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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10
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2answers
169 views

Could you suggest books, papers or problems that could be used as good “general” motivating examples of calculus application?

I would like to stress the kind of reference I am looking for: In statistics there are lots of motivating (and sometimes unexpected) examples that are interesting for everyone such as Birthday Problem,...
23
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7answers
3k views

When should we first teach variables in school math? And how?

From a pedagogical point of view, when is the "right" moment to introduce letters and variables to school children? Let's say we taught arithmetic, the four operations, did computation exercises, or ...
4
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0answers
72 views

What are the best expository pieces related to the Van Hiele models?

The Van Hiele model (wikipage) "is a theory that describes how students learn geometry." I would appreciate further insights into the original model, later models that expanded or re-worked it, and ...
5
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1answer
85 views

Looking for a classic paper “Vinner and Hershkowitz”

I can't find this ZDM article: Vinner, S., & Hershkowitz, R. (1983). On concept formation in geometry. Zentralblatt für Didaktik der mathematik, 83(1), 20-25. Could you help me? I was ...
20
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7answers
1k views

Good examples of functions defined as definite integrals of elementary functions?

I am writing some Calculus content, and I would like a "big list" of useful functions which are defined by definite integrals, but are not elementary functions. Two examples of such functions are $$ ...
8
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2answers
205 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
839 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
990 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
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1answer
169 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
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1answer
102 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
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1answer
297 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
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3answers
121 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
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1answer
205 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
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2answers
189 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
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2answers
174 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
221 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
409 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
167 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
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3answers
268 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
173 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
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6answers
576 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
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2answers
340 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
350 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
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1answer
238 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
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3answers
4k 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
302 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
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1answer
115 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 ...
13
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3answers
320 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
2k 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
373 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
303 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
513 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
154 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
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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 ...
7
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3answers
176 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
557 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
81 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
281 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
192 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
307 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
1k 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
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0answers
79 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
417 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
482 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
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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
votes
1answer
145 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
442 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
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
290 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 ...