# Questions tagged [teaching]

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257 views

### How to teach linear programming and reductions?

Do you know any textbook with problems+solutions to support teaching of linear programming and reductions, and in particular, cover standard and slack forms, formulation of problems as linear programs,...
629 views

### How to (or should one) distinguish between lowercase and uppercase letters orally when lecturing?

I sometimes teach calculus in English whereas it's not my native language. For example, during a course about antiderivatives, how do you (orally) pronounce $f$ vs $F$? Which are the best? "the ...
80 views

### How to address opportunities for improvement with a teacher

My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching. For example, this question has no context from previous questions ...
178 views

### Introductory exercise for the addition of large natural numbers

I'm starting a repetition with my students in 5th grade after they learned in elementary school how to sum up larger natural numbers (also 5- to 6-digits) by writing down that calculation. As ...
112 views

### Road map to teach undergrads a first course in real analysis that concludes with convergence of fourier series

I am planning to teach (unofficially, I am a Grad student) a course in real analysis. Aim of the course is to understand the convergence of Fourier series. I want to start with the notion of ...
265 views

### Examples of informal explanations that cause misconceptions

Every good teacher knows that giving an informal explanation (that is, an explanation not based on strict definitions and maybe making use of metaphors, intuition, or everyday language) of a ...
554 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 there minds) what ...
156 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 ...
339 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 ...
263 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 ...
542 views

### Rhombuses, kites etc

As a high school teacher, I sometimes wonder about the usefulness of certain topics. Some topics seem to be in the textbook because they have always been there, not because they lead anywhere ...
2k views

### Diagram of Methods to Solve Differential Equations

I am currently trying to build a flow chart to visualize all tests there are to tell whether an ordinary differential equation is solvable and how to solve it. This is for tutoring purposes. The ...
355 views

### Enlighten younger students about the concept of “procedural justice” in mathematics?

I am tutoring a 16-year-old student from my home country (in Asia) in, roughly speaking, precalculus. I would like to give him a feeling of procedural justice, so to speak, in modern mathematics, ...
332 views

### Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

A friend of mine that teaches math has made many times the following experiment : drawing two circles on the blackboard representing two sets A and B such that A and B are disjoint writing on the ...
528 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 ...
3k views

### How to convince students of the implication truth values? [duplicate]

How can I convince students that "P implies Q" is true when P is false, independent of what truth value Q takes? Is there any real life or a convincing argument for this? I have given the analogy ...
222 views

### How to overcome the frustration in teaching and doing research at the same time

I understand that this website is designated particularly for teaching-related topics. However as many of us do agree that being a lecturer, we are supposed to run both teaching and research duties at ...
307 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. ...
2k views

### Teaching indefinite integrals that require special-casing

I encountered the following concern when teaching indefinite integrals. I believe that many of us may overlook this. May I be wrong? Let's consider the following example. Find the indefinite ...
400 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 ...
131 views

### What makes education in Finland so good?

This is a question more about education in general than math education but there is no general education Stack Exchange website so I decided to write this question here. If this question is more ...
222 views

### How to motivate students to do proofs?

I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this. How can ...
172 views

### Revision Lecture, what are the aims?

I will give a 2-hour long revision lecture on a Mathematics area. The aim of this lecture is to help the students prepare for the exam test. The course was rather long, covering 5 chapters and a ...
649 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 ...
466 views

### Topics in Mathematics for a 15 minute demonstration

I need to appear for an interview for the post of Assistant Professor in Mathematics in an undergraduate college. My Backgorund : I have studied topics like Algebra comprising of Group Theory,Ring ...
189 views

### How to introduce Group Theory to a general audience in 15 minutes?

How to introduce Group Theory to a general audience in 15 minutes? I know that it will be quite tough to introduce Groups to a general audience in such a short time. So what will be a good way to ...
148 views

### For what subjects and grade levels is the take-home exam suitable?

I'm starting my job as a mathematics teacher in an intermediate school. I want to follow some new way of assessment and I'm really curious about take-home exams; are they suitable for any subjects? ...
844 views

### Should young math students be taught an abstract concept of form?

Should a more general concept of the "form" of an equation or expression, be taught to math students as young as elementary school? I'm a fairly new tutor--do more experienced teachers think this ...
97 views

### More intermediate steps or check well-understanding

I work as a math tutor mostly for talented high-school students that are passionate about mathematics and want to learn more of it beyond school programs. They are very smart kids, but I noticed that ...
352 views

### Teaching math by serving it as games with rules first, not intuition?

Just now I'm thinking a crazy reversed idea: Is it good to teach math to elementary students without starting from its real world motivation or making it intuitive first, but rather by realizing that ...
474 views

### Students understand during course but can't solve exam

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...
111 views

### Pythagorean triples

What is the most motivating way to introduct Pythagorean triples to undergraduate students? I am looking for an approach that will have an impact. Good interesting or real life examples will help. Is ...
15k 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 ...
169 views

### CoTeaching Elementary Linear Algebra

I and my colleague will teach an elementary linear algebra next few weeks, but the way our course is planned mostly is by turn teaching. By that I mean, my partner will teach the first 8 weeks of the ...
355 views

### Integral calculus from the modern viewpoint

This is a soft question. What is the purpose of teaching techniques of integration at the college level? More specifically, in the sense of putting integration into practice, what value does ...
80 views

### One course/subject, one class, two lecturers

This is my first question here, so please correct me if I'm wrong in my way of asking. My question is suggested directly by the title. In my college institution, for each subject, half of the ...
231 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 ...
193 views

### Should students teach other students?

I am interested in creating a curriculum that helps cultivate students abilities to teach one another. Specifically good one-on-one instruction includes elements like: Examples, Pictures, Humor, ...
178 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 ...
134 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) ...
593 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 ...
179 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 ...
599 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 ...
176 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?
194 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 ...
199 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 ...
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-...
118 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 ...
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 ...