# All Questions

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### Has Benezet's teaching experiment ever been reproduced?

In the 1930's, Louis Bénézet, a superintendent of several schools in New Hampshire made the interesting experiment of teaching no formal arithmetic until grade 6: In the fall of 1929 I made up my ...
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### Is AP Calculus AB really necessary?

High school student here... This coming school year I'm scheduled to start AP Calculus AB and then my school is looking into taking Multivariable Calculus at a local university. The school's calculus ...
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### CoTeaching Elementary Linear Algebra

I and my colleague will teach an elementary linear algebra next few weeks, but the way our course is planned mostly is by turn teaching. By that I mean, my partner will teach the first 8 weeks of the ...
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Q1. Which statement is about the sets N and Q (a) N=Q (b)Q subset N (c) N subset Q (d) non of them Q2.An upper bound for the set {P€O:p^2<9} (a) 3 (b) -3 (c) -1 Q3. Which of the ...
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### Project ideas for prime numbers [on hold]

I and my friend had decided to do a project based on prime numbers in science Fair. We are highschool students. We have already collected details about some prime finding ways, prime number encryption,...
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I am looking for multiple choice question (MCQ) based tests on some Mathematics' topics (details below), which could be downloaded in most preferably tex (LaTex) format or doc/docx format. Kindly ...
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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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### Evaluation and feedback using Optical Mark Recognition systems in secondary school

OMR in exit tickets I plan to use an OMR, Optical Mark Recognition systems at the end of (some of) my classes. I want to use the same OMR system for exit tickets scattered over the academic year (...
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### Curriculum for self taught Maths degree

Someone has made this template for a self taught CS degree. I am a CS grad and found it quite good. As I don't have much idea about a proper pathway to learn degree level mathematics in my own. Please ...
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### Why emphasize moment generating function over characteristic function in a probability course?

I've noticed that some undergraduate introductory probability textbooks and courses emphasize or seem to prefer the moment generating function $m(t) = \mathbf E(e^{tX})$ of a random variable $X$ ...
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### Existing Tools for Math Expression Equivalence Logic

Note - this question was posted here and garnered some decent replies before it was closed as off-topic in Stack Overflow. Online systems, such as ALEKS, Cengage's WebAssign, and even Khan Academy ...
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### exponential equations

I'm looking for exponential equations that require the application of the properties of logarithms and can be solved without a calculator (by evaluating the logarithm). example: 27 = 3^(5x) . 9^(x^2^...
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### What are standard (or good) textbooks for undergraduate graph theory?

I'll be teaching graph theory this fall for the first time. The only undergraduate graph theory book I am familiar with is Doug West's book, which I like. But I'd like to consult some other ...
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### Should students be given partial scores when they gave an incomplete proof by contradiction?

In a quiz, there was a question asking students to show something doesn’t exist. A lot of them gave proofs by contradiction. Initially, I designed the marking scheme so that an incomplete proof by ...
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### Why are proofs written in flowery language incomprehensible?

Let's take an example in Wu-Ki Tung, Group theory in physics: Theorem 3.4: Irreducible representations of any abelian group must be of dimension one. Proof: Let $U(G)$ be an irreducible ...
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### Is There Such Thing as Learning Disability in Math?

I am currently tutoring a student who is really lacking in math. At first I thought she was just resistant; perhaps she thought that her teacher had no choice but to pass her. What truly stunned me ...
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### Integral calculus from the modern viewpoint

This is a soft question. What is the purpose of teaching techniques of integration at the college level? More specifically, in the sense of putting integration into practice, what value does ...
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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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### Online quiz with slightly different questions for each student

I am looking for an online quiz that can generate multiple versions of a multiple choice question. What I want is: The same question can have a different text for each student Alternatives are ...
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### What is the value in creating distinguishing terminology between the $x$, $y$, and $(x, y)$ values of a possible point of extremum?

I've been out of a math program for about four years now. My wife is starting a CS degree, and finished her first calculus course last semester. I tutored calculus throughout my entire undergrad, ...
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### Encouraging students to learn probability

Background: I’m not exactly a Math educator, but I’m currently a TA of an elementary algebra course aiming at students of age 14-15. I found that a lot of people have misconception about probability ...
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It seems like the internet has made it very difficult to prevent cheating -- simply looking up the solutions to textbook problems -- on undergraduate math homework. So there is a danger that grading ...
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### What is the best term for “probability measure” in an undergrad introduction to probability course?

The function $P$ that takes an event $A$ as input and returns the probability $P(A)$ as output is called a "probability measure" when we are developing probability using measure theory. I have also ...
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### How to present the order of factors and summands for the usual multiplication procedure

In the following multiplication example, \begin{align} 34\;& \\\underline{\times\;\; 7\;}& \end{align} first one would multiply the units digits, producing the partial product $28$ as ...
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### Better strategy on math graduate school

I'm just starting graduate school (master in mathematics) and there we have absolute freedom in choosing the number of courses that we can attend each term. In consequence, I'm wondering what is the ...
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### Polar form before Cartesian form when introducing complex numbers

When I teach complex numbers to undergraduate engineering students, I invariably start, as appears to be customary, with $a + bi$ (or $a + bj$ for electrical engineers) and then follow up with the ...
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### Learning math historically

What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...
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### Trends in math education: Majors? Applied math? Statistics?

I would be quite interested in learning of trends (in the U.S. or internationally) of student interest at the undergraduate level in pure math vs. applied math, say, measured by majors at graduation. ...
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### Good real-life examples of transformations of function graphs

I am a gradudate student teaching college algebra at a larger state school and transformations of graphs of function, i.e.: given the graph of a function $y =f(x)$, what do the graphs $y = f(x) \pm C$,...
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### Are there any books on how mathematicians reason about infinite sets? [closed]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 457. For an account ...
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### How can students self-learn creativity in math that “demand more than just deduction”? [closed]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 112.   You might ...
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### Should I describe the function $x \mapsto f(x_0) + f'(x_0)(x - x_0)$ as “linear” in a freshman calculus class?

One of the most important ideas of calculus is $$f(x) \approx f(x_0) + f'(x_0)(x - x_0).$$ The approximation is good when $x$ is close to $x_0$. This approximation is very useful because the ...
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### On fractions and least common multiple

At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of primer number, prime factorization and calculus of least common multiple. In ...
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### Why don’t all professors let students use notes, books, etc. on exams?

Last semester I had a teacher who let us use any type of information in the exam, for example the course notes, books, solved exercises, etc. The only thing he did not let us use was something ...
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### Small 'new things' to confront talented high-schoolers with

Something my students* often struggle with is how to react on being confronted by 'new things', including functions, notation or definitions for which they are given sufficient definition but with ...
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### Teaching logic through “high school algebra”?

I am going to be teaching a discrete math class in the fall. One of the major goals of the course is a solid understanding of the basics of logic: the precise meanings of "and", "or", "not", "implies"...
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### How to become really interested in math [closed]

I'm a high school senior. What can I do to be really interested in mathematics ? I know some of my batch-mates (from meeting them at several math Olympiads) are like insanely good at math (know lots ...
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### Urn (containing colored balls) generator?

I am looking for a nice app that would enable me to create "automatically" nice urns filled with balls of two different colors, following the illustration below (actual colors do not matter, being ...
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### What are the uses of calculus in every day life? [closed]

Can anybody say me what is differentiation and integration and what is the use of these ?
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### Subject advice in Number Theory [closed]

At my University, we have the optional feature to write a project like a Bachelor Thesis. This semester have finished and I would like to work in the summer in project like this. So, I'm searching for ...
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### Simple, elegant ways to teach the idea of what functions are for the first time

The context In my country, when the concept of function needs to be introduced in math classes, most teachers will simply talk about $f(x)=c$, $f(x)=ax+b$ and $f(x)=1/x$ (constant, linear and inverse ...
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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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### Supplemental text for undergraduate real analysis

Context: I am an assistant professor at a small college in the US. Next semester I am teaching real analysis for the first time, and we are using Steven R. Lay's book. (It also happens to be the ...
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I am doing exercises with middle grade students and looking at their capacities to create arguments for simple number theory conjectures. I want three tasks, and I have two so far: 1. The sum of three ...
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### One course/subject, one class, two lecturers

This is my first question here, so please correct me if I'm wrong in my way of asking. My question is suggested directly by the title. In my college institution, for each subject, half of the ...
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### Why bother completing the square to find the minimum/maximum of a quadratic function?

Given a question like Find the coordinates of the minimum point on the curve $y=3x^2+2x+9$. students are often taught to solve this by completing the square. The class I am currently teaching ...
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### Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?

I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of ...
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### Why is problem solving important for all of us?

I am looking for academic references related to this questions. In fact, I need to write a paper which shows the importance of problem-solving approach for everyone. Certainly, this should include ...