All Questions
3,625
questions
4
votes
1
answer
158
views
Does there exist a (statistic) topology induced by students on the space of algebraic formulas? :)
It's kind of a serious question even if the title seems silly.
As math educators, we all know that students link together different algebraic expression thinking that they mean the same thing, e.g.
\...
- 713
1
vote
1
answer
46
views
Sourcing and verifying calculus applications
There are many questions on this site about specific (or not-so-specific) applications of calculus to the "real world". However, one issue I've noticed in using textbooks for this purpose ...
- 5,962
1
vote
2
answers
81
views
Antiderivative of $1/x$, with or without absolute value?
Many textbooks include $\int \frac{1}{x} dx = \ln |x| + c$ in their list of antiderivative formulas, with the absolute value. Correspondingly, they do the same with the antiderivative of $\tan x$ or ...
- 11
1
vote
3
answers
108
views
Plainly by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{dodgerblue}{|\vec{b}| - |\vec{r}|}$?
Yearly, I teach 16 year olds this diagram beneath (improvement of this) that reappears on standardized tests IN BLACK AND WHITE below with different lengths, letters, and orientation. Tests require ...
- 25
9
votes
5
answers
2k
views
Is there a resource for learning to read mathematical notation/equations/formulae?
Ideally, I am looking for an online resource. But a book or any other would help already.
Background: I am a senior teaching assistant in the field of business and statistics. Most of my students have ...
1
vote
1
answer
71
views
What can be considered as common knowledge in an online Mathematics course?
As I prepare to instruct an online Mathematics course next year, I'm currently writing the syllabus. Right now, I'm writing about student participation in the Learning Management System, which takes ...
- 11
2
votes
5
answers
904
views
Geometrical verifications for Algebraic formulae
What is the importance of using approaches related to Geometric Algebra in teaching,is it only useful when introducing Algebra to the students or can it be helpful to improve creative skills in ...
- 755
1
vote
2
answers
142
views
I'm in dilemma while solving arithmetic problems [closed]
I'm competitive exam student learning Quantative aptitude what should i choose over solving more questions and skipping the one i can't solve or spending hours on one question till i solve it and then ...
- 11
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 ...
- 921
1
vote
4
answers
200
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 ...
- 147
-4
votes
1
answer
105
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 ...
- 95
4
votes
2
answers
144
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 ...
- 6,129
0
votes
1
answer
88
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 ...
- 19
1
vote
1
answer
58
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 ...
- 1,802
6
votes
7
answers
509
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 ...
- 427
4
votes
3
answers
361
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 ...
- 927
3
votes
2
answers
77
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 ...
- 1,120
9
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 ...
- 193
1
vote
1
answer
157
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 ...
- 1,802
4
votes
3
answers
259
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
0
votes
4
answers
338
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 ...
- 29
-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 ...
- 1,802
6
votes
1
answer
141
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 ...
- 161
4
votes
2
answers
105
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 ...
- 1,036
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 ...
- 231
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 ...
- 253
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 ...
- 8,856
1
vote
3
answers
243
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 ...
- 1,802
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
0
votes
0
answers
32
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 ...
- 755
0
votes
2
answers
65
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 $y$-...
- 361
2
votes
2
answers
321
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.
- 147
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) ...
- 167
4
votes
7
answers
269
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?
- 1,802
2
votes
2
answers
218
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 ...
- 925
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 ...
- 11
3
votes
3
answers
229
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
1
vote
2
answers
254
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 ...
- 755
9
votes
0
answers
125
views
Course materials for developing a mathematical theory from "natural questions to ask"
Educational setting.
I'm teaching math courses - typically consisting of lectures, weekly homework sheets, and an exercise class where the homework questions are discussed - for undergraduate and ...
- 1,637
-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 “...
0
votes
1
answer
214
views
Limitations of applying the factor theorem
Here are three situations in which students might try to apply the factor theorem.
Proving that $x + 1$ is a factor of the polynomial $x^3 + x + 2$ can be done using the factor theorem by showing ...
- 755
7
votes
3
answers
993
views
What are the different ways that teachers' conceptions of mathematics can influence students' learning?
I'm looking for studies on how and to what degree a teacher's conception of what mathematics is influences their way of teaching and, in the case of students, how this conception influences their ...
- 1,802
7
votes
5
answers
2k
views
Should I really just "shut up and calculate"? On learning at a good pace without sacrificing rigour
This question is about getting realistic expectations for how a university student actually does and should learn maths. I'm becoming increasingly suspicious that my approach is detrimental, but I don'...
- 448
9
votes
5
answers
1k
views
Models for spherical geometry
Context: I am an associate professor at a small liberal arts institution in the US.
I am currently preparing to teach geometry this fall. Our course is mostly focused on Euclidean geometry (it's ...
- 1,339
1
vote
0
answers
61
views
If a student earns a non-ABET accredited engineering degree, when can they take the FE or PE exam?
I just recently had a student (U.S. university) ask "How long would I have to wait until I could be eligible to take the FE or PE exam if I earned a non-ABET accredited engineering degree?" ...
- 71
1
vote
1
answer
209
views
A Question about Answer Keys
I am a HS math teacher and just started a job that adopted a new curriculum at the last minute. It gave us the tasks but did not provide any answer keys. Of course, I know how to work through the math ...
6
votes
4
answers
634
views
What mathematical topics are important for succeeding in an undergrad PDE course?
I am a student helping to develop a remedial course for other students who have recently failed the undergraduate PDE course at our university. The topics are provided from the syllabus in the ...
- 71
0
votes
1
answer
163
views
What would constitute as a good justification of why a divergent limit is divergence for highschool teaching?
For example, consider $\lim_{x \to -\infty} \frac{x}{e^x}$, what would constitute as a good justification that the limit diverges too infinity?
It's pretty easy to justify convergent limits ...
7
votes
3
answers
2k
views
What's it called when multiple concepts are combined into a single problem?
A lot of students complain about "never being shown that before". What's the idea called when you test multiple concepts or one or two new ones along with some old ones in a word problem, ...
- 303
1
vote
1
answer
162
views
Are there differences between graphs, diagrams and charts?
"Can you explain the distinctions between graphs, diagrams, and charts, and provide definitions for each of these concepts? Specifically, is every graph considered a diagram? Are graphs ...
- 1,802