All Questions
3,512
questions
0
votes
1
answer
45
views
Interpreting the derivative as instantaneous rate of change in real phenomena
When interpreting the meaning of the derivative in real phenomena, it may seem that the interpretation is in conflict with the definition of the derivative itself. The confusion is caused by the units ...
1
vote
1
answer
28
views
Best category theory textbook for undergraduate students
Title is pretty self explanatory. All recommendations welcome. Comments and answers which reject the premise of the question will be met with eye rolling.
If I don't see a good enough answer I'll have ...
- 252
1
vote
5
answers
131
views
What is an example of something you might see outside of math class and how would you model that thing as a set?
In mathematics, we have sets, such as $\begin{Bmatrix}1, 2, 3 \end{Bmatrix}$ or the real-numbers, usually denoted as $\mathbb{R}$.
When teaching students about sets for the first time, it can ...
- 137
14
votes
3
answers
4k
views
Parentheses around negative numbers
We teach students that a notation like
$$17 - -59$$ is not acceptable or at least not good. Instead we want them to write $$17-(-59)$$
The main reason seems to be that it's more readable if you ...
- 149
0
votes
0
answers
43
views
What books were used to teach the old Scholarship level exams in the UK?
The scholarship level looks like it could have some interesting questions:
https://en.wikipedia.org/wiki/Scholarship_level
Any ideas on what books or resources were used to teach this level?
3
votes
2
answers
254
views
How to teach that $10000x^2$ c$^2$m$^2$ is wrong?
How do you teach to teenagers or kids that if we have a square with side length $x$ m (that is, $100x$ cm), then its area is $x^2$ m$^2,$ but not $10000x^2$ c$^2$m$^2$ ?
- 31
2
votes
4
answers
223
views
Teaching Clifford Algebra Instead of Imaginary/Complex Numbers
For those unaware, Clifford Algebra (also known as Geometric Algebra) is able to generalize vectors and rotations in n-dimensional space, and simplifies a great many formulas. However, I was curious ...
- 1,101
4
votes
2
answers
227
views
Impact of GPT4 and future AI development on math curricula in schools
At least since pocket calculators were available there is an ongoing debate in math education of how meaningfull it is to continue to teach students how to calculations only using a paper and pencil. ...
- 824
1
vote
3
answers
132
views
Questions to test highest level of competency
In mathematics we ask so many types of questions to check the student's knowledge of the subject. More oftenly we ask to define terms, state a formula or application of theorems. What would you ...
- 623
34
votes
14
answers
12k
views
How to give exercises when students can use ChatGPT
I tried some math exercises we will give to students and ChatGPT does really well answering these. It excels at proofs and often gives details that were not our the example solution, and makes some ...
- 418
0
votes
1
answer
131
views
Student finding it difficult to recall theorem exactly
I've been trying to teach my sister school maths, and one difficulty I find is, she is unable to state precise formulation of theorems, and sometimes confuse the assumption and the implication. This ...
0
votes
2
answers
139
views
Multiple proofs for the same problem
One way of encouraging students to explore mathematics can be letting them to use different approaches to solve the same problem. If students can find alternatives from different areas of mathematics ...
- 623
6
votes
2
answers
656
views
Mathematical induction without simplifying equations or inequalities
We discuss lot of questions related to mathematical expressions consisting equations or inequalities in mathematical induction. What are the examples where we can apply mathematical induction as the ...
- 623
4
votes
1
answer
127
views
How do you describe your experience using OER textbooks for calculus?
If you have used commercial as well as OPENSTAX OER textbooks for calculus I would like to know about your experience. How would you compare the two? Were there any disadvantages to using OpenStax?
- 924
2
votes
1
answer
276
views
The effects of telling the public that Mathematics is everywhere [closed]
Question: What are some arguments for and against telling the public that Mathematics is everywhere? I would like to know if there is any evidence that telling the public Mathematics is everywhere ...
2
votes
3
answers
150
views
Geometrical approaches in algebra
Usually we describe proofs in algebra by algebraic means, I think it may be useful to introduce geometrical approaches to those proofs to improve creativity skills of students, what are the examples ...
- 623
13
votes
5
answers
2k
views
When writing log, do you indicate the base, even when 10?
I’ve been working with many students on logarithms and have noted that log has a base of 10 unless specified. Further, I commented that putting a 10 as a subscript to log is redundant, or at least not ...
6
votes
1
answer
415
views
Homework in a Flipped Classroom
I'm in the middle of teaching first-semester Calculus where, for the first time, I'm trying to implement a flipped classroom. (Background: Small university in U.S.; Calc 1 for STEM majors, 50 minute ...
- 6,948
9
votes
5
answers
816
views
What should I call the "important" values of x?
When analyzing the functions
$f(x) = \sqrt{x-5}$
$g(x) = \frac{1}{x-5}$
$h(x) = 2^{x-5}$
we know that it is useful to think about what happens at $x = 5$.
For the function $f$, this logic will ...
- 20.3k
1
vote
0
answers
153
views
What to cover on a first ordinary differential equations module?
I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books, have Laplace Transforms which is fine but I would not use LT to solve ...
- 1,235
7
votes
6
answers
318
views
Pi Day is approaching: What are some interesting math questions whose answer is exactly $\pi$?
In anticipation of Pi Day, which is (of course) March 14, I would like to ask:
What are some interesting math questions whose answer is exactly $\pi$?
The questions can be for any age group.
Of ...
- 609
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?
...
- 365
4
votes
0
answers
116
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 ...
- 924
6
votes
0
answers
99
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? ...
- 924
0
votes
0
answers
81
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 ...
- 623
7
votes
1
answer
200
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 ...
- 1,117
0
votes
3
answers
613
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 ...
- 623
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
197
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 ...
- 623
3
votes
1
answer
327
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 ...
- 199
3
votes
3
answers
186
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 ...
- 167
3
votes
2
answers
628
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
627
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 ...
- 623
0
votes
1
answer
158
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-...
- 829
3
votes
2
answers
152
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
29
votes
6
answers
2k
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 ...
- 20.3k
8
votes
2
answers
210
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
973
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 ...
- 1,748
6
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 $\iff$? Cause that is what let’s them say $-5$ is a solution to ...
- 247
14
votes
8
answers
4k
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
297
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 ...
- 1,358
3
votes
5
answers
451
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 ...
- 249
20
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 ...
- 303
4
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, ...
- 43
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/...
- 924
8
votes
1
answer
187
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 ...
- 3,713
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
2k
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
29
votes
19
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 ...
- 399