All Questions

Filter by
Sorted by
Tagged with
0 votes
1 answer
140 views

‘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 ...
user avatar
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 ...
Nate Armstrong's user avatar
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 ...
Joel Croteau's user avatar
3 votes
0 answers
64 views

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 ...
Labba's user avatar
  • 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 ...
Davis Yoshida's user avatar
2 votes
0 answers
131 views

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 ...
Maesumi's user avatar
  • 1,084
3 votes
0 answers
123 views

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 ...
KCd's user avatar
  • 3,258
2 votes
1 answer
172 views

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 ...
Janaka Rodrigo's user avatar
2 votes
1 answer
180 views

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-...
Ashish Shukla's user avatar
16 votes
7 answers
5k views

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 $...
user avatar
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 ...
FoiledIt24's user avatar
  • 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 ...
Janaka Rodrigo's user avatar
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?
The Real Masochist's user avatar
1 vote
2 answers
118 views

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 ...
Clive Long's user avatar
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 ...
Aeryk's user avatar
  • 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 ...
Timothy Chow's user avatar
0 votes
1 answer
58 views

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,...
Humberto José Bortolossi's user avatar
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 ...
Humberto José Bortolossi's user avatar
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 ...
Humberto José Bortolossi's user avatar
5 votes
0 answers
143 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'...
underflow's user avatar
  • 151
3 votes
2 answers
189 views

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 ...
Paul's user avatar
  • 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 ...
Oofy2000's user avatar
  • 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 ...
user2676187's user avatar
4 votes
1 answer
184 views

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 ...
user929304's user avatar
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 ...
Janaka Rodrigo's user avatar
3 votes
1 answer
145 views

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 ...
Humberto José Bortolossi's user avatar
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 ...
faceclean's user avatar
  • 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 ...
Mahdi Majidi-Zolbanin's user avatar
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 ...
Dan Christensen's user avatar
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 ...
Mahdi Majidi-Zolbanin's user avatar
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 ...
cheyne's user avatar
  • 250
0 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 ...
Samuel Muldoon's user avatar
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 ...
realGottlob's user avatar
0 votes
0 answers
88 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?
Convex Leopard's user avatar
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$^2$ ?
guest's user avatar
  • 41
1 vote
4 answers
401 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 ...
johnnyb's user avatar
  • 1,217
5 votes
1 answer
354 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. ...
Julia's user avatar
  • 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 ...
Janaka Rodrigo's user avatar
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 ...
allo's user avatar
  • 476
0 votes
1 answer
171 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 ...
tryst with freedom's user avatar
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 ...
Janaka Rodrigo's user avatar
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 ...
Janaka Rodrigo's user avatar
4 votes
1 answer
153 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?
Maesumi's user avatar
  • 1,084
1 vote
1 answer
345 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 ...
Mahdi Majidi-Zolbanin's user avatar
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 ...
Janaka Rodrigo's user avatar
14 votes
5 answers
3k 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 ...
JTP - Apologise to Monica's user avatar
7 votes
1 answer
465 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 ...
Aeryk's user avatar
  • 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 ...
Chris Cunningham's user avatar
1 vote
0 answers
169 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 ...
matqkks's user avatar
  • 1,245
7 votes
6 answers
374 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 ...
Dan's user avatar
  • 821

15 30 50 per page
1 2 3
4
5
74