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votes
1answer
43 views

How to improve mathematical skills(University level)?

I am doing Ph.D in Mathematics, I feel I lack few of the skills, if I can improve those skills I think I can do better as a Math scholar. I need some suggestion on these following(below I am talking ...
8
votes
2answers
111 views

Instilling a Growth Mindset in a Student Diagnosed With Dyscalculia

I have had two students so far with a documented disability called dyscalculia. However, I am a strong proponent in the idea that our primary goal as educators should be the development of something ...
0
votes
1answer
57 views

Calculus book for basic calculus and repetition from videregående

Does there exist a textbook in Norwegian (bokmål and nynorsk should both be fine) that covers the more advanced mathematics (needed for calculus) from videregående (secondary school, includes both ...
0
votes
1answer
66 views

High school maths textbook for talented students

I am looking for a math textbook. I'm 15 and I'd like to complete algebra 2 geometry and perhaps something about probability/ number theory or trigonometry would be nice too. Later I wanna do ...
2
votes
1answer
69 views

Applied ODEs for Numerical Methods

I am looking for a list of ODEs to use as examples in the teaching of a numerical methods course for engineers. I am looking for first and second order examples - the more applied (to engineering) ...
1
vote
1answer
88 views

Questions about the calculus AP [on hold]

I'm not sure if this is the proper place to ask this question, but I figured I'll try anyway. If I have the option of taking a Calculus AP class, and am thinking of pursuing a career in either ...
0
votes
1answer
70 views

Proper paper for exercises and exams [closed]

Does it matter what paper students use for handwritten exercises and exams? Should some sort of grid be allowed or recommended? Should it be enforced across the whole class?
3
votes
1answer
82 views

Are there any math journals or magazines with math problems for middle school or university?

Are there any math journals or magazines with math problems for middle school or university ?
-6
votes
0answers
41 views

Value out of percentage with existing value [closed]

Please help to find a right problem equation to solve this task.
25
votes
12answers
6k views

How to give my students a straightedge instead of a ruler

I'm having a "challenge" in my geometry classes getting students to avoid using rulers as measuring devices in constructions. As natural as that usage is, they're only supposed to use them to connect ...
7
votes
3answers
191 views

Would a 1990's educated person need additional content knowledge to tutor high school mathematics today?

Have there been any major content (not pedagogy) changes in the basic US high school mathematics curriculum since the mid-1990's? More specifically, if I wanted to become a tutor of high school math ...
0
votes
1answer
92 views

Is “The Petersen Graph” by Holton and Sheehan a good text for graph-theory students? Any requisite knowledge for mastering the text?

This book has been recommended to me by a guiding hand/mentor mathematician when I showed interest in his field, and he seemed to really like this book however he doesn't really know me and my ...
0
votes
0answers
28 views

Using mathjax on a standard PC [closed]

Are there any apps or downloadable programs that allow the use of mathjax on a computer - making it easier to type up equations and problems?
4
votes
2answers
1k views

Asking students to define “unique”

Context: This is for introductory linear algebra course, near the beginning. As a sort of "exit survey" after one of my lectures, I would like to ask my students to try and define what "unique" is ...
5
votes
4answers
143 views

Pedagogical considerations behind current order of presentation of trigonometry

A pre-calculus book (Precalculus ed 1 By Miller and Gerken), presents trigonometry in the following order: 1- Angles 2- Trigonometric functions defined on the unit circle 3- Right triangle ...
4
votes
1answer
73 views

Can anyone recommend good software for verifying row reduction steps?

I work as a tutor for linear algebra. Students will often have a problem that requires them to row reduce, and they'll make an arithmetic mistake somewhere. Often they'll ask for my help finding ...
4
votes
0answers
89 views

The word “numeral”, is it being taught and does the word exist for it in your language?

I am a mathematics educator from Lithuania and I have recently realized that there is no separate word in our language for the word "numeral". To be more precise there is no term to describe the ...
2
votes
7answers
196 views

How to show $3(\log_2 n)^5 < \sqrt{n}$

I am teaching final year high school students and needed to persuade them of the following fact: There exists an $n_0 > 0$ such that for all $n>n_0$, $$3(\log_2 n)^5 < \sqrt{n}$$ Plotting ...
10
votes
5answers
799 views

A different symbol for the indefinite integral/antiderivative?

Examples. An indefinite integral (or antiderivative) of $\cos$ is $\sin$: $$\int \cos = \sin.$$ Edit: There has been much unexpected confusion with the above statement. I define the above statement ...
3
votes
3answers
106 views

How to choose random student to answer questions?

I would like to choose some random students in class to answer questions. I don't want to make some students feel that they are targeted. So I used to use a software to choose random student name. ...
1
vote
2answers
54 views

Retain problems and combat regression in learning

Regressive Learning It's a really stressful situation. I can achieve but not retain expertise in maths problems. History 6 months back, I studied integration in Calculus at college. I learnt it all ...
7
votes
13answers
2k views

A PEMDAS issue request for explanation

This question made the rounds recently - $8÷2(2+2)=?$ Now, I glanced at this, answered "1" and then saw the full article printed in the New York Times, The Math Equation That Tried to Stump the ...
11
votes
9answers
1k views

Why do you need to distinguish between apparently identical objects in probability?

In the math class I taught today I was asked a question, and I was unable to give a good answer. The problem was as follows: A certain factory produces throat tablets. In each pack, there are from 48 ...
10
votes
6answers
292 views

How should students say in words the notation for a limit?

$$\lim_{x\rightarrow a} f(x)=L$$ Which way should students best get in the habit of? The limit of $f(x)$, as $x$ approaches $a$, equals $L$ The limit of $f(x)$ equals $L$, as $x$ approaches $a$ The ...
8
votes
4answers
468 views

Easy examples of correspondence between global and local, as preparation for Gauss's theorem and Stokes's theorem

I'm teaching freshman electricity and magnetism this semester, and as usual in this type of course, I will need to teach my students a lot of vector calculus before they see it in a math course. The ...
6
votes
1answer
76 views

Studies on more simple problems, or fewer difficult problems?

I'm a new adjunct faculty member. I haven't taught math yet (I'm teaching a related subject for now), but I've been thinking about my approach to teaching Calculus I should I be asked to teach it in ...
3
votes
2answers
119 views

Finland's performance on international competitions

Why it is said that Finland has a particularly good education system, but Finland's performance on international mathematics competitions is quite often at relatively intermediate level?
3
votes
3answers
123 views

Is there a pre-calculus introduction to the formal definition of a limit?

To give an example of what I mean, I'll answer a similarly worded question: “is there a pre-calculus introduction to the derivative?” I would say yes, since there already are the ideas of a slopes of ...
8
votes
1answer
396 views

Is there research on the efficacy of taking good notes in math class?

I teach at community college, and have often encountered others talking about helping students learn to take good notes. I have never felt that I took good notes as a student. I was too busy thinking ...
9
votes
1answer
423 views

An alternative to “two column” geometry proofs

I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam)...
5
votes
3answers
140 views

Graph theory teaching materials for young students

Does anyone have any good sources to teach upper primary so grade 7 students basics on graph theory? The only ones I can find are for like upper middle school and high school, and having trouble ...
3
votes
1answer
200 views

The most transparent exposition of Bayes' Theorem

I am seeking the most transparent exposition of Bayes' Theorem (for undergraduates). I would prefer to avoid mentioning "prior" and "posterior," and instead focus on frequencies. The Wikipedia entry ...
6
votes
1answer
179 views

Will there ever be a revision of Common Core?

Although the implementation of curricula and assessments that align to the Common Core has been a slow roll-out across many states, the standards themselves are close to ten years old now. I don't ...
7
votes
3answers
4k views

Can we save the word “unique”?

Increasing numbers of students seem to be using the word "unique" incorrectly. A common example: Question. Define the term "one-to-one" for a function $f$. Answer. Every $x$ has a unique $f(...
7
votes
1answer
184 views

When (and why) did geometric means of more than two numbers exit the secondary curriculum?

In contemporary US secondary mathematics textbooks, geometric means occasionally make a brief appearance. For example: In Geometry, students learn that when an altitude is dropped to the hypotenuse ...
8
votes
4answers
204 views

Should school syllabus include chapters partially?

In my locality, many schools have this tendency to partially include this and that chapter in the syllabus (for almost every subject). For example, (most of the chapters are subdivided in two or more ...
10
votes
4answers
364 views

Why is absolute value difficult?

My understanding is that students find absolute value to be challenging to learn or understand. Off the top of my head, I can come up with two possible reasons for this. Absolute value is a piecewise ...
6
votes
8answers
1k views

Adding things to bunches of things vs multiplication

"Suppose you bought four boxes of pencils having five pencils in each, how many pencils do you have altogether?" — "Nine." — "How come?" — "Because 4 plus 5 is 9." — "But you cannot add boxes to ...
16
votes
5answers
8k views

What is the most difficult concept to grasp in Calculus 1?

I would say it is not the Fundamental Theorem of Calculus, but rather some notion connecting limits and continuity, perhaps the $(\epsilon,\delta)$-definitions of limits and continuity. But I would be ...
2
votes
1answer
173 views

Software for validating answers from students

To start with, I'm not sure whether this is the correct stackexchange site to ask this, but I can't find one for physics teachers and my problem could easily be extended to math teachers with the same ...
2
votes
3answers
112 views

Self-Study of Calculus Two

I just finished self study of Calculus One and I am looking to begin Calculus Two. Is there a free platform that can help me with this?
1
vote
6answers
403 views

Is there a more telling name for “Calculus 2”?

I see a lot of places where "Calculus 1" is referred to as "Introduction to Calculus", or "Single-variable Calculus." "Calculus 3" is referred to as "Multiple-variable calculus." Is there an ...
12
votes
6answers
3k views

Is it a bad idea to offer variants of a final exam based on the type of allowed calculators?

Background/rant: I am in charge of teaching our single quarter course on vector calculus (don't ask me why the department head thinks the area can be covered in half a semester). The two biggest ...
3
votes
2answers
84 views

Forming a Study Model for a Self-Study Beginner

I am very new to this platform so I may have misunderstood thr concept or might seem a bit off but please bear with me because I know what I want for certain. I always wanted to study mathematics ...
40
votes
19answers
5k views

How to help new students accept function notation

I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation. Their main ...
7
votes
2answers
157 views

Examples of application problems of coordinate geometry in the complex plane?

I am currently writing some basic introductory texts to complex numbers for third-year high school students (Denmark). My main goal is to introduce complex numbers as a practical tool that both ...
10
votes
2answers
276 views

Introductory real analysis before or after introductory abstract algebra?

What are the pros and cons for students of taking introductory real analysis before or after introductory abstract algebra, assuming they are going to take both? I recognize that the overlap between ...
3
votes
4answers
263 views

Best Way to Learn Trigonometry

What are the best resources to learn trigometry? I recently decided to pursue a BS in mathematics at uni. I used to fail all my math classes with D's or F's until I started teaching myself, and so far ...
5
votes
4answers
150 views

How to make a mathematical dynamic graph?

How to make a mathematical dynamic graph? I have seen a lot of mathematics teaching videos containing a lot of mathematical dynamic graphs; I think it is very interesting, and it is very attractive! ...
11
votes
4answers
353 views

Why are the contents of contest maths so different from contents of degree-level maths?

I wonder why topics examined in high school math contests are so different from the maths learned by those who are seriously studying a math major at a university. Firstly, contests like IMO, ARML, ...

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