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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8
votes
2answers
200 views

Coverage of Fundamentals of Lines and Planes

I was helping a high school student with some fundamental concepts of planes and lines, when I realized I am rusty on some definitions myself. I found some minimal coverage in his high school math and ...
19
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2answers
819 views

Can students tell the difference between the “definition if” and the “theorem if”?

The word "if" is used in two meanings in mathematics: Definition. A topological space is compact if every open cover has a finite subcover. Theorem. A topological space is compact if it is ...
11
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1answer
792 views

Method for teaching factorization

A while back I stumbled on teacher's website that advocated a different way to teach factorization. Rather than jumping straight to factorization practice, the teacher first had their student's ...
11
votes
1answer
164 views

Has any research been done on the topic of “fact-based” versus “rule-based” understanding?

Consider the following piece of reasoning: $$x+3 = 5$$ $$x=5-3$$ Based on my own experience back in school, and helping people with their math homework, as well as in talking to other people about ...
9
votes
1answer
100 views

Is there an introductory book on linear algebra that makes use of simple concrete examples to teach the underlying theory?

I'm a third year philosophy student and considering pursuing an academic career. I'm comfortable with formal logic, set theory, and the calculations taught in high-school math. I've noticed that my ...
14
votes
1answer
274 views

Spiral learning in real analysis

Has there been any attempts at developing a curriculum for teaching analysis (here let us be narrow and say real analysis in the sense of rigorous integral and differential calculus) in a multipass, ...
7
votes
3answers
120 views

Looking for a reference for highschool level readers

I was wondering if there exists a book that talks to highschool level audience who wish to study pure mathematics for their undergraduate years. I'm not talking about problem solving kind of books (I'...
5
votes
1answer
202 views

Research on reciprocal teaching of mathematics?

Reciprocal teaching seems to have started as method of teaching how to read difficult texts (with respect to the level of the reader). Has reciprocal teaching been applied to teaching mathematics? Is ...
8
votes
2answers
185 views

Second Order Differential Equation Example Request

I am looking for some non-complicated second order differential equations to illustrate certain techniques for control engineering. It doesn’t matter if the differential equations are linear or non-...
7
votes
2answers
163 views

Are there more modern or computation oriented applications of complex analysis in science and engineering?

No doubt that complex analysis is a tremendously useful with plenty of applications in engineering and physics. Common raw applications of complex analysis includes: evaluation of ordinary and ...
10
votes
5answers
216 views

Lesson-planning: Teaching probability concepts via geometry

I am intending to teach a lesson covering some topic related to "Probability via Geometry" and, if possible, I would appreciate references or materials (or good ideas) that can help me. The target ...
15
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2answers
401 views

Logic in symbols or words

Making precise logical statements is an important part of teaching and learning mathematics. There are many ways to write such statements, and let me divide them into two main types1: writing in ...
6
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4answers
158 views

Recommendations for free, basic resource on discrete probability for a discrete structures class?

I'm teaching a course this fall on Discrete Structures for Computer Science. It's taught out of the math department but is a service course for the CS department with 90-95% of students being CS ...
14
votes
3answers
251 views

How to measure the understandability of a proof?

Is there a way to measure the understandability of a proof? From a search in the internet I have only found methods for measuring the understandability of software or tests for measuring the ...
6
votes
1answer
166 views

Resources for Pell's equation

What is the best way to introduce Pell’s equation on a first elementary number theory course? Are there any practical applications of Pell’s equation? What are the really interesting questions about ...
11
votes
6answers
497 views

Reference requests: Is there a text that is even more advanced than books on “advanced engineering mathematics”

Advanced engineering mathematics is a subject of its own, building up from simple notions of functions, series, integration techniques and brief review of linear algebra which leads to transform ...
8
votes
2answers
332 views

Symmetric version of product and quotient differentiation rules

The usual way of writing the product rule and the quotient rule in differentiation is $$(fg)'=f'g+fg'$$ $$\left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^2}\quad\text{where}\quad g\ne 0$$ A few years ago, ...
18
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3answers
332 views

Critiquing Proof Style During Class

I would like to spend a day with my students analyzing mathematical writing. One way I might accomplish this is to offer multiple proofs (some good, some poor) of the same simple statement and ask ...
8
votes
1answer
235 views

Quantity as the basic concept for applied mathematics

I read about the Theory of Quantity in the booklet Principles of Mathematics Education written by Kô Ginbayashi in 1984. (A summary of it is here.) Instead of using pure numbers as the basic concept,...
10
votes
3answers
3k views

What is a good book to learn all of prealgebra?

I am an old man trying to learn math, starting off with prealgebra and need a good comprehensive book for it. The book should NOT contain annoying images like in most American textbooks or anything ...
4
votes
2answers
191 views

List of math competition problems by topic

I am working with a student who is very interested in math competitions, and I am teaching him Algebra I. I feel like doing competition problems related to a given topic is an excellent way to force ...
8
votes
1answer
59 views

Sources for embedding secondary math into technical classes?

I've taken a job for the next school year, which will involve embedding secondary math (algebra, geometry and trigonometry) into technical programs such as drafting and electrician school. Does ...
6
votes
1answer
113 views

Reference request: Textbooks in mathematics for future kindergarten teachers

The title says it all, but some more details. We need good textbooks for a mathematics course for future kindergarten teachers. The actual course is titled (my translation) "Text, language and ...
12
votes
3answers
311 views

Resources for reading mathematics out loud in different languages

Are there reference books or online material for reading mathematics out loud in different languages? For example, the expression1) $$ \int x^2dx=\frac13x^3 $$ is understandable to anyone who has ...
14
votes
4answers
1k views

Teaching a very enthusiastic and bright 5 year old

I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never tought at this age and I am unfamiliar with the ...
22
votes
3answers
371 views

Mathematic reasoning in nonEnglish/non Western languages

I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language ...
8
votes
3answers
282 views

Have there been longitudinal studies comparing outcomes of various teaching methods?

There have been many innovative teaching methods tried from time to time. Twenty years ago was Calculus reform, now is flipped classrooms. We also have a resurgence of the Moore method under the name ...
15
votes
4answers
502 views

Thought experiment: Utopian college-level math curriculum without external constraints

An old favourite topic of mine to daydream about on pleasant afternoons is this: If you could completely redesign the university-level mathematics curriculum from the ground up to be as good as it ...
9
votes
1answer
153 views

Is there any footage of Let's Make a Deal illustrating the Monty Hall problem?

The Monty Hall problem is a classic probability riddle and I will be gleefully explaining it to my class of discrete math students. It is apparently based on his classic game show Let's Make a Deal. ...
35
votes
5answers
2k views

Effects of early study of advanced books

Context: There was recently a question on Math.SE: Inferior to Other Younger and Brighter Kids which starts as follows: I'm a high school student (Junior/Grade 11) and I'm currently studying ...
6
votes
3answers
175 views

References on British, German and French educational system

I'm writing a comparative study between mathematical teaching in my country (which sucks by the way) with others. However, I don't want to make it about today, globalization gives us a good notion of ...
10
votes
4answers
540 views

Creativity in mathematics

I have recently been engaging more and more with my creative side by drawing, writing, and (trying to) playing piano. I have come to see mathematics as much more of a creative field of study than I ...
1
vote
1answer
80 views

In which order should I read these topics? [closed]

In which order should these topic be read if one have to understand mathematics topic well? Differential Equations Game Theory Graph Theory Linear Programming Probability Statistics Vector ...
7
votes
1answer
277 views

Why are manhole covers circular?

The answer to the question in the title, that then it will not easily fall down into the manhole (just try with ellipsoidal or square covers ...), is a property of circles I never learnt in school. ...
11
votes
1answer
184 views

Has someone written an essay on the role of axioms in mathematics (suitable for undergrads)?

I'm just starting up the academic year (yes, it starts in February here in the Southern Hemisphere) teaching a 2nd-year Introduction to Pure Mathematics class. For general background, I would like to ...
16
votes
1answer
295 views

How to assign grades to proofs: what do(es) the literature/experts suggest?

I am teaching an introductory course on proofs in mathematics in a mid-size American public university, and trying to develop some kind of consistent grading meta-scheme for grading proofs. I am ...
5
votes
3answers
980 views

Honors project idea for linear algebra

At my institution there is an Honors program which encourages (or requires) students to petition classes for Honors. Basically, what this amounts to is the student has to write a 10 page (not set in ...
3
votes
0answers
78 views

Student input in secondary teacher evaluations

this is something I have been wondering about for a while now. In my school district (urban setting in Pennsylvania) student input amounts to exactly 0% of the final assessment for observed teachers. ...
13
votes
5answers
403 views

Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
5
votes
3answers
124 views

System of Equations Generator

I often find myself spending too much time coming up with systems of equations for exercises for my students to practice on (that come out to nice integers). For two variables this is trivial, albeit ...
21
votes
3answers
973 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
votes
1answer
128 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
votes
2answers
294 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
votes
0answers
76 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
votes
2answers
273 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
votes
2answers
333 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
votes
3answers
397 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
votes
0answers
271 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
votes
2answers
263 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
votes
3answers
465 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. ...