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8
votes
0answers
67 views

Analogies for grad, div, curl, and Laplacian?

I want to try making some calculation-less questions about vector calculus identities that are solely based upon picture diagrams of vector fields, or fields that could be sketched out by hand. The ...
2
votes
1answer
120 views

Logic and proofs in secondary school

Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
3
votes
5answers
1k views

How to get better at proofs

As an undergrad student of applied mathematics, I have something to say that make's me ashamed of myself. I suck at proving things in mathematics and i know that if I don't get better in doing this ...
-2
votes
0answers
30 views

Integral of an exponential modulus [closed]

I try to comprehend a step on an integral. The calculation follows: $\int\limits_{0}^{t} \mid \exp{(At)} \mid dt$ I wonder, in complex case, that $\mid \exp(\cdot)\mid$ do not coincide with $\exp(\...
4
votes
0answers
99 views

Ideal Features of Online Homework Platform?

If you could build an ideal online homework platform for mathematics, what combination of features should it have in order to be effective at levels from high school through undergraduate, and why? ...
-5
votes
0answers
19 views

If $x= a\tan^2y+ b\sec^2y$ the find $x+a/x-b$ [closed]

If $x= a\tan^2y+ b\sec^2y$ the find $x+a/x-b$.
1
vote
4answers
181 views

Why is a translated exponential function considered an exponential function?

I am tutoring a student preparing to take Calculus 1 at a university. This student hasn't taken precalculus for a year, so I have been drilling him on definitions, rules, and theorems from a college ...
12
votes
11answers
4k views

When do college students learn rigorous proofs?

I teach in a regional university. In my department, students take their "proof course" (a course that sole focus on writing proofs) in the third or even fourth year. All the courses before ...
3
votes
1answer
126 views

English translation of Sung-Dae Hong's The Art of Mathematics

The Art of Mathematics by Sung-Dae Hong is the standard high-school mathematics textbook in South Korea. The series gets new editions and reprints since 1966. Wikipedia has a page for it. Had it ever ...
12
votes
2answers
217 views

The use of “$\therefore$” and “$\because$”

In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost ...
16
votes
4answers
3k views

What are some of the open problems that can be suitably introduced in a calculus course?

I feel it may be a good idea to introduce some related open problems in a calculus course. Surely I am not expecting my students to solve any one of them, though I cannot say it is absolutely ...
19
votes
5answers
915 views

What are the best practices for giving online tests?

Many of us our coming off our first semester of required-online classes; and at some of our institutions we are preparing for what is most likely a required-online semester in the fall. (That is: The ...
3
votes
1answer
163 views

Help finding good deep mathematics problems

Once, when I Was doing calculus 2, someone challenged me to calculate and prove the Gaussian integral, with a few hints, and a few days, I managed to. It was a great feeling to solve a “deep” multi ...
3
votes
5answers
409 views

Grad school after doing an online bachelor's degree without support for undergraduate research

[I originally posted this is the Mathematics Stack Exchange and was told to post it here instead] This might seem like an odd topic for this forum, but I'm losing my mind. I am about eight months away ...
23
votes
4answers
3k views

What websites allow students to purchase solutions to problems?

I am a college instructor who's just had an outbreak of academic dishonesty connected to students posting take-home exam problems on a platform called Chegg. Chegg collects a membership fee from ...
7
votes
1answer
141 views

Math Education for Students who use Right-to-Left Written Languages

Does anyone know of any studies or have personal experience dealing with difficulties (if any) faced by students studying mathematics if they come from countries which use languages written from right-...
1
vote
2answers
143 views

Workbooks for advanced high school math topics

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them): Logic and sets (propositional calculus, ...
7
votes
1answer
254 views

How, now, shall we teach math online?

Now that everyone has had the experience of teaching math in an online/remote/synchronous/asynchronous format, and looking forward to more of this in the Summer and Fall terms, how do we change our ...
5
votes
4answers
329 views

Falling into the calculus trap

I am a student, in my last year of school(17 years old) When I was about 13 years old I fell into the calculus trap by starting off learning trigonometry on my own, when I was supposed to factor ...
3
votes
4answers
181 views

Textbook to study group theory as a part of Discrete Mathematics

I am a student from CS background. I have been following "Discrete Mathematics and its Applications" by Kenneth Rosen, though it is a good book, but it does not cover group theory. I would like to ...
0
votes
0answers
70 views

Better instruction for an identity equation worksheet

I would like to construct a good worksheet for my students. I am thinking of creating an instruction that will cover all problems related to identity equations. Here is how I initially constructed ...
1
vote
1answer
128 views

Future way of learning mathematics (towards graduate level)

Recently, there is an idea sparkling out from my mind due to the COVID-19 outbreak. In the past, we typically attend a course, complete homework and assignment, then finish the semester with a final ...
4
votes
3answers
126 views

self-reliance and psychology in learning math

It's hard to be more descriptive with the title without making it excessively long. What I'm wondering is this: what is the "right attitude" or "right psychology" when confronted with a mathematical ...
6
votes
5answers
186 views

Concrete way to teach addition and subtraction of fractions

I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...
6
votes
4answers
197 views

What are other strategies for a 7 year old for addition and subtraction besides counting fingers?

We recently received feedback from our 7 year old daugther's school teacher. One of the things mentioned was that our daughter still counts her fingers when she does addition and subtraction. The ...
2
votes
1answer
100 views

Advanced textbook for vector fields [closed]

I am currently reading Spivak Calculus on Manifolds and Munkres Analysis on Manifolds. I am looking for a more advanced text, especially on vector fields as they relate to the great conserved fields ...
3
votes
0answers
93 views

How must the “ungrading” idea be adapted to work in a math class?

After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...
2
votes
2answers
825 views

Curriculum in USA vs. Canada

(1) When do students in Canada learn about the four triangle centres (centers), circumcenter, incenter, orthocenter, and centroid? In the USA (more precisely, Indiana), the math curriculums are by ...
3
votes
1answer
103 views

Refreshing math knowledge

How do I refresh advanced math I learned at a graduate level? I once was able to do the full solution of a particle in a parabolic well and other advanced math, however 20 years later I'm struggling ...
0
votes
1answer
78 views

Applications of unreducible fractions in Basic School

An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (...
6
votes
6answers
831 views

Efficient methods to receive and grade online mathematics assessments?

I am UK-based but I guess this issue currently affects all maths educators and has probably been addressed by those how have been delivering courses through online channels for the past few years. ...
9
votes
1answer
205 views

What are some resources for “ungrading” in a math class?

Most of the stuff I'm finding online about ungrading are either general descriptions of its virtues, or personal accounts from instructors from subjects other than math. Does anyone know any resources ...
4
votes
2answers
139 views

Graphing program for conceptualizing calculus

I'm taking integral calculus at the moment. I was understanding everything quite well until we started learning about finding volume of a solid of revolution. I understand the concept, but practicing ...
1
vote
1answer
109 views

Undergraduate Interview Maths Questions [closed]

I am trying to compile a document of preparation questions to use in mock interviews with students applying to study Maths at top UK Universities. I have many questions already, but it is always ...
3
votes
1answer
105 views

Teaching Approach at primary, middle and higher level

I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre primary) to middle to higher classes. I understand at every level one ...
30
votes
6answers
3k views

How to motivate an adolescent who has fallen behind in conceptual development?

I tutor a 16 year old girl. As far as I can tell, she has average talent and interest in math. However, her knowledge of math is that of a 10 year old or even below. She knows the basic operations on ...
8
votes
4answers
202 views

Math 3d animation software

I am looking for 3d-math animation software that is specifically meant for Visualization: That is geometry-based software that can aid in making visualizations as in https://www.youtube.com/watch?v=...
1
vote
1answer
194 views

What to call a symbol that denotes an “undisclosed” given number? [closed]

Students like to categorize notations to pin down their understanding of exactly what these notations stand for. Thus, given the expressions $f(x_{0})=f(x)|_{x\leftarrow x_{0}}$, $x=x_0+h$, or $lim_{x\...
5
votes
3answers
289 views

Looking for a HIERARCHY of math subjects

If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc. What do you suggest is a good structure, for ...
5
votes
2answers
261 views

Have there been attempts to base early math education on category theory?

The New Math curriculum built math eduction on set theory. Have there been any attempts to do something similar with category theory? I was fortunate to grow up in a relatively enlightened ...
3
votes
1answer
87 views

Is SQL relevant to statisticians' work?

I hope this is the right place for posting this, but if not, please let me know! I recently took a second class in Python programming which, toward the end, also taught a little bit of SQL. As it ...
1
vote
0answers
79 views

Is there a 'statistics theory' course plan for practitioners?

My job is starting to have me delve into categories that require things like regression analyses on data sets, essentially i'm being introduced to "Data Science" type material. Coming from a computer ...
9
votes
2answers
1k views

“Feynman effect” in teaching mathematics

In his book "Surely you're joking Mr. Feynman", Richard Feynman relates the following story. As he was supervising a group of calculators for Manhattan project, he at some point gave them a lecture on ...
16
votes
7answers
3k views

Why do some linear algebra courses focus on matrices rather than linear maps?

I hope the essence of the question is clear from the title. There are obvious advantages to making the linear map the central notion of a linear algebra course: the notion can be illustrated with ...
5
votes
3answers
172 views

Can you ace one branch of math, while bumbling another branch? [closed]

This r/math post spurred this question. To concretize the meaning of "ace", assume success means earning professorial tenure at a Top 100 world university. your liked stronger branch doesn't exactly ...
20
votes
1answer
471 views

How do I track down the sources of solutions which students have used to cheat on exams?

I recently taught an introduction to real analysis. I assigned a (covid-induced) take-home final, which included the question: Define the set S by $$ \bigcup_{n=1}^\infty \left\{ \frac{a}{2^n}\...
6
votes
1answer
164 views

Solving open problems through a misunderstanding

We all know the (apparently verified1) anecdote recounting George Dantzig arriving late to a lecture (by Jerzy Neyman), and later solving two open problems written on the board, mistaking them for ...
-4
votes
1answer
90 views

Legality of posting dictated video of publisher's slides [closed]

I typically will write my own slides for a course, and then may make a screen recorded video of me talking over the slides. Now I'm planning on doing a screen recording over slides the publisher has ...
18
votes
6answers
5k views

How rigorous should high school calculus be?

In the UK, calculus taught in secondary school focuses mainly on computation of derivatives and integrals and solving simple differential equations. There is a small amount of discussion about limits ...
12
votes
1answer
699 views

Proof by contradiction - more than one case

I am looking for some examples of when proof by contradiction is used in a problem with more than one case. In all the elementary examples, there are only two options (eg rational/irrational, ...

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