All Questions
3,690
questions
0
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1
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140
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‘Induction on’ vs ‘Induction with respect to’ in math
I heard one mathematician who said “induction on 𝑛” and another who said “induction with respect to 𝑛”. Do these two expressions mean exactly the same thing mathematically?
If so, then are they ...
guest
4
votes
4
answers
333
views
Good analogies for teaching error correcting codes
I'm trying to find a good real-world analogy (or even good visualization) for teaching about error correcting codes and erasure encodings. The most natural way to talk about it really is in terms of ...
- 143
19
votes
4
answers
4k
views
Why do we teach linear algebra in precalculus classes?
When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't ...
- 307
3
votes
0
answers
64
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Are there any fun toy applications of representation and character theory for finite groups to physics?
Representation theory has very deep ties with physics, leading to incredibly profound and admittedly cool results such as the classification of particles in the Standard Model via mass and spin by ...
- 131
3
votes
0
answers
175
views
Assigning essays in take home exams
I was talking to a college student I know who is currently taking linear algebra. He told me that during his take home midterm/final exams he was assigned essay questions, which surprised me quite a ...
- 211
2
votes
0
answers
131
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What is the origin of "Core Assessment" for freshman university classes?
As a math faculty in a public institution in TX, USA, I am supposed to conduct a "Core Assessment" for most of my freshman classes. This typically entails an assignment to be completed by ...
- 1,084
3
votes
0
answers
123
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congruency: how widely used?
Today I was made aware of the term "congruency" as a word related to congruence in the same way that equality is related to equation. I have never seen the term "congruency" used ...
- 3,258
2
votes
1
answer
172
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Importance of etymological approach to terminology
Here I have two issues related to this post.
How can etymological approach to a language be used to improve creativity skills of mathematics in students;
I think, knowing the evolution which has ...
- 955
2
votes
1
answer
180
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Rediscovering euqation of line [closed]
I am studying (self learner) linear equations/equation of line and my idea is to discover the equations myself rather than try and understand ready-made equations available in text books. I am using X-...
- 345
16
votes
7
answers
5k
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Why don’t we teach a topological view of continuity instead of epsilon-delta?
I would like a critique of this approach to teaching continuity to calculus 1 students.
Show them that for an increasing function on (a,b) we have that (a,b) is contained in the set of solutions to $...
user22312
11
votes
5
answers
1k
views
Are Error-Analysis Lessons Effective?
I recently came across a thought-provoking video where Simon Sinek explains that the human brain struggles to process negative statements. In the video, Sinek states that skiers should not spend their ...
- 1,283
0
votes
2
answers
272
views
Differentiation in integer solutions
What would you suggest as examples to demonstrate as applications of differentiation in finding integer solutions of an equation for advanced level students?
Here you have one example which I have ...
- 955
2
votes
1
answer
193
views
What is the terminology for integers with the same oddness or evenness?
If two integers are either both negative or both positive, we can say they have the same sign.
How about two integers that are either both odd or both even? Is there any term for them?
1
vote
2
answers
118
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Any online resources explaining why rearrangement of terms occurs in a particular order
Does anyone know of links to resources to explain why basic algebra rearrangement operations take place in a certain order?
A simple, seemingly absurd example, but not uncommon follows.
Say the ...
- 532
1
vote
1
answer
51
views
Discrete Probability Modeling with Desmos or Spreadsheets
In my Finite Math course* almost every section includes a part where students have to create a file (from scratch) in Desmos or in Google Sheets. For example, they use Desmos to plot piecewise linear ...
- 7,500
18
votes
7
answers
3k
views
Do any middle-school texts indicate that irrationality requires proof?
I believe that most middle-school math curricula have at least a brief section about irrational numbers, in which students are taught (among other things) that $\sqrt{2}$ is irrational and $\pi$ is ...
- 493
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votes
1
answer
58
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What are "must read"/classical refences on data aggregation/disaggregation in statistics?
I am looking for "must read"/classical references on data aggregation/disaggregation in statistics, particularly, what they are exactly, why they are done and how statistical measures (media,...
- 1,931
1
vote
0
answers
99
views
simpson paradox in classroom: reports?
he Simpson's Paradox is a statistical phenomenon in which a trend or relationship observed within a dataset disappears or reverses when the dataset is divided into smaller groups. It occurs when a ...
- 1,931
3
votes
5
answers
878
views
Simple examples of how a good notation or diagram can help to solve math problems
I am looking for simple examples of situations where a good notation/diagram was fundamental for solving an elementary problem in mathematics (I am looking for examples accessible to a basic school ...
- 1,931
5
votes
0
answers
143
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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'...
- 151
3
votes
2
answers
189
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What is a theoretical contribution in mathematics-education research?
I am an early-career mathematics-education researcher. Recently, I received a request for major revisions for a manuscript I had submitted on opportunities to learn provided by undergraduate ...
- 39
2
votes
2
answers
638
views
Process of finding limits for multivariable functions
I was tutoring a student today and they asked a question which made me curious.
We were working on the following question together.
After explaining that we must look at the limit along the x axis, I ...
- 153
1
vote
2
answers
640
views
Is Morris Kline's 'Calculus: An Intuitive and Physical Approach' a Good Book to Learn Calculus From ?'
Would I have to read a standard textbook in addition -- i.e., Stewart, etc. -- or would this be sufficient ? My interest is in applications (dynamical systems theory and physics in general).The book ...
- 11
4
votes
1
answer
184
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Resources for teaching decimal numbers
I am currently teaching special classes to students whose ages range from 11 to 15 and there is quite a wide spectrum in their levels of maths. The lessons are given in English and we do not have a ...
- 243
1
vote
1
answer
567
views
Triples or triplets in Pythagoras theorem
We usually say (3,4,5) , (5,12,13) as Pythagorean triples. What is much better way to refer those sets of numbers, Pythagorean triples or Pythagorean triplets?
According to the normal usage we say ...
- 955
3
votes
1
answer
145
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What is the best didactical way to read decimal numbers?
What is the best didactic and number sense-promoting method for reading decimal numbers?
For instance, is it best to teach students to read the number 3.14 as 'three and fourteen hundredths' instead ...
- 1,931
8
votes
4
answers
2k
views
Seeking Advice on Allowing Students to Skip a Quiz in Linear Algebra Course
I am currently teaching a linear algebra course at a university and have chosen to assess my students using five quizzes throughout the semester, instead of assigning homework. I have encountered a ...
- 537
4
votes
0
answers
166
views
Studies on the change in effectiveness of pedagogical practices over time
Are there any studies that have investigated this question?
Why certain pedagogical practices that used to be effective up to a few years ago, may suddenly become less or even no longer effective?
I ...
- 1,019
2
votes
4
answers
487
views
A better example of a logical implication
(Updated)
An example of a logical (material) implication that is commonly used is: "If it is raining outside, then the ground is wet." The problem with this example is that it could be ...
- 1,074
3
votes
3
answers
339
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 ...
- 1,019
0
votes
4
answers
415
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 ...
- 250
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votes
5
answers
196
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 ...
- 183
14
votes
4
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
88
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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
3
answers
436
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$^2$ ?
- 41
1
vote
4
answers
401
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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 ...
- 1,217
5
votes
1
answer
354
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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. ...
- 1,128
1
vote
3
answers
156
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 ...
- 955
37
votes
14
answers
13k
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 ...
- 476
0
votes
1
answer
171
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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
159
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 ...
- 955
5
votes
2
answers
681
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 ...
- 955
4
votes
1
answer
153
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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?
- 1,084
1
vote
1
answer
345
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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 ...
- 1,019
2
votes
3
answers
168
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 ...
- 955
14
votes
5
answers
3k
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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 ...
7
votes
1
answer
465
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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 ...
- 7,500
8
votes
5
answers
872
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 ...
- 21.2k
1
vote
0
answers
169
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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 ...
- 1,245
7
votes
6
answers
374
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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 ...
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