All Questions
3,690
questions
11
votes
4
answers
4k
views
Is there a fair way to increase the grade of students who did not do well in exams?
How can I fairly compensate a student who showed passion and dedication for my undergraduate course but performed poorly on the final exam, without unfairly advantaging them over other students?
...
- 569
5
votes
0
answers
126
views
Is it possible to learn some basic mathematics using an app?
I am interested in developing an app for students that are starting a grade career involving mathematics. It is a real problem that they start with almost no knowgladge of basic mathematics and there ...
11
votes
2
answers
2k
views
How do/should administrators estimate the cost of producing an online introductory mathematics class?
With the advent of the Internet administrators used to allocate release time or summer salary for making online course content. The pandemic made a Sal Khan out of most of us and making online content ...
- 1,084
6
votes
0
answers
104
views
Is there ADA-compliance certification for mathematics text books?
What factors are there to consider when adopting a text as far as ADA (Americans with Disabilities Act) is concerned? Is there a certification? What do you look for in the digital version of the text? ...
- 1,084
0
votes
1
answer
136
views
Online platforms for teachers to discuss matters related to mathematics
As we all agree mathematics educators community is doing a great service as an international platform regarding teachers issues related to mathematics education. Not all but only personally motivated ...
- 955
7
votes
1
answer
1k
views
Difference between the Cambridge IGCSE 0580 and 0607 mathematics courses
I am a high school mathematics teacher, in our school students take the Cambridge IGCSE 0580 exam. After IGCSE our school offers the IB Diploma programme and I am thinking about proposing the ...
- 1,228
0
votes
3
answers
743
views
Definite integrals with equal limits
As a property of definite integrals, we teach that definite integrals are zero if the lower and upper limits are the same (Wolfram mathworld says this too). Is this valid in general?
In the case of ...
- 955
7
votes
4
answers
2k
views
If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
I’m currently getting my Master’s in Math at Portland State University so that I can teach community college mathematics. I’m specifically hoping to teach calculus, statistics, and linear algebra, so ...
- 261
2
votes
2
answers
303
views
Lateral thinking in mathematics
Especially in mathematics, we give a set of definitions and rules, and ask our students to prove a particular statement or to solve equations or inequalities.
By this kind of system we limit students ...
- 955
3
votes
1
answer
361
views
Best demonstration of $\pi$ ever; is this common?
When I was in 6th grade (U.S. so 12-13 years old), I took a summer school class. The teacher gave us all different sized spools (spools that hold sewing thread but were empty). We each made a mark on ...
- 229
3
votes
3
answers
219
views
Applications of Triangle Inequality for high-school students?
The Triangle Inequality ($|x+y|\leq|x|+|y|$) is useful later on in the student's math education (e.g. in proving results about limits).
But for the high-school student, are there any useful and ...
user18187
3
votes
2
answers
660
views
Elementary Teacher Math specialist/ Basic Math Minor
I'm the math department chair at a small university. Our general education program is non-traditional. The university is split into three areas. Students are expected to complete a major in one of the ...
- 121
6
votes
3
answers
789
views
Composite functions
How would you describe the existence of a composite function $f(g(x))$in terms of range of $g$ and domain of $f$ . Does range of $g$ need to be subset of domain of $f$ or is it sufficient if the two ...
- 955
0
votes
1
answer
211
views
How to formalize high-school (Euclidean) geometry?
I have unsuccessfully attempted several times over the years to formalize high-school (Euclidean) geometry, or even a working subset of it. Think very simple, diagramless geometry.
The usual two-...
- 1,074
3
votes
2
answers
159
views
Word for an object being extended: Given F, a function that extends F is called an extension and F is called the extension __?
If a field L extends a subfield K then L is called an extension of K and K is called the extension's base field. See extension field for a definition.
What is the analog of "base field" when ...
- 31
30
votes
6
answers
3k
views
f(x+h) in the difference quotient
When teaching students how to compute the difference quotient in a precalculus or calculus class, we need them to evaluate the expression
$$\frac{f(x+h) - f(x)}{h}$$
for various simple functions, like ...
- 21.2k
8
votes
2
answers
230
views
A few quick sentences to inspire an 8 year old in Maths
I have always been passionate and fascinated with maths, my job revolves around the subject, but I'm not an educator. Today I met the 8 year old son of a friend, I had the opportunity to speak to him ...
- 81
5
votes
1
answer
1k
views
Law of large numbers as a middle school topic?
My daughter (a biologist) is presently teaching also math at a middle school (9th grade, so about 14 years olds). Now the topic in probability seems to be the law of large numbers! More and more I ...
- 1,758
7
votes
4
answers
4k
views
What implication arrows, if any, should I require in teaching?
Q: Solve $x+5=0$.
A: $x+5=0\implies x=-5$.
This answer would be given full marks.
Isn’t it better to tell students to use $\equiv$ or $\iff$? Because that is what lets them say $-5$ is a solution to ...
- 257
14
votes
8
answers
5k
views
Teaching math too soon in middle school and high school
I'm a retired university math prof and I now have a retirement job teaching at a small private high school. This is my 4th year. This school teaches Algebra 1 to 8th graders. Geometry to 9th ...
- 481
2
votes
1
answer
353
views
Do Greek students use Greek letters to denote angles?
In western schools is a tradition to use Greek letters to denote angles. I wonder what about Greek schools do they also use Greek letters to denote angles or do they prefer other kind of alphabet to ...
- 1,931
3
votes
5
answers
508
views
Why do we explicitly state the equality of two things when we know they're equal
Recently my brother in high school and I were talking about some math when he said
If we know two things are the same i.e. equal why do we need to state
that they're the same? What he was trying to ...
- 447
21
votes
7
answers
2k
views
Is there a canonical name for a polynomial-like expression allowing for negative powers?
When introducing the techniques of differentiation, polynomials come up all the time as great examples to familiarize students with the "power rule" and the linearity of differentiation.
A ...
- 313
3
votes
3
answers
1k
views
How to teach using brackets in sums?
How one should teach using brackets in summation?
For example, why is it correct to write $\sum_i a_ib_i$ but $\sum_i a_i+b_i$ should be written as $\sum_i (a_i+b_i)$ But $\sum_i\frac{a_i+b_i}{2}$ is, ...
- 41
6
votes
3
answers
3k
views
Are there examples of central symmetry, without axial symmetry, in nature?
Examples of axial symmetry abound, but I could not find an example of pure central symmetry (that is, without axial symmetry)! Do you know of any? A butterfly shows axial symmetry, what shows point/...
- 1,084
7
votes
1
answer
215
views
Research into how students read algebraic expressions
In answering another question What is the justification to teach the (redundant) use of parentheses in multiplications? I was left wondering what we actually know about students' progression in terms ...
- 3,982
6
votes
1
answer
1k
views
What is the justification to teach the (redundant) use of parentheses in multiplications?
Example: 5 x 18 = (5 x 10) + (5 x 8) instead of 5 x 10 + 5 x 8?
- 61
9
votes
4
answers
3k
views
Should math for elementary teachers content be taught under the direction of the math department?
I recently was appointed math department chair at a small university. We have a 3 credit math for elementary teachers content course. Administration told us they will change this course into an ...
- 121
31
votes
20
answers
8k
views
‘Lies to children’ in mathematics and statistics education
In teaching, we sometimes necessarily oversimplify concepts. Terry Pratchett famously referred to this as Lies to children:
A lie-to-children is a statement that is false, but which nevertheless ...
- 419
1
vote
2
answers
381
views
When teaching online, how does the teacher teach visual concepts?
What would one suggest for online math teaching to draw diagrams? Is Tikz or Matplotlib too slow for helping to visualize problems during the lesson?
- 21
3
votes
2
answers
333
views
Common mistakes in probability
$\DeclareMathOperator\Var{Var}\DeclareMathOperator\Bern{Bern}\DeclareMathOperator\Pois{Pois}$Question: What not-trivial mistakes do students often make when solving problems in probability theory, ...
- 179
2
votes
2
answers
285
views
Introduction of group action as morphism of groups
The usual definition of a group action is as follows.
Let $G$ be a group and $A$ be a set. An action of $G$ on $A$ is defined to be a map $\rho:G\times A\rightarrow A$ satisfying certain conditions.
I ...
1
vote
1
answer
98
views
Best Free Direction Field Plotter?
Can you recommend one for a first or second year calculus course?
Ideally the website that can plot direction fields:
is free
is 100% WYSIWYG (does not require any coding or markup or anything of the ...
- 564
3
votes
3
answers
216
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 ...
- 369
0
votes
2
answers
188
views
Example of a phenomenon from real life where there is a limit going to infinity
I haven't been able to find examples in real life where we have a function or sequence such that the limit goes to infinity when the independent variable goes to infinity. The only one so far is ...
- 121
13
votes
9
answers
1k
views
Is it meaningful to add a number to itself a fractional number of times?
(Migrated from the math stack exchange, where I received an apt-seeming suggestion to pose the question here, at the math-educators stack exchange)
I introduce my young kids to basic math concepts in ...
- 293
4
votes
1
answer
622
views
How does learning math differ from learning second foreign languages (L2)?
Peer-reviewed publications analogize learning math to learning a L2. But what are the DisAnalogies and CounterArguments? How can you distinguish learning math from learning L2?
Luciana Oliveira, ...
- 357
1
vote
2
answers
220
views
A high school level proof that $a/b > 0$ [closed]
Is there a high school level proof of the following?
If $a,b > 0$ then $a/b > 0.$
- 311
11
votes
3
answers
2k
views
Arithmetic books for adults
I'm trying to learn arithmetic from scratch again. Even though I can use it, I'm not sure if I can teach it to someone and I believe if you can't teach something properly, there might be loopholes in ...
- 447
0
votes
1
answer
216
views
Which are the most used Greek letters in math textbooks?
I am looking for a list of the most frequent Greek letters used in high school and college textbooks or some other corpora. I've realized my students don't know Greek letters and I would like to teach ...
- 1,931
8
votes
4
answers
293
views
Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?
I sometimes come across equations like
$x^\circ = 180^\circ - \frac{360^\circ}{n}$
where I would write
$x = 180^\circ - \frac{360^\circ}{n}$,
or like
$3 \text{ cm} + x \text{ cm} = 5 \text{ cm}$
where ...
- 1,881
12
votes
6
answers
5k
views
Is patching up a student's poor solution better than providing a good solution?
A student benefits from their attempt at a solution or proof being checked by the teacher. My own view is that, if the student's work is poor, it is best just to provide a model solution or proof in ...
- 249
4
votes
2
answers
413
views
Proof by Contradiction vs. Proof of Negation
In constructive mathematics we make a distinction between "proof of negation" and "proof by contradiction". You can read a great account of the difference in this blog post of ...
- 24.4k
2
votes
2
answers
229
views
How to introduce the use of Greek letters in high school?
I am looking for any hints or experience reports or materials/potential difficulties about how to introduce the use of Greek letters in high school Math/Physics.
- 1,931
3
votes
3
answers
521
views
What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?
The following is an elementary-level Math Kangaroo multiple choice question:
What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?
A. 9
B. 10
C. 11
D....
- 39
27
votes
6
answers
4k
views
Students confusing "object types" in introductory proofs class
In my intro to proofs (and discrete mathematics) class, I see a common mistake where students make nonsensical statements because, for lack of a better term, they confuse the types of the mathematical ...
- 381
11
votes
7
answers
1k
views
Introductory Books easier than Dover
I'm looking to books introducing different topics of math with fun for my son, to give him a taste of different areas.
My son roughly understands A-level topics until single variable calculus (of ...
- 655
0
votes
1
answer
112
views
Where can I find a summary of typical material (e.g., mathematics) taught in US elementaries and high schools?
The reasons for my question are complicated but basically I need information about different subjects, mostly languages (Eng, Spa, Fre), math, and sciences, as taught in different grades in elementary/...
- 11
1
vote
0
answers
122
views
Math curricula\programs or any experience using "The Road to Reality" as the\a primary textbook
Primarily a reference request, collaborator search-tips requests, and question-improvement request (including improveent by deletion and re-posting to more appropriate stack, meta, wiki, etc). Rank ...
29
votes
6
answers
2k
views
Calculus problems arising from real research problems
I am visiting my in-laws for the holidays. My sister in law is a statistician. She asked me to take a stab at a calculus problem which was coming up in her research. The Lambert $W_0$ function is ...
- 24.4k