All Questions

Filter by
Sorted by
Tagged with
3 votes
1 answer
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 ...
user avatar
  • 39
3 votes
2 answers
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. ...
user avatar
5 votes
3 answers
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, ...
user avatar
  • 1,009
4 votes
1 answer
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 ...
user avatar
1 vote
2 answers
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 ...
user avatar
2 votes
0 answers
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 ...
user avatar
5 votes
3 answers
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. ...
user avatar
-2 votes
0 answers
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 ...
user avatar
12 votes
14 answers
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 ...
user avatar
  • 2,107
17 votes
4 answers
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 ...
user avatar
  • 273
2 votes
3 answers
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 ...
user avatar
-1 votes
5 answers
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 ...
user avatar
9 votes
1 answer
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 ...
user avatar
  • 191
3 votes
3 answers
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, ...
user avatar
0 votes
3 answers
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?
user avatar
  • 11
11 votes
6 answers
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 ...
user avatar
  • 1,049
6 votes
2 answers
141 views

Where can I find a collection of bad/misleading data visualizations?

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 ...
user avatar
  • 4,362
7 votes
3 answers
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 ...
user avatar
  • 4,362
3 votes
5 answers
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" ...
user avatar
10 votes
2 answers
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 ...
user avatar
  • 251
3 votes
4 answers
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 ...
user avatar
  • 135
0 votes
6 answers
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 ...
user avatar
3 votes
2 answers
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 ...
user avatar
3 votes
5 answers
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 ...
user avatar
8 votes
0 answers
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 ...
user avatar
  • 301
7 votes
1 answer
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). ...
user avatar
  • 1,919
9 votes
2 answers
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 ...
user avatar
  • 4,015
10 votes
6 answers
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 ...
user avatar
  • 769
3 votes
1 answer
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 ...
user avatar
9 votes
0 answers
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 ...
user avatar
5 votes
0 answers
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 ...
user avatar
  • 51
7 votes
7 answers
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 ...
user avatar
1 vote
1 answer
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?...
user avatar
  • 4,015
7 votes
7 answers
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 ...
user avatar
  • 4,362
0 votes
1 answer
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 ...
user avatar
8 votes
5 answers
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 ...
user avatar
  • 183
3 votes
2 answers
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 ...
user avatar
2 votes
2 answers
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 ...
user avatar
3 votes
1 answer
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 ...
user avatar
  • 4,362
14 votes
3 answers
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 ...
user avatar
4 votes
1 answer
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 ...
user avatar
  • 1,834
5 votes
3 answers
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 ...
user avatar
14 votes
5 answers
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 ...
user avatar
7 votes
3 answers
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 ...
user avatar
4 votes
1 answer
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 ...
user avatar
16 votes
18 answers
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 ...
user avatar
4 votes
1 answer
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....
user avatar
  • 141
14 votes
5 answers
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 ...
user avatar
5 votes
3 answers
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 ...
user avatar
  • 53
13 votes
12 answers
6k views

How should I grade true-or-false questions if the student's writing is unclear?

See the attached image: I am having a difficult time grading this paper as I am not sure if the student intentionally wrote the answers in such a way that each answer looks like both "T" (...
user avatar
  • 4,015

15 30 50 per page
1
2 3 4 5
67