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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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 ...
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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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Teaching a very enthusiastic and bright 5 year old
I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never taught at this age and I am unfamiliar with the ...
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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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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 ...
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When should we first teach variables in school math? And how?
From a pedagogical point of view, when is the "right" moment to introduce letters and variables to school children?
Let's say we taught arithmetic, the four operations, did computation exercises, or ...
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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 ...
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Literature on learning from errors in mathematics
In teaching undergraduate mathematics, I implemented some strategies to encourage the students to look at errors they made or at "typical errors" in the current topic. One attempt was to compile a ...
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A study comparing effects of calculator usage on later math skills?
Each year my university tries to decide whether or not it will have calculator and CAS based introductory math courses (the calculus sequence, linear algebra, and ODE) or not. Other than some hearsay ...
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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 ...
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Physical vs. Virtual manipulatives in the high school classroom
I notice that geometry students frequently have difficulty with representations of 3-dimensional objects in 2 dimensions. Today, we worked with physical manipulatives in order to help visualize where ...
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Moving From Rote Learning To Creative Thinking
My mathematics education was essentially rote, you learned the formulas and applied them almost algorithmically to the problems you were presented with; the teacher dictated a method and you followed ...
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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 ...
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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 ...
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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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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 ...
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Which universities teach true infinitesimal calculus?
My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
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Best textbooks to introduce measure theory and Lebesgue integration?
What are the best textbooks to introduce measure theory and Lebesgue integration to undergraduate math majors? Many students in such a class will go on to graduate school and be required to take a ...
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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 ...
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Discovery-based and inquiry-based learning
In general, I think (and I am told by students) that I am good as a tutor. However, I would like to become more rigorously familiar with the discovery-based and inquiry-based learning applied to ...
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Is there any evidence about the effectiveness of "table proofs" in pre-college mathematics education?
I remember when I took geometry in high school, like most students it's where I was formally introduced to proofs. However, the way we went about them was strange, it really felt like symbol ...
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Calculation versus writing in mathematics
Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas ...
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How does a reliance on calculators affect student performance?
Overheard in the Math Office while another Professor was helping a student with Statistics:
Always use a calculator when doing decimal arithmetic because you'll eventually make a mistake if you do ...
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Recommendations for inquiry based/aided discovery textbooks
I've recently dipped my toes into the world of number theory; and I've bought a book that to me is quite unconventional: R. P. Burn, A Pathway into Number Theory. I've yet to put the book through its ...
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What are some fun/nonstandard examples of arithmetic/geometric series?
I am teaching those topics (arithmetic/geometric series) just now, and want some
not so standard (fun) examples, which can be used essentially at high school/beginning calculus level. I'm ...
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Is there a program like ALEKS for mathematical logic?
ALEKS (http://www.aleks.com/) is a good way of learning procedural math, because it is very systematic and forces you to master the dependencies of a kind of problem before working on that kind of ...
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Creativity in mathematics
I have recently been engaging more and more with my creative side by drawing, writing, and (trying to) playing piano. I have come to see mathematics as much more of a creative field of study than I ...
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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 ...
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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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Students who know high-level math before going to college
There is a high school in the city I live in which has some high-level math courses in their curriculum. It's a special math class mentored by some university lecturers, and the children basically do ...
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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 ...
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Any support for mathematical "learning types?"
Back when I was an undergrad calculus TA, I participated in a general TA training class. We were taught to be mindful of different "learning types," such as visual learners, audio learners, and ...
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Separating the roles of "teacher" and "assessor"
Teachers at the university level (at least what I've seen in the US) are responsible for both
teaching students the material for a course, and
assessing the students' understanding of the course ...
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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 ...
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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 ...
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Evidence for or against the claim that some students are "algebra people" and others are "geometry people"
Where I live and work, there is a widely-accepted and often-repeated claim that there are two kinds of students: "algebra people" and "geometry people". This claim sometimes gets expressed in ...
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How to assign grades to proofs: what do(es) the literature/experts suggest?
I am teaching an introductory course on proofs in mathematics in a mid-size American public university, and trying to develop some kind of consistent grading meta-scheme for grading proofs. I am ...
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Reference request for studies on gender in math examples, homework problems, or math exams
I am looking for a study or reference on gender in math problems given in mathematics.
In math texts or even on math exams, if there is a word problem involving people, these people or "characters" ...
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What experimental studies have been done on the Kumon method of teaching and learning mathematics?
My dissertation involved, among other things, the East Asian way of teaching and learning mathematics. (See, for example, Leung (2001).) I was particularly interested in the Kumon method. Although I ...
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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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Resources for reading mathematics out loud in different languages
Are there reference books or online material for reading mathematics out loud in different languages?
For example, the expression1)
$$
\int x^2dx=\frac13x^3
$$
is understandable to anyone who has ...
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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 ...
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Research on how mathematics skills transfer to other areas
Briefly: I am looking for research on the extent to which learning mathematics (let's say "college algebra" if we want to be specific) impacts problem solving skills, abstract reasoning, etc.
Less ...
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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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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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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 ...
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Mathematics Education Graduate Program List and Rankings
U.S. News and World Report publishes school rankings for many different disciplines, including mathematics. Is there any ranking for mathematics education graduate programs?
Weaker question: Is there ...
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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 ...
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Mathematics and the hermeneutic circle
Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations.
This leads me to ...
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Ideological Teaching in Logic Courses
Logic and its sub-fields are closely related to philosophy. There is an undeniable mutual interaction between one's philosophical point of view and his/her approach in teaching mathematical logic. In ...
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