed. I would like to ask what is -- ...
13
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3answers
488 views

Immersive attention when learning mathematics

In Jennifer Roberts' article The Power of Patience: Teaching students the value of deceleration and immersive attention she talks about intentionally slowing down to contemplate deeply a work of art. ...
8
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5answers
305 views

Good resources for coaching for mathematics competitions (Highschool Level)

I'm teaching in China, and I have been told that I will be leading the students in mathematics competitions. I feel very ill prepared for this. I never did mathematics competitions in either high ...
2
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1answer
85 views

Mathematics necessary for signal processing

What is the mathematics needed to delve in signal processing? I don't know if it correct to dig toward purism downwards or stay at the applied level. Specifically, in complex analysis I find the $\...
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4answers
2k views

Prerequisites of mathematical analysis [closed]

What topics should I read before studying mathematical analysis? I want to have a solid foundation in terminology, notation and concepts in general. Please suggest titles for books.
12
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1answer
351 views

Teaching K-8 math in the style of “A Mathematician’s Lament”

Here's a link to the full paper, colloquially known as Lockhart's Lament: Link: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf In the context of K-8 learning materials that take ...
15
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2answers
775 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
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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
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1answer
185 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
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1answer
125 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
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0answers
239 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
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3answers
204 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 ...
9
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2answers
622 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? ...
8
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2answers
223 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
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0answers
261 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
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2answers
288 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
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3answers
750 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
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2answers
798 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
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3answers
1k 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
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5answers
753 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 ...
12
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2answers
812 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
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2answers
584 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
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1answer
137 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
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5answers
4k 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
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2answers
97 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 ...
21
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6answers
658 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
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1answer
131 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
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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-...
7
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2answers
1k 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
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1answer
366 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
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0answers
189 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
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1answer
70 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
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3answers
509 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 ...
15
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1answer
737 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
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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
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3answers
236 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
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2answers
664 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 ...
28
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4answers
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
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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
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1answer
478 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
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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
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3answers
730 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 ...