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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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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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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 ...
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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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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 ...
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"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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"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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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 ...
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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 ...
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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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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).
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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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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 ...
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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-...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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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Introduction of the power set as a collection of *labels* or *names* for subsets
The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
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Resources for high school teachers about APOS theory
As far as I can find, the major resources available to the layteacher about APOS (Action, Process, Object, Schema) theory refer to "undergraduate" concepts such as group theory and vector spaces (such ...
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What did math educators think about the transition to widespread classroom use of calculators?
When we have discussions about which technology to include in our classrooms today, we are often somewhat conflicted with many standard arguments and worries being presented on both sides. To help ...
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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 ...
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Quantifying arthmetical skill
Question for a research project:
What is the standard way of quantifying a student's skill in arithmetic ranging from having to look up numbers on a times-table to computing large sums in their head ...