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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-4 votes
2 answers
222 views

Is it nonsensical to try to 'prove' Euler's 'formula' in real numbers? What is Wikipedia/proofwiki even doing? [closed]

Edit re the close vote: I guess this 1 of those questions whose on-topic-ness depends on the answer. If the answer is no, then well maybe it's off-topic. But if the answer is yes, then I believe it's ...
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5 votes
2 answers
162 views

Where can I find a collection of bad/misleading data visualizations?

Are there any collections or blogs of bad data visualizations? I know I've seen such misleading graphics in the news or in print, made misleading either maliciously or thoughtlessly, but I usually see ...
  • 4,462
10 votes
2 answers
612 views

Real-world applications of taxicab metric

The taxicab metric can be used to measure distances in idealized gridded cities. However, usually this serves only as a fun exercise for students. I'm looking for engaging (as non-technical as ...
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10 votes
10 answers
911 views

What are examples of math-themed sci-fi appropriate for students?

What are examples of sci-fi books or short stories that have a mathematics theme? I'd like to have a pool of examples in mind that I could refer students to. The only example I've got in mind right ...
  • 4,462
3 votes
1 answer
59 views

Resource for International Comparison of Math Education Logistics

Are there resources that compares/lists crunchy facts about the logistics of math education in different regions or countries? I'm talking facts like: Do they use paper homework versus and online ...
  • 4,462
8 votes
1 answer
153 views

Ball rolling down curve simulator

I am preparing a seminar on mathematical discovery for beginner's students, and one of the topics I plan to cover is the brachistocronic/tautochronic curve. For this purpose, I would like to let the ...
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2 votes
0 answers
97 views

Where can I find examples of statistics projects? [duplicate]

I am going to teach an undergraduate statistics course for the first time next semester. I would like students to do a project by applying some of the things they learned to real-world data. Is there ...
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5 votes
1 answer
247 views

For 15 year olds, are there exercises — with full solutions — on the Fence Post or Off by One error?

Which books contain practice questions — preferably with full solutions — to assist 15 year olds with the Fence Post or Off by One error? Most students at my institution have not heard of this name, ...
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2 votes
0 answers
66 views

Where can I find the solutions manual to Beginning Statistics with Data Analysis by Mosteller, Fienberg and Rourke?

I am planning to teach a course on Statistics using Beginning Statistics with Data Analysis by Mosteller, Fienberg and Rourke. On page xii of the book, the authors said "A solutions manual is ...
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16 votes
9 answers
3k views

What is the rationale for distinguishing between proper and improper fractions?

I cannot recall ever hearing the terms "improper fraction" and "proper fraction" outside of an elementary and middle school setting. At some point in my mathematics education ...
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10 votes
3 answers
770 views

Are there research studies that attempt to determine the value of a "Growth Mindset?"

A "growth mindset" can be defined this way, see this article: In a fixed mindset students believe their basic abilities, their intelligence, their talents, are just fixed traits. They have ...
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12 votes
0 answers
153 views

What studies exist, comparing the efficacy of exercise sheets with or without worked solutions?

I've been tutoring mathematics at university level for over 10 years, and one of the more common requests from students is worked solutions for sheets of exercises. Most educators I've worked with ...
6 votes
0 answers
192 views

Are there measurements of how much mathematics people remember after high-school?

These days I got curious about something: Are there measurements of how much mathematics people remember after high-school?
5 votes
1 answer
299 views

Research on Waldorf/Steiner mathematics education

I am mildly interested in research on mathematics education in the Waldorf/Steiner educational context, primarily in the upper secondary school setting, but not exclusively. Information about Waldorf/...
1 vote
1 answer
74 views

Reference request: an introduction to triangular, square, and other figurate numbers

There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that ...
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0 votes
3 answers
195 views

Highly intuitive yet comprehensive and easily readable (student friendly) book on linear algebra which do not focus much on applications, just basics

I came to know about Gilbert Strang's two books, "Introduction to Linear Algebra" and "Linear Algebra and its Applications". The first is the one used as the text in the 18.06 ...
1 vote
1 answer
180 views

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
22 votes
7 answers
3k views

How do you coach students who often make small errors?

Some students are prone to making small calculation errors. Not errors in understanding, but errors like adding or multiplying integers incorrectly, or dropping a negative sign. Unsystematic errors in ...
  • 4,462
59 votes
15 answers
7k views

Is there a virtue to learning how to compute by hand?

I have been professionally tutoring a wide range of students (from elementary school through graduate school) for many years. Most of them are from the United States. I generally focus on helping my ...
  • 823
11 votes
2 answers
229 views

Reference on study habits; cramming vs studying a bit every day

I am teaching Linear Algebra this semester, with pre-recorded classes and weekly meetings, and the students have a few short and simple exercises to solve every week, which count a bit (20%) to their ...
5 votes
1 answer
323 views

Is there any video lecture series on Graph Theory which uses "Introduction to Graph Theory" by Douglas West? as the text

I am interested in learning graph theory, and from many resources I came to know that Douglas West's Introduction to Graph Theory is a good textbook. But since I am doing self-study, it is at times ...
5 votes
1 answer
222 views

Sensible amount of repetition 7 year old

We are now in lock-down, so while homeschooling my son I get to se exactly what he does for math. He has been getting a huge amount of repetitive practicing of really simple math, despite being quite ...
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8 votes
3 answers
277 views

Seeking references for why it is good that students understand why mathematical rules work

I am currently advising a student at his final project (it is a graduation course for people who will become math teachers). We've chosen to pick some basic mathematical rules which are (or at least ...
8 votes
1 answer
203 views

Effects of AI based education in mathematics in PISA like studies

One of the biggest revolutions in education in the last few years seems to be the use of artificial intelligence to offer adaptive individualized learning environments as done by companies like ...
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7 votes
6 answers
679 views

Statistics, for the mathematically rigorous

I don't know where I can find a rigorous statistics course or textbook. The closest thing I can think of is measure-theoretic probability theory, but I wouldn't really call that "statistics"....
2 votes
0 answers
82 views

Reference request for 1960s-1970s Australia/NZ primary-level textbooks

Where could I find a list, and ideally discussion, of primary school mathematics schemes (textbook series) in common use in Australia and New Zealand in the period immediately following decimalization ...
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6 votes
2 answers
223 views

Measuring the effectiveness of one-on-one instruction?

I've been recently thinking a lot about what would be the "best possible instruction method", and in regards to that, I've been drawn the question of what would be possible if a student had ...
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5 votes
0 answers
196 views

A video game for teaching the concept of a mathematical proof

Two students in my game development course would like, as a final project, to develop a video game for teaching mathematics. In contrast to the many other games for teaching maths, which focus mainly ...
5 votes
1 answer
759 views

Choice of textbook for an undergraduate abstract algebra course

Currently a 5th year PhD student, and I've been fighting tooth and nail to teach one of our junior-year honors sections in undergraduate algebra next fall (desperately hopeful we'll be able to return ...
2 votes
1 answer
118 views

Recommendation for Discrete Mathematics

I'm taking a Mathematical Structures course as a 2nd year math major. Our course textbook is Discrete mathematics and Its Applications, by Rosen. It's been very difficult finding good content on ...
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3 votes
0 answers
102 views

References for visualizing numbers in base 10 flats

Base 10 blocks (units, rods, flats and cubes) are a widespread manipulative material for teaching place value. However, piling rods on top of each other is not very stable, so it is not easy to build ...
4 votes
1 answer
169 views

Is there a study on how often modern teaching methods versus traditional methods are used in a math classes?

Most of the students I've encountered seem to have had the same sort of math education I've had, the standard lecture, book readings, homework problems and exams. In my own experience and in my ...
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9 votes
2 answers
581 views

Fear of notation and hazily-appeared writing in Mathematics

I am looking for literature related to fear of notation in mathematics. It is even heard that the font size and font type make a reader reluctant to study mathematical literature, often lecture notes,...
1 vote
1 answer
54 views

Reference Request: Suitability of a text and corresponding video lecture series request for "Matroid Theory"

I am an undergraduate student from the CS background. While reading a portion of the text "Introduction to Algorithms" by Cormen et. al. I came across a section of Matroids. I was unable to ...
8 votes
2 answers
256 views

Math Education for Students who use Right-to-Left Written Languages

Does anyone know of any studies or have personal experience dealing with difficulties (if any) faced by students studying mathematics if they come from countries which use languages written from right-...
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3 votes
4 answers
490 views

Textbook to study group theory as a part of Discrete Mathematics

I am a student from CS background. I have been following "Discrete Mathematics and its Applications" by Kenneth Rosen, though it is a good book, but it does not cover group theory. I would like to ...
14 votes
3 answers
747 views

What are some resources for "ungrading" in a math class?

Most of the stuff I'm finding online about ungrading are either general descriptions of its virtues, or personal accounts from instructors from subjects other than math. Does anyone know any resources ...
  • 4,462
9 votes
2 answers
1k views

"Feynman effect" in teaching mathematics

In his book "Surely you're joking Mr. Feynman", Richard Feynman relates the following story. As he was supervising a group of calculators for Manhattan project, he at some point gave them a lecture on ...
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3 votes
2 answers
183 views

Has a List of Fundamental Mathematical Skills been compiled?

... in the literature. I an wondering is there a (considered) list of "fundamental mathematical skills". I am not sure can I give a solid definition of "fundamental mathematical skill". What I mean ...
5 votes
1 answer
159 views

Scoring students' work is counter-productive

The Mathematics Assessment Project (MAP) has created lesson plans for high school lessons in maths based around formative assessment. They make the following remark about marking students' work in ...
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5 votes
2 answers
161 views

Tips and References for a 15 days Course on Math

I'm going to participate in a course (as a teacher) where I'm suppose to teach high school math to high school students in about 15 days during the year. Each class has about 1 hour long. Now, I think ...
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5 votes
2 answers
162 views

Are there any more mathematical journals or websites with the "problems and solutions"?

Are there any more mathematical journals or websites with the "problems and solutions"? such as , the American Mathematical Monthly and Crux Mathematicorum
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26 votes
6 answers
2k views

What is the quantitative data on effectiveness of "modern" teaching methods?

What research has been done on how much and in what circumstances various non-lecture types of teching are effective with regards to student knowledge and performance? Meta/review studies preferred ...
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3 votes
6 answers
355 views

What do I study in calculus beyond the minimum required for undergraduate engineering?

I am majoring in aerospace engineering. I love math a lot, especially calculus. I have a lot of free time right now and I want to learn more stuff in calculus that would be helpful for my major but I ...
-3 votes
1 answer
199 views

A role for a non-symmetric equality relation in teaching mathematics? [closed]

First, I will simply observe that it seems to be standard practice, in elementary set theory, to define relations to be sets of ordered pairs. If we had the option of introducing a "symmetric ...
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3 votes
1 answer
122 views

Are there any textbooks on multivariable calculus that introduce all non-trivial definitions and all non-trivial proofs with a "first draft"?

The idea is that a student who is reading from beginning to end will always be provided with a train of thought. The student will have no motivation to stop, and memorize an unexplained product of ...
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20 votes
8 answers
3k views

How can I learn to write better questions to test for conceptual understanding?

I'm worried that I'm bad at realizing when a question I've written requires little or no conceptual understanding to answer. Like, when I'm writing a question for a homework assignment or exam, I'll ...
  • 4,462
8 votes
1 answer
257 views

How to study for university level math olympiads and competitions?

I participated in some high-school-level math competitions, but I never invested much of my time in them at that time, something that I regret immensely. Now that I am an engineering grad student, I ...
10 votes
2 answers
283 views

Pros and cons of randomised question generation

I am developing an assessment piece where the content is the same but the particular numbers are different for each student. It involves finding Triangle Centers given points using coordinate geometry....
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12 votes
1 answer
386 views

Best practices in teaching math to future elementary teachers

This question is about references in current best practices in teaching math to future elementary teachers at a university level. I am asking it because I do not see any question so far on this site ...
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