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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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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 ...
20
votes
2answers
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 ...
12
votes
3answers
919 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 ...
21
votes
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 ...
35
votes
5answers
1k 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 ...
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 ...
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 ...
11
votes
2answers
628 views

Physical vs. Virtual manipulatives in the high school classroom

I notice that geometry students frequently have difficulty with representations of 3-dimensional objects in 2 dimensions. Today, we worked with physical manipulatives in order to help visualize where ...
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 ...
1
vote
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.
13
votes
3answers
601 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 ...
16
votes
5answers
715 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
10answers
899 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 ...
12
votes
3answers
639 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 ...
15
votes
2answers
358 views

Comparison of different concepts of integral

As the following math stack exchange question (and answers) show: https://math.stackexchange.com/questions/703212/is-dxdy-really-a-multiplication-of-dx-and-dy There are a lot of different ways to ...
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 ...
7
votes
5answers
242 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 ...
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 ...
11
votes
3answers
589 views

Teaching algebra to visually impaired or blind students

I am currently writing an independent project investigating the teaching and learning of algebra for students with a visual impairment. I am struggling to find literature specifically about teaching ...
14
votes
3answers
390 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 ...
10
votes
4answers
521 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 ...
11
votes
1answer
156 views

Where can I find primary sources from the New Math movement in the 60s?

I'm interested in learning about the New Math movement from a historical perspective. I've located some secondary sources about the topic, mainly parodies, highly critical restrospective articles, or ...
20
votes
3answers
946 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 ...
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 ...
14
votes
1answer
601 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 ...
10
votes
4answers
670 views

Is Calculus Necessary?

That title is a quote from Fred Roberts: Fred Roberts. "Is Calculus Necessary?" Proceedings of the Fourth International Congress on Mathematical Education. 1980. p.52ff. "Calculus is not ...
16
votes
1answer
290 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 ...
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 ...
8
votes
4answers
378 views

Elementary physics course for pure math student

Are there any mathematical departments which present the course "elementary physics" for pure math undergraduate students, separately? Is there a way to present this course with the most pure ...
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 ...
12
votes
3answers
305 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 ...
10
votes
2answers
260 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 ...
7
votes
1answer
135 views

Subtraction Methods in School Mathematics

I have studied long ago different method for subtracting numbers, for instance the borrow method or the Austrian method (I hope I am using the right names; I am not an English native speaker and these ...
19
votes
5answers
432 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 ...
16
votes
2answers
270 views

Literature on learning from errors in mathematics

In teaching undergraduate mathematics, I implemented some strategies to encourage the students to look at errors they made or at "typical errors" in the current topic. One attempt was to compile a ...
15
votes
1answer
181 views

Reference request for studies on gender in math examples, homework problems, or math exams

I am looking for a study or reference on gender in math problems given in mathematics. In math texts or even on math exams, if there is a word problem involving people, these people or "characters" ...
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 ...
14
votes
4answers
303 views

Why is polynomial factorization over the integers part of secondary school curricula?

By "polynomial factorization over the integers", I mean problems and solutions like the following: Problem: Find a factorization into irreducible polynomials for $24x^2 +x - 10$ and ...
13
votes
2answers
619 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 ...
12
votes
2answers
269 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
4answers
5k 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 ...
12
votes
2answers
327 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 ...
5
votes
4answers
779 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. ...
3
votes
2answers
768 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. ...
16
votes
3answers
393 views

Evidence for or against the claim that some students are “algebra people” and others are “geometry people”

Where I live and work, there is a widely-accepted and often-repeated claim that there are two kinds of students: "algebra people" and "geometry people". This claim sometimes gets expressed in ...
13
votes
5answers
384 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 ...
11
votes
1answer
475 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 ...
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 ...
4
votes
1answer
122 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 ...
2
votes
1answer
218 views

Are kindergartners supposed to be steered from squares being rectangles?

Question 1: What are the literature, status, debates, references, etc regarding this matter please? Apparently, some (woohoo weasel words!) consider that squares are rectangles too advanced a topic ...