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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5
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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 ...
6
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1answer
173 views

Is there any high school level summer program that teaches Analysis?

All summer programs I know for high-school students focuses on number theory, combinatorics, graph theory, logic, and all kinds of topics in discrete mathematics. (I am mainly interested in UK, US, ...
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2answers
83 views

What do I study in calculus

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 ...
6
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2answers
287 views

Difference in difficulty between removing and adding structures?

In Fantasy math, Peter Saveliev remarks: Removing structures from consideration is hard; adding is much easier. Compare how you start with point-set topology -- by removing the geometry from the ...
18
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2answers
482 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 ...
-3
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1answer
143 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 ...
3
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1answer
93 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 ...
15
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2answers
763 views

The Fundamental Theorem of Calculus and Vegetables

When I was an undergraduate, someone presented to me a proof of the Fundamental Theorem of Calculus using entirely vegetables. I found this incredibly fun at the time, but I can't remember who ...
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4answers
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 ...
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4answers
1k 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 ...
19
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8answers
2k 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
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2answers
194 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
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5answers
283 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 ...
29
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7answers
13k views

What are the comparative advantages of open-book versus closed-book exams?

I would like to know the advantages and disadvantages of open-book exams as compared to closed-book exams, particularly in standard undergraduate courses like calculus or linear algebra. My practice ...
10
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2answers
263 views

How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
19
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6answers
591 views

Becoming a better instructor: where to start?

I just finished a PhD in math at a top department, but not one that placed much emphasis on graduate student teaching. Grad students here teach only as TAs, and the training is minimal. I got great ...
8
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1answer
228 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 ...
11
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1answer
236 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 ...
6
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2answers
139 views

Studies about group tutoring sessions

I’m not sure if this question belongs here, so I apologize if it doesn’t. I work in a tutoring center at my university where we tutor every subject. Mathematics is in high demand, and occasionally my ...
9
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2answers
215 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....
10
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1answer
631 views

Effectiveness of multiple-choice versus short answer questions

I want to know if there is any research on whether students' learn better by answering selected response (multiple choice) questions than constructed response (written) questions. My gut feeling is ...
7
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2answers
218 views

Material on tutoring university level math classes

Can anyone recommend online or printed sources on anything related to teaching university level math tutorials (that accompany a lecture course taught by someone more senior, but I'd also be happy ...
5
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4answers
298 views

Is the education system in Finland particularly good?

Inspired by this question: What makes education in Finland so good? Finland has marketed itself as a top country in education. Indeed, at some time, the Pisa results in Finland were quite good. ...
8
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4answers
400 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 ...
1
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1answer
94 views

Roadmap to studying PDEs for analyzing Quantum Physics better

I am studying the basics of Quantum Physics (involving the characteristics of Schrodinger's Wave equation without actually analyzing it rigorously mathematically) this semester. I was wondering, ...
11
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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 ...
5
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0answers
274 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, ...
11
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3answers
649 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 ...
2
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2answers
101 views

Are questions on overlapping solids of revolutions without prior definitions and instructions fair given that there are divided interpretations?

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the ...
5
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1answer
527 views

Midterm in Mathematics Courses

Can someone point me to papers indicating whether or not a midterm is an important part of a course? I suspect I can find many 'experiential anecdotes' that midterms are good/bad/moot but I would ...
7
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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. ...
10
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20answers
7k 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 ...
4
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0answers
229 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 ...
5
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2answers
134 views

Published papers for Intro Stat students to read

I am looking for studies and experiments in the literature that I can share with undergraduate students in an intro statistics course. I do not expect students to understand everything, and I plan to ...
4
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0answers
127 views

What effect does giving numerical or written grades have on learning?

When I was in school, pupils were given numerical grades, or the equivalent of numerical grades but disguised as words, on their performance in various school subjects and also behaviour. A key ...
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 ...
31
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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 ...
14
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2answers
335 views

“Always/Sometimes/Never” vs. “True/False” questions for mathematical reasoning

Has anyone performed a study on the differences between student interpretations of these words? Background: When I taught high school geometry and later undergraduate precalculus, I noticed that ...
6
votes
0answers
124 views

Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?

For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs) I can understand that in more ...
3
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1answer
134 views

Books similar to “Teaching Developmentally”, but for high school math

I've been extremely excited by my reading of the book Elementary and Middle School Mathematics: Teaching Developmentally by Johan A. Van de Walle et al. Does anyone know of similar books (or other ...
10
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4answers
699 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 ...
5
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7answers
2k 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 $y=mx+y_0$,...
2
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0answers
67 views

Reference for study about good teachers in a US state

Several years ago I have read about a study in a US state where standard test scores were used to identify teachers whose students consistently improved far above the average and then film and analyse ...
5
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1answer
106 views

Tables of primitives with indication of solution method

I am looking for an extensive source (often called "table of integrals") listing primitives of various classes of functions including the "elementary" ones (rational functions, functions involving ...
7
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4answers
417 views

Examples of Research Level Math Discoveries Done by Undergraduate Students

A good way for motivating young students in undergraduate level is telling them that you can do great works! Question. What are good examples of research level mathematical discoveries done by ...
9
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0answers
120 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
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0answers
140 views

Textbooks explicitly showing the injections for the sum of sets

Asking for methods to produce the sum of natural numbers from the disjoint union of sets, it seems that the obvious way is to use the general definition, as coproduct, of the sum of sets. The accepted ...
13
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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 ...
8
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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-...
11
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6answers
498 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 ...