Questions tagged [teaching]

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2
votes
1answer
184 views

"Basic ideas" as a concept in teaching maths?

In Germany there exists a concept whose name might be translated as "basic ideas." The core of the concept is to offer the students an idea of what they are learning, e.g. in the context of ...
5
votes
3answers
386 views

Limit of questions that a student should ask in class without upsetting professor?

Days ago a professor told me to ask in class when I don't understand something and that he could keep explaining until it's clear for me. Being honest I'm a little slow to understand mathematics in ...
3
votes
2answers
156 views

Ideas for high-school proof class?

I have a math degree and have been hired to teach a proof class at a summer program. Our goal is to help the students learn the material they need for school (they take an algebra class separately) ...
5
votes
2answers
272 views

How to explain NP-hardness and NP-completeness to students

Computer science is becoming more and more important for mathematicians nowadays. Terms like big data, algorithm, artificial intelligence and others are frequently on the news. Many mathematical ...
4
votes
2answers
230 views

What is the ideal teaching style for Calculus exercises only?

A Calculus class for 1st year students may have two subclasses (with two different lecturers) : The main class (which covers the theories and concept), and the 'response' class (which provides and ...
11
votes
4answers
221 views

What are the best places online where math educators can discuss their experience?

As a math teacher I often experiment new things (for instance non obvious ways to use technology in the classroom, or new ways to teach something), and I think it would be useful if I could share my ...
10
votes
3answers
438 views

How to teach Leibniz and Newton's notation

There has been many posts here and in MSE about different notations of differentiation. See for example this, this and this. However, those questions only deal with the common misunderstanding about ...
12
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6answers
724 views

teach that $\frac10$ not defined properly

there're some students, who belive that $$\frac10 = \infty $$ I need to teach them that this is not true and $\frac10 $ is undefined, mathematically and give a good picture (for their minds) what is ...
28
votes
10answers
8k views

How should a student's inefficient calculation be pointed out?

One time I watched a student solve the equation $0 = (x-2)^2-9$ for $x$ like this. $$\begin{align*} 0 &= (x-2)^2-9 \\0 &= (x^2-4x+4)-9 \\0 &= x^2-4x-5 \\0 &= (x+1)(x-...
5
votes
3answers
372 views

L'Hopital's Rule: Why do we need it?

I'm preparing a design/teaching experiment for my Curriculum Design Course right now. I've decided to cover L'Hopital's rule with a student I've been working with for a year, so skill wise he's ready ...
7
votes
2answers
178 views

Should basic exercises be solved before formulas are introduced?

I was watching (as a fellow teacher) a lecture on arithmetic progression. It so happened that a formula was rapidly introduced and used. The formula was $a_i = a_1 + (i-1)r$ (I trust the terms ...
4
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2answers
455 views

How to explain Chinese remainder theorem?

I want to explain Chinese remainder theorem to master level computer science students. There are two versions of CRT one is number theoretic and second requires the definition of ideals, groups etc. ...
12
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3answers
2k views

How to teach abstract algebra for the first time?

I am a Ph.D student in computer science. I am TAing one course this semester, which requires the basics of abstract algebra like rings, fields, ideals, and basic theorems about them. I have done two ...
8
votes
2answers
249 views

How can I get a better result making math videos with a tablet?

First question in this stack. Here it goes: So, I had this 2 or 3 year old intuos tablet and I said why not? And started doing my own videos. I've been making my own videos for my students last couple ...
4
votes
0answers
108 views

Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]

I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question. I've been tasked with helping to redesign a math curriculum for an enrichment ...
5
votes
4answers
261 views

How to become a good teacher in the classroom when first starting to teach?

This semester is my first time to teach Calculus II in a classroom which contains around 25 students. (In fact, this is a discussion class.) I didn't have much experience about teaching. For instance, ...
8
votes
1answer
180 views

How can I deal with the time pressure of teaching a short course?

I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad ...
16
votes
1answer
368 views

Addressing fundamental math errors

I am looking for ways I can correct fundamental math mistakes. I am currently tutoring someone taking a course which is a cross between first year calculus and grade 12 functions. In high school he ...
15
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6answers
599 views

Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?

I am teaching Calculus I and will be teaching it again. To me, the $\varepsilon$-$\delta$ definition of limit is one of the key ideas of Calculus; learning calculus without learning $\varepsilon$-$\...
11
votes
4answers
647 views

What is most motivating way to introduce Fermat's Little Theorem

What is the best way to introduce Fermat’s Little Theorem (F$l$T) to students? What can I use as an opening paragraph which will motivate and have an impact on why students should learn this theorem ...
15
votes
7answers
822 views

How should I introduce the concept of a function to a precalculus student?

My brother has not taken a math class in $10-15$ years. He is studying for the GRE so I have been teaching him a chapter or two from my precalculus book. So far, he has learned (and excelled at) basic ...
10
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6answers
3k views

Greatest common divisor applications

What are some real-life applications of gcd? I am looking for a motivating way of introducing this topic in an elementary number theory course.
5
votes
3answers
289 views

How to teach to draw graphs of quadratic equations without knowing calculus?

In the country I'm living we learn how to draw the graph of quadratic equations such as $y=x^2$ or $y=x^2+5x+3$ before knowing calculus (in fact we don't even learn calculus until we begin the ...
13
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3answers
255 views

Repeating basic material in exercise class at university

I am a teaching assistant in mathematics at a university in Continental Europe. The course for which I am an assistant is a third year course, so usually the students are expected to know the basic ...
5
votes
2answers
215 views

At what educational stage are angles greater than 180 introduced?

Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles $> 180^\circ$. For example, when do they reason with an angle of $270^\...
11
votes
1answer
923 views

How to denote angle?

I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like $\angle ABC$. But sometimes I have difficulties to understand whether they mean an angle or its ...
3
votes
1answer
238 views

How to ask a student a question to get the answer '...integer not continuous...'

Context: a very basic level statistics package computer lab. A scatter plot is produced for one integer variable versus another integer variable. The students are asked why the points form a grid ...
6
votes
3answers
684 views

Is there a more intuitive way to solve combined rates of work problems?

I am helping my brother study for the GRE and we have come across some problems like this in my old precalculus textbook: 1) Karen and Betty have been hired to pain a house. Working together, they ...
8
votes
3answers
295 views

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of: notes written during the lecture ...
37
votes
13answers
18k views

Why do we teach complex numbers?

In algebra II, USA, we teach our students complex numbers. However, after algebra II, they never use complex numbers until pretty much complex analysis. The whole point of teaching them complex ...
5
votes
1answer
648 views

Is the current education system as bad as most critics and famous pure mathematicians try to convey? [closed]

Throughout elementary, middle and high school mathematics is quite merely about memorizing concepts and formulas, understanding the theorems (without their proofs) and applying acquired knowledge in ...
2
votes
0answers
182 views

Core-Plus Mathematics: Similar Resources for grades 7-9

I'm looking for rich educational resources similar to core-plus mathematics, for grades 7, 8, and 9. Is there any such material?
1
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3answers
92 views

Determining sets to show sufficiency of a condition?

$p \to q$ that means (among others) $p$ is a sufficient condition for $q$. To show the sufficiency, I teach my study by determining the set for $p$, the set for $q$ first and comparing their ...
4
votes
2answers
6k views

Notation of line segment and its length

I have sometimes seen a notation where $AB$ could mean either the line segment or its length. Why do the same notation can be mean both? Should one teach pupils to use for example notation $d(A,B)$ or ...
2
votes
0answers
83 views

What should I teach 13 to 15 years old pupils to learn competition mathematics? [closed]

I would like to teach some young and talented pupils basics of competition mathematics. What kind of methods, topics and theorems should I teach to those who are good at school mathematics but have no ...
15
votes
6answers
886 views

What is a better way to explain these claims about limit are not true in general?

As a TA who led calculus* 1 and 2 discussion section and holds office hour** in the previous year, I heard the following (wrong) arguments several times. $\displaystyle \lim_{x\to \infty} \sqrt{x+1}-\...
3
votes
2answers
1k views

Teaching Models for Mathematics (like 5 E's in Science)

I want to find and know about teaching models in mathematics. There's such a model for teaching science: the 5 E's model: Any suggestion (books, references, etc.) would be greatly appreciated.
4
votes
2answers
557 views

Why "plug in numbers" when solving inequality?

Let me use this example, Solve $x^3-4x>0$ After factorization, we have $$(x+2)x(x-2)>0$$, in order to have product of several numbers positive, even(0,2,4,...) of them have to be negative ...
14
votes
4answers
2k views

Is it better to provide students with guided notes or to have them write their own notes, or both?

When I taught calculus, I posted my notes after the lecture. Then I had the students fill out a mid-quarter evaluation, and a lot of them wanted me to post my notes before class. What I started ...
11
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4answers
852 views

Teaching algebra to visually impaired or blind students

I am currently writing an independent project investigating the teaching and learning of algebra for students with a visual impairment. I am struggling to find literature specifically about teaching ...
7
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3answers
210 views

References for graduate education

A search in Google returns lots of studies and thinkings about teaching in undergraduate schools. Could anybody come up with any research/references about teaching in graduate schools (graduate ...
15
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7answers
3k views

Students strictly follow the steps and notations in sample problems without understanding them

It's just an observation, but I'll be highly appreciated if anyone with experience in teaching (or TA-ing) lower-division calculus can explain this phenomenon in detail. I'm one of a TAs who's ...
10
votes
2answers
277 views

How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
8
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4answers
567 views

Elementary physics course for pure math student

Are there any mathematical departments which present the course "elementary physics" for pure math undergraduate students, separately? Is there a way to present this course with the most pure ...
12
votes
1answer
276 views

How can I be more prolific as a maths teacher with my visual handicap?

I have a chronic visual handicap and am in need of adequate level of accessibility support while learning and teaching mathematics from and to the visually challenged as well as the sighted. I'm ...
14
votes
4answers
954 views

As a TA, how to reduce imprecise notations/statements in students' exams

I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams. When grading the midterm, I found large number of students showed some ...
3
votes
0answers
51 views

clasification of teaching licensures and certifications particularly for teacher-students

There is a lot of certification and licensure tests for teaching (math and etc) particularly for teachers and teacher-students (PACT, Praxis & PPAT, edTPA, RESA, ... in US and TAT in India and etc)...
8
votes
1answer
869 views

Should $\varphi$ be monotone in the integration by substitution?

I'm trying to calculate $$\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\sin t \cos^3 t\,dt$$ using integration by substitution $$\int_{\varphi([a;b])} f(x)dx=\int_{[a;b]} f\left(\varphi(t)\right)|\varphi'(t)|...
6
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4answers
2k views

Why convert to sums of two squares?

Why bother writing a given integer as the sum of two squares? Does this have any practical application? Is there an introduction on a first year number theory course which would motivate students to ...

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