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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21 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 ...
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1answer
143 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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4answers
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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 ...
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1answer
206 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 ...
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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
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2answers
162 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
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1answer
142 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 ...
5
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2answers
139 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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2answers
111 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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6answers
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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 ...
3
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6answers
236 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 ...
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1answer
154 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
101 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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8answers
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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 ...
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1answer
237 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 ...
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2answers
233 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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1answer
246 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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1answer
99 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, ...
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4answers
318 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. ...
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0answers
279 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, ...
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2answers
106 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
531 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 ...
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2answers
145 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 ...
5
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2answers
140 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 ...
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0answers
134 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 ...
6
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1answer
302 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 ...
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2answers
580 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
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0answers
126 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
138 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 ...
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 $y=mx+y_0$,...
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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
114 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 ...
9
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0answers
123 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
141 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 ...
3
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1answer
239 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 ...
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3answers
182 views

Resources on solving systems of polynomial equations in multivariable calculus setting

Whenever I teach multivariable calculus I find students really struggle with both finding critical points and the method of Lagrange multipliers. I think that the reason is the same: solving systems ...
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4answers
362 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 ...
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0answers
103 views

Which book to use concurrently with each of these mathematics texts?

I'm in search of a good book that I can read --- and recommend to my proteges to read --- along with each one of the following books. Topology by James R. Munkres, 2nd edition Introductory ...
13
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4answers
295 views

Pedagogical advice/articles for graduate student teaching assistants

Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their ...
6
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0answers
158 views

Adding one to numbers bigger than ten

If someone asks you Tell me the next number (add one) after the number one million two hundred thirty-one thousand ninety-nine, do you known if it is a common error that the first number that ...
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3answers
171 views

Which book has functions and their respective graphs? [closed]

I am looking for a book, which has different many different types of functions and their graphs (like, Weierstrass function, Takagi function).
6
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1answer
190 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, ...
9
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1answer
153 views

Experimental results about the variability of grades on a math exam

"[Myth] that exams are objectively graded. Daniel Stark and Edward Elliot sent two English essays to 200 high school teachers for grading. They got back 142 grades. For one paper, the grades ranged ...
4
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1answer
111 views

Is there a class curriculum that studies the work of a mathematician?

Are there classes dedicated to understanding the work of a particular mathematician? I have seen courses dedicated to a theorem (I saw for example one that sought to prove and understand the Atiyah-...
12
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3answers
159 views

Tasks that encourage argumentation

I am looking for resources that have tasks such as the one below that encourage argumentation. I want tasks that 8th graders could do but would also be appropriate for high school students. I want to ...
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0answers
373 views

What is known about discrimination and difficulty in test questions?

I am interested in looking at any design resources or "guiding principles" on the distribution of different types of question difficulties on evaluative examinations. We can use Item Response Theory ...
7
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2answers
221 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 ...
12
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1answer
198 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 ...
2
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1answer
124 views

Reference or term for connected sage-on-the-stage?

I heard that there is evidence that a "connected sage-on-the-stage" teaching style is at least as effective as guide-on-the-side / flipped classrooms. I have been unable to find significant references ...
4
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0answers
95 views

Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]

I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question. I've been tasked with helping to redesign a math curriculum for an enrichment ...

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