All Questions
3,617
questions
1
vote
4
answers
189
views
Naming the procedure of converting the place values of digits
Let's say I have the numeral 2.263,3 thousands, and convert it to 2.263.300 units.
How do we describe what I have done to the numeral regarding units ?
I know it has to do with the place values of the ...
- 201
6
votes
7
answers
412
views
Is 'For all $x$' an abuse of language in math?
I chose to ask this question on MESE because I think it's not about mathematics per se but more about how it should be communicated.
Quantified statements in mathematics are often written for ...
- 201
6
votes
4
answers
5k
views
What benefit is there to obfuscate the geometry with algebra?
Consider:
In a right triangle:
sin(2x + 4) = cos (46)
What is the value of x?
The question above is from standardized tests for a geometry course. If my goal is to have students understand ...
- 919
4
votes
3
answers
257
views
Looking for web app resources for symbolic Gaussian elimination
I am looking for a web app software that takes step-by-step directions from a student to perform the linear combination operation on a matrix with symbolic coefficients (as opposed to just numbers). ...
- 1,036
17
votes
4
answers
12k
views
Applications of Vector Calculus to Economics/Finance
I will be teaching a course focusing on multivariable integration soon, for the millionth time. The most difficult topic in such a course is certainly Vector Calculus, by which I mean line and surface ...
-4
votes
1
answer
103
views
Does the "Middle School Mathematics domains" refer to (I) through (V) topics?
Does the "Middle School Mathematics domains" on page 3 of https://www.ets.org/content/dam/ets-org/pdfs/praxis/5164.pdf refer to the the following 5 topics/categories?
(I) Numbers and ...
- 6,110
9
votes
5
answers
4k
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 ...
- 103
5
votes
3
answers
363
views
Modeling vs. Application vs. Context
Our undergraduate mathematics program has recently seen a large drop-off in majors (suspected reason: our growing (but separate) undergraduate statistics program is seen as being a more employable ...
- 6,110
4
votes
2
answers
136
views
The key didactical ideas on mathematical modelling?
This question concerns teaching teachers who often already teach mathematics, but are now studying to get a formal qualification for it, and hopefully some more competency as well.
What are the key ...
- 19
25
votes
14
answers
9k
views
How to teach pure mathematics to a well-educated adult who did badly in maths at school
My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is ...
- 2,536
0
votes
1
answer
84
views
Why do problems should be solved by pen and paper before coding? [closed]
I heard that before you can handle data automatically, you have to know how to handle it manually.
Why is it impossible to find a problem and build some machine learning algorithm to find a proper ...
- 1,556
21
votes
2
answers
2k
views
Can we avoid confusion over using "let" as a quantifier?
I've encountered the following misunderstanding.
I pose a question (to undergraduates in the U.S.), for example:
Let $P$ be a polygon of $n$ vertices.
Is it true that every triangulation of $P$
has ...
- 1,767
1
vote
1
answer
55
views
Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students
Can anyone recommend good and didactic references that delve into the dualism between deterministic and stochastic phenomena? Ideally, I'm seeking materials that provide a conceptual explanation along ...
- 1,556
4
votes
3
answers
318
views
Graphing lines by finding integer points
I always say that the most difficult part of graphing or plotting points is labelling your axis/es. In the case of plotting the graph of a linear equation with integer coefficients in 2 variables it ...
- 7,423
8
votes
2
answers
2k
views
Explaining Sigma-Notation
I attempted to introduce the summation notation $\Sigma$ to my students. The notation was unfamiliar to the students beforehand. I worked through many examples with them, but for most of them, working ...
- 23.6k
19
votes
11
answers
3k
views
Books that every aspirant mathematician should read
I am a student and I would love to become a research mathematician one day.
So I would like to ask you---experts in mathematics but also in
education---what are some influential ($\star$) books that ...
- 105
0
votes
4
answers
326
views
Why are negative numbers introduced before quotients in the real number subsets?
This is a question regarding why the order of the real number subsets commonly used in the mathematics community is such:
$$ \mathbb{N}\subseteq\mathbb{Z}\subseteq\mathbb{Q}\subseteq\mathbb{R} $$
Here ...
- 101
3
votes
2
answers
76
views
Utillizing Lakatos' "Proofs and Refutations" in Secondary Education
These days I am reading Imre Lakatos's Proofs and Refutations and I can't stop thinking how one could utilize it in the classroom (mostly high school). Some stray half-baked ideas I have had so far ...
- 291
1
vote
1
answer
153
views
Is there any university or college in any country where failure and dropout rates in Calculus are not so high?
Calculus is a foundational mathematics course that is often seen as a bottleneck for STEM majors. However, it is also a course that is notorious for its high dropout rates. In the United States, for ...
- 6,110
5
votes
2
answers
466
views
Experimental Evidence that Mathematical Reasoning is Important
Most Standards (e.g. Common Core Standards in the U.S.)
explicitly promote the teaching of “mathematical reasoning”, with a usually vague description of what exactly that is. Does anyone know of ...
- 3,439
13
votes
7
answers
1k
views
What are some good books on mathematical pedagogy?
I suspect that; just as one must "do" mathematics to learn mathematics, one must have practice teaching mathematics to become a great mathematics instructor.
Still, a good book on ...
- 494
4
votes
2
answers
103
views
Recommended online software for Euler method/ODEs
Solving a first order ODE with the Euler method is simple enough, if the student is to do it for a few rounds, however for anything substantial a programmable calculator or access to a programming ...
- 205
6
votes
1
answer
139
views
Remote Teaching by Video Conferencing
I am in my early 70's and licensed to teach 8-12 math in Texas. I have an advanced degree in the same area. I used to teach in high school decades ago but have since quit because the student's ...
- 1,478
-5
votes
1
answer
202
views
references and examples of questions that shows what mathematics is not
there is a large literature about what Mathematics is. but what about what mathematics is not.
for instance the question displayed in the following image is, for me an example of what mathematics is ...
- 1,556
19
votes
5
answers
3k
views
Source of conceptual, multiple choice calculus questions
I'd like to give my Calculus 1 class periodic multiple choice questions that really test conceptual understanding. Ideally, I'd like these questions to require very little computation. I know that a ...
- 19.4k
15
votes
6
answers
2k
views
What is important to keep in mind in grading proof-based courses?
I am an undergraduate grader at my institution where I have been entrusted with grading a section of an undergraduate analysis course; it's usual for this role to be offered exclusively to graduate ...
- 3,626
7
votes
5
answers
3k
views
How to properly define volume for beginner calculus students?
I'm interested in opinions based on experience about how to introduce volume for beginner calculus students. Below I present some observations and specific questions.
In Stewart's book, the volume of ...
- 1,092
24
votes
5
answers
6k
views
Correcting how a student writes symbols
One of my college students writes the Greek letter $\pi$ as a script n with a bar over it, like $\bar{n}$. [There is actual space between the letter and the bar.] I have never seen this before, and ...
32
votes
12
answers
5k
views
For calculus students, what should be the intuition or motivation behind series?
I've noticed that series are one of the most difficult portions of calculus for new students to learn.
I think the level of abstraction has to do with this. Limits, derivatives, and integrals, as ...
- 21
1
vote
3
answers
242
views
Is it correct to state that a cone has no faces?
Faces are attributes of polyhedra, so it doesn't make sense to ask how many faces a cone has.
Are there traditional scholars that use faces attached to cones? How do different countries deal with the ...
- 6,110
0
votes
2
answers
63
views
How to intuitively connect Linear Equation in two variables and the graph of them? [closed]
I struggle with connecting graphs of linear equation with algebraic form like $x+y=p$.
How do I develop the intuition that it represents a line that is sloping down and passes through value $p$ on $y$-...
- 1,556
0
votes
0
answers
30
views
Apps to make mathematics much interesting by sharing creative ideas with others
I think proofs without words is much important topic when we want to improve students interest in subject using their skills other than in mathematics. Recently I could able to find that kind of proof ...
- 727
4
votes
7
answers
265
views
How to convince a student without calculus that great circles are geodesics in a sphere?
how to convince or demonstrate to a high school student who does not know differential and integral calculus that the geodesics of a sphere are arcs of great circles?
- 2,039
5
votes
1
answer
2k
views
In math exams, how rigorous should the questions be?
We have theoretical questions in our exams (often in ABCD format).
For example, I can state the question:
For an indefinite integral, does it hold that $\int f(g(x)) \cdot g'(x) \, dx = \int f(x) ...
- 1,364
2
votes
2
answers
319
views
Geometric line: constructing fractions
I am interested in teaching maths visually. in page 36 of Growing ideas of number (by John N Crossley) the following image appears, yet I cannot fully grasp how to interpreted it.
- 2,404
17
votes
9
answers
7k
views
Why is differential calculus often presented before integral calculus?
Why is differential calculus often presented before integral calculus?
Note: I'm still learning calculus at the moment.
It seems that many elementary calculus texts describe differential calculus ...
- 4,586
1
vote
2
answers
252
views
Responding to students' questions that aren't directly relevant to their exams
What would you suggest as the best way to deal with students' questions that seem irrelevant to their upcoming exams?
When I was studying for my university-entrance exam, I came across a couple of ...
- 727
1
vote
1
answer
91
views
highschool's mathematics journal which citable in Google Scholar
I'm a high school Mathematics teacher and I want to issue some research articles for highschool students to improve their math problem resolve skills. Is there any valuable Math journal for high ...
- 2,039
2
votes
2
answers
214
views
Scepticism as the cornerstone for not making mistakes in arithmetic/algebra etc, especially for students who relentlessly make every possible error
As a maths tutor, some students I have tutored don't just make the odd mistake in arithmetic (including fractions) and algebra: they make every possible mistake and regularly.
My go-to approach for ...
- 777
34
votes
11
answers
2k
views
Epsilons and deltas in a first calculus course
In a freshman calculus course for non-majors;
Is it to the benefit of the students to include discussion of epsilons and deltas?
To what extent, if any, should they be used? For example, just to ...
- 1,660
11
votes
7
answers
3k
views
How can we best motivate the study of polynomials to high-school students?
We all know how important and ubiquitous polynomials are in mathematics. However, when faced with a (not so much in love with the subject) 14-year-old asking us why they should care about these things,...
- 161
3
votes
3
answers
228
views
Is there a preferred way to format a negative exponent?
Say there's an exam question whose answer is $x$ to the power of negative one. Two ways of writing this are $x^{-1}$ and $\frac{1}{x}$.
I know that questions will sometimes request an answer without ...
- 131
-4
votes
1
answer
133
views
How to explain square meters?
How can we explain to students these ideas?
A square with 4 sides measuring 25 cm each does not have an area of 1 square meter.
A shape which is not a square can have an area of 1 square meter.
Is “...
- 777
29
votes
12
answers
8k
views
How to give my students a straightedge instead of a ruler
I'm having a "challenge" in my geometry classes getting students to avoid using rulers as measuring devices in constructions. As natural as that usage is, they're only supposed to use them to connect ...
- 7,423
16
votes
5
answers
471
views
Amount of concrete calculations on board?
Imagine that you are teaching a high school class in the last years of high school, an undergraduate class in university, or you are a tutor of a small group at university.
Should one provide ...
CommunityBot
- 1
2
votes
5
answers
1k
views
At what age are most children able to convert between rational fractions and decimals?
At what age are most children able/taught to convert between rational fractions and decimals?
For example
Convert 0.25 to a fraction consisting only of whole numbers.
What is 3/4 expressed in ...
- 21
11
votes
3
answers
558
views
Terminology for parts of limit notation
When we talk about: $$\lim_{x\to{c}}f(x)=L.$$ Is there a formal name for the number "$c$"?
I know that the notation means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It ...
- 7,423
38
votes
18
answers
9k
views
How do I show students the Beauty of Mathematics?
I teach many high school students, and all of them complain about being unable to fully understand mathematical concepts. I try to show them the joy of learning and deepen their understanding through ...
- 191
3
votes
3
answers
204
views
Relearning math after long COVID using AoPS or developmental math textbooks?
This is a little bit of a niche topic.
I've dealt with a pretty bad dose of long COVID that has caused some serious gaps in my mathematics (basically causing terrible arithmetic skills and a really ...
CommunityBot
- 1
5
votes
0
answers
129
views
Comparison of texbook for "how to write proofs"
I posted this question in the math stackexchange https://math.stackexchange.com/questions/4681694/comparison-of-textbooks-on-how-to-write-proofs and one person suggested that I cross-post it here. I'...
CommunityBot
- 1