All Questions
3,312
questions
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 ...
- 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.
...
- 28k
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, ...
- 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 ...
- 75
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 ...
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 ...
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.
...
user11702
-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 ...
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 ...
- 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 ...
- 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 ...
-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 ...
- 21
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 ...
- 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, ...
- 633
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?
- 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 ...
- 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 ...
- 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 ...
- 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" ...
Chris Shiherlis
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 ...
- 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 ...
- 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 ...
- 25
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 ...
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 ...
- 139
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 ...
- 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). ...
- 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 ...
- 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 ...
- 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 ...
user11702
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 ...
- 91
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 ...
- 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 ...
- 299
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?...
- 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 ...
- 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 ...
- 269
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 ...
- 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 ...
- 133
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 ...
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 ...
- 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 ...
- 309
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 ...
- 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 ...
user11702
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 ...
user11702
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 ...
- 211
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 ...
- 143
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 ...
- 3,613
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....
- 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 ...
- 791
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 ...
- 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" (...
- 4,015