# All Questions

3,312 questions
Filter by
Sorted by
Tagged with
45 views

### How to study for a mathematics undergraduate entrance examination?

TL;DR: Tell me which topics should i study the most, based on this three tests: Mathematics (A): 2020 2019 2018 This question may sound a bit weird, since the natural answer would be "study ...
• 39
1k views

### Is the Wronskian still assumed for graduate education?

About thirty years ago, in a practice GRE (Graduate Record Exam) math test in the US, a question assumed the student knew the definition of the Wronskian. I had never heard of this determinant before. ...
893 views

### How can I improve my Retake Policy?

I teach Pre-Calculus at a public high school in the United States. This school year, I allowed my students to retake any assessment regardless of how they performed on their first attempt. However, ...
• 1,009
85 views

### How to create a platform for students asking questions quickly and privately?

When studying math in class, many students have a few moments falling behind, and they are reluctant to ask a quick question. Do we have a way (like an online web page or tool) for students to quicky ...
1 vote
161 views

### Importance of exploring skills in mathematics

How can you improve exploring skills in high school mathematics education in order to guide students to get better opportunities to become mathematicians ? Here are my suggestions, Let students to ...
97 views

### Generating exercises about extrema of $f(x,y)$

(I have asked this question on math.stackexchange.com and according to a suggestion from comments I am re-asking it here.) I can generate many examples of functions $f(x,y)$ for which finding local ...
313 views

### Is there anything one can do for students who have given up?

In each class, there are often a few students who seem to have given up early on. In my recent discrete math class, when I asked a student a question, he said he was working on his graduation project. ...
80 views

### How do you teach the order of a series of events?

I’m looking for research-backed methods for teaching which order a series of events are in. Notably, ordinality in my case is far more important than cardinality. Even better if the technique allows ...
3k views

### Examples of relations that are not functions

When teaching functions, one key aspect of the definition of a function is the fact that each input is assigned exactly one output. I always felt that the "exactly one" part is confusing to ...
• 2,107
5k views

### Explaining why volume of cone is a third of cylinder

I came across this video explaining to kids why the volume of a cone is a third of the cylinder of same cross-sectional radius and height. Essentially the explainer presents pre-created cylindrical ...
• 273
582 views

### Equation of a straight line on two dimensional Cartesian plane

What is the most appropriate way to write equation of a straight line through a given point $(\alpha,\beta)$? If you write it using the standard form $y- \beta = m (x - \alpha )$ Where m is the ...
269 views

### Is it considered a mistake to use different correct notation for writing intervals?

Standard definition of writing interval states that it should be written (a,b) where a<b Due to this being arbitrary and just a convention that we all use, would it be considered a mistake to write ...
229 views

### How well can students learn abstract concepts through concrete examples?

In my own personal experience in teaching linear algebra, where many students encounter abstract ideas for the first time, I find that most students have trouble consolidating observations from ...
• 191
3k views

### What are some examples of great functions that are not too elementary (easy)?

I am teaching precalculus/basic calculus to my class (high schoolers of around 18 years of age), and I'm always searching for nice functions to plot and study (finding the domain, the function's sign, ...
• 633
152 views

### A good way to learn differential equations rigorously

What would be a good books of learning differential equations for a student who likes to learn things rigorously and has a good background on analysis and topology?
• 11
497 views

### What are best practices for building a dedicated space for mathematics majors?

The math department at my institution (a private, four-year college with a total enrollment of about 4000) is in the process of brainstorming about a dedicated study/community space for our math ...
• 1,049
141 views

Are there any collections or blogs of bad data visualizations? I know I've seen such misleading graphics in the news or in print, made misleading either maliciously or thoughtlessly, but I usually see ...
• 4,362
357 views

### How can you elicit the $\log x = {\log} \cdot x$ error?

You know the error, when you're watching a student work through an algebraic calculation to solve for a variable trapped in the argument of a function, usually $\log$ or a trig function, and you watch ...
• 4,362
2k views

### What term describes the relationship between tenth, hundredth, thousandth and the number ten?

What term describes the relationship between tenth, hundredth, thousandth, et cetera (1/10, 1/100, 1/1000, ...) and the number ten? (Despite what some may say, I don't accept that "decimal" ...
591 views

### Real-world applications of taxicab metric

The taxicab metric can be used to measure distances in idealized gridded cities. However, usually this serves only as a fun exercise for students. I'm looking for engaging (as non-technical as ...
• 251
362 views

### Student forgets to remove dx after integrating

I am tutoring another US college student in a Calculus 1 class. Initially, she was having trouble with basic concepts, but after much prodding most of the conceptual difficulties seem to have been ...
• 135
817 views

### Finding an analogy to explain the function of a binary adder

I want to find an intuitive analogy to explain how binary addition (more precise: an adder circuit in a computer) works. The point here is to explain the abstract process of adding something by ...
• 25
199 views

### How to understand the book and the material to the deepest possible level?

I'm a first year mathematics major and I have a problem with my learning process. In my university, I only have books and questions that the university published, so I have to learn the most of the ...
1k views

### Do we need to practice equation derivation while learning math if equations will be chunked and automatized?

When I was learning the Pythagorean theorem(at time A), I was just told to memorize it. I used it often before trying to derive the equation(at time B), and I think actually I have forgotten the ...
• 139
165 views

### References for mathematical notation for foreign students in the U.S

I teach quite a few foreign students at a U.S. university. Frequently students are placed in our most remedial math class due to not having placement scores and failing to test out of the course. I ...
• 301
117 views

### Resources for Teaching Parameterization of Curves/Surfaces

In classes like Calc 3 or Computer Graphics, I want my students to be comfortable describing common curves and surfaces parametrically (such as lines, triangles, circles, or surfaces of revolution). ...
• 1,919
278 views

### Is it normal for a child to strongly prefer addition to subtraction?

My six-year-old daughter enjoys addition but not subtraction. When we walk together, I like to give her some "mental mathematics" questions, such as "What is 13 plus 33" and she ...
• 4,015
4k views

### What should be memorized in math and what should be reference table?

I can never figure out what should be a memorization concept and what should be in a reference table. For example, in calculus, you are expected to memorize all the derivatives and integrals but in ...
• 769
216 views

### What kind of general advice for studying math we can offer undergraduate studens who do not major in math?

I have received request from a student, who is not in math major, asking me for advice on How to keep motivated when studying math (calculus, linear algebra, etc.) What does one need to do beyond ...
222 views

### Long division layout in French-speaking Switzerland

This question is addressed to those familiar with mathematics teaching in French-speaking Switzerland. The main textbook in use in grades 3 to 5 in the canton of Vaud from 1957 to about 1972 appears ...
113 views

### After building the probability space, how to motivate for random variables? [closed]

Having put my audience through developing a probability space $(\Omega, \mathcal{F}, P)$, where $\Omega$ is the sample space of a random trial, $\mathcal{F}$ is a $\sigma$-field on it, and P is a ...
• 51
252 views

### Creative problems in 2D vector geometry

What are some "interesting" and creative problems or exercises on specifically 2-dimensional vector geometry that a high school student might find compelling to solve? The class' current ...
1 vote
201 views

### Why do so many children's book confuse discs with circles? [duplicate]

The difference between a disc (disk) and a circle is crystal clear to me: However, in many children's books, a disc is usually called a circle: Why do many children's book confuse discs with circles?...
• 4,015
799 views

### What are examples of math-themed sci-fi appropriate for students?

What are examples of sci-fi books or short stories that have a mathematics theme? I'd like to have a pool of examples in mind that I could refer students to. The only example I've got in mind right ...
• 4,362
92 views

### Best PreCalculus Textbook

What is your favorite PreCalculus textbook for someone that needs to get their algebra skills up to snuff? Something comprehensive with some tricky problems. Stewart? Sullivan? Blitzer? Something ...
• 269
3k views

### Should an undergraduate math program contain a course on Lebesgue integration?

Is it standard for a math undergraduate program to have a course on Lebesgue integration? Does Riemann integral suffice for undergraduates? The reason of my question is I read a paper by Bartle titled ...
• 183
83 views

### Program for visualizing trajectories for a 2D system of linear differential equations

I am looking for a program so that when you give it a 2D system of linear differential equations and an initial condition, it can show an animation of the trajectory of a particle starting at that ...
• 133
111 views

### Is there a good Animation to explain Rotational Symmetry of Equilateral triangle

I am willing to teach that the Order of rotational Symmetry of Equilateral triangle as $3$ using Animation. Any suggestions of good applet which demonstrates the rotation of equilateral triangle with ...
57 views

### Resource for International Comparison of Math Education Logistics

Are there resources that compares/lists crunchy facts about the logistics of math education in different regions or countries? I'm talking facts like: Do they use paper homework versus and online ...
• 4,362
161 views

### Middle school math games for the parking lot

I'm looking for math games that a group of students in grades 5 to 10 (ages 11 to 15, say) could play in a gym or parking lot. My school has a STEM Day each year and I get tasked with cooking up some ...
• 309
138 views

### AP Calculus BC Guidance

Hello wonderful educators. I am hoping to get some help on a tough situation I am in. So first, a little bit of background facts: This is my first time teaching an AP class. I've adjuncted for Calc I ...
• 1,834
341 views

### Should we use quizzes to replace homeworks?

I posted a question regarding what to do when students have done poorly in a mid-term exam. One suggestion I got is to use frequent tests to reduce the risk of one poorly designed exam. Then I did a ...
6k views

### What should I do if students did very poorly in the mid-term exam?

In the linear algebra course I taught, I have three exams. In the first exam, which is probably too hard, students did poorly. So many students said they have lost confidence. To encourage them, I ...
155 views

### Visual aids for understanding group theory

I want ideas for pictorial representation of groups which can help one understand the different group theorems. Here are some examples of the type of thing I am looking for. In this video by socratica ...
148 views

### Valid Reasons in Two-Column Geometry Proofs

I'm wondering about the relationship between Eculid's work and modern high school geometry. In "two column proofs," certain reasons are considered acceptible for steps in the proof, such as ...
2k views

### Concrete vectors spaces without an obvious basis or many "obvious" bases?

I am teaching a class on linear algebra to sophomore and junior science majors, and am having some trouble illustrating the difference between $\mathbb{R}^n$ and an n-dimensional vector space. The ...
• 3,613
94 views

### Conferences dealing w/challenges of teaching higher level math to STEM audiences

I'm interested in knowing whether there are conferences that have, among other topics, the difficulty of teaching higher level mathematical concepts to folks with prior established skills in STEM, e.g....
• 141
2k views

### Use of language: "perfect square". is this useful or a hindrance? [closed]

I have recently been noticing the tendency to use the term "perfect square" when "square number" is really what is meant. Usually I have seen it at elementary level: introductory ...
• 791
607 views

### Should one teach to use equality or isomorphism in particular groups?

I am wondering the following. Suppose we have some particular space $X$ and $x_1,x_2,x_3,x_4\in X$ has the law of composition that works like Klein four-group. Is it correct to say that the structure ...
• 53