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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17
votes
7answers
578 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 ...
3
votes
0answers
151 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, ...
2
votes
0answers
60 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 ...
4
votes
1answer
224 views

Research on Waldorf/Steiner mathematics education

I am broadly 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/...
6
votes
2answers
214 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 ...
16
votes
9answers
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 ...
8
votes
3answers
548 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 ...
9
votes
8answers
668 views

Definition of the term, equation

What is the definition of an equation (as a mathematical terminology)? I have been using this term, equation, for a long time. I don't even remember when and where I have learned this term (Possibly, ...
12
votes
0answers
138 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
0answers
175 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?
14
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4answers
6k 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 ...
1
vote
1answer
71 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 ...
0
votes
3answers
179 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 ...
2
votes
1answer
163 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,...
24
votes
5answers
2k views

Should we "program" calculus students, like the physicists seem to want us to?

If it is true that we first learn formalism...how to do things that we don't understand, should we regard teaching students mathematics as programming dumb machines with formal rules (to the greatest ...
22
votes
7answers
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 ...
58
votes
15answers
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 ...
11
votes
2answers
209 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 ...
26
votes
2answers
1k 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 ...
5
votes
1answer
216 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 ...
7
votes
8answers
3k views

What is an intercept?

I have always taught my students that the $y$-intercept of a line is the $y$-coordinate of the point of intersection of a line with the $y$-axis, that is, for the line given by the equation $y=mx+y_0$,...
8
votes
1answer
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 ...
10
votes
1answer
216 views

Recommend a vector calculus textbook/resource with an algebraic geometry flavor

Is there a resource or textbook that presents the basics of vector calculus, specifically the gradient, directional derivatives, curves and surfaces, and extrema, from a more algebraic geometry ...
5
votes
1answer
216 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 ...
8
votes
3answers
268 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 ...
7
votes
4answers
429 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
0answers
73 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 ...
5
votes
0answers
157 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 ...
13
votes
23answers
16k views

Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

I am asking this question here to obtain a nice reference list. I am asking for examples of words which have different connotations or meanings in Mathematics compared to English as taught in ...
5
votes
1answer
562 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 ...
7
votes
3answers
4k 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 ...
6
votes
0answers
368 views

What books properly address the properties of $a^b$?

Many students think $\sqrt{a} \sqrt{b}=\sqrt{a\ b}$ $\sqrt{a^2}=a$ $\frac{1}{\sqrt{a}}=\sqrt{\frac{1}{a}}$ but none of the above are true when (a) and (b) are negative. To avoid such problems, ...
24
votes
3answers
2k 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 ...
14
votes
10answers
1k 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 ...
14
votes
6answers
223 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 ...
2
votes
1answer
95 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 ...
3
votes
0answers
96 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 ...
36
votes
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 ...
4
votes
1answer
352 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 ...
4
votes
1answer
161 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 ...
7
votes
1answer
273 views

Native language, writing, and mathematical problem solving

This question is meant to explore the intuition that mathematical thought does not most naturally proceed from writing in one's native language. The hackneyed and not entirely satisfying slogan that ...
9
votes
2answers
564 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,...
29
votes
4answers
4k 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 ...
7
votes
1answer
379 views

"Indicated Arithmetic" or "Delayed Evaluation"

In the recent past, I've come across a pedagogical strategy for teaching/learning algebra that is sometimes called "Indicated Arithmetic" or "Delayed Evaluation". However, I've been unable to find any ...
8
votes
2answers
251 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-...
1
vote
1answer
53 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 ...
3
votes
4answers
400 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 ...
11
votes
1answer
419 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 ...
9
votes
2answers
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 ...
3
votes
2answers
179 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 ...

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